module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT, PLANCK_CONSTANT
using Polymers.Physics.SingleChain: ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Fjc.Thermodynamics: FJC
@testset "physics::single_chain::fjc::thermodynamics::test::base::init" begin
@test isa(
FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
),
Any,
)
end
@testset "physics::single_chain::fjc::thermodynamics::test::base::number_of_links" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
@test FJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::base::link_length" begin
for _ = 1:parameters.number_of_loops
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::base::hinge_mass" begin
for _ = 1:parameters.number_of_loops
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test FJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::base::all_parameters" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
@test all(
FJC(number_of_links, link_length, hinge_mass).number_of_links ==
number_of_links &&
FJC(number_of_links, link_length, hinge_mass).link_length == link_length &&
FJC(number_of_links, link_length, hinge_mass).hinge_mass == hinge_mass,
)
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
force_out = model.isometric.legendre.force(end_to_end_length, temperature)
residual_abs = force - force_out
residual_rel = residual_abs / force
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_force_out = model.isometric.legendre.nondimensional_force(
nondimensional_end_to_end_length_per_link,
)
residual_abs = nondimensional_force - nondimensional_force_out
residual_rel = residual_abs / nondimensional_force
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
helmholtz_free_energy_legendre =
model.isotensional.gibbs_free_energy(force, temperature) +
force * end_to_end_length
helmholtz_free_energy_legendre_out =
model.isometric.legendre.helmholtz_free_energy(end_to_end_length, temperature)
residual_abs =
helmholtz_free_energy_legendre - helmholtz_free_energy_legendre_out +
BOLTZMANN_CONSTANT *
temperature *
log(
8.0 * pi^2 * hinge_mass * link_length^2 * BOLTZMANN_CONSTANT * temperature /
PLANCK_CONSTANT^2,
)
residual_rel = residual_abs / helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
end_to_end_length_per_link =
model.isotensional.end_to_end_length_per_link(force, temperature)
helmholtz_free_energy_per_link_legendre =
model.isotensional.gibbs_free_energy_per_link(force, temperature) +
force * end_to_end_length_per_link
helmholtz_free_energy_per_link_legendre_out =
model.isometric.legendre.helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
residual_abs =
helmholtz_free_energy_per_link_legendre -
helmholtz_free_energy_per_link_legendre_out +
BOLTZMANN_CONSTANT *
temperature *
log(
8.0 * pi^2 * hinge_mass * link_length^2 * BOLTZMANN_CONSTANT * temperature /
PLANCK_CONSTANT^2,
) / number_of_links
residual_rel = residual_abs / helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
relative_helmholtz_free_energy_legendre =
model.isotensional.relative_gibbs_free_energy(force, temperature) +
force * end_to_end_length
relative_helmholtz_free_energy_legendre_out =
model.isometric.legendre.relative_helmholtz_free_energy(
end_to_end_length,
temperature,
)
residual_abs =
relative_helmholtz_free_energy_legendre -
relative_helmholtz_free_energy_legendre_out
residual_rel = residual_abs / relative_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
end_to_end_length_per_link =
model.isotensional.end_to_end_length_per_link(force, temperature)
relative_helmholtz_free_energy_per_link_legendre =
model.isotensional.relative_gibbs_free_energy_per_link(force, temperature) +
force * end_to_end_length_per_link
relative_helmholtz_free_energy_per_link_legendre_out =
model.isometric.legendre.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
residual_abs =
relative_helmholtz_free_energy_per_link_legendre -
relative_helmholtz_free_energy_per_link_legendre_out
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.isotensional.nondimensional_end_to_end_length(nondimensional_force)
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_helmholtz_free_energy_legendre =
model.isotensional.nondimensional_gibbs_free_energy(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length
nondimensional_helmholtz_free_energy_legendre_out =
model.isometric.legendre.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_legendre -
nondimensional_helmholtz_free_energy_legendre_out + log(
8.0 * pi^2 * hinge_mass * link_length^2 * BOLTZMANN_CONSTANT * temperature /
PLANCK_CONSTANT^2,
)
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_helmholtz_free_energy_per_link_legendre =
model.isotensional.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
nondimensional_helmholtz_free_energy_per_link_legendre_out =
model.isometric.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
residual_abs =
nondimensional_helmholtz_free_energy_per_link_legendre -
nondimensional_helmholtz_free_energy_per_link_legendre_out +
log(
8.0 * pi^2 * hinge_mass * link_length^2 * BOLTZMANN_CONSTANT * temperature /
PLANCK_CONSTANT^2,
) / number_of_links
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length =
model.isotensional.nondimensional_end_to_end_length(nondimensional_force)
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_relative_helmholtz_free_energy_legendre =
model.isotensional.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
) + nondimensional_force * nondimensional_end_to_end_length
nondimensional_relative_helmholtz_free_energy_legendre_out =
model.isometric.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy_legendre -
nondimensional_relative_helmholtz_free_energy_legendre_out
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_legendre
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::legendre::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
rand(parameters.number_of_links_minimum:parameters.number_of_links_maximum)
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_relative_helmholtz_free_energy_per_link_legendre =
model.isotensional.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
nondimensional_relative_helmholtz_free_energy_per_link_legendre_out =
model.isometric.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
residual_abs =
nondimensional_relative_helmholtz_free_energy_per_link_legendre -
nondimensional_relative_helmholtz_free_energy_per_link_legendre_out
residual_rel =
residual_abs / nondimensional_relative_helmholtz_free_energy_per_link_legendre
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.isometric.force(end_to_end_length, temperature)
end_to_end_length_out = model.isotensional.end_to_end_length(force, temperature)
residual_abs = end_to_end_length - end_to_end_length_out
residual_rel = residual_abs / end_to_end_length
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.isometric.force(end_to_end_length, temperature)
end_to_end_length_per_link = nondimensional_end_to_end_length_per_link * link_length
end_to_end_length_per_link_out =
model.isotensional.end_to_end_length_per_link(force, temperature)
residual_abs = end_to_end_length_per_link - end_to_end_length_per_link_out
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_force =
model.isometric.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links
nondimensional_end_to_end_length_out =
model.isotensional.nondimensional_end_to_end_length(nondimensional_force)
residual_abs =
nondimensional_end_to_end_length - nondimensional_end_to_end_length_out
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_force =
model.isometric.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_end_to_end_length_per_link_out =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
residual_abs =
nondimensional_end_to_end_length_per_link -
nondimensional_end_to_end_length_per_link_out
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::force" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
force_out = model.isometric.force(end_to_end_length, temperature)
residual_abs = force - force_out
residual_rel = residual_abs / force
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_force_out =
model.isometric.nondimensional_force(nondimensional_end_to_end_length_per_link)
residual_abs = nondimensional_force - nondimensional_force_out
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.isometric.force(end_to_end_length, temperature)
helmholtz_free_energy =
model.isometric.helmholtz_free_energy(end_to_end_length, temperature)
helmholtz_free_energy_out =
model.isotensional.gibbs_free_energy(force, temperature) +
force * end_to_end_length
residual_abs = helmholtz_free_energy - helmholtz_free_energy_out
residual_rel = residual_abs / helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
end_to_end_length_per_link = nondimensional_end_to_end_length_per_link * link_length
force = model.isometric.force(end_to_end_length, temperature)
helmholtz_free_energy_per_link =
model.isometric.helmholtz_free_energy_per_link(end_to_end_length, temperature)
helmholtz_free_energy_per_link_out =
model.isotensional.gibbs_free_energy_per_link(force, temperature) +
force * end_to_end_length_per_link
residual_abs = helmholtz_free_energy_per_link - helmholtz_free_energy_per_link_out
residual_rel = residual_abs / helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
force = model.isometric.force(end_to_end_length, temperature)
relative_helmholtz_free_energy =
model.isometric.relative_helmholtz_free_energy(end_to_end_length, temperature)
relative_helmholtz_free_energy_out =
model.isotensional.relative_gibbs_free_energy(force, temperature) +
force * end_to_end_length
residual_abs = relative_helmholtz_free_energy - relative_helmholtz_free_energy_out
residual_rel = residual_abs / relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links * link_length
end_to_end_length_per_link = nondimensional_end_to_end_length_per_link * link_length
force = model.isometric.force(end_to_end_length, temperature)
relative_helmholtz_free_energy_per_link =
model.isometric.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
relative_helmholtz_free_energy_per_link_out =
model.isotensional.relative_gibbs_free_energy_per_link(force, temperature) +
force * end_to_end_length_per_link
residual_abs =
relative_helmholtz_free_energy_per_link -
relative_helmholtz_free_energy_per_link_out
residual_rel = residual_abs / relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links
nondimensional_force =
model.isometric.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_helmholtz_free_energy =
model.isometric.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_out =
model.isotensional.nondimensional_gibbs_free_energy(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_helmholtz_free_energy - nondimensional_helmholtz_free_energy_out
residual_rel = residual_abs / nondimensional_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force =
model.isometric.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_helmholtz_free_energy_per_link =
model.isometric.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
)
nondimensional_helmholtz_free_energy_per_link_out =
model.isotensional.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_helmholtz_free_energy_per_link -
nondimensional_helmholtz_free_energy_per_link_out
residual_rel = residual_abs / nondimensional_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links
nondimensional_force =
model.isometric.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_relative_helmholtz_free_energy =
model.isometric.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_helmholtz_free_energy_out =
model.isotensional.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
) + nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_relative_helmholtz_free_energy -
nondimensional_relative_helmholtz_free_energy_out
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_end_to_end_length_per_link =
parameters.nondimensional_end_to_end_length_per_link_reference +
parameters.nondimensional_end_to_end_length_per_link_scale * (0.5 - rand())
nondimensional_force =
model.isometric.nondimensional_force(nondimensional_end_to_end_length_per_link)
nondimensional_relative_helmholtz_free_energy_per_link =
model.isometric.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
nondimensional_relative_helmholtz_free_energy_per_link_out =
model.isotensional.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
) + nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_relative_helmholtz_free_energy_per_link -
nondimensional_relative_helmholtz_free_energy_per_link_out
residual_rel = residual_abs / nondimensional_relative_helmholtz_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
gibbs_free_energy = model.isotensional.gibbs_free_energy(force, temperature)
gibbs_free_energy_out =
model.isometric.helmholtz_free_energy(end_to_end_length, temperature) -
force * end_to_end_length
residual_abs = gibbs_free_energy - gibbs_free_energy_out
residual_rel = residual_abs / gibbs_free_energy
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
end_to_end_length_per_link = end_to_end_length / number_of_links
gibbs_free_energy_per_link =
model.isotensional.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_out =
model.isometric.helmholtz_free_energy_per_link(end_to_end_length, temperature) -
force * end_to_end_length_per_link
residual_abs = gibbs_free_energy_per_link - gibbs_free_energy_per_link_out
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
relative_gibbs_free_energy =
model.isotensional.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_out =
model.isometric.relative_helmholtz_free_energy(end_to_end_length, temperature) -
force * end_to_end_length
residual_abs = relative_gibbs_free_energy - relative_gibbs_free_energy_out
residual_rel = residual_abs / relative_gibbs_free_energy
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.isotensional.end_to_end_length(force, temperature)
end_to_end_length_per_link = end_to_end_length / number_of_links
relative_gibbs_free_energy_per_link =
model.isotensional.relative_gibbs_free_energy_per_link(force, temperature)
relative_gibbs_free_energy_per_link_out =
model.isometric.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
) - force * end_to_end_length_per_link
residual_abs =
relative_gibbs_free_energy_per_link - relative_gibbs_free_energy_per_link_out
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links
nondimensional_gibbs_free_energy =
model.isotensional.nondimensional_gibbs_free_energy(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_out =
model.isometric.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_out
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_gibbs_free_energy_per_link =
model.isotensional.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_out =
model.isometric.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_out
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_end_to_end_length =
nondimensional_end_to_end_length_per_link * number_of_links
nondimensional_relative_gibbs_free_energy =
model.isotensional.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
)
nondimensional_relative_gibbs_free_energy_out =
model.isometric.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
) - nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_relative_gibbs_free_energy -
nondimensional_relative_gibbs_free_energy_out
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::thermodynamic_limit::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links = parameters.number_of_links_maximum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
nondimensional_force =
parameters.nondimensional_force_reference +
parameters.nondimensional_force_scale * (0.5 - rand())
nondimensional_end_to_end_length_per_link =
model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
nondimensional_relative_gibbs_free_energy_per_link =
model.isotensional.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
)
nondimensional_relative_gibbs_free_energy_per_link_out =
model.isometric.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
) - nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_relative_gibbs_free_energy_per_link -
nondimensional_relative_gibbs_free_energy_per_link_out
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_rel) <= parameters.rel_tol_thermodynamic_limit
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_strong_potential_isometric::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.modified_canonical.force(
end_to_end_length,
potential_stiffness,
temperature,
) - model.isometric.force(end_to_end_length, temperature)
)^2
end
function integrand_denominator(end_to_end_length)
return model.modified_canonical.force(
end_to_end_length,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_strong_potential_isometric::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.modified_canonical.nondimensional_force(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
) - model.isometric.nondimensional_force(
nondimensional_end_to_end_length_per_link,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return model.modified_canonical.nondimensional_force(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_strong_potential_isometric::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.modified_canonical.relative_helmholtz_free_energy(
end_to_end_length,
potential_stiffness,
temperature,
) - model.isometric.relative_helmholtz_free_energy(
end_to_end_length,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return model.modified_canonical.relative_helmholtz_free_energy(
end_to_end_length,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_strong_potential_isometric::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.modified_canonical.relative_helmholtz_free_energy_per_link(
end_to_end_length,
potential_stiffness,
temperature,
) - model.isometric.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return model.modified_canonical.relative_helmholtz_free_energy_per_link(
end_to_end_length,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_strong_potential_isometric::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.modified_canonical.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
) - model.isometric.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return model.modified_canonical.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_strong_potential_isometric::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.modified_canonical.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
) -
model.isometric.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return model.modified_canonical.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.force(
potential_distance,
potential_stiffness,
temperature,
)
return (
model.modified_canonical.end_to_end_length(
potential_distance,
potential_stiffness,
temperature,
) - model.isotensional.end_to_end_length(force, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.modified_canonical.end_to_end_length(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.force(
potential_distance,
potential_stiffness,
temperature,
)
return (
model.modified_canonical.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
) - model.isotensional.end_to_end_length_per_link(force, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.modified_canonical.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force = model.modified_canonical.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.isotensional.nondimensional_end_to_end_length(
nondimensional_force,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.modified_canonical.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force = model.modified_canonical.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.modified_canonical.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance_ref =
parameters.nondimensional_potential_distance_large_1 *
number_of_links *
link_length
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
force_ref = model.modified_canonical.force(
potential_distance_ref,
potential_stiffness,
temperature,
)
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.force(
potential_distance,
potential_stiffness,
temperature,
)
return (
model.modified_canonical.gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) - model.modified_canonical.gibbs_free_energy(
potential_distance_ref,
potential_stiffness,
temperature,
) - model.isotensional.gibbs_free_energy(force, temperature) +
model.isotensional.gibbs_free_energy(force_ref, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.modified_canonical.gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) - model.modified_canonical.gibbs_free_energy(
potential_distance_ref,
potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance_ref =
parameters.nondimensional_potential_distance_large_1 *
number_of_links *
link_length
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
force_ref = model.modified_canonical.force(
potential_distance_ref,
potential_stiffness,
temperature,
)
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.force(
potential_distance,
potential_stiffness,
temperature,
)
return (
model.modified_canonical.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) - model.modified_canonical.gibbs_free_energy_per_link(
potential_distance_ref,
potential_stiffness,
temperature,
) - model.isotensional.gibbs_free_energy_per_link(force, temperature) +
model.isotensional.gibbs_free_energy_per_link(force_ref, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.modified_canonical.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) - model.modified_canonical.gibbs_free_energy_per_link(
potential_distance_ref,
potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.force(
potential_distance,
potential_stiffness,
temperature,
)
return (
model.modified_canonical.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) - model.isotensional.relative_gibbs_free_energy(force, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.modified_canonical.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.force(
potential_distance,
potential_stiffness,
temperature,
)
return (
model.modified_canonical.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) - model.isotensional.relative_gibbs_free_energy_per_link(
force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.modified_canonical.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_potential_distance_ref =
parameters.nondimensional_potential_distance_large_1
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
nondimensional_force_ref = model.modified_canonical.nondimensional_force(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force = model.modified_canonical.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) - model.modified_canonical.nondimensional_gibbs_free_energy(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
temperature,
) - model.isotensional.nondimensional_gibbs_free_energy(
nondimensional_force,
temperature,
) + model.isotensional.nondimensional_gibbs_free_energy(
nondimensional_force_ref,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return (
model.modified_canonical.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) - model.modified_canonical.nondimensional_gibbs_free_energy(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_potential_distance_ref =
parameters.nondimensional_potential_distance_large_1
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
nondimensional_force_ref = model.modified_canonical.nondimensional_force(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force = model.modified_canonical.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -
model.modified_canonical.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
temperature,
) - model.isotensional.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + model.isotensional.nondimensional_gibbs_free_energy_per_link(
nondimensional_force_ref,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return (
model.modified_canonical.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) - model.modified_canonical.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force = model.modified_canonical.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.isotensional.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.modified_canonical.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_weak_potential_isotensional::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force = model.modified_canonical.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.isotensional.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.modified_canonical.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.isometric.force(end_to_end_length, temperature) -
model.modified_canonical.asymptotic.strong_potential.force(
end_to_end_length,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return model.isometric.force(end_to_end_length, temperature)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::nondimensional_force" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.isometric.nondimensional_force(
nondimensional_end_to_end_length_per_link,
) -
model.modified_canonical.asymptotic.strong_potential.nondimensional_force(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return model.isometric.nondimensional_force(
nondimensional_end_to_end_length_per_link,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.isometric.helmholtz_free_energy(end_to_end_length, temperature) -
model.isometric.helmholtz_free_energy(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
temperature,
) -
model.modified_canonical.asymptotic.strong_potential.helmholtz_free_energy(
end_to_end_length,
potential_stiffness,
temperature,
) +
model.modified_canonical.asymptotic.strong_potential.helmholtz_free_energy(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return (
model.isometric.helmholtz_free_energy(end_to_end_length, temperature) -
model.isometric.helmholtz_free_energy(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.isometric.helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
) - model.isometric.helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
temperature,
) -
model.modified_canonical.asymptotic.strong_potential.helmholtz_free_energy_per_link(
end_to_end_length,
potential_stiffness,
temperature,
) +
model.modified_canonical.asymptotic.strong_potential.helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return (
model.isometric.helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
) - model.isometric.helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.isometric.relative_helmholtz_free_energy(
end_to_end_length,
temperature,
) -
model.modified_canonical.asymptotic.strong_potential.relative_helmholtz_free_energy(
end_to_end_length,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return model.isometric.relative_helmholtz_free_energy(
end_to_end_length,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(end_to_end_length)
return (
model.isometric.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
) -
model.modified_canonical.asymptotic.strong_potential.relative_helmholtz_free_energy_per_link(
end_to_end_length,
potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(end_to_end_length)
return model.isometric.relative_helmholtz_free_energy_per_link(
end_to_end_length,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO * number_of_links * link_length,
parameters.nondimensional_potential_distance_small *
number_of_links *
link_length,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::nondimensional_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.isometric.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
) - model.isometric.nondimensional_helmholtz_free_energy(
parameters.nondimensional_potential_distance_small,
temperature,
) -
model.modified_canonical.asymptotic.strong_potential.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
temperature,
) +
model.modified_canonical.asymptotic.strong_potential.nondimensional_helmholtz_free_energy(
parameters.nondimensional_potential_distance_small,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return (
model.isometric.nondimensional_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
temperature,
) - model.isometric.nondimensional_helmholtz_free_energy(
parameters.nondimensional_potential_distance_small,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::nondimensional_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.isometric.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
) - model.isometric.nondimensional_helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small,
temperature,
) -
model.modified_canonical.asymptotic.strong_potential.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
temperature,
) +
model.modified_canonical.asymptotic.strong_potential.nondimensional_helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return (
model.isometric.nondimensional_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
temperature,
) - model.isometric.nondimensional_helmholtz_free_energy_per_link(
parameters.nondimensional_potential_distance_small,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::nondimensional_relative_helmholtz_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.isometric.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
) -
model.modified_canonical.asymptotic.strong_potential.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return model.isometric.nondimensional_relative_helmholtz_free_energy(
nondimensional_end_to_end_length_per_link,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_strong_potential_isometric::nondimensional_relative_helmholtz_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_end_to_end_length_per_link)
return (
model.isometric.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
) -
model.modified_canonical.asymptotic.strong_potential.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
nondimensional_potential_stiffness,
)
)^2
end
function integrand_denominator(nondimensional_end_to_end_length_per_link)
return model.isometric.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_end_to_end_length_per_link,
)^2
end
numerator = integrate(
integrand_numerator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
denominator = integrate(
integrand_denominator,
ZERO,
parameters.nondimensional_potential_distance_small,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_large)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_large * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.asymptotic.weak_potential.force(
potential_distance,
potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.end_to_end_length(
potential_distance,
potential_stiffness,
temperature,
) - model.isotensional.end_to_end_length(force, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.modified_canonical.asymptotic.weak_potential.end_to_end_length(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.asymptotic.weak_potential.force(
potential_distance,
potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
) - model.isotensional.end_to_end_length_per_link(force, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.modified_canonical.asymptotic.weak_potential.end_to_end_length_per_link(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::nondimensional_end_to_end_length" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force =
model.modified_canonical.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.isotensional.nondimensional_end_to_end_length(
nondimensional_force,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.modified_canonical.asymptotic.weak_potential.nondimensional_end_to_end_length(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::nondimensional_end_to_end_length_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force =
model.modified_canonical.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.isotensional.nondimensional_end_to_end_length_per_link(
nondimensional_force,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.modified_canonical.asymptotic.weak_potential.nondimensional_end_to_end_length_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance_ref =
parameters.nondimensional_potential_distance_large_1 *
number_of_links *
link_length
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
force_ref = model.modified_canonical.asymptotic.weak_potential.force(
potential_distance_ref,
potential_stiffness,
)
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.asymptotic.weak_potential.force(
potential_distance,
potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) -
model.modified_canonical.asymptotic.weak_potential.gibbs_free_energy(
potential_distance_ref,
potential_stiffness,
temperature,
) - model.isotensional.gibbs_free_energy(force, temperature) +
model.isotensional.gibbs_free_energy(force_ref, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.modified_canonical.asymptotic.weak_potential.gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) -
model.modified_canonical.asymptotic.weak_potential.gibbs_free_energy(
potential_distance_ref,
potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
potential_distance_ref =
parameters.nondimensional_potential_distance_large_1 *
number_of_links *
link_length
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
force_ref = model.modified_canonical.asymptotic.weak_potential.force(
potential_distance_ref,
potential_stiffness,
)
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.asymptotic.weak_potential.force(
potential_distance,
potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) -
model.modified_canonical.asymptotic.weak_potential.gibbs_free_energy_per_link(
potential_distance_ref,
potential_stiffness,
temperature,
) - model.isotensional.gibbs_free_energy_per_link(force, temperature) +
model.isotensional.gibbs_free_energy_per_link(force_ref, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return (
model.modified_canonical.asymptotic.weak_potential.gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) -
model.modified_canonical.asymptotic.weak_potential.gibbs_free_energy_per_link(
potential_distance_ref,
potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.asymptotic.weak_potential.force(
potential_distance,
potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
) - model.isotensional.relative_gibbs_free_energy(force, temperature)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.modified_canonical.asymptotic.weak_potential.relative_gibbs_free_energy(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
potential_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_potential_stiffness
function integrand_numerator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
force = model.modified_canonical.asymptotic.weak_potential.force(
potential_distance,
potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
) - model.isotensional.relative_gibbs_free_energy_per_link(
force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
potential_distance =
number_of_links * link_length * nondimensional_potential_distance
return model.modified_canonical.asymptotic.weak_potential.relative_gibbs_free_energy_per_link(
potential_distance,
potential_stiffness,
temperature,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::nondimensional_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_potential_distance_ref =
parameters.nondimensional_potential_distance_large_1
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
nondimensional_force_ref =
model.modified_canonical.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force =
model.modified_canonical.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -
model.modified_canonical.asymptotic.weak_potential.nondimensional_gibbs_free_energy(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
temperature,
) - model.isotensional.nondimensional_gibbs_free_energy(
nondimensional_force,
temperature,
) + model.isotensional.nondimensional_gibbs_free_energy(
nondimensional_force_ref,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return (
model.modified_canonical.asymptotic.weak_potential.nondimensional_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -
model.modified_canonical.asymptotic.weak_potential.nondimensional_gibbs_free_energy(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::nondimensional_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_potential_distance_ref =
parameters.nondimensional_potential_distance_large_1
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
nondimensional_force_ref =
model.modified_canonical.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force =
model.modified_canonical.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -
model.modified_canonical.asymptotic.weak_potential.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
temperature,
) - model.isotensional.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
) + model.isotensional.nondimensional_gibbs_free_energy_per_link(
nondimensional_force_ref,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return (
model.modified_canonical.asymptotic.weak_potential.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
temperature,
) -
model.modified_canonical.asymptotic.weak_potential.nondimensional_gibbs_free_energy_per_link(
nondimensional_potential_distance_ref,
nondimensional_potential_stiffness,
temperature,
)
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::nondimensional_relative_gibbs_free_energy" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force =
model.modified_canonical.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.isotensional.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.modified_canonical.asymptotic.weak_potential.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::fjc::thermodynamics::test::modified_canonical_asymptotic_weak_potential_isotensional::nondimensional_relative_gibbs_free_energy_per_link" begin
for _ = 1:parameters.number_of_loops
number_of_links =
parameters.number_of_links_maximum - parameters.number_of_links_minimum
link_length =
parameters.link_length_reference + parameters.link_length_scale * (0.5 - rand())
hinge_mass =
parameters.hinge_mass_reference + parameters.hinge_mass_scale * (0.5 - rand())
model = FJC(number_of_links, link_length, hinge_mass)
function residual_rel(nondimensional_potential_stiffness)
function integrand_numerator(nondimensional_potential_distance)
nondimensional_force =
model.modified_canonical.asymptotic.weak_potential.nondimensional_force(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)
return (
model.modified_canonical.asymptotic.weak_potential.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
) - model.isotensional.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
)
)^2
end
function integrand_denominator(nondimensional_potential_distance)
return model.modified_canonical.asymptotic.weak_potential.nondimensional_relative_gibbs_free_energy(
nondimensional_potential_distance,
nondimensional_potential_stiffness,
)^2
end
numerator = integrate(
integrand_numerator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
denominator = integrate(
integrand_denominator,
parameters.nondimensional_potential_distance_large_1,
parameters.nondimensional_potential_distance_large_2,
POINTS,
)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_potential_stiffness_small)
residual_rel_2 = residual_rel(
parameters.nondimensional_potential_stiffness_small * parameters.log_log_scale,
)
log_log_slope =
-log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(log_log_slope + 1.0) <= parameters.log_log_tol
end
end
end