module Test
using Test
using Polymers.Physics: BOLTZMANN_CONSTANT
using Polymers.Physics.SingleChain: ONE, ZERO, POINTS, integrate, parameters
using Polymers.Physics.SingleChain.Ufjc.LogSquared.Thermodynamics.Isotensional:
LOGSQUAREDFJC
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::base::init" begin
@test isa(
LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
),
Any,
)
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::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 LOGSQUAREDFJC(
number_of_links,
parameters.link_length_reference,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).number_of_links == number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::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 LOGSQUAREDFJC(
parameters.number_of_links_minimum,
link_length,
parameters.hinge_mass_reference,
parameters.link_stiffness_reference,
).link_length == link_length
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::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 LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
hinge_mass,
parameters.link_stiffness_reference,
).hinge_mass == hinge_mass
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::base::link_stiffness" begin
for _ = 1:parameters.number_of_loops
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test LOGSQUAREDFJC(
parameters.number_of_links_minimum,
parameters.link_length_reference,
parameters.hinge_mass_reference,
link_stiffness,
).link_stiffness == link_stiffness
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
@test all(
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).number_of_links == number_of_links &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_length == link_length &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).hinge_mass == hinge_mass &&
LOGSQUAREDFJC(
number_of_links,
link_length,
hinge_mass,
link_stiffness,
).link_stiffness == link_stiffness,
)
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::nondimensional::end_to_end_length" 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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
residual_abs = end_to_end_length / link_length - nondimensional_end_to_end_length
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::nondimensional::end_to_end_length_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs =
end_to_end_length_per_link / link_length -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::nondimensional::gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
residual_abs =
gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::nondimensional::gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::nondimensional::relative_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs =
relative_gibbs_free_energy / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::nondimensional::relative_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy_per_link / BOLTZMANN_CONSTANT / temperature -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::per_link::end_to_end_length" 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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
residual_abs = end_to_end_length / number_of_links - end_to_end_length_per_link
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::per_link::nondimensional_end_to_end_length" 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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_end_to_end_length / number_of_links -
nondimensional_end_to_end_length_per_link
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::per_link::gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
residual_abs = gibbs_free_energy / number_of_links - gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::per_link::relative_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
relative_gibbs_free_energy / number_of_links -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::per_link::nondimensional_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy / number_of_links -
nondimensional_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::per_link::nondimensional_relative_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_relative_gibbs_free_energy / number_of_links -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::relative::gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_0 = model.gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
residual_abs = gibbs_free_energy - gibbs_free_energy_0 - relative_gibbs_free_energy
residual_rel = residual_abs / gibbs_free_energy_0
@test abs(residual_abs) <=
BOLTZMANN_CONSTANT * temperature * number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::relative::gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_0 = model.gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
residual_abs =
gibbs_free_energy_per_link - gibbs_free_energy_per_link_0 -
relative_gibbs_free_energy_per_link
residual_rel = residual_abs / gibbs_free_energy_per_link_0
@test abs(residual_abs) <= BOLTZMANN_CONSTANT * temperature * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::relative::nondimensional_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_0 =
model.nondimensional_gibbs_free_energy(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_0 -
nondimensional_relative_gibbs_free_energy
residual_rel = residual_abs / nondimensional_gibbs_free_energy_0
@test abs(residual_abs) <= number_of_links * parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::relative::nondimensional_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_0 =
model.nondimensional_gibbs_free_energy_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_0 -
nondimensional_relative_gibbs_free_energy_per_link
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link_0
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::zero::relative_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_0 = model.relative_gibbs_free_energy(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature * number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::zero::relative_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
relative_gibbs_free_energy_per_link_0 = model.relative_gibbs_free_energy_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
@test abs(relative_gibbs_free_energy_per_link_0) <=
ZERO * BOLTZMANN_CONSTANT * temperature
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::zero::nondimensional_relative_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_0 =
model.nondimensional_relative_gibbs_free_energy(ZERO, temperature)
@test abs(nondimensional_relative_gibbs_free_energy_0) <= ZERO * number_of_links
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::zero::nondimensional_relative_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_relative_gibbs_free_energy_per_link_0 =
model.nondimensional_relative_gibbs_free_energy_per_link(ZERO, temperature)
@test abs(nondimensional_relative_gibbs_free_energy_per_link_0) <= ZERO
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::connection::end_to_end_length" 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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_from_derivative =
-(
model.relative_gibbs_free_energy(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy(force - 0.5 * h, temperature)
) / h
residual_abs = end_to_end_length - end_to_end_length_from_derivative
residual_rel = residual_abs / end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::connection::end_to_end_length_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link_from_derivative =
-(
model.relative_gibbs_free_energy_per_link(force + 0.5 * h, temperature) -
model.relative_gibbs_free_energy_per_link(force - 0.5 * h, temperature)
) / h
residual_abs =
end_to_end_length_per_link - end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::connection::nondimensional_end_to_end_length" 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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
h = parameters.rel_tol
nondimensional_end_to_end_length_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_relative_gibbs_free_energy(
nondimensional_force - 0.5 * h,
temperature,
)
) / h
residual_abs =
nondimensional_end_to_end_length -
nondimensional_end_to_end_length_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::connection::nondimensional_end_to_end_length_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
h = parameters.rel_tol
nondimensional_end_to_end_length_per_link_from_derivative =
-(
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
) / h
residual_abs =
nondimensional_end_to_end_length_per_link -
nondimensional_end_to_end_length_per_link_from_derivative
residual_rel = residual_abs / nondimensional_end_to_end_length_per_link
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre::gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
gibbs_free_energy = model.gibbs_free_energy(force, temperature)
gibbs_free_energy_legendre =
model.legendre.helmholtz_free_energy(force, temperature) -
force * end_to_end_length
residual_abs = gibbs_free_energy - gibbs_free_energy_legendre
residual_rel = residual_abs / gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre::gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
gibbs_free_energy_per_link = model.gibbs_free_energy_per_link(force, temperature)
gibbs_free_energy_per_link_legendre =
model.legendre.helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link
residual_abs = gibbs_free_energy_per_link - gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre::relative_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length = model.end_to_end_length(force, temperature)
end_to_end_length_0 = model.end_to_end_length(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy = model.relative_gibbs_free_energy(force, temperature)
relative_gibbs_free_energy_legendre =
model.legendre.relative_helmholtz_free_energy(force, temperature) -
force * end_to_end_length +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length * end_to_end_length_0
residual_abs = relative_gibbs_free_energy - relative_gibbs_free_energy_legendre
residual_rel = residual_abs / relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre::relative_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
end_to_end_length_per_link = model.end_to_end_length_per_link(force, temperature)
end_to_end_length_per_link_0 = model.end_to_end_length_per_link(
ZERO * BOLTZMANN_CONSTANT * temperature / link_length,
temperature,
)
relative_gibbs_free_energy_per_link =
model.relative_gibbs_free_energy_per_link(force, temperature)
relative_gibbs_free_energy_per_link_legendre =
model.legendre.relative_helmholtz_free_energy_per_link(force, temperature) -
force * end_to_end_length_per_link +
ZERO * BOLTZMANN_CONSTANT * temperature / link_length *
end_to_end_length_per_link_0
residual_abs =
relative_gibbs_free_energy_per_link -
relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre::nondimensional_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_gibbs_free_energy =
model.nondimensional_gibbs_free_energy(nondimensional_force, temperature)
nondimensional_gibbs_free_energy_legendre =
model.legendre.nondimensional_helmholtz_free_energy(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length
residual_abs =
nondimensional_gibbs_free_energy - nondimensional_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre::nondimensional_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link =
model.nondimensional_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link
residual_abs =
nondimensional_gibbs_free_energy_per_link -
nondimensional_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre::nondimensional_relative_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length =
model.nondimensional_end_to_end_length(nondimensional_force, temperature)
nondimensional_end_to_end_length_0 =
model.nondimensional_end_to_end_length(ZERO, temperature)
nondimensional_relative_gibbs_free_energy =
model.nondimensional_relative_gibbs_free_energy(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length +
ZERO * nondimensional_end_to_end_length_0
residual_abs =
nondimensional_relative_gibbs_free_energy -
nondimensional_relative_gibbs_free_energy_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre::nondimensional_relative_gibbs_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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
nondimensional_end_to_end_length_per_link =
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
nondimensional_end_to_end_length_per_link_0 =
model.nondimensional_end_to_end_length_per_link(ZERO, temperature)
nondimensional_relative_gibbs_free_energy_per_link =
model.nondimensional_relative_gibbs_free_energy_per_link(
nondimensional_force,
temperature,
)
nondimensional_relative_gibbs_free_energy_per_link_legendre =
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force,
temperature,
) - nondimensional_force * nondimensional_end_to_end_length_per_link +
ZERO * nondimensional_end_to_end_length_per_link_0
residual_abs =
nondimensional_relative_gibbs_free_energy_per_link -
nondimensional_relative_gibbs_free_energy_per_link_legendre
residual_rel = residual_abs / nondimensional_relative_gibbs_free_energy_per_link
@test abs(residual_abs) <= parameters.abs_tol &&
abs(residual_rel) <= parameters.rel_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre_connection::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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
force = nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
h = parameters.rel_tol * BOLTZMANN_CONSTANT * temperature / link_length
force_from_derivative =
(
model.legendre.relative_helmholtz_free_energy(
force + 0.5 * h,
temperature,
) -
model.legendre.relative_helmholtz_free_energy(force - 0.5 * h, temperature)
) / (
model.end_to_end_length(force + 0.5 * h, temperature) -
model.end_to_end_length(force - 0.5 * h, temperature)
)
residual_abs = force - force_from_derivative
residual_rel = residual_abs / force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::legendre_connection::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())
link_stiffness =
parameters.link_stiffness_reference +
parameters.link_stiffness_scale * (0.5 - rand())
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
nondimensional_force_max =
link_stiffness / BOLTZMANN_CONSTANT / temperature * link_length^2 / exp(1)
nondimensional_force = nondimensional_force_max * rand()
h = parameters.rel_tol
nondimensional_force_from_derivative =
(
model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.legendre.nondimensional_relative_helmholtz_free_energy_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
) / (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force + 0.5 * h,
temperature,
) - model.nondimensional_end_to_end_length_per_link(
nondimensional_force - 0.5 * h,
temperature,
)
)
residual_abs = nondimensional_force - nondimensional_force_from_derivative
residual_rel = residual_abs / nondimensional_force
@test abs(residual_rel) <= h
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::asymptotic::end_to_end_length" 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())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return (
model.end_to_end_length(force, temperature) -
model.asymptotic.end_to_end_length(force, temperature)
)^2
end
function integrand_denominator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return model.end_to_end_length(force, temperature)^2
end
nondimensional_link_stretch_max = exp(1)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(0.5 * log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::asymptotic::end_to_end_length_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())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return (
model.end_to_end_length_per_link(force, temperature) -
model.asymptotic.end_to_end_length_per_link(force, temperature)
)^2
end
function integrand_denominator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return model.end_to_end_length_per_link(force, temperature)^2
end
nondimensional_link_stretch_max = exp(1)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(0.5 * log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::asymptotic::nondimensional_end_to_end_length" 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())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
return (
model.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
) - model.asymptotic.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_force)
return model.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)^2
end
nondimensional_link_stretch_max = exp(1)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(0.5 * log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::asymptotic::nondimensional_end_to_end_length_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())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
return (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
) - model.asymptotic.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_force)
return model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)^2
end
nondimensional_link_stretch_max = exp(1)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * parameters.log_log_scale,
)
log_log_slope = log(residual_rel_2 / residual_rel_1) / log(parameters.log_log_scale)
@test abs(0.5 * log_log_slope + 1.0) <= parameters.log_log_tol
end
end
@testset "physics::single_chain::ufjc::log_squared::thermodynamics::isotensional::test::asymptotic_reduced::end_to_end_length" 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())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return (
model.end_to_end_length(force, temperature) -
model.asymptotic.reduced.end_to_end_length(force, temperature)
)^2
end
function integrand_denominator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return model.end_to_end_length(force, temperature)^2
end
nondimensional_link_stretch_max = exp(1)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * 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::ufjc::log_squared::thermodynamics::isotensional::test::asymptotic_reduced::end_to_end_length_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())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return (
model.end_to_end_length_per_link(force, temperature) -
model.asymptotic.reduced.end_to_end_length_per_link(force, temperature)
)^2
end
function integrand_denominator(nondimensional_force)
force =
nondimensional_force * BOLTZMANN_CONSTANT * temperature / link_length
return model.end_to_end_length_per_link(force, temperature)^2
end
nondimensional_link_stretch_max = exp(1)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * 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::ufjc::log_squared::thermodynamics::isotensional::test::asymptotic_reduced::nondimensional_end_to_end_length" 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())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
return (
model.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
) - model.asymptotic.reduced.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_force)
return model.nondimensional_end_to_end_length(
nondimensional_force,
temperature,
)^2
end
nondimensional_link_stretch_max = exp(1)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * 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::ufjc::log_squared::thermodynamics::isotensional::test::asymptotic_reduced::nondimensional_end_to_end_length_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())
temperature =
parameters.temperature_reference + parameters.temperature_scale * (0.5 - rand())
function residual_rel(nondimensional_link_stiffness)
link_stiffness =
BOLTZMANN_CONSTANT * temperature / link_length^2 *
nondimensional_link_stiffness
model = LOGSQUAREDFJC(number_of_links, link_length, hinge_mass, link_stiffness)
function integrand_numerator(nondimensional_force)
return (
model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
) - model.asymptotic.reduced.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)
)^2
end
function integrand_denominator(nondimensional_force)
return model.nondimensional_end_to_end_length_per_link(
nondimensional_force,
temperature,
)^2
end
nondimensional_link_stretch_max = exp(1)
nondimensional_force_max = nondimensional_link_stretch_max
numerator =
integrate(integrand_numerator, ZERO, nondimensional_force_max, POINTS)
denominator =
integrate(integrand_denominator, ZERO, nondimensional_force_max, POINTS)
return sqrt(numerator / denominator)
end
residual_rel_1 = residual_rel(parameters.nondimensional_link_stiffness_big)
residual_rel_2 = residual_rel(
parameters.nondimensional_link_stiffness_big * 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