"""
The worm-like chain (WLC) model thermodynamics in the isotensional ensemble.
"""
module Isotensional
using DocStringExtensions
using ......Polymers: PROJECT_ROOT
include("legendre/mod.jl")
"""
The structure of the thermodynamics of the WLC model in the isotensional ensemble.
$(FIELDS)
"""
struct WLC
"""
The number of links in the chain ``N_b``.
"""
number_of_links::UInt8
"""
The length of each link in the chain ``\\ell_b`` in units of nm.
"""
link_length::Float64
"""
The mass of each hinge in the chain ``m`` in units of kg/mol.
"""
hinge_mass::Float64
"""
The persistance length of the chain in units of nm.
"""
persistance_length::Float64
nondimensional_persistance_length::Float64
"""
The thermodynamic functions of the model in the isotensional ensemble approximated using a Legendre transformation.
"""
legendre::Any
"""
The expected force ``f`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length::Function
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied force ``f`` and temperature ``T``.
"""
end_to_end_length_per_link::Function
"""
The expected nondimensional end-to-end length ``N_b\\gamma=\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length::Function
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_end_to_end_length_per_link::Function
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy::Function
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
gibbs_free_energy_per_link::Function
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy::Function
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``.
"""
relative_gibbs_free_energy_per_link::Function
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy::Function
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``.
"""
nondimensional_gibbs_free_energy_per_link::Function
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy::Function
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``.
"""
nondimensional_relative_gibbs_free_energy_per_link::Function
end
"""
The expected force ``f`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and persistance length ``\\ell_p``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
persistance_length::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, persistance_length_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
persistance_length_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
persistance_length,
force,
temperature,
)
end
"""
The expected end-to-end length per link ``\\xi/N_b=\\ell_b\\gamma`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, and persistance length ``\\ell_p``.
$(TYPEDSIGNATURES)
"""
function end_to_end_length_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
persistance_length::Union{Float64,Vector,Matrix,Array},
force::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, link_length_i, persistance_length_i, force_i, temperature_i) ->
ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
persistance_length_i,
force_i,
temperature_i,
),
number_of_links,
link_length,
persistance_length,
force,
temperature,
)
end
"""
The expected nondimensional end-to-end length ``N_b\\gamma\\equiv\\xi/\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional persistance length ``\\zeta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_persistance_length::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_persistance_length_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_nondimensional_end_to_end_length,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_persistance_length_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_persistance_length,
nondimensional_force,
)
end
"""
The expected nondimensional end-to-end length per link ``\\gamma\\equiv\\xi/N_b\\ell_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional persistance length ``\\zeta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_end_to_end_length_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_persistance_length::Union{Float64,Vector,Matrix,Array},
nondimensional_force::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(number_of_links_i, nondimensional_persistance_length_i, nondimensional_force_i) ->
ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_nondimensional_end_to_end_length_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_persistance_length_i,
nondimensional_force_i,
),
number_of_links,
nondimensional_persistance_length,
nondimensional_force,
)
end
"""
The Gibbs free energy ``\\varphi`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and persistance length ``\\ell_p``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
persistance_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
persistance_length,
end_to_end_length,
temperature,
)
end
"""
The Gibbs free energy per link ``\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and persistance length ``\\ell_p``.
$(TYPEDSIGNATURES)
"""
function gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
persistance_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
persistance_length,
end_to_end_length,
temperature,
)
end
"""
The relative Gibbs free energy ``\\Delta\\varphi\\equiv\\varphi(f,T)-\\varphi(0,T)`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b`` link length ``\\ell_b``, and persistance length ``\\ell_p``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
persistance_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
persistance_length,
end_to_end_length,
temperature,
)
end
"""
The relative Gibbs free energy per link ``\\Delta\\varphi/N_b`` as a function of the applied force ``f`` and temperature ``T``,
parameterized by the number of links ``N_b`` link length ``\\ell_b``, and persistance length ``\\ell_p``.
$(TYPEDSIGNATURES)
"""
function relative_gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
persistance_length::Union{Float64,Vector,Matrix,Array},
end_to_end_length::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
persistance_length_i,
end_to_end_length_i,
temperature_i,
),
number_of_links,
link_length,
persistance_length,
end_to_end_length,
temperature,
)
end
"""
The nondimensional Gibbs free energy ``N_b\\varrho=\\beta\\varphi`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional persistance length ``\\zeta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_persistance_length::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_nondimensional_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_persistance_length,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional Gibbs free energy per link ``\\varrho\\equiv\\beta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta`` and temperature ``T``,
parameterized by the number of links ``N_b``, link length ``\\ell_b``, hinge mass ``m``, and nondimensional persistance length ``\\zeta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
link_length::Union{Float64,Vector,Matrix,Array},
hinge_mass::Union{Float64,Vector,Matrix,Array},
nondimensional_persistance_length::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
temperature::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_nondimensional_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64, Float64, Float64, Float64),
number_of_links_i,
link_length_i,
hinge_mass_i,
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
temperature_i,
),
number_of_links,
link_length,
hinge_mass,
nondimensional_persistance_length,
nondimensional_end_to_end_length_per_link,
temperature,
)
end
"""
The nondimensional relative Gibbs free energy ``N_b\\Delta\\varrho=\\beta\\Delta\\varphi`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the nondimensional persistance length ``\\zeta``.
```
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_persistance_length::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_persistance_length,
nondimensional_end_to_end_length_per_link,
)
end
"""
The nondimensional relative Gibbs free energy per link ``\\Delta\\varrho\\equiv\\beta\\Delta\\varphi/N_b`` as a function of the applied nondimensional force ``\\eta``,
parameterized by the number of links ``N_b`` and nondimensional persistance length ``\\zeta``.
$(TYPEDSIGNATURES)
"""
function nondimensional_relative_gibbs_free_energy_per_link(
number_of_links::Union{UInt8,Vector,Matrix,Array},
nondimensional_persistance_length::Union{Float64,Vector,Matrix,Array},
nondimensional_end_to_end_length_per_link::Union{Float64,Vector,Matrix,Array},
)::Union{Float64,Vector,Matrix,Array}
return broadcast(
(
number_of_links_i,
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
) -> ccall(
(
:physics_single_chain_wlc_thermodynamics_isotensional_nondimensional_relative_gibbs_free_energy_per_link,
string(PROJECT_ROOT, "target/release/libpolymers"),
),
Float64,
(UInt8, Float64, Float64),
number_of_links_i,
nondimensional_persistance_length_i,
nondimensional_end_to_end_length_per_link_i,
),
number_of_links,
nondimensional_persistance_length,
nondimensional_end_to_end_length_per_link,
)
end
"""
Initializes and returns an instance of the thermodynamics of the WLC model in the isotensional ensemble.
$(TYPEDSIGNATURES)
"""
function WLC(
number_of_links::UInt8,
link_length::Float64,
hinge_mass::Float64,
persistance_length::Float64,
)
nondimensional_persistance_length = persistance_length / number_of_links / link_length
return WLC(
number_of_links,
link_length,
hinge_mass,
persistance_length,
nondimensional_persistance_length,
Legendre.WLC(number_of_links, link_length, hinge_mass, persistance_length),
(force, temperature) -> end_to_end_length(
number_of_links,
link_length,
persistance_length,
force,
temperature,
),
(force, temperature) -> end_to_end_length_per_link(
number_of_links,
link_length,
persistance_length,
force,
temperature,
),
(nondimensional_force) -> nondimensional_end_to_end_length(
number_of_links,
nondimensional_persistance_length,
nondimensional_force,
),
(nondimensional_force) -> nondimensional_end_to_end_length_per_link(
number_of_links,
nondimensional_persistance_length,
nondimensional_force,
),
(force, temperature) -> gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
persistance_length,
force,
temperature,
),
(force, temperature) -> gibbs_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
persistance_length,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy(
number_of_links,
link_length,
persistance_length,
force,
temperature,
),
(force, temperature) -> relative_gibbs_free_energy_per_link(
number_of_links,
link_length,
persistance_length,
force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy(
number_of_links,
link_length,
hinge_mass,
nondimensional_persistance_length,
nondimensional_force,
temperature,
),
(nondimensional_force, temperature) -> nondimensional_gibbs_free_energy_per_link(
number_of_links,
link_length,
hinge_mass,
nondimensional_persistance_length,
nondimensional_force,
temperature,
),
(nondimensional_force) -> nondimensional_relative_gibbs_free_energy(
number_of_links,
nondimensional_persistance_length,
nondimensional_force,
),
(nondimensional_force) -> nondimensional_relative_gibbs_free_energy_per_link(
number_of_links,
nondimensional_persistance_length,
nondimensional_force,
),
)
end
end