polymers 0.3.7

Polymers Modeling Library
Documentation 
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#[cfg(feature = "extern")]
pub mod ex;

#[cfg(feature = "python")]
pub mod py;

mod test;

/// The worm-like chain (WLC) model thermodynamics in the isotensional ensemble approximated using a Legendre transformation.
pub mod legendre;

use std::f64::consts::PI;
use crate::math::
{
    inverse_newton_raphson_powered,
    integrate_1d
};
use crate::physics::
{
    PLANCK_CONSTANT,
    BOLTZMANN_CONSTANT
};
use crate::physics::single_chain::
{
    ONE,
    ZERO,
    POINTS
};
use super::isometric::nondimensional_force as isometric_nondimensional_force;
use super::isometric::nondimensional_helmholtz_free_energy as isometric_nondimensional_helmholtz_free_energy;
use super::isometric::nondimensional_relative_helmholtz_free_energy as isometric_nondimensional_relative_helmholtz_free_energy;

/// The structure of the thermodynamics of the WLC model in the isotensional ensemble.
pub struct WLC
{
    /// The mass of each hinge in the chain in units of kg/mol.
    pub hinge_mass: f64,

    /// The length of each link in the chain in units of nm.
    pub link_length: f64,

    /// The number of links in the chain.
    pub number_of_links: u8,

    /// The persistance length of the chain in units of nm.
    pub persistance_length: f64,

    nondimensional_persistance_length: f64,

    /// The thermodynamic functions of the model in the isotensional ensemble approximated using a Legendre transformation.
    pub legendre: self::legendre::WLC
}

/// The expected end-to-end length as a function of the applied force and temperature, parameterized by the number of links, link length, and persistance length.
pub fn end_to_end_length(number_of_links: &u8, link_length: &f64, persistance_length: &f64, force: &f64, temperature: &f64) -> f64
{
    link_length*nondimensional_end_to_end_length(number_of_links, &(persistance_length/((*number_of_links as f64)*link_length)), &(force*link_length/BOLTZMANN_CONSTANT/temperature))
}

/// The expected end-to-end length per link as a function of the applied force and temperature, parameterized by the number of links, link length, and persistance length.
pub fn end_to_end_length_per_link(number_of_links: &u8, link_length: &f64, persistance_length: &f64, force: &f64, temperature: &f64) -> f64
{
    link_length*nondimensional_end_to_end_length_per_link(number_of_links, &(persistance_length/((*number_of_links as f64)*link_length)), &(force*link_length/BOLTZMANN_CONSTANT/temperature))
}

/// The expected nondimensional end-to-end length as a function of the applied nondimensional force, parameterized by the number of links and nondimensional persistance length.
pub fn nondimensional_end_to_end_length(number_of_links: &u8, nondimensional_persistance_length: &f64, nondimensional_force: &f64) -> f64
{
    let f = &|nondimensional_end_to_end_length_per_link: &f64| isometric_nondimensional_force(number_of_links, nondimensional_persistance_length, nondimensional_end_to_end_length_per_link);
    let fp = &|nondimensional_end_to_end_length_per_link: &f64| (isometric_nondimensional_force(number_of_links, nondimensional_persistance_length, &(nondimensional_end_to_end_length_per_link + 1e-8)) - isometric_nondimensional_force(number_of_links, nondimensional_persistance_length, &(nondimensional_end_to_end_length_per_link - 1e-8)))/2e-8;
    let gamma_hat = inverse_newton_raphson_powered(nondimensional_force, f, fp, &0.9999, &1e-5, &100, 2);
    if !(0.0..=1.0).contains(&gamma_hat)
    {
        panic!("Root finding failed!");
    }
    let scale = (*number_of_links as f64)*nondimensional_force*gamma_hat - isometric_nondimensional_relative_helmholtz_free_energy(nondimensional_persistance_length, &gamma_hat);
    let integrand_denominator = |nondimensional_end_to_end_length_per_link: &f64|
    {
        let beta_delta_psi = isometric_nondimensional_relative_helmholtz_free_energy(nondimensional_persistance_length, nondimensional_end_to_end_length_per_link);
        let beta_f_xi = (*number_of_links as f64)*nondimensional_force*nondimensional_end_to_end_length_per_link;
        ((beta_f_xi - scale - beta_delta_psi).exp() - (-beta_f_xi - scale - beta_delta_psi).exp())*nondimensional_end_to_end_length_per_link/nondimensional_force
    };
    let integrand_numerator = |nondimensional_end_to_end_length_per_link: &f64|
    {
        let beta_delta_psi = isometric_nondimensional_relative_helmholtz_free_energy(nondimensional_persistance_length, nondimensional_end_to_end_length_per_link);
        let beta_f_xi = (*number_of_links as f64)*nondimensional_force*nondimensional_end_to_end_length_per_link;
        let exp_1 = (beta_f_xi - scale - beta_delta_psi).exp();
        let exp_2 = (-beta_f_xi - scale - beta_delta_psi).exp();
        ((exp_1 + exp_2)*(*number_of_links as f64)*nondimensional_end_to_end_length_per_link - (exp_1 - exp_2)/nondimensional_force)*nondimensional_end_to_end_length_per_link/nondimensional_force
    };
    integrate_1d(&integrand_numerator, &ZERO, &ONE, &POINTS)/integrate_1d(&integrand_denominator, &ZERO, &ONE, &POINTS)
}

/// The expected nondimensional end-to-end length per link as a function of the applied nondimensional force, parameterized by the number of links and nondimensional persistance length.
pub fn nondimensional_end_to_end_length_per_link(number_of_links: &u8, nondimensional_persistance_length: &f64, nondimensional_force: &f64) -> f64
{
    nondimensional_end_to_end_length(number_of_links, nondimensional_persistance_length, nondimensional_force)/(*number_of_links as f64)
}

/// The Gibbs free energy as a function of the applied force and temperature, parameterized by the number of links, link length, hinge mass, and persistance length.
pub fn gibbs_free_energy(number_of_links: &u8, link_length: &f64, hinge_mass: &f64, persistance_length: &f64, force: &f64, temperature: &f64) -> f64
{
    nondimensional_gibbs_free_energy(number_of_links, link_length, hinge_mass, &(persistance_length/((*number_of_links as f64)*link_length)), &(force*link_length/BOLTZMANN_CONSTANT/temperature), temperature)*BOLTZMANN_CONSTANT*temperature
}

/// The Gibbs free energy per link as a function of the applied force and temperature, parameterized by the number of links, link length, hinge mass, and persistance length.
pub fn gibbs_free_energy_per_link(number_of_links: &u8, link_length: &f64, hinge_mass: &f64, persistance_length: &f64, force: &f64, temperature: &f64) -> f64
{
    nondimensional_gibbs_free_energy_per_link(number_of_links, link_length, hinge_mass, &(persistance_length/((*number_of_links as f64)*link_length)), &(force*link_length/BOLTZMANN_CONSTANT/temperature), temperature)*BOLTZMANN_CONSTANT*temperature
}

/// The relative Gibbs free energy as a function of the applied force and temperature, parameterized by the number of links, link length, and persistance length.
pub fn relative_gibbs_free_energy(number_of_links: &u8, link_length: &f64, persistance_length: &f64, force: &f64, temperature: &f64) -> f64
{
    nondimensional_relative_gibbs_free_energy(number_of_links, &(persistance_length/((*number_of_links as f64)*link_length)), &(force*link_length/BOLTZMANN_CONSTANT/temperature))*BOLTZMANN_CONSTANT*temperature
}

/// The relative Gibbs free energy per link as a function of the applied force and temperature, parameterized by the number of links, link length, and persistance length.
pub fn relative_gibbs_free_energy_per_link(number_of_links: &u8, link_length: &f64, persistance_length: &f64, force: &f64, temperature: &f64) -> f64
{
    nondimensional_relative_gibbs_free_energy_per_link(number_of_links, &(persistance_length/((*number_of_links as f64)*link_length)), &(force*link_length/BOLTZMANN_CONSTANT/temperature))*BOLTZMANN_CONSTANT*temperature
}

/// The nondimensional Gibbs free energy as a function of the applied nondimensional force and temperature, parameterized by the number of links, link length, hinge mass, and nondimensional persistance length.
pub fn nondimensional_gibbs_free_energy(number_of_links: &u8, link_length: &f64, hinge_mass: &f64, nondimensional_persistance_length: &f64, nondimensional_force: &f64, temperature: &f64) -> f64
{
    let f = &|nondimensional_end_to_end_length_per_link: &f64| isometric_nondimensional_force(number_of_links, nondimensional_persistance_length, nondimensional_end_to_end_length_per_link);
    let fp = &|nondimensional_end_to_end_length_per_link: &f64| (isometric_nondimensional_force(number_of_links, nondimensional_persistance_length, &(nondimensional_end_to_end_length_per_link + 1e-8)) - isometric_nondimensional_force(number_of_links, nondimensional_persistance_length, &(nondimensional_end_to_end_length_per_link - 1e-8)))/2e-8;
    let fpp = &|x: &f64| (fp(&(x + 1e-8)) - fp(&(x - 1e-8)))/2e-8;
    let gamma_hat = inverse_newton_raphson_powered(nondimensional_force, f, fp, &0.9999, &1e-5, &100, 2);
    if !(0.0..=1.0).contains(&gamma_hat)
    {
        panic!("Root finding failed!");
    }
    let scale = (*number_of_links as f64)*nondimensional_force*gamma_hat - isometric_nondimensional_helmholtz_free_energy(number_of_links, link_length, hinge_mass, nondimensional_persistance_length, &gamma_hat, temperature);
    let log_integral = if nondimensional_force > &100.0
    {
        -((8.0*PI.powi(2)/fpp(&gamma_hat)).sqrt()).ln() - (0.5*(*number_of_links as f64)*gamma_hat/nondimensional_force).ln()
    }
    else
    {
        let integrand = |nondimensional_end_to_end_length_per_link: &f64|
        {
            let beta_psi = isometric_nondimensional_helmholtz_free_energy(number_of_links, link_length, hinge_mass, nondimensional_persistance_length, nondimensional_end_to_end_length_per_link, temperature);
            let beta_f_xi = (*number_of_links as f64)*nondimensional_force*nondimensional_end_to_end_length_per_link;
            0.5*((beta_f_xi - scale - beta_psi).exp() - (-beta_f_xi - scale - beta_psi).exp())*(*number_of_links as f64)*nondimensional_end_to_end_length_per_link/nondimensional_force
        };
        -(4.0*PI*integrate_1d(&integrand, &ZERO, &ONE, &POINTS)).ln()
    };
    log_integral - scale - (4.0*(-1.0/nondimensional_persistance_length).exp().acos().sin()*PI.powi(2)*hinge_mass*link_length.powi(2)*BOLTZMANN_CONSTANT*temperature/PLANCK_CONSTANT.powi(2)).ln()
}

/// The nondimensional Gibbs free energy per link as a function of the applied nondimensional force and temperature, parameterized by the number of links, link length, and hinge mass, and nondimensional persistance length.
pub fn nondimensional_gibbs_free_energy_per_link(number_of_links: &u8, link_length: &f64, hinge_mass: &f64, nondimensional_persistance_length: &f64, nondimensional_force: &f64, temperature: &f64) -> f64
{
    nondimensional_gibbs_free_energy(number_of_links, link_length, hinge_mass, nondimensional_persistance_length, nondimensional_force, temperature)/(*number_of_links as f64)
}

/// The nondimensional relative Gibbs free energy as a function of the applied nondimensional force, parameterized by the number of links and nondimensional persistance length.
pub fn nondimensional_relative_gibbs_free_energy(number_of_links: &u8, nondimensional_persistance_length: &f64, nondimensional_force: &f64) -> f64
{
    nondimensional_gibbs_free_energy(number_of_links, &1.0, &1.0, nondimensional_persistance_length, nondimensional_force, &300.0) - nondimensional_gibbs_free_energy(number_of_links, &1.0, &1.0, nondimensional_persistance_length, &ZERO, &300.0)
}

/// The nondimensional relative Gibbs free energy per link as a function of the applied nondimensional force, parameterized by the number of links and nondimensional persistance length.
pub fn nondimensional_relative_gibbs_free_energy_per_link(number_of_links: &u8, nondimensional_persistance_length: &f64, nondimensional_force: &f64) -> f64
{
    nondimensional_gibbs_free_energy_per_link(number_of_links, &1.0, &1.0, nondimensional_persistance_length, nondimensional_force, &300.0) - nondimensional_gibbs_free_energy_per_link(number_of_links, &1.0, &1.0, nondimensional_persistance_length, &ZERO, &300.0)
}

/// The implemented functionality of the thermodynamics of the WLC model in the isotensional ensemble.
impl WLC
{
    /// Initializes and returns an instance of the thermodynamics of the WLC model in the isotensional ensemble.
    pub fn init(number_of_links: u8, link_length: f64, hinge_mass: f64, persistance_length: f64) -> Self
    {
        WLC
        {
            hinge_mass,
            link_length,
            number_of_links,
            persistance_length,
            nondimensional_persistance_length: persistance_length/(number_of_links as f64)/link_length,
            legendre: self::legendre::WLC::init(number_of_links, link_length, hinge_mass, persistance_length)
        }
    }
    /// The expected end-to-end length as a function of the applied force and temperature.
    pub fn end_to_end_length(&self, force: &f64, temperature: &f64) -> f64
    {
        end_to_end_length(&self.number_of_links, &self.link_length, &self.persistance_length, force, temperature)
    }
    /// The expected end-to-end length per link as a function of the applied force and temperature.
    pub fn end_to_end_length_per_link(&self, force: &f64, temperature: &f64) -> f64
    {
        end_to_end_length_per_link(&self.number_of_links, &self.link_length, &self.persistance_length, force, temperature)
    }
    /// The expected nondimensional end-to-end length as a function of the applied nondimensional force.
    pub fn nondimensional_end_to_end_length(&self, nondimensional_force: &f64) -> f64
    {
        nondimensional_end_to_end_length(&self.number_of_links, &self.nondimensional_persistance_length, nondimensional_force)
    }
    /// The expected nondimensional end-to-end length per link as a function of the applied nondimensional force.
    pub fn nondimensional_end_to_end_length_per_link(&self, nondimensional_force: &f64) -> f64
    {
        nondimensional_end_to_end_length_per_link(&self.number_of_links, &self.nondimensional_persistance_length, nondimensional_force)
    }
    /// The Gibbs free energy as a function of the applied force and temperature.
    pub fn gibbs_free_energy(&self, force: &f64, temperature: &f64) -> f64
    {
        gibbs_free_energy(&self.number_of_links, &self.link_length, &self.hinge_mass, &self.persistance_length, force, temperature)
    }
    /// The Gibbs free energy per link as a function of the applied force and temperature.
    pub fn gibbs_free_energy_per_link(&self, force: &f64, temperature: &f64) -> f64
    {
        gibbs_free_energy_per_link(&self.number_of_links, &self.link_length, &self.hinge_mass, &self.persistance_length, force, temperature)
    }
    /// The relative Gibbs free energy as a function of the applied force and temperature.
    pub fn relative_gibbs_free_energy(&self, force: &f64, temperature: &f64) -> f64
    {
        relative_gibbs_free_energy(&self.number_of_links, &self.link_length, &self.persistance_length, force, temperature)
    }
    /// The relative Gibbs free energy per link as a function of the applied force and temperature.
    pub fn relative_gibbs_free_energy_per_link(&self, force: &f64, temperature: &f64) -> f64
    {
        relative_gibbs_free_energy_per_link(&self.number_of_links, &self.link_length, &self.persistance_length, force, temperature)
    }
    /// The nondimensional Gibbs free energy as a function of the applied nondimensional force and temperature.
    pub fn nondimensional_gibbs_free_energy(&self, nondimensional_force: &f64, temperature: &f64) -> f64
    {
        nondimensional_gibbs_free_energy(&self.number_of_links, &self.link_length, &self.hinge_mass, &self.nondimensional_persistance_length, nondimensional_force, temperature)
    }
    /// The nondimensional Gibbs free energy per link as a function of the applied nondimensional force and temperature.
    pub fn nondimensional_gibbs_free_energy_per_link(&self, nondimensional_force: &f64, temperature: &f64) -> f64
    {
        nondimensional_gibbs_free_energy_per_link(&self.number_of_links, &self.link_length, &self.hinge_mass, &self.nondimensional_persistance_length, nondimensional_force, temperature)
    }
    /// The nondimensional relative Gibbs free energy as a function of the applied nondimensional force.
    pub fn nondimensional_relative_gibbs_free_energy(&self, nondimensional_force: &f64) -> f64
    {
        nondimensional_relative_gibbs_free_energy(&self.number_of_links, &self.nondimensional_persistance_length, nondimensional_force)
    }
    /// The nondimensional relative Gibbs free energy per link as a function of the applied nondimensional force.
    pub fn nondimensional_relative_gibbs_free_energy_per_link(&self, nondimensional_force: &f64) -> f64
    {
        nondimensional_relative_gibbs_free_energy_per_link(&self.number_of_links, &self.nondimensional_persistance_length, nondimensional_force)
    }
}