1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216

#[cfg(feature = "extern")]
pub mod ex;

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

mod test;

/// The freely-jointed chain (FJC) model thermodynamics in the isometric ensemble approximated using a Legendre transformation.
pub mod legendre;

/// The freely-jointed chain (FJC) model thermodynamics in the isometric ensemble calculated using Monte Carlo methods.
pub mod monte_carlo;

use super::
{
    treloar_sums,
    treloar_sum_0_with_prefactor
};
use std::f64::consts::PI;
use crate::physics::
{
    PLANCK_CONSTANT,
    BOLTZMANN_CONSTANT
};
use crate::physics::single_chain::ZERO;

/// The structure of the thermodynamics of the FJC model in the isometric ensemble.
pub struct FJC
{
    /// 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 thermodynamic functions of the model in the isometric ensemble approximated using a Legendre transformation.
    pub legendre: legendre::FJC
}

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

/// The expected nondimensional force as a function of the applied nondimensional end-to-end length per link, parameterized by the number of links.
pub fn nondimensional_force(number_of_links: &u8, nondimensional_end_to_end_length_per_link: &f64) -> f64
{
    let sums = treloar_sums(number_of_links, nondimensional_end_to_end_length_per_link, &[0, 1]);
    let number_of_links_f64 = *number_of_links as f64;
    (1.0/nondimensional_end_to_end_length_per_link + (0.5*number_of_links_f64 - 1.0)*sums[1]/sums[0])/number_of_links_f64
}

/// The Helmholtz free energy as a function of the applied end-to-end length and temperature, parameterized by the number of links, link length, and hinge mass.
pub fn helmholtz_free_energy(number_of_links: &u8, link_length: &f64, hinge_mass: &f64, end_to_end_length: &f64, temperature: &f64) -> f64
{
    nondimensional_helmholtz_free_energy(number_of_links, link_length, hinge_mass, &(end_to_end_length/((*number_of_links as f64)*link_length)), temperature)*BOLTZMANN_CONSTANT*temperature
}

/// The Helmholtz free energy per link as a function of the applied end-to-end length and temperature, parameterized by the number of links, link length, and hinge mass.
pub fn helmholtz_free_energy_per_link(number_of_links: &u8, link_length: &f64, hinge_mass: &f64, end_to_end_length: &f64, temperature: &f64) -> f64
{
    nondimensional_helmholtz_free_energy_per_link(number_of_links, link_length, hinge_mass, &(end_to_end_length/((*number_of_links as f64)*link_length)), temperature)*BOLTZMANN_CONSTANT*temperature
}

/// The relative Helmholtz free energy as a function of the applied end-to-end length and temperature, parameterized by the number of links and link length.
pub fn relative_helmholtz_free_energy(number_of_links: &u8, link_length: &f64, end_to_end_length: &f64, temperature: &f64) -> f64
{
    nondimensional_relative_helmholtz_free_energy(number_of_links, &(end_to_end_length/((*number_of_links as f64)*link_length)))*BOLTZMANN_CONSTANT*temperature
}

/// The relative Helmholtz free energy per link as a function of the applied end-to-end length and temperature, parameterized by the number of links and link length.
pub fn relative_helmholtz_free_energy_per_link(number_of_links: &u8, link_length: &f64, end_to_end_length: &f64, temperature: &f64) -> f64
{
    nondimensional_relative_helmholtz_free_energy_per_link(number_of_links, &(end_to_end_length/((*number_of_links as f64)*link_length)))*BOLTZMANN_CONSTANT*temperature
}

/// The nondimensional Helmholtz free energy as a function of the nondimensional end-to-end length per link and temperature, parameterized by the number of links, link length, and hinge mass.
pub fn nondimensional_helmholtz_free_energy(number_of_links: &u8, link_length: &f64, hinge_mass: &f64, nondimensional_end_to_end_length_per_link: &f64, temperature: &f64) -> f64
{
    -(equilibrium_distribution(number_of_links, link_length, &(nondimensional_end_to_end_length_per_link*(*number_of_links as f64)*link_length))).ln() - ((*number_of_links as f64) - 1.0)*(8.0*PI.powi(2)*hinge_mass*link_length.powi(2)*BOLTZMANN_CONSTANT*temperature/PLANCK_CONSTANT.powi(2)).ln()
}

/// The nondimensional Helmholtz free energy per link as a function of the nondimensional end-to-end length per link and temperature, parameterized by the number of links, link length, and hinge mass.
pub fn nondimensional_helmholtz_free_energy_per_link(number_of_links: &u8, link_length: &f64, hinge_mass: &f64, nondimensional_end_to_end_length_per_link: &f64, temperature: &f64) -> f64
{
    nondimensional_helmholtz_free_energy(number_of_links, link_length, hinge_mass, nondimensional_end_to_end_length_per_link, temperature)/(*number_of_links as f64)
}

/// The nondimensional relative Helmholtz free energy as a function of the nondimensional end-to-end length per link, parameterized by the number of links.
pub fn nondimensional_relative_helmholtz_free_energy(number_of_links: &u8, nondimensional_end_to_end_length_per_link: &f64) -> f64
{
    (nondimensional_equilibrium_distribution(number_of_links, &ZERO)/nondimensional_equilibrium_distribution(number_of_links, nondimensional_end_to_end_length_per_link)).ln()
}

/// The nondimensional relative Helmholtz free energy per link as a function of the nondimensional end-to-end length per link, parameterized by the number of links.
pub fn nondimensional_relative_helmholtz_free_energy_per_link(number_of_links: &u8, nondimensional_end_to_end_length_per_link: &f64) -> f64
{
    nondimensional_relative_helmholtz_free_energy(number_of_links, nondimensional_end_to_end_length_per_link)/(*number_of_links as f64)
}

/// The equilibrium probability density of end-to-end vectors as a function of the end-to-end length, parameterized by the number of links and link length.
pub fn equilibrium_distribution(number_of_links: &u8, link_length: &f64, end_to_end_length: &f64) -> f64
{
    let contour_length = (*number_of_links as f64)*link_length;
    nondimensional_equilibrium_distribution(number_of_links, &(end_to_end_length/contour_length))/contour_length.powi(3)
}

/// The nondimensional equilibrium probability density of nondimensional end-to-end vectors per link as a function of the nondimensional end-to-end length per link, parameterized by the number of links.
pub fn nondimensional_equilibrium_distribution(number_of_links: &u8, nondimensional_end_to_end_length_per_link: &f64) -> f64
{
    treloar_sum_0_with_prefactor(number_of_links, nondimensional_end_to_end_length_per_link)
}

/// The equilibrium probability density of end-to-end lengths as a function of the end-to-end length, parameterized by the number of links and link length.
pub fn equilibrium_radial_distribution(number_of_links: &u8, link_length: &f64, end_to_end_length: &f64) -> f64
{
    let contour_length = (*number_of_links as f64)*link_length;
    nondimensional_equilibrium_radial_distribution(number_of_links, &(end_to_end_length/contour_length))/contour_length
}

/// The nondimensional equilibrium probability density of nondimensional end-to-end lengths per link as a function of the nondimensional end-to-end length per link, parameterized by the number of links.
pub fn nondimensional_equilibrium_radial_distribution(number_of_links: &u8, nondimensional_end_to_end_length_per_link: &f64) -> f64
{
    4.0*PI*nondimensional_end_to_end_length_per_link.powi(2)*nondimensional_equilibrium_distribution(number_of_links, nondimensional_end_to_end_length_per_link)
}

/// The implemented functionality of the thermodynamics of the FJC model in the isometric ensemble.
impl FJC
{
    /// Initializes and returns an instance of the thermodynamics of the FJC model in the isometric ensemble.
    pub fn init(number_of_links: u8, link_length: f64, hinge_mass: f64) -> Self
    {
        FJC
        {
            hinge_mass,
            link_length,
            number_of_links,
            legendre: legendre::FJC::init(number_of_links, link_length, hinge_mass)
        }
    }
    /// The expected force as a function of the applied end-to-end length and temperature.
    pub fn force(&self, end_to_end_length: &f64, temperature: &f64) -> f64
    {
        force(&self.number_of_links, &self.link_length, end_to_end_length, temperature)
    }
    /// The expected nondimensional force as a function of the applied nondimensional end-to-end length per link.
    pub fn nondimensional_force(&self, nondimensional_end_to_end_length_per_link: &f64) -> f64
    {
        nondimensional_force(&self.number_of_links, nondimensional_end_to_end_length_per_link)
    }
    /// The Helmholtz free energy as a function of the applied end-to-end length and temperature.
    pub fn helmholtz_free_energy(&self, end_to_end_length: &f64, temperature: &f64) -> f64
    {
        helmholtz_free_energy(&self.number_of_links, &self.link_length, &self.hinge_mass, end_to_end_length, temperature)
    }
    /// The Helmholtz free energy per link as a function of the applied end-to-end length and temperature.
    pub fn helmholtz_free_energy_per_link(&self, end_to_end_length: &f64, temperature: &f64) -> f64
    {
        helmholtz_free_energy_per_link(&self.number_of_links, &self.link_length, &self.hinge_mass, end_to_end_length, temperature)
    }
    /// The relative Helmholtz free energy as a function of the applied end-to-end length and temperature.
    pub fn relative_helmholtz_free_energy(&self, end_to_end_length: &f64, temperature: &f64) -> f64
    {
        relative_helmholtz_free_energy(&self.number_of_links, &self.link_length, end_to_end_length, temperature)
    }
    /// The relative Helmholtz free energy per link as a function of the applied end-to-end length and temperature.
    pub fn relative_helmholtz_free_energy_per_link(&self, end_to_end_length: &f64, temperature: &f64) -> f64
    {
        relative_helmholtz_free_energy_per_link(&self.number_of_links, &self.link_length, end_to_end_length, temperature)
    }
    /// The nondimensional Helmholtz free energy as a function of the applied nondimensional end-to-end length per link and temperature.
    pub fn nondimensional_helmholtz_free_energy(&self, nondimensional_end_to_end_length_per_link: &f64, temperature: &f64) -> f64
    {
        nondimensional_helmholtz_free_energy(&self.number_of_links, &self.link_length, &self.hinge_mass, nondimensional_end_to_end_length_per_link, temperature)
    }
    /// The nondimensional Helmholtz free energy per link as a function of the applied nondimensional end-to-end length per link and temperature.
    pub fn nondimensional_helmholtz_free_energy_per_link(&self, nondimensional_end_to_end_length_per_link: &f64, temperature: &f64) -> f64
    {
        nondimensional_helmholtz_free_energy_per_link(&self.number_of_links, &self.link_length, &self.hinge_mass, nondimensional_end_to_end_length_per_link, temperature)
    }
    /// The nondimensional relative Helmholtz free energy as a function of the applied nondimensional end-to-end length per link.
    pub fn nondimensional_relative_helmholtz_free_energy(&self, nondimensional_end_to_end_length_per_link: &f64) -> f64
    {
        nondimensional_relative_helmholtz_free_energy(&self.number_of_links, nondimensional_end_to_end_length_per_link)
    }
    /// The nondimensional relative Helmholtz free energy per link as a function of the applied nondimensional end-to-end length per link.
    pub fn nondimensional_relative_helmholtz_free_energy_per_link(&self, nondimensional_end_to_end_length_per_link: &f64) -> f64
    {
        nondimensional_relative_helmholtz_free_energy_per_link(&self.number_of_links, nondimensional_end_to_end_length_per_link)
    }
    /// The equilibrium probability density of end-to-end vectors as a function of the end-to-end length.
    pub fn equilibrium_distribution(&self, end_to_end_length: &f64) -> f64
    {
        equilibrium_distribution(&self.number_of_links, &self.link_length, end_to_end_length)
    }
    /// The nondimensional equilibrium probability density of nondimensional end-to-end vectors per link as a function of the nondimensional end-to-end length per link.
    pub fn nondimensional_equilibrium_distribution(&self, nondimensional_end_to_end_length_per_link: &f64) -> f64
    {
        nondimensional_equilibrium_distribution(&self.number_of_links, nondimensional_end_to_end_length_per_link)
    }
    /// The equilibrium probability density of end-to-end lengths as a function of the end-to-end length.
    pub fn equilibrium_radial_distribution(&self, end_to_end_length: &f64) -> f64
    {
        equilibrium_radial_distribution(&self.number_of_links, &self.link_length, end_to_end_length)
    }
    /// The nondimensional equilibrium probability density of nondimensional end-to-end lengths per link as a function of the nondimensional end-to-end length per link.
    pub fn nondimensional_equilibrium_radial_distribution(&self, nondimensional_end_to_end_length_per_link: &f64) -> f64
    {
        nondimensional_equilibrium_radial_distribution(&self.number_of_links, nondimensional_end_to_end_length_per_link)
    }
}