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
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
use pyo3::prelude::*;
use numpy::
{
IntoPyArray,
PyArrayDyn,
PyReadonlyArrayDyn
};
use crate::physics::BOLTZMANN_CONSTANT;
pub fn register_module(py: Python<'_>, parent_module: &PyModule) -> PyResult<()>
{
let isotensional = PyModule::new(py, "isotensional")?;
super::asymptotic::py::register_module(py, isotensional)?;
super::legendre::py::register_module(py, isotensional)?;
parent_module.add_submodule(isotensional)?;
isotensional.add_class::<EFJC>()?;
Ok(())
}
/// The extensible freely-jointed chain (EFJC) model thermodynamics in the isotensional ensemble.
#[pyclass]
#[derive(Copy, Clone)]
pub struct EFJC
{
/// The mass of each hinge in the chain in units of kg/mol.
#[pyo3(get)]
pub hinge_mass: f64,
/// The length of each link in the chain in units of nm.
#[pyo3(get)]
pub link_length: f64,
/// The number of links in the chain.
#[pyo3(get)]
pub number_of_links: u8,
/// The stiffness of each link in the chain in units of J/(molâ‹…nm^2).
#[pyo3(get)]
pub link_stiffness: f64,
/// The thermodynamic functions of the model in the isotensional ensemble approximated using an asymptotic approach.
#[pyo3(get)]
pub asymptotic: super::asymptotic::py::EFJC,
/// The thermodynamic functions of the model in the isotensional ensemble approximated using a Legendre transformation.
#[pyo3(get)]
pub legendre: super::legendre::py::EFJC
}
#[pymethods]
impl EFJC
{
#[new]
pub fn init(number_of_links: u8, link_length: f64, hinge_mass: f64, link_stiffness: f64) -> Self
{
EFJC
{
hinge_mass,
link_length,
number_of_links,
link_stiffness,
asymptotic: super::asymptotic::py::EFJC::init(number_of_links, link_length, hinge_mass, link_stiffness),
legendre: super::legendre::py::EFJC::init(number_of_links, link_length, hinge_mass, link_stiffness)
}
}
/// The expected end-to-end length as a function of the applied force and temperature,
///
/// .. math::
/// \xi(f, T) = -\frac{\partial\varphi}{\partial f}.
///
/// Args:
/// force (numpy.ndarray): The force :math:`f`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The end-to-end length :math:`\xi`.
///
pub fn end_to_end_length<'py>(&self, py: Python<'py>, force: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
force.as_array().mapv(|force: f64| super::end_to_end_length(&self.number_of_links, &self.link_length, &self.link_stiffness, &force, &temperature)).into_pyarray(py)
}
/// The expected end-to-end length per link as a function of the applied force and temperature.
///
/// Args:
/// force (numpy.ndarray): The force :math:`f`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The end-to-end length per link :math:`\xi/N_b=\ell_b\gamma`.
///
pub fn end_to_end_length_per_link<'py>(&self, py: Python<'py>, force: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
force.as_array().mapv(|force: f64| super::end_to_end_length_per_link(&self.link_length, &self.link_stiffness, &force, &temperature)).into_pyarray(py)
}
/// The expected nondimensional end-to-end length as a function of the applied nondimensional force.
///
/// Args:
/// nondimensional_force (numpy.ndarray): The nondimensional force :math:`\eta\equiv\beta f\ell_b`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The nondimensional end-to-end length :math:`N_b\gamma=\xi/\ell_b`.
///
pub fn nondimensional_end_to_end_length<'py>(&self, py: Python<'py>, nondimensional_force: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
nondimensional_force.as_array().mapv(|nondimensional_force: f64| super::nondimensional_end_to_end_length(&self.number_of_links, &(self.link_stiffness*self.link_length.powi(2)/BOLTZMANN_CONSTANT/temperature), &nondimensional_force)).into_pyarray(py)
}
/// The expected nondimensional end-to-end length per link as a function of the applied nondimensional force, calculated from :footcite:t:`balabaev2009extension,buche2022freely` as
///
/// .. math::
/// \gamma(\eta) = -\frac{\partial\varrho}{\partial\eta} = \mathcal{L}(\eta) + \frac{\eta}{\kappa}\left[1 + \frac{1 - \mathcal{L}(\eta)\coth(\eta)}{1 + (\eta/\kappa)\coth(\eta)}\right] + \frac{\partial}{\partial\eta}\,\ln\left[1+g(\eta)\right],
///
/// where :math:`\mathcal{L}(x)=\coth(x)-1/x` is the Langevin function, and :math:`g(\eta)` is defined as
///
/// .. math::
/// g(\eta) \equiv \frac{e^{\eta}\left(\frac{\eta}{\kappa} + 1\right) \,\mathrm{erf}\left(\frac{\eta+\kappa}{\sqrt{2\kappa}}\right) - e^{-\eta}\left(\frac{\eta}{\kappa} - 1\right) \,\mathrm{erf}\left(\frac{\eta-\kappa}{\sqrt{2\kappa}}\right)}{4\sinh(\eta)\left[1 + (\eta/\kappa)\coth(\eta)\right]} - \frac{1}{2}.
///
/// Args:
/// nondimensional_force (numpy.ndarray): The nondimensional force :math:`\eta\equiv\beta f\ell_b`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The nondimensional end-to-end length per link :math:`\gamma\equiv \xi/N_b\ell_b`.
///
pub fn nondimensional_end_to_end_length_per_link<'py>(&self, py: Python<'py>, nondimensional_force: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
nondimensional_force.as_array().mapv(|nondimensional_force: f64| super::nondimensional_end_to_end_length_per_link(&(self.link_stiffness*self.link_length.powi(2)/BOLTZMANN_CONSTANT/temperature), &nondimensional_force)).into_pyarray(py)
}
/// The Gibbs free energy as a function of the applied force and temperature,
///
/// .. math::
/// \varphi(f, T) = -kT\ln Z(f, T).
///
/// Args:
/// force (numpy.ndarray): The force :math:`f`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The Gibbs free energy :math:`\varphi`.
///
pub fn gibbs_free_energy<'py>(&self, py: Python<'py>, force: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
force.as_array().mapv(|force: f64| super::gibbs_free_energy(&self.number_of_links, &self.link_length, &self.hinge_mass, &self.link_stiffness, &force, &temperature)).into_pyarray(py)
}
/// The Gibbs free energy per link as a function of the applied force and temperature.
///
/// Args:
/// force (numpy.ndarray): The force :math:`f`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The Gibbs free energy per link :math:`\varphi/N_b`.
///
pub fn gibbs_free_energy_per_link<'py>(&self, py: Python<'py>, force: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
force.as_array().mapv(|force: f64| super::gibbs_free_energy_per_link(&self.link_length, &self.hinge_mass, &self.link_stiffness, &force, &temperature)).into_pyarray(py)
}
/// The relative Gibbs free energy as a function of the applied force and temperature.
///
/// Args:
/// force (numpy.ndarray): The force :math:`f`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The relative Gibbs free energy :math:`\Delta\varphi\equiv\varphi(f,T)-\varphi(0,T)`.
///
pub fn relative_gibbs_free_energy<'py>(&self, py: Python<'py>, force: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
force.as_array().mapv(|force: f64| super::relative_gibbs_free_energy(&self.number_of_links, &self.link_length, &self.link_stiffness, &force, &temperature)).into_pyarray(py)
}
/// The relative Gibbs free energy per link as a function of the applied force and temperature.
///
/// Args:
/// force (numpy.ndarray): The force :math:`f`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The relative Gibbs free energy per link :math:`\Delta\varphi/N_b`.
///
pub fn relative_gibbs_free_energy_per_link<'py>(&self, py: Python<'py>, force: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
force.as_array().mapv(|force: f64| super::relative_gibbs_free_energy_per_link(&self.link_length, &self.link_stiffness, &force, &temperature)).into_pyarray(py)
}
/// The nondimensional Gibbs free energy as a function of the applied nondimensional force and temperature.
///
/// Args:
/// nondimensional_force (numpy.ndarray): The nondimensional force :math:`\eta\equiv\beta f\ell_b`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The nondimensional Gibbs free energy :math:`\beta\varphi=N_b\varrho`.
///
pub fn nondimensional_gibbs_free_energy<'py>(&self, py: Python<'py>, nondimensional_force: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
nondimensional_force.as_array().mapv(|nondimensional_force: f64| super::nondimensional_gibbs_free_energy(&self.number_of_links, &self.link_length, &self.hinge_mass, &(self.link_stiffness*self.link_length.powi(2)/BOLTZMANN_CONSTANT/temperature), &nondimensional_force, &temperature)).into_pyarray(py)
}
/// The nondimensional Gibbs free energy per link as a function of the applied nondimensional force and temperature.
///
/// Args:
/// nondimensional_force (numpy.ndarray): The nondimensional force :math:`\eta\equiv\beta f\ell_b`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The nondimensional Gibbs free energy per link :math:`\varrho\equiv\beta\varphi/N_b`.
///
pub fn nondimensional_gibbs_free_energy_per_link<'py>(&self, py: Python<'py>, nondimensional_force: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
nondimensional_force.as_array().mapv(|nondimensional_force: f64| super::nondimensional_gibbs_free_energy_per_link(&self.link_length, &self.hinge_mass, &(self.link_stiffness*self.link_length.powi(2)/BOLTZMANN_CONSTANT/temperature), &nondimensional_force, &temperature)).into_pyarray(py)
}
/// The nondimensional relative Gibbs free energy as a function of the applied nondimensional force.
///
/// Args:
/// nondimensional_force (numpy.ndarray): The nondimensional force :math:`\eta\equiv\beta f\ell_b`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The nondimensional relative Gibbs free energy :math:`\beta\Delta\varphi=N_b\Delta\varrho`.
///
pub fn nondimensional_relative_gibbs_free_energy<'py>(&self, py: Python<'py>, nondimensional_force: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
nondimensional_force.as_array().mapv(|nondimensional_force: f64| super::nondimensional_relative_gibbs_free_energy(&self.number_of_links, &(self.link_stiffness*self.link_length.powi(2)/BOLTZMANN_CONSTANT/temperature), &nondimensional_force)).into_pyarray(py)
}
/// The nondimensional relative Gibbs free energy per link as a function of the applied nondimensional force, given by :footcite:t:`buche2022freely` as
///
/// .. math::
/// \Delta\varrho(\eta) = -\frac{\eta^2}{2\kappa} - \ln\left[w^+(\eta) + w^-(\eta)\right],
///
/// where the functions :math:`w^+(\eta)` and :math:`w^-(\eta)` are defined as as
///
/// .. math::
/// w^\pm(\eta) \equiv e^{\pm\eta}\left(\frac{1}{\kappa} \pm \frac{1}{\eta}\right) \left[1 \pm \mathrm{erf}\left(\frac{\eta\pm\kappa}{\sqrt{2\kappa}}\right)\right].
///
/// Args:
/// nondimensional_force (numpy.ndarray): The nondimensional force :math:`\eta\equiv\beta f\ell_b`.
/// temperature (float): The temperature :math:`T`.
///
/// Returns:
/// numpy.ndarray: The nondimensional relative Gibbs free energy per link :math:`\Delta\varrho\equiv\beta\Delta\varphi/N_b`.
///
pub fn nondimensional_relative_gibbs_free_energy_per_link<'py>(&self, py: Python<'py>, nondimensional_force: PyReadonlyArrayDyn<f64>, temperature: f64) -> &'py PyArrayDyn<f64>
{
nondimensional_force.as_array().mapv(|nondimensional_force: f64| super::nondimensional_relative_gibbs_free_energy_per_link(&(self.link_stiffness*self.link_length.powi(2)/BOLTZMANN_CONSTANT/temperature), &nondimensional_force)).into_pyarray(py)
}
}