EFRC isometric Monte Carlo

src/physics/single_chain/efrc/mod.rs

@@ -0,0 +1,2 @@
+/// The extensible freely-rotating chain (EFRC) model thermodynamics.
+pub mod thermodynamics;

src/physics/single_chain/efrc/thermodynamics/isometric/mod.rs

@@ -0,0 +1,2 @@
+/// The extensible freely-rotating chain (EFRC) model thermodynamics in the isometric ensemble calculated using Monte Carlo methods.
+pub mod monte_carlo;

src/physics/single_chain/efrc/thermodynamics/isometric/monte_carlo/mod.rs

@@ -0,0 +1,87 @@
+mod test;
+
+use rand::prelude::*;
+
+use rand_distr::{Normal, Distribution};
+
+use std::f64::consts::TAU as TWO_PI;
+
+use crate::physics::single_chain::frc::thermodynamics::isometric::monte_carlo::cross;
+
+pub fn random_configuration<const NUMBER_OF_LINKS: usize>(theta: &f64, dist: Normal<f64>, rng: &mut ThreadRng) -> [[f64; 3]; NUMBER_OF_LINKS]
+{
+    let mut lambda: f64 = 0.0;
+    let mut phi: f64 = 0.0;
+    let mut phi_cos: f64 = 0.0;
+    let mut phi_sin: f64 = 0.0;
+    let theta_cos: f64 = theta.cos();
+    let theta_sin: f64 = theta.sin();
+    let mut configuration = [[0.0; 3]; NUMBER_OF_LINKS];
+    let mut position = [0.0; 3];
+    let mut r = [1.0, 0.0, 0.0];
+    let mut t = [0.0; 3];
+    let mut u = [0.0; 3];
+    let mut v = [0.0; 3];
+    let mut u_normalization = 0.0;
+    let mut r_n = [1.0, 0.0, 0.0];
+    let mut r_normalization = 0.0;
+    configuration.iter_mut().for_each(|coordinate|{
+        lambda = dist.sample(rng);
+        r_n = r;
+        r_normalization = r_n.iter().map(|r_n_i| r_n_i * r_n_i).sum::<f64>().sqrt();
+        r_n.iter_mut().for_each(|r_n_i| *r_n_i /= r_normalization);
+        phi = TWO_PI * rng.gen::<f64>();
+        phi_cos = phi.cos();
+        phi_sin = phi.sin();
+        t = std::array::from_fn(|_| rng.gen::<f64>());
+        u = cross(&r_n, &t);
+        u_normalization = u.iter().map(|u_i| u_i * u_i).sum::<f64>().sqrt();
+        u.iter_mut().for_each(|u_i| *u_i /= u_normalization);
+        v = cross(&r_n, &u);
+        r.iter_mut().zip(r_n.iter().zip(u.iter().zip(v.iter()))).for_each(|(r_i, (r_n_i, (u_i, v_i)))|
+            *r_i = lambda * ((u_i * phi_cos + v_i * phi_sin) * theta_sin + *r_n_i * theta_cos)
+        );
+        position.iter_mut().zip(r.iter()).for_each(|(position_i, r_i)|
+            *position_i += r_i
+        );
+        coordinate.iter_mut().zip(position.iter()).for_each(|(coordinate_i, position_i)|
+            *coordinate_i = *position_i
+        );
+    });
+    configuration
+}
+
+pub fn random_nondimensional_end_to_end_length<const NUMBER_OF_LINKS: usize>(theta: &f64, dist: Normal<f64>, rng: &mut ThreadRng) -> f64
+{
+    random_configuration::<NUMBER_OF_LINKS>(theta, dist, rng)[NUMBER_OF_LINKS - 1].iter().map(|entry| entry * entry).sum::<f64>().sqrt()
+}
+
+pub fn nondimensional_equilibrium_radial_distribution<const NUMBER_OF_BINS: usize, const NUMBER_OF_LINKS: usize>(gamma_max: &f64, kappa: &f64, theta: &f64, number_of_samples: usize) -> ([f64; NUMBER_OF_BINS], [f64; NUMBER_OF_BINS])
+{
+    let mut rng = rand::thread_rng();
+    let dist = Normal::new(1.0, 1.0/kappa.sqrt()).unwrap();
+    let number_of_links_f64 = NUMBER_OF_LINKS as f64;
+    let mut bin_centers = [0.0_f64; NUMBER_OF_BINS];
+    bin_centers.iter_mut().enumerate().for_each(|(bin_index, bin_center)|
+        *bin_center = gamma_max * ((bin_index as f64) + 0.5)/(NUMBER_OF_BINS as f64)
+    );
+    let mut bin_counts = [0_u128; NUMBER_OF_BINS];
+    let mut gamma: f64 = 0.0;
+    (0..number_of_samples).for_each(|_|{
+        gamma = random_nondimensional_end_to_end_length::<NUMBER_OF_LINKS>(theta, dist, &mut rng)/number_of_links_f64;
+        for (bin_center, bin_count) in bin_centers.iter().zip(bin_counts.iter_mut())
+        {
+            if &gamma < bin_center
+            {
+                *bin_count += 1;
+                break
+            }
+        }
+    });
+    let normalization = gamma_max * (number_of_samples as f64)/(NUMBER_OF_BINS as f64);
+    let mut bin_probabilities = [0.0_f64; NUMBER_OF_BINS];
+    bin_probabilities.iter_mut().zip(bin_counts.iter()).for_each(|(bin_probability, bin_count)|
+        *bin_probability = (*bin_count as f64)/normalization
+    );
+    (bin_centers, bin_probabilities)
+}

src/physics/single_chain/efrc/thermodynamics/isometric/monte_carlo/test.rs

@@ -0,0 +1,45 @@
+#![cfg(test)]
+
+use super::*;
+
+use std::f64::consts::PI;
+
+const GAMMA_MAX: f64 = 1.5;
+const KAPPA: f64 = 50.0;
+const NUMBER_OF_BINS: usize = 100;
+const NUMBER_OF_LINKS: usize = 8;
+const NUMBER_OF_SAMPLES: usize = 100000;
+const THETA: f64 = PI/8.0;
+
+#[test]
+fn monte_carlo_random_configuration()
+{
+    let mut rng = rand::thread_rng();
+    let dist = Normal::new(1.0, 1.0/KAPPA.sqrt()).unwrap();
+    let configuration = random_configuration::<NUMBER_OF_LINKS>(&THETA, dist, &mut rng);
+    assert_eq!(configuration.len(), NUMBER_OF_LINKS);
+    assert_eq!(configuration[0].len(), 3);
+}
+
+#[test]
+fn monte_carlo_random_nondimensional_end_to_end_length()
+{
+    let mut rng = rand::thread_rng();
+    let dist = Normal::new(1.0, 1.0/KAPPA.sqrt()).unwrap();
+    let gamma = random_nondimensional_end_to_end_length::<NUMBER_OF_LINKS>(&THETA, dist, &mut rng)/(NUMBER_OF_LINKS as f64);
+    assert!(gamma >= 0.0);
+    assert!(gamma <= GAMMA_MAX);
+}
+
+#[test]
+fn monte_carlo_nondimensional_equilibrium_radial_distribution()
+{
+    let (gamma, g_eq) = nondimensional_equilibrium_radial_distribution::<NUMBER_OF_BINS, NUMBER_OF_LINKS>(&GAMMA_MAX, &KAPPA, &THETA, NUMBER_OF_SAMPLES);
+    assert_eq!(gamma.len(), NUMBER_OF_BINS);
+    assert_eq!(g_eq.len(), NUMBER_OF_BINS);
+    gamma.iter().zip(g_eq.iter()).for_each(|(gamma_i, g_eq_i)|{
+        assert!(gamma_i > &0.0);
+        assert!(gamma_i < &GAMMA_MAX);
+        assert!(g_eq_i >= &0.0);
+    });
+}

src/physics/single_chain/efrc/thermodynamics/mod.rs

@@ -0,0 +1,2 @@
+/// The extensible freely-rotating chain (EFRC) model thermodynamics in the isometric ensemble.
+pub mod isometric;

src/physics/single_chain/mod.rs

@@ -21,6 +21,9 @@ pub mod ufjc;
 /// The freely-rotating chain (FRC) single-chain model.
 pub mod frc;
 
+/// The extensible freely-rotating chain (EFRC) single-chain model.
+pub mod efrc;
+
 /// The worm-like chain (WLC) single-chain model.
 pub mod wlc;
 

tests/efjc.rs

@@ -10,7 +10,7 @@ const NUMBER_OF_SAMPLES: usize = 10000000;
 fn monte_carlo_nondimensional_equilibrium_radial_distribution()
 {
     let (gamma, g_eq) = nondimensional_equilibrium_radial_distribution::<NUMBER_OF_BINS, NUMBER_OF_LINKS>(&GAMMA_MAX, &KAPPA, NUMBER_OF_SAMPLES);
-    gamma.iter().zip(g_eq.iter()).for_each(|output|{
+    gamma.iter().zip(g_eq.iter()).for_each(|output|
         println!("{:?}", output)
-    });
+    );
 }

tests/efrc.rs

@@ -0,0 +1,39 @@
+use polymers::physics::single_chain::
+{
+    frc::thermodynamics::isometric::monte_carlo::nondimensional_equilibrium_radial_distribution as frc_nondimensional_equilibrium_radial_distribution,
+    efrc::thermodynamics::isometric::monte_carlo::nondimensional_equilibrium_radial_distribution
+};
+
+use std::f64::consts::PI;
+
+const GAMMA_MAX: f64 = 1.5;
+const KAPPA: f64 = 50.0;
+const KAPPA_LARGE: f64 = 1e5;
+const NUMBER_OF_BINS: usize = 1000;
+const NUMBER_OF_LINKS: usize = 8;
+const NUMBER_OF_SAMPLES: usize = 10000000;
+const THETA: f64 = PI/8.0;
+const TOL: f64 = 5e-2;
+
+#[test]
+fn monte_carlo_nondimensional_equilibrium_radial_distribution()
+{
+    let (gamma, g_eq) = nondimensional_equilibrium_radial_distribution::<NUMBER_OF_BINS, NUMBER_OF_LINKS>(&GAMMA_MAX, &KAPPA, &THETA, NUMBER_OF_SAMPLES);
+    gamma.iter().zip(g_eq.iter()).for_each(|output|
+        println!("{:?}", output)
+    );
+}
+
+
+#[test]
+fn monte_carlo_nondimensional_equilibrium_radial_distribution_frc_limit()
+{
+    let gamma_max = (2.0 - 2.0*(PI - THETA).cos()).sqrt()/2.0;
+    let (_, g_eq) = nondimensional_equilibrium_radial_distribution::<NUMBER_OF_BINS, NUMBER_OF_LINKS>(&gamma_max, &KAPPA_LARGE, &THETA, NUMBER_OF_SAMPLES);
+    let (_, g_eq_frc) = frc_nondimensional_equilibrium_radial_distribution::<NUMBER_OF_BINS, NUMBER_OF_LINKS>(&THETA, NUMBER_OF_SAMPLES);
+    let mut residual = 0.0;
+    g_eq.iter().zip(g_eq_frc.iter()).for_each(|(g_eq_i, g_eq_frc_i)|{
+        residual = (g_eq_i - g_eq_frc_i).abs();
+        assert!(residual < TOL || residual/g_eq_frc_i < TOL || g_eq_i < &TOL);
+    });
+}