MCMC FRC

src/physics/single_chain/frc/mod.rs

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

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

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

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

@@ -0,0 +1,84 @@
+mod test;
+
+use rand::prelude::*;
+
+use std::f64::consts::PI;
+use std::f64::consts::TAU as TWO_PI;
+
+pub fn cross(u: &[f64; 3], v: &[f64; 3]) -> [f64; 3]
+{
+    [u[1] * v[2] - u[2] * v[1],
+     u[2] * v[0] - u[0] * v[2],
+     u[0] * v[1] - u[1] * v[0]]
+}
+
+pub fn random_configuration<const NUMBER_OF_LINKS: usize>(theta: &f64, rng: &mut ThreadRng) -> [[f64; 3]; NUMBER_OF_LINKS]
+{
+    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;
+    configuration.iter_mut().for_each(|coordinate|{
+        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, &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, &u);
+        r.iter_mut().zip(u.iter().zip(v.iter())).for_each(|(r_i, (u_i, v_i))|
+            *r_i = (u_i * phi_cos + v_i * phi_sin) * theta_sin + *r_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, rng: &mut ThreadRng) -> f64
+{
+    random_configuration::<NUMBER_OF_LINKS>(theta, 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>(theta: &f64, number_of_samples: usize) -> ([f64; NUMBER_OF_BINS], [f64; NUMBER_OF_BINS])
+{
+    let mut rng = rand::thread_rng();
+    let number_of_links_f64 = NUMBER_OF_LINKS as f64;
+    let gamma_max = (2.0 - 2.0*(PI - theta).cos()).sqrt()/2.0;
+    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, &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 = (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/frc/thermodynamics/isometric/monte_carlo/test.rs

@@ -0,0 +1,43 @@
+#![cfg(test)]
+
+use super::*;
+
+use std::f64::consts::PI;
+
+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 configuration = random_configuration::<NUMBER_OF_LINKS>(&THETA, &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 gamma = random_nondimensional_end_to_end_length::<NUMBER_OF_LINKS>(&THETA, &mut rng)/(NUMBER_OF_LINKS as f64);
+    let gamma_max = (2.0 - 2.0*(PI - THETA).cos()).sqrt()/2.0;
+    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>(&THETA, NUMBER_OF_SAMPLES);
+    assert_eq!(gamma.len(), NUMBER_OF_BINS);
+    assert_eq!(g_eq.len(), NUMBER_OF_BINS);
+    let gamma_max = (2.0 - 2.0*(PI - THETA).cos()).sqrt()/2.0;
+    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/frc/thermodynamics/mod.rs

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

src/physics/single_chain/mod.rs

@@ -18,6 +18,9 @@ pub mod swfjc;
 /// The arbitrary link potential freely-jointed chain (uFJC) single-chain model.
 pub mod ufjc;
 
+/// The freely-rotating chain (FRC) single-chain model.
+pub mod frc;
+
 /// The worm-like chain (WLC) single-chain model.
 pub mod wlc;
 

tests/frc.rs

@@ -0,0 +1,26 @@
+use polymers::physics::single_chain::
+{
+    frc::thermodynamics::isometric::monte_carlo::nondimensional_equilibrium_radial_distribution,
+    wlc::thermodynamics::isometric::WLC
+};
+
+const KAPPA: f64 = 5.0/11.0;
+const NUMBER_OF_BINS: usize = 1000;
+const NUMBER_OF_LINKS: usize = 256;
+const NUMBER_OF_SAMPLES: usize = 10000000;
+const TOL: f64 = 5e-2;
+
+#[test]
+fn monte_carlo_nondimensional_equilibrium_radial_distribution_wlc_limit()
+{
+    let theta = (2.0/(NUMBER_OF_LINKS as f64)/KAPPA).sqrt();
+    let (gamma, g_eq) = nondimensional_equilibrium_radial_distribution::<NUMBER_OF_BINS, NUMBER_OF_LINKS>(&theta, NUMBER_OF_SAMPLES);
+    let mut check = 0.0;
+    let mut residual = 0.0;
+    let wlc = WLC::init(1, 1.0, 1.0, KAPPA);
+    gamma.iter().zip(g_eq.iter()).for_each(|(gamma_i, g_eq_i)|{
+        check = wlc.nondimensional_equilibrium_radial_distribution(&gamma_i);
+        residual = (g_eq_i - &check).abs();
+        assert!(residual < TOL || residual/check < TOL || g_eq_i < &TOL);
+    });
+}