Langevin dynamics for rigid bodies of arbitrary shape

Abstract

We present an algorithm for carrying out Langevin dynamics simulations on complex rigid bodies by incorporating the hydrodynamic resistance tensors for arbitrary shapes into an advanced rotational integration scheme. The integrator gives quantitative agreement with both analytic and approximate hydrodynamic theories for a number of model rigid bodies and works well at reproducing the solute dynamical properties (diffusion constants and orientational relaxation times) obtained from explicitly solvated simulations.

New Langevin and gradient thermostats for rigid body dynamics

“…In Ref. 20 the authors consider Langevin dynamics for rigid bodies using the rotational integration scheme based on the Lie-Poisson integrator 2,12 . It is slightly more expensive than the quaternion representation which is the minimal non-singular description of rotations.…”

The passive diffusion ofLeptospira interrogans

“…Notation-wise, in the equations above, ⊗ denotes the outer tensor product, t is time, k b is the Boltzmann constant, T is the absolute temperature, and δ(t) is the Dirac delta function. Einstein's and Langevin's results have since been extended to look at the diffusion of rods [4], helicoidal bodies [5], helices [6] and arbitrarily shapes [7,8,9,10]. The influence of fluid and particle inertia was also theoretically investigated [11], predicting the short time Brownian ballistic regime.…”

Velocity Fluctuations in Helical Propulsion: How Small Can a Propeller Be

“…To include the effect of thermal noise, we used the method described in ref 31 and introduced the random force term F R , described by a Gaussian distribution with zero mean and the variance, given by ⟨F R (t) F R ′ (t′)⟩ = 2kTΓδ(t − t′). The smallest time step Δt used in the simulation is taken to be much smaller than the lowest time scale in the system, which is τ r3 = 1/(2D r3 ), approximately equal to 0.08 s for the propellers used in these experiments.…”