Wavelet Monte Carlo dynamics

Abstract

The Wavelet Monte Carlo dynamics (WMCD) algorithm is developed from scratch to simulate hydrodynamically coupled Brownian particles at low Reynolds numbers. The basic premise is to construct a regularised version of the Oseen tensor out of a distribution of 3-dimensional vector wavelets that displace groups of particles so as to evolve the system in time while correlating the motion of all particles according to their separation. In doing so, the Oseen tensor is made implicit in the simulation code and the computational complexity of WMCD scales with system size N as N lnN (or even linearly in fractal systems), comparing favourably to existing Brownian dynamics algorithms, while the absence of any solvent degrees of freedom also leads to favourable comparisons with explicit-solvent methods. WMCD therefore holds promise to simulate system sizes beyond the reach of the alternatives. Key extensions to the basic algorithm are presented - none of which affect the computational complexity - including additional Fourier moves and smart Monte Carlo biasing to improve the algorithm's dynamical fidelity, as well as schemes to build in polydispersity and hydrodynamic coupling of particle rotations. WMCD is then used in a comprehensive study of the diffusion of isolated polymer chains, using the properties of the centre of mass velocity autocorrelation to identify distinct short and long-time regimes driving the reduction of diffusivity from the Kirkwood value. Using similar methods in a very different context, WMCD is also used to study the enhanced diffusion of passive particles in active suspensions. Here again the velocity autocorrelation proves useful in understanding the underlying physics, with three driving mechanisms identified depending on relative particle sizes. Of particular note is the importance of thermal fluctuations, often neglected in active matter research but central to WMCD