Pychastic: Precise Brownian Dynamics using TaylorItō integrators in Python
Abstract
In the last decade, Pythonpowered physics simulations ecosystem has been growing steadily, allowing greater interoperability, and becoming an important tool in numerical exploration of physical phenomena, particularly in soft matter systems. Driven by the need for fast and precise numerical integration in colloidal dynamics, here we formulate the problem of Brownian Dynamics (BD) in a mathematically consistent formalism of the Itō calculus, and develop a Python package to assist numerical computations. We show that, thanks to the automatic differentiation packages, the classical truncated TaylorItō integrators can be implemented without the burden of computing the derivatives of the coefficient functions beforehand. Furthermore, we show how to circumvent the difficulties of BD simulations such as calculations of the divergence of the mobility tensor in the diffusion equation and discontinuous trajectories encountered when working with dynamics on $S^2$ and $SO(3)$. The resulting Python package, Pychastic, is capable of performing BD simulations including hydrodynamic interactions at speeds comparable to dedicated implementations in lowerlevel programming languages, but with a much simpler enduser interface.
 Publication:

arXiv eprints
 Pub Date:
 September 2022
 DOI:
 10.48550/arXiv.2209.04332
 arXiv:
 arXiv:2209.04332
 Bibcode:
 2022arXiv220904332W
 Keywords:

 Condensed Matter  Soft Condensed Matter;
 Condensed Matter  Statistical Mechanics;
 Physics  Chemical Physics;
 Physics  Computational Physics
 EPrint:
 submitted to SciPost Physics Codebases