Theory and Simulation of Soft Matter, Hydrodynamics, and Biophysics Joost de Graaf

Hydrodynamically Interacting Particles via JAX-based Fast Stokesian Dynamics

Stokesian Dynamics (SD) is a powerful computational framework for simulating the motion of particles in a viscous Newtonian fluid under Stokes-flow conditions. Traditional SD implementations can be computationally expensive as they rely on the inversion of large mobility matrices to determine hydrodynamic interactions. Recently, however, the simulation of thermalized systems with large numbers of particles has become feasible [Fiore and Swan, J. Fluid. Mech. 878, 544 (2019)]. Their "fast Stokesian dynamics" (FSD) method leverages a saddle-point formulation to ensure overall scaling of the algorithm that is linear in the number of particles O(N); performance relies on dedicated graphics-processing-unit computing. In this work, we present a different route toward implementing FSD, which instead leverages the Just-in-Time (JIT) compilation capabilities of Google JAX. We refer to this implementation as JFSD and perform benchmarks on it to verify that it has the right scaling and is sufficiently fast by the standards of modern computational physics. In addition, we provide a series of physical test cases that help ensure accuracy and robustness, as the code undergoes further development. Thus, JFSD is ready to facilitate the study of hydrodynamic effects in particle suspensions across the domains of soft, active, and granular matter.

The software can be found in this repository and may be straightforwardly installed on machines with a GPU. For more information on the use of JAX, we refer to the developer's website.

Fluid-Derived Lattice Simulations for Growing Bacterial Colonies

Bacterial colonies can form a wide variety of shapes and structures based on ambient and internal conditions. To help understand the mechanisms that determine the structure of and the diversity within these colonies, various numerical modeling techniques have been applied. The most commonly used ones are continuum models, agent-based models, and lattice models. Continuum models are usually computationally fast, but disregard information at the level of the individual, which can be crucial to understanding diversity in a colony. Agent-based models resolve local details to a greater level, but are computationally costly. Lattice-based approaches strike a balance between these two limiting cases. However, this is known to come at the price of introducing undesirable artifacts into the structure of the colonies. For instance, square lattices tend to produce square colonies even where an isotropic shape is expected. In this work, we aim to overcome these limitations and therefore study lattice-induced orientational symmetry in a class of hybrid numerical methods that combine aspects of lattice-based and continuum descriptions. We characterize these artifacts and show that they can be circumvented through the use of a disordered lattice which derives from an unstructured fluid. The main advantage of this approach is that the lattice itself does not imbue the colony with a preferential directionality. We demonstrate that our implementation enables the study of colony growth involving millions of individuals within hours of computation time on an ordinary desktop computer, while retaining many of the desirable features of agent-based models. Furthermore, our method can be readily adapted for a wide range of applications, opening up new avenues for studying the formation of colonies with diverse shapes and complex internal interactions.