In the article "Rapid sampling of stochastic displacements in Brownian dynamics simulations", Fiore et al. present a new technique for sampling the stochastic thermal displacements in Brownian Dynamics simulations with hydrodynamic interactions represented at the Rotne-Prager-Yamawaka (RPY) level of approximation. This technique, called Positively-Split Ewald sampling, samples the Brownian displacements from a superposition of two indepedent distributions: a wave space (far-field or long-ranged) contribution, computed using techniques from fluctuating hydrodynamics and non-uniform fast Fourier transforms; and a real space (near-field or short-ranged) correction, computed using a Krylov subspace method. The total computational complexity of the algorithm scales linearly with the number of particles modeled. The PSE algorithm enables simulations of up to 4 million colloidal particles. A high-performance implementation of the PSE algorithm on graphics processing units (GPUs), written as a plugin for the software package HOOMD-blue is freely available on GitHub.
A GPU algorithm for Brownian Dynamics of composite-bead rigid particles is implemented. Arbitrarily shaped colloidal particles or macromolecules can be modeled as rigid assemblies of beads from surface tessellation. Hydrodynamic interactions among the beads are modeled with RPY tensor applying the PSE algorithm. Correct hydrodynamic and transport properties are successfully captured as demonstrated in the article "Rapid calculation of hydrodynamic and transport properties in concentrated solutions of colloidal particles and macromolecules". The software package can be downloaded here.
In the article "Modeling hydrodynamic self-propulsion with Stokesian Dynamics. Or teaching Stokesian Dynamics to swim," Swan, Brady and Moore demonstrate how models of swimming microorganisms can be constructed from rigid particles that move along a prescribed gait. The hydrodynamic interactions between particles serve as a surrogate for a solution of the Stokes equations dictating the fluid flow around the swimmer. These interactions are accounted for faithfully with the Stokesian Dynamics method. Click this link to view some movies of swimmers modeled in the article. A software package capable replicating these model swimmers as well as others is available.
A common practice in soft matter physics is to use colloidal probes to measure inter- and intra-molecular forces. For instance, A colloidal bead may be tethered to a microscope slide with DNA. When a force is applied to the bead, the DNA is stretched and a force-extension curve can be inferred. The key then is to know the force exerted on the bead. One method of "pulling" on the bead is to generate a flow field which drags it along the slide. When far from the surface of the slide, the drag coefficient of the bead is well know. In the article "Nonequilibrium distributions and hydrodynamic coupling distort the measurement of nanoscale forces near interfaces," Swan and Furst show that when the bead is near the interface, its Brownian motion makes knowledge of its drag coefficient difficult. They derive a new model for the force-extension curve associated with a bead tethered by a Hookean spring that accounts for the this stochastic motion explicitly. A software package capable of replicating the results of this model is available.