Search

We present a novel computational framework for the simulation of rigid spherical Janus particle suspensions in Stokes flow. For a wide array of Janus particle types, we show long-range interactions may be resolved using fast, spectrally accurate boundary integral methods. We incorporate this to our rigid body Stokes platform, which resolves hydrodynamic interactions and contact. Our approach features the use of spherical harmonic expansions for spectrally accurate integral operator evaluation, complementarity-based collision resolution, and optimal O (n) scaling with the number of particles when accelerated via fast summation techniques. We demonstrate the versatility of our simulation platform through three test cases involving Janus particle systems prominent in applications: amphiphilic, bipolar electric and phoretic particles. For each test case, we formulate Janus particle interactions in boundary integral form and use our framework to demonstrate examples of self-assembly and complex collective behavior characteristic of these systems. [ABSTRACT FROM AUTHOR]

An efficient direct solver for volume integral equations with O ( N ) complexity for a broad range of problems is presented. The solver relies on hierarchical compression of the discretized integral operator, and exploits that off-diagonal blocks of certain dense matrices have numerically low rank. Technically, the solver is inspired by previously developed direct solvers for integral equations based on “recursive skeletonization” and “Hierarchically Semi-Separable” (HSS) matrices, but it improves on the asymptotic complexity of existing solvers by incorporating an additional level of compression. The resulting solver has optimal O ( N ) complexity for all stages of the computation, as demonstrated by both theoretical analysis and numerical examples. The computational examples further display good practical performance in terms of both speed and memory usage. In particular, it is demonstrated that even problems involving 10 7 unknowns can be solved to precision 10 − 10 using a simple Matlab implementation of the algorithm executed on a single core. [ABSTRACT FROM AUTHOR]