Title: Numerically simulating particles with short-ranged interactions
Abstract: Particles with diameters of nanometres to micrometres form the building blocks of many of the materials around us, and can be designed in a multitude of ways to form new ones. Such particles commonly live in fluids, where they jiggle about randomly because of thermal fluctuations in the fluid, and interact with each other via numerous mechanisms. One challenge in simulating such particles is that the range over which they interact attractively is often much shorter than their diameters, so the stochastic differential equations describing the particles’ dynamics are stiff, requiring timesteps much smaller than the timescales of interest. I will introduce methods to accelerate these simulations, which instead solve the limiting equations as the range of the attractive interaction goes to zero. In this limit a system of particles is described by a diffusion process on a collection of manifolds of different dimensions, connected by “sticky” boundary conditions. I will show how to simulate low-dimensional sticky diffusion processes, and will show how such methods give new insight into our experimental measurements of the dynamics of colloids. Finally I will discuss some ongoing challenges such as extending these methods to high dimensions and incorporating hydrodynamic interactions.
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