Seminar Event Detail

Applied Interdisciplinary Mathematics (AIM)

Date:  Friday, March 01, 2019
Location:  1084 East Hall (3:00 PM to 4:00 PM)

Title:  Interaction between charged dielectric spheres: algorithms and computer simulations

Abstract:   Modern particle-based simulations increasingly incorporate polarization charges arising from spatially nonuniform permittivity, for the study ranging from colloidal suspensions to protein-protein interactions, etc. Numerical calculation of these induced many-body effects typically requires large amount of computational effort. For the special case of dielectric spheres, we will present two different approaches for solving the 3D Poisson equation, including 1. a semi-analytical hybrid method which combines the method of images and method of moments. Singularity in the multipole expansion is removed through the addition of image charges for close sphere pairs, making the problem well-conditioned. 2. a more general and flexible numerical boundary element method, higher order accuracy is achieved by combining the singularity subtraction and extrapolation techniques.

We further use our methods to explore the role of dielectric effect in the interaction between charged dielectric spheres. Through a few concrete numerical examples, we will show that the dielectric effect can lead to interesting phenomena such as like-charge attraction and qualitatively different self-assembled structures.


Speaker:  Zecheng Gan
Institution:  University of Michigan

Event Organizer:   Robert Krasny


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