Time & Date: 10:00 - 11:00 am, June 17 (Friday)

Venue: Zoom Online Meeting

Zoom meeting ID: 954 9836 3071

Passcode: 20220617

Host: Prof. Dong WANG

Speaker: Prof. Yanxiang ZHAO

Abstract: We propose a nonlocal Ohta-Kawasaki model to study the nonlocal effect on the pattern formation of some binary systems with general long-range interactions. While the nonlocal Ohta-Kawasaki model displays similar bubble patterns as the standard Ohta-Kawasaki model, by performing Fourier analysis, we find that the optimal number of bubbles for the nonlocal model may have an upper bound no matter how large the repulsive strength is. The existence of such an upper bound is characterized by the eigenvalues of the nonlocal kernels. Additionally we explore the conditions under which the nonlocal horizon parameter may promote or demote the bubble splitting, and apply the analysis framework to several case studies for various nonlocal operators.

Biography: Dr. Yanxiang ZHAO is an associate professor of mathematics department at George Washington University. His research interests include numerical analysis, scientific computing and mathematical modeling with applications in biophysics, materials science and biochemistry.