Nonlocal Models of Physics (virtual)

Modeling Problems with Anomalies and Singularities In recent years, nonlocal models have drawn increasing attention from scientific and engineering communities, especially in modeling problems with anomalies and singularities. Their applications can be found in a wide range of fields, including quantum physics, material sciences, turbulence, geophysics, and biology. Nonlocal models are usually characterized by integral operators, which introduce considerable challenges in both analyses and computations. In this talk, I will introduce our recently developed computational methods for nonlocal models characterized by the fractional Laplacian. Both finite difference method and meshfree method will be presented for their numerical approximation. Numerical analysis and experiments will be provided to demonstrate the effectiveness of our methods. Finally, physics applications including coexistence of normal and anomalous diffusion and wave propagation in nonlocal media will be also discussed.