Speaker: Yanzhi Zhang, Missouri University of Science and Technology, Rolla, USA

Time : 16:00 - 17.00 CET (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

Zoom :  A zoom meeitng link will appear here, one hour before the talk

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: Variable-order fractional Laplacian, meshfree methods, radial basis functions, anomalous diffusion

Abstract: The transition between different diffusion states is a common feature in highly heterogeneous, fractal-like media. This phenomenon is observed across various fields, including dusty plasma, living human cells, hydrology, proteins, and polymer liquids. The application of nonlocal fractional models to study anomalous diffusion transitions is a relatively recent advancement. In particular, the variable-order fractional Laplacian plays a key role in understanding heterogeneous systems. In this talk, we will explore the challenges and current progress in studying anomalous diffusion in heterogeneous media. We will also introduce our meshfree methods for solving the variable-order Laplacian and discuss their properties. Additionally, we will apply these methods to investigate the solution behaviors of variable-order fractional PDEs in different contexts. 

Biography: Dr. Yanzhi Zhang is a Gary Havener Endowed Professor  in the Department of Mathematics and Statistics at Missouri University of Science and Technology (Missouri S&T). She received her Ph.D. in Computational Mathematics from the National University of Singapore in 2006, completed a postdoctoral appointment in the Department of Scientific Computing at Florida State University, and joined the faculty at Missouri S&T in 2010. Dr. Zhang’s current research interests include data-informed modeling for seismic waves, reduced-order modeling, fractional and nonlocal PDEs, and multiscale/multiphysics modeling and simulation.

Bibliography

[1] Y. Wu and Y. Zhang. “Variable-order Laplacian and its computations with meshfree methods”. Journal of Scientific Computing 99 (2024), article 18.
[2] J. Burkardt, Y. Wu, and Y. Zhang, “A unified meshfree pseudospectral method for solving both classical and fractional PDEs”. SIAM Journal of Scientific Computing, 43 (2021), pp. A1389– A1411.