KI-Net Organizational Meeting

NCSU Node: Current and Future Research

Alina Chertock

North Carolina State University

Our research focuses on development of high-resolution numerical methods for problems that admit solutions of very complicated structures. The new techniques are based on particle methods, finite-volume methods and their hybridization, as well as on a combination of stochasticand numerical tools. The developed computational methods are being implemented in a variety of applications closely related to network dynamics, biological processes, and geophysical problems.

In particular, one of the objectives of the current work is to systematically develop and analyze the hierarchy of pedestrian traffic models, which consists of three levels: (i) Microscopic description, (ii) Mesoscopic description and (iii) Macroscopic PDE description. Another direction we are exploring is related to chemotaxis models, where we are interested in studying the collective behavior of a suspension of oxygen-driven bacteria in an aquatic fluid. We also work on simulating various wave phenomena including propagation of internal waves in ocean and atmosphere.