nonlinear models

Deterministic particle approximation for nonlinear transport equations

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Building L3 R3119

Approximating the solution to an evolutionary partial differential equation by a set of "moving particles" has several advantages. It validates the use of a continuity equation in an "individuals-based" modeling setting, it provides a link between Lagrangian and Eulerian description, and it defines a "natural" numerical approach to those equations. I will describe recent rigorous results in that context. The main one deals with one-dimensional scalar conservation laws with nonnegative initial data, for which we prove that the a suitably designed "follow-the-leader" particle scheme approximates entropy solutions in the sense of Kruzkov in the many particle limit. Said result represents a new way to solve scalar conservation laws with bounded and integrable initial data. The same method applies to second order traffic flow models, to nonlocal transport equations, and to the Hughes model for pedestrian movements.

A novel design of antenna array developed by KAUST scientists

1 min read ·
At the sensors lab, Prof. K.N. Salama and Prof. A. Shamim led a team of KAUST founding masters students Farhan Abdul Ghaffar and Muhammad Umair Khalid to develop an aperture coupled patch antenna array SoP.

Khaled Salama

Professor Salama is a prominent leader in the development of intelligent sensors, biosensors and very large-scale integration (VLSI) architectures for bioimaging and instrumentation. He is one of the founders of the Electrical and Computer Engineering (ECE) Program at KAUST.