# Physical Mathematics Laboratory

Our research interests are in gasdynamics, shock and detonation waves, fluid dynamics, nonlinear waves. We use mathematical and computational tools to understand the physics of the phenomena of interest. The underlying models are typically described by hyperbolic systems of PDE. Recently, we have also started experiments in our Physical Mathematics Laboratory. These are mostly fluid dynamics experiments, in particular, on Faraday instability and shallow-water flows with hydraulic jumps.

Ongoing projects include:

- simplifed modeling of detonation waves, detonation analogs
- theory of detonation, in particular, gaseous detonation in systems with heat and momentum losses
- two-dimensional detonation stabilized in supersonic flow
- theory and high-resolution computation of detonation instability in mixtures with complex chemistry
- traffic flow theory based on hyperbolic continuum models
- nonlinear free-surface waves, in particular involving hydraulic jumps
- theory and computation of dispersive PDE, as in modeling Bose-Einstein condensation
- asymptotic behavior of solutions of (mostly hyperbolic) PDE

Our group has access to a 384 core cluster based on AMD's latest processors. KAUST's IBM BG/P supercomputer is also available for larger scale computations.

The Physical Mathematics Laboratory is equiped with Phantom V310 and V1610 high-speed cameras from Vision Research and a 2D PIV system by LaVision. These are used in visualization of water wave propagation, bouncing drop experiments, etc.

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- L. Faria, A. Kasimov, R. Rosales,
*Study of a model equation in detonation theory*. (to appear in SIAM J. Applied Math)

- A. Kasimov, L. Faria, R. Rosales,
*Model for shock wave chaos*, PRL 110, 104104, 2013

- R. Semenko, L. Faria, A. Kasimov, B. Ermolaev,
*Set-valued solutions for non-ideal detonation,*(submitted)

- B. Said-Houari, A. Kasimov,
*Damping by heat conduction in the Timoshenko system: Fourier and Cattaneo are the same*. J. Diff. Equations, 255(4), 611–632, 2013

- B. Seibold, M. Flynn, A. Kasimov, R. Rosales,
*Constructing set-valued fundamental diagrams from Jamiton solutions in second order traffic models*. Special issue of Networks and Heterogeneous Media, 8(3), 745-772, 2013

See preprint in Arxiv.