# 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 a 512 core cluster based on AMD's latest processors.

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.

- L. M. Faria, A. R. Kasimov, R. R. Rosales, Study of a model equation in detonation theory: multidimensional effects (to appear in SIAM J. Applied Maths, ArXiv preprint)

- L. Faria, A. Kasimov, R. Rosales,
*Theory of weakly nonlinear self-sustained detonations*, J. Fluid Mech., 784, 163-198, 2015.

- R. Semenko, L. Faria, A. Kasimov, B. Ermolaev,
*Set-valued solutions for non-ideal detonation*, Shock Waves, 2015.

- J. Sierra, A. Kasimov, P. Markowich, R.-M. Weishäupl,
*On the Gross-Pitaevskii equation with pumping and decay: stationary states and their stability*, Journal of Nonlinear Science, 25(3), 709-739, 2015.

- A. Kasimov, S. Korneev,
*Detonation in supersonic radial outflow,*J. Fluid Mech., 760, 313-341, 2014

- L. Faria, A. Kasimov, R. Rosales,
*Study of a model equation in detonation theory*. SIAM J. Applied Math, 74(2), 547–570, 2014.

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