Physical Mathematics Laboratory
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Our research activities revolve around partial differential equations and their applications in fluid dynamics, reacting gas dynamics, linear and nonlinear wave propagation, dispersive systems, and reaction-diffusion phenomena. We use a wide spectrum of methods in the study of PDE: asymptotic, functional-analytic, and computational. Whenever possible, we also carry out experiments in our fluid dynamics laboratory to go along with theoretical and computational studies.
Specific topics currently being studied include:
- hyperbolic balance laws, existence and stability of self-sustained shock waves;
- theory of detonation (linear stability analysis, asymptotic theory of weakly curved detonations);
- high-resolution computation of detonation instability;
- dispersive PDE, in particular, nonlinear Schroedinger equation with application to Bose-Einstein condensation;
- reaction-diffusion systems in population biology;
- asymptotic behavior of solutions of hyperbolic and hyperbolic-parabolic/hyperbolic-elliptic systems of PDE.
Significant computational resources are also available to the group, including access to KAUST's IBM BG/P supercomputer with 64K cores (Shaheen) and a 96 node linux cluster with two Intel Nehalem quad-core processors per each node.
Our experimental laboratory is equiped with facilities to perform fluid dynamical experiments, for example, involving water waves in non-uniform channels, hydraulic jumps, rotating flows, etc. Phantom V310 high-speed camera and 2D PIV system by LaVision are used for visualization of the flows.