Research our contributions to discovery
Chaotic mixing of granular materials; 3D nonlinear dynamical systems and chaos
This was the topic of the TMNT-Lab Director's PhD dissertation. He applied advanced techniques from the theory of nonlinear dynamical systems to the problem of mixing and segregation of granular materials. Research supported by the National Science Foundation.
Nonlinear Fourier analysis and transforms for ocean acoustics modeling (NONFATFOAM)
The extension of normal mode analysis to nonlinear systems is a pressing unsolved problem in engineering. The theory of nonlinear evolution equations offers an approach to generalize classical Fourier analysis on a case-by-case basis, providing a novel approach towards signal processing of nonlinear time series.
Hyperbolic heat conduction
Amongst several mathematical contributions to this field, mistakes were found in a paper claiming cloaking of hyperbolic heat waves. Research proudly performed on nights & weekends without expending any taxpayer funds.
Nonlinear acoustics and shock formation
Amongst many accomplishments and contributions to this field, new weakly-nonlinear acoustic equations were derived for both lossless gasses and liquids, without suffering from the shortcomings of the approximations credited to Kuznetsov and Lighthill–Westervelt (though this attribution is somewhat incorrect).
Numerical methods for hyperbolic systems of conservation laws
This was the topic of the TMNT-Lab Director's MS research — implementing a fully-discrete non-oscillatory central scheme for hyperbolic systems of conservation on unstructured triangular meshes, including introducing a "genuinely multidimensional" non-oscillatory minimum-angle plane reconstruction (MAPR).
Wavelets and wavelet methods for signal processing and solution of PDEs
Legacy project, now archived.