Brown University Joint Materials/Solid Mechanics Seminar Series
Department of Otolaryngology and Communicative Sciences
Scientific Computing Seminar
Computational Sciences Branch, Air Vehicles Directorate,
Air Force Research Laboratory, Wright-Patterson AFB, Ohio 45433
Abstract: This presentation will discuss recent progress in the development of a set of versatile schemes aimed at the solution of multi-disciplinary problems on general curvilinear geometries. Fourth and sixth-order accurate Pade-type schemes, coupled with low-pass (up to 10th-order) spatial filters have been incorporated into both implicit and explicit time-marching solvers. The filtering technique overcomes previous limitations associated with numerical instability arising from non-linearity, boundary condition implementation and mesh non-uniformity, while retaining the desired high spatial accuracy. Extensions to treat moving meshes, as well as multi-domain and overset grid strategies have yielded a powerful common platform to solve problems in turbulence, acoustics, computational electromagnetics and fluid-structure interactions. Several results obtained in the Computational Sciences Branch will be described, and ongoing research will be outlined.
Department of Mathematics and TICAM
Abstract: Nonlinear dispersive wave equations arise from both hearing and optics, and finite energy particle like solutions play key roles for information transmission and processing. Analysis and numerical simulation of these wave solutions will be shown for qualitative and quantitative understanding of their robustness and interactions. The PDE in hearing is a nonlinear nonlocal cochlear model of the transmission line type for capturing the multitone interactions and resulting tonal suppression effects. The model can serve as a module for voice signal processing. It is a one space dimensional damped forced dispersive PDE based on mechanics and phenomenology of hearing. It describes the motion of basilar membrane (BM) in the cochlea driven by in-put pressure waves. The elastic damping is a nonlinear and nonlocal functional of BM displacement. The PDE model in optics is the two space dimensional sine-Gordon equation which admits long lived short pulses, the so called light bullets, as observed in Maxwell equations.
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