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Papers by Roy Baty

Journal of Sound and Vibration, May 1, 1997

Bulletin of the American Physical Society, 2015

Quarterly Journal of Mechanics and Applied Mathematics, 2017

Bulletin of the American Physical Society, 2016

The Quarterly Journal of Mechanics and Applied Mathematics, 2019

As modern hydrodynamic codes increase in sophistication, the availability of realistic test probl... more As modern hydrodynamic codes increase in sophistication, the availability of realistic test problems becomes increasingly important. In gas dynamics, one common unrealistic aspect of most test problems is the ideal gas assumption, which is unsuited to many real applications, especially those involving high pressure and speed metal deformation. Our work considers the collapsing cavity and converging shock test problems, showing to what extent the ideal gas assumption can be removed from their specification. It is found that while most materials simply do not admit simple (that is scaling) solutions in this context, there are infinite-dimensional families of materials which do admit such solutions. We characterize such materials, derive the appropriate ordinary differential equations and analyze the associated nonlinear eigenvalue problem. It is shown that there is an inherent tension between boundedness of the solution, boundedness of its derivatives and the entropy condition. The sp...

This article applies nonstandard analysis to derive jump conditions for one-dimensional, divergin... more This article applies nonstandard analysis to derive jump conditions for one-dimensional, diverging, magnetogasdynamic shock waves emerging on the surface of a star. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions for the flow parameters occur smoothly across this interval. Predistributions of the Heaviside function and the Dirac delta measure are used to model the flow variables across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the flow parameters. It is shown here that the equations modeling a family of magnetogasdynamic shock waves yield products of generalized functions that may be analyzed consistently using nonstandard predistributions.

International Journal of Aeroacoustics

This article applies nonstandard analysis to study the generalized solutions of entropy and energ... more This article applies nonstandard analysis to study the generalized solutions of entropy and energy across one-dimensional shock waves in a compressible, inviscid, perfect gas. Nonstandard analysis is an area of modern mathematics that studies number systems that contain both infinitely large and infinitely small numbers. For an inviscid shock wave, it is assumed that the shock thickness occurs on an infinitesimal interval and that the jump functions for the field variables are smoothly defined on this interval. A weak converse to the existence of the entropy peak is derived and discussed. Generalized solutions of the Euler equations for entropy and energy are then derived for both theoretical and realistic normalized velocity profiles.