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Applied Mathematics

1991

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Articles 31 - 36 of 36

Full-Text Articles in Physical Sciences and Mathematics

Self-Activation And Inhibition: A Simple Nonlinear Model, J. A. Adam Jan 1991

Self-Activation And Inhibition: A Simple Nonlinear Model, J. A. Adam

Mathematics & Statistics Faculty Publications

Self-activation and self-inhibition of cell number density (or growth factor concentration) due to a spatially localized source are studied. Both the time-independent and time-dependent models are examined, and the linear stability of the resulting three steady states of the former is discussed.

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Nonlinear-Interaction Of A Detonation Vorticity Wave, D. G. Lasseigne, T. L. Jackson, M. Y. Hussaini Jan 1991

Nonlinear-Interaction Of A Detonation Vorticity Wave, D. G. Lasseigne, T. L. Jackson, M. Y. Hussaini

Mathematics & Statistics Faculty Publications

The interaction of an oblique, overdriven detonation wave with a vorticity disturbance is investigated by a direct two-dimensional numerical simulation using a multidomain, finite-difference solution of the compressible Euler equations. The results are compared to those of linear theory, which predict that the effect of exothermicity on the interaction is relatively small except possibly near a critical angle where linear theory no longer holds. It is found that the steady-state computational results whenever obtained in this study agree with the results of linear theory. However, for cases with incident angle near the critical angle, moderate disturbance amplitudes, and/or sudden transient …

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On A Unique Tree Representation For P4-Extendible Graphs, B. Jamison, S. Olariu Jan 1991

On A Unique Tree Representation For P4-Extendible Graphs, B. Jamison, S. Olariu

Computer Science Faculty Publications

Several practical applications in computer science and computational linguistics suggest the study of graphs that are unlikely to have more than a few induced paths of length three. These applications have motivated the notion of a cograph, defined by the very strong restriction that no vertex may belong to an induced path of length three. The class of P4-extendible graphs that we introduce in this paper relaxes this restriction, and in fact properly contains the class of cographs, while still featuring the remarkable property of admitting a unique tree representation. Just as in the case of cographs, the …

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A Duality Approach To Best Uniform Convex Approximation, S. E. Weinstein, Yuesheng Xu Jan 1991

A Duality Approach To Best Uniform Convex Approximation, S. E. Weinstein, Yuesheng Xu

Mathematics & Statistics Faculty Publications

Let C[a, b] be the space of continuous functions on [a, b] endowed with the uniform norm llƒll ∞ = sup{ Iƒ(x)1 :x∈ [a, b]}. Let K be the set of convex functions defined on [a, b]. A function g* ∈ K is said to be a best uniform convex approximation to ƒ ∈ C[a, b] if ∥ƒ - g*∥ ∞ = inf { ∥ƒ - g∥∞ : g ∈ K}.

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Parametric Instability Of Supersonic Shear Layers Induced By Periodic Mach Waves, Fang Q. Hu, Christopher K. W. Tam Jan 1991

Parametric Instability Of Supersonic Shear Layers Induced By Periodic Mach Waves, Fang Q. Hu, Christopher K. W. Tam

Mathematics & Statistics Faculty Publications

It is suggested that parametric instability can be induced in a confined supersonic shear layer by the use of a periodic Mach wave system generated by a wavy wall. The existence of such an instability solution is demonstrated computationally by solving the Floquet system of equations. The solution is constructed by means of a Fourier-Chebyshev expansion. Numerical convergence is assured by using a very large number of Fourier and Chebyshev basis functions. The computed growth rate of the induced flow instability is found to vary linearly with the amplitude of the mach waves when the amplitude is not excessively large. …

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A Mathematical Model For Outgassing And Contamination, W. Fang, M. Shillor, E. Stahel, E. Epstein, C. Ly, J. Mcniel, Edward D. Zaron Jan 1991

A Mathematical Model For Outgassing And Contamination, W. Fang, M. Shillor, E. Stahel, E. Epstein, C. Ly, J. Mcniel, Edward D. Zaron

Civil and Environmental Engineering Faculty Publications and Presentations

A model for the mathematical description of the processes of outgassing and contamination in a vacuum system is proposed. The underlying assumptions are diffusion in the source, convection and diffusion in the cavity, mass transfer across the source-cavity interface, and a generalization of the Langmuir isotherm for the sorption kinetics on the target. Three approximations are considered where the asymptotic behavior of the model for large time is shown as well as the dependence and sensitivity of the model on some of the parameters. Some numerical examples of the full model are then presented together with a proof of the …

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