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Articles 91 - 100 of 100
Full-Text Articles in Physical Sciences and Mathematics
Self-Activation And Inhibition: A Simple Nonlinear Model, J. A. Adam
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.
Stability Of A Viscoelastic Burgers Flow, D. Glenn Lasseigne, W. E. Olmstead
Stability Of A Viscoelastic Burgers Flow, D. Glenn Lasseigne, W. E. Olmstead
Mathematics & Statistics Faculty Publications
The system of equations proposed by Burgers to model turbulent flow in a channel is extended to include viscoelastic affects. The stability and bifurcation properties are examined in the neighborhood of the critical Reynolds number. For highly elastic fluids, the bifurcated state is periodic with a shift in frequency.
Best Quasi-Convex Uniform Approximation, S. E. Weinstein, Yuesheng Xu
Best Quasi-Convex Uniform Approximation, S. E. Weinstein, Yuesheng Xu
Mathematics & Statistics Faculty Publications
No abstract provided.
A Characterization Of The Solution Of A Fredholm Integral Equation With L∞ Forcing Term, Hideaki Kaneko, Richard Noren, Yuesheng Xu
A Characterization Of The Solution Of A Fredholm Integral Equation With L∞ Forcing Term, Hideaki Kaneko, Richard Noren, Yuesheng Xu
Mathematics & Statistics Faculty Publications
In this paper we investigate the regularity properties of the Fredholm equation (Formula Presented) . The kernel is the product of the smooth function k and the singular function gα (Formula Presented). The forcing function f is in L∞. We obtain a decomposition of the solution as the sum of two functions—one with a discontinuity reflecting that of the forcing function—and the other a regular function. Our results extend those of C. Schneider [6], who assumes a condition that is stronger than f ∈ C[a, b] ∩ Cm(a,b) (for some integer m). © 1990 …
Uniform L1 Behavior In Classes Of Integrodifferential Equations With Convex Kernels, Richard Noren
Uniform L1 Behavior In Classes Of Integrodifferential Equations With Convex Kernels, Richard Noren
Mathematics & Statistics Faculty Publications
No abstract provided.
Ignition Of A Combustible Solid With Reactant Consumption, D. Glenn Lasseigne, W. E. Olmstead
Ignition Of A Combustible Solid With Reactant Consumption, D. Glenn Lasseigne, W. E. Olmstead
Mathematics & Statistics Faculty Publications
The effects of excessive reactant consumption on the ignition of a combustible solid are introduced through a revised scaling of the heat release constant. Large activation energy asymptotics then yields a new one-parameter integral equation governing the temperature evolution near ignition. Analysis of the integral equation reveals a critical value of the parameter which distinguishes between the cases of ignition and nonignition. © 1987 Society for Industrial and Applied Mathematics
On The Existence Of Periodic And Eventually Periodic Solutions Of A Fluid Dynamic Forced Harmonic Oscillator, Charlie H. Cooke
On The Existence Of Periodic And Eventually Periodic Solutions Of A Fluid Dynamic Forced Harmonic Oscillator, Charlie H. Cooke
Mathematics & Statistics Faculty Publications
For certain flow regimes, the nonlinear differential equation Y¨=F(Y)−G, Y≥0, G>0 and constant, models qualitatively the behaviour of a forced, fluid dynamic, harmonic oscillator which has been a popular department store attraction. The device consists of a ball oscillating suspended in the vertical jet from a household fan. From the postulated form of the model, we determine sets of attraction and exploit symmetry properties of the system to show that all solutions are either initially periodic, with the ball never striking the fan, or else eventually approach a periodic limit cycle, after a sufficient number of bounces away from …
Sufficiency Of A Numerical Downstream Continuation, Charlie H. Cooke
Sufficiency Of A Numerical Downstream Continuation, Charlie H. Cooke
Mathematics & Statistics Faculty Publications
(First paragraph) Customarily one does not impose n-th order boundary conditions on the solution of initial/boundary value problems whose characterizing partial differential equations are also n-th order. However, conjecture that such problems are not well-posed, or that a solution might not exist, is not always justified [l]. Perhaps a physically more natural example is provided by problems of computational fluid dynamics. Here boundary conditions which correctly should be applied at an infinite distance downstream from the region of interest are for computational convenience often applied at a finite location [2]. Results of numerical experimentation on viscous flows governed by …
Complementary Extremum Principles, J. Swetits, C. Rogers
Complementary Extremum Principles, J. Swetits, C. Rogers
Mathematics & Statistics Faculty Publications
Important complementary extremum principles are generated without recourse to general variational theory. The results are illustrated by an application to a class of boundary value problems in Magnetohydrodynamics.
Solar Magnetoatmospheric Waves-A Simplified Mathematical Treatment, John A. Adam
Solar Magnetoatmospheric Waves-A Simplified Mathematical Treatment, John A. Adam
Mathematics & Statistics Faculty Publications
The inhomogeneous wave equation for a special class of magnetoatmospheric waves is formally solved, and the principle of stationary phase used to provide information on the group velocity properties of such waves. General results are presented concerning the associated mechanical energy flux. The basic problem considered is relevant to waves initiated by sudden events in the solar atmosphere.