Now showing items 1-10 of 19
A Lyapunov Functional for the Cubic Nonlinearity Activator-Inhibitor Model Equation
The cubic nonlinearity activator-inhibitor model equation is a simpleexample of a pattern-forming system for which strong mathematical resultscan be obtained. Basic properties of solutions and the derivation ofa Lyapunov ...
Harnack's Inequality for Cooperative Weakly Coupled Elliptic Systems
We consider cooperative, uniformly elliptic systems, with bounded coefficients and coupling in the zeroth-order terms. We establish two analogues of Harnack's inequality for this class of systems. A weak version is obtained ...
An Object-Oriented Programming Approach to Implement Global Spectral Methods: Application to Dynamic Simulation of a Chemical Infiltration Process
Boundary-value problems (BVPs) in relatively simple geometriescan be solved using global spectral methods. These discretizationmethods are applicable to a wide range of problems and are suitablefor a "rapid prototyping" ...
Influence of Gas Composition on Wafer Temperature Control in a Tungsten Chemical Vapor Deposition Reactor
Experimental measurements of wafer temperature in a single-wafer,lamp-heated CVD system were used to study the wafer temperature responseto gas composition. A physically based simulation procedure for theprocess gas and ...
The Pompeiu Problem, What's New?
Survey of recent developments on the Pompeiu problem and the Schiffer problem. This problem has surprising interactions with inverse scattering, image processing and other applied problems.
Software and Other Teaching Tools Applied to Modeling and Analysis of Distributed Parameter Systems
Over the last two years, we have been developing a library of Matlab subprograms integrated with on-line lecture notes in the form of WWW documents which are used in both undergraduate and graduate-level Chemical Engineering ...
Spatially Resolved Compressor Characteristics for Modeling and Control of Blade-Scale Flow Instabilities
A numerical techniques cable of simulating blade-scale compression system flow instabilities over times scales spanning tens of rotor revolutions is presented. Simulations of stall inception, growth to fully-developed ...
Monodromic differential equations
Lecture presented at Taniguchi Symposium, Katata, June 1995. Deals with new kind of differential equations for multivalued functions. The monodromy operator is allowed to enter into the equation. Related to resurgence and ...
Analysis of a complex activator-inhibitor equation
Basic properties of solutions and a Lyapunov functionalare presented for a complex activator-inhibitor equation witha cubic nonlinearity.Potential applications include control of coupled-oscillator arrays(for quasi-optical ...
Control of Large Actuator Arrays Using Pattern-Forming Systems
Pattern-forming systems are used to model many diverse phenomena from biology,chemistry and physics. These systems of differential equations havethe property that as a bifurcation (or control) parameter passes through ...