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Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Applied Mathematics

Boundary value problems

2016

Articles 1 - 2 of 2

Full-Text Articles in Physical Sciences and Mathematics

Transients In The Synchronization Of Asymmetrically Coupled Oscillator Arrays, Carlos E. Cantos, David K. Hammond, J.J.P. Veerman Sep 2016

Transients In The Synchronization Of Asymmetrically Coupled Oscillator Arrays, Carlos E. Cantos, David K. Hammond, J.J.P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We consider the transient behavior of a large linear array of coupled linear damped harmonic oscillators following perturbation of a single element. Our work is motivated by modeling the behavior of flocks of autonomous vehicles. We first state a number of conjectures that allow us to derive an explicit characterization of the transients, within a certain parameter regime Ω. As corollaries we show that minimizing the transients requires considering non-symmetric coupling, and that within Ω the computed linear growth in N of the transients is independent of (reasonable) boundary conditions.

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Method Of The Riemann-Hilbert Problem For The Solution Of The Helmholtz Equation In A Semi-Infinite Strip, Ashar Ghulam Jan 2016

Method Of The Riemann-Hilbert Problem For The Solution Of The Helmholtz Equation In A Semi-Infinite Strip, Ashar Ghulam

LSU Doctoral Dissertations

In this dissertation, a new method is developed to study BVPs of the modified Helmholtz and Helmholtz equations in a semi-infinite strip subject to the Poincare type, impedance and higher order boundary conditions. The main machinery used here is the theory of Riemann Hilbert problems, the residue theory of complex variables and the theory of integral transforms. A special kind of interconnected Laplace transforms are introduced whose parameters are related through branch of a multi-valued function. In the chapter 1 a brief review of the unified transform method used to solve BVPs of linear and non-linear integrable PDEs in convex …

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