Date of Award

5-18-2007

Degree Type

Dissertation

Degree Name

Ph.D.

Degree Program

Engineering and Applied Science

Department

Physics

Major Professor

Puri, Ashok

Second Advisor

Jilkov, Vesselin

Third Advisor

Kocic, Vlajko

Fourth Advisor

Malkinski, Leszek

Fifth Advisor

Rees, Charles

Sixth Advisor

Murphy, Joseph

Abstract

In this paper we develop a finite-difference scheme to approximate radially symmetric solutions and (1 + 1)-dimensional solutions of the initial-value problem with smooth initial conditions Ý2w Ýt2. Þ2w. ƒÀ Ý Ýt..Þ2w + ƒÁ Ýw Ýt + m2w + GŒ(w) = 0, subject to : ( w(Px, 0) = ƒÓ(Px), Px ¸ D, Ýw Ýt (Px, 0) = ƒÕ(Px), Px ¸ D, in an open sphere D around the origin, where the internal and external damping coefficients ƒÀ and ƒÁ, respectively, are constant. The functions ƒÓ and ƒÕ are radially symmetric in D, they are small at infinity, and rƒÓ(r) and rƒÕ(r) are also assumed to be small at infinity. We prove that our scheme is consistent order O( t2) + O( r2) for GŒ identically equal to zero, and provide a necessary condition for it to be stable order n. A cornerstone of our investigation will be the study of potential applications of our model to discrete versions involving nonlinear systems of coupled oscillators. More concretely, we make use of the process of nonlinear supratransmission of energy in these chain systems and our numerical techniques in order to transmit binary information. Our simulations show that, under suitable parametric conditions, the transmission of binary signals can be achieved successfully.

Rights

The University of New Orleans and its agents retain the non-exclusive license to archive and make accessible this dissertation or thesis in whole or in part in all forms of media, now or hereafter known. The author retains all other ownership rights to the copyright of the thesis or dissertation.

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