Numerical Analysis and Applications of the Process of Nonlinear Supratransmission in Mechanical Systems of Coupled Oscillators with Damping

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,...

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Main Author: Macias, Diaz Jorge
Format: Others
Published: ScholarWorks@UNO 2007
Online Access:http://scholarworks.uno.edu/td/1077
http://scholarworks.uno.edu/cgi/viewcontent.cgi?article=2058&context=td
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spelling ndltd-uno.edu-oai-scholarworks.uno.edu-td-20582016-10-21T17:05:12Z Numerical Analysis and Applications of the Process of Nonlinear Supratransmission in Mechanical Systems of Coupled Oscillators with Damping Macias, Diaz Jorge 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. 2007-05-18T07:00:00Z text application/pdf http://scholarworks.uno.edu/td/1077 http://scholarworks.uno.edu/cgi/viewcontent.cgi?article=2058&context=td University of New Orleans Theses and Dissertations ScholarWorks@UNO
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format Others
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description 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.
author Macias, Diaz Jorge
spellingShingle Macias, Diaz Jorge
Numerical Analysis and Applications of the Process of Nonlinear Supratransmission in Mechanical Systems of Coupled Oscillators with Damping
author_facet Macias, Diaz Jorge
author_sort Macias, Diaz Jorge
title Numerical Analysis and Applications of the Process of Nonlinear Supratransmission in Mechanical Systems of Coupled Oscillators with Damping
title_short Numerical Analysis and Applications of the Process of Nonlinear Supratransmission in Mechanical Systems of Coupled Oscillators with Damping
title_full Numerical Analysis and Applications of the Process of Nonlinear Supratransmission in Mechanical Systems of Coupled Oscillators with Damping
title_fullStr Numerical Analysis and Applications of the Process of Nonlinear Supratransmission in Mechanical Systems of Coupled Oscillators with Damping
title_full_unstemmed Numerical Analysis and Applications of the Process of Nonlinear Supratransmission in Mechanical Systems of Coupled Oscillators with Damping
title_sort numerical analysis and applications of the process of nonlinear supratransmission in mechanical systems of coupled oscillators with damping
publisher ScholarWorks@UNO
publishDate 2007
url http://scholarworks.uno.edu/td/1077
http://scholarworks.uno.edu/cgi/viewcontent.cgi?article=2058&context=td
work_keys_str_mv AT maciasdiazjorge numericalanalysisandapplicationsoftheprocessofnonlinearsupratransmissioninmechanicalsystemsofcoupledoscillatorswithdamping
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