DSpace Repository

Energy transmission in Hamiltonian systems of globally interacting particles with Klein-Gordon on-site potentials

Show simple item record

dc.contributor.author Mac´ıas-D´ıaz, Jorge E.
dc.contributor.author Bountis, Anastasios
dc.contributor.author Christodoulidi, Helen
dc.date.accessioned 2019-12-12T03:37:06Z
dc.date.available 2019-12-12T03:37:06Z
dc.date.issued 2019-04-03
dc.identifier.citation Jorge E. Mac´ıas-D´ıaz, Anastasios Bountis,and Helen Christodoulidi (2019) Energy transmission in Hamiltonian systems of globally interacting particles with Klein-Gordon on-site potentials. Mathematics in Engineering.Volume: 1, Issue: 2, Pages: 343-358 en_US
dc.identifier.uri http://nur.nu.edu.kz/handle/123456789/4402
dc.description.abstract We consider a family of 1-dimensional Hamiltonian systems consisting of a large number of particles with on-site potentials and global (long range) interactions. The particles are initially at rest at the equilibrium position, and are perturbed sinusoidally at one end using Dirichlet data, while at the other end we place an absorbing boundary to simulate a semi-infinite medium. Using such a lattice with quadratic particle interactions and Klein-Gordon type on-site potential, we use a parameter 0 ≤ α < ∞as a measure of the “length” of interactions, and show that there is a sharp threshold above which energy is transmitted in the form of large amplitude nonlinear modes, as long as driving frequencies Ω lie in the forbidden band-gap of the system. This process is called nonlinear supratransmission and is investigated here numerically to show that it occurs at higher amplitudes the longer the range of interactions, reaching a maximum at a value α = αmax . 1.5 that depends on Ω. Below this αmax supratransmission thresholds decrease sharply to values lower than the nearest neighbor α = ∞ limit. We give a plausible argument for this phenomenon and conjecture that similar results are present in related systems such as the sine-Gordon, the nonlinear Klein-Gordon and the double sine-Gordon type. en_US
dc.language.iso en en_US
dc.publisher Mathematics in Engineering en_US
dc.rights Attribution-NonCommercial-ShareAlike 3.0 United States *
dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/us/ *
dc.subject nonlinear supratransmission en_US
dc.subject globally interacting systems en_US
dc.subject on-site potentials en_US
dc.title Energy transmission in Hamiltonian systems of globally interacting particles with Klein-Gordon on-site potentials en_US
dc.type Article en_US
workflow.import.source science


Files in this item

The following license files are associated with this item:

This item appears in the following Collection(s)

Show simple item record

Attribution-NonCommercial-ShareAlike 3.0 United States Except where otherwise noted, this item's license is described as Attribution-NonCommercial-ShareAlike 3.0 United States

Video Guide

Submission guideSubmission guide

Submit your materials for publication to

NU Repository Drive

Browse

My Account

Statistics