PittsburghV1, France, Analysis, bibRecord, 000060

Breathers in a locally resonant granular chain with precompression

Identifieur interne : 000060 ( France/Analysis ); précédent : 000059; suivant : 000061

Breathers in a locally resonant granular chain with precompression

Auteurs : Lifeng Liu [États-Unis] ; Guillaume James [France] ; Panayotis Kevrekidis [États-Unis] ; Anna Vainchtein [États-Unis]

Source :

Physica D: Nonlinear Phenomena [ 0167-2789 ] ; 2016-09-15.

RBID : Hal:hal-01417945

Abstract

We study a locally resonant granular material in the form of a precompressed Hertzian chain with linearinternal resonators. Using an asymptotic reduction, we derive an effective nonlinear Schrödinger (NLS)modulation equation. This, in turn, leads us to provide analytical evidence, subsequently corroboratednumerically, for the existence of two distinct types of discrete breathers related to acoustic or opticalmodes: (a) traveling bright breathers with a strain profile exponentially vanishing at infinity and (b)stationary and traveling dark breathers, exponentially localized, time-periodic states mounted on topof a non-vanishing background. The stability and bifurcation structure of numerically computed exactstationary dark breathers is also examined. Stationary bright breathers cannot be identified using the NLSequation, which is defocusing at the upper edges of the phonon bands and becomes linear at the loweredge of the optical band.

Url:

https://hal.archives-ouvertes.fr/hal-01417945

DOI: 10.1016/j.physd.2016.05.007

Affiliations:

Links toward previous steps (curation, corpus...)

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Links to Exploration step

Hal:hal-01417945

Le document en format XML

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<author><name sortKey="Vainchtein, Anna" sort="Vainchtein, Anna" uniqKey="Vainchtein A" first="Anna" last="Vainchtein">Anna Vainchtein</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-110124" status="VALID">          <orgName>Department of Mathematics</orgName>
          <desc>            <address>              <addrLine>School of Arts and Sciences University of Pittsburgh 301 Thackeray Hall, Pittsburgh, PA 15260</addrLine>
              <country key="US"></country>
            </address>
            <ref type="url">http://www.mathematics.pitt.edu/</ref>
          </desc>
          <listRelation>            <relation active="#struct-378064" type="direct"></relation>
          </listRelation>
        <tutelles><tutelle active="#struct-378064" type="direct"><org type="institution" xml:id="struct-378064" status="INCOMING">          <orgName>University of Pittsburgh</orgName>
          <desc>            <address>              <country key="FR"></country>
            </address>
          </desc>
        </org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>États-Unis</country>
<placeName><settlement type="city">Pittsburgh</settlement>
<region type="state">Pennsylvanie</region>
</placeName>
<orgName type="university">Université de Pittsburgh</orgName>
</affiliation>
</author>
</analytic>
<idno type="DOI">10.1016/j.physd.2016.05.007</idno>
<series><title level="j">Physica D: Nonlinear Phenomena</title>
<idno type="ISSN">0167-2789</idno>
<imprint><date type="datePub">2016-09-15</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass></textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">We study a locally resonant granular material in the form of a precompressed Hertzian chain with linearinternal resonators. Using an asymptotic reduction, we derive an effective nonlinear Schrödinger (NLS)modulation equation. This, in turn, leads us to provide analytical evidence, subsequently corroboratednumerically, for the existence of two distinct types of discrete breathers related to acoustic or opticalmodes: (a) traveling bright breathers with a strain profile exponentially vanishing at infinity and (b)stationary and traveling dark breathers, exponentially localized, time-periodic states mounted on topof a non-vanishing background. The stability and bifurcation structure of numerically computed exactstationary dark breathers is also examined. Stationary bright breathers cannot be identified using the NLSequation, which is defocusing at the upper edges of the phonon bands and becomes linear at the loweredge of the optical band.</div>
</front>
</TEI>
<affiliations><list><country><li>France</li>
<li>États-Unis</li>
</country>
<region><li>Auvergne-Rhône-Alpes</li>
<li>Massachusetts</li>
<li>Pennsylvanie</li>
<li>Rhône-Alpes</li>
</region>
<settlement><li>Amherst (Massachusetts)</li>
<li>Grenoble</li>
<li>Pittsburgh</li>
</settlement>
<orgName><li>Université Grenoble-Alpes</li>
<li>Université Joseph Fourier</li>
<li>Université de Grenoble</li>
<li>Université de Pittsburgh</li>
<li>Université du Massachusetts</li>
</orgName>
</list>
<tree><country name="États-Unis"><region name="Pennsylvanie"><name sortKey="Liu, Lifeng" sort="Liu, Lifeng" uniqKey="Liu L" first="Lifeng" last="Liu">Lifeng Liu</name>
</region>
<name sortKey="Kevrekidis, Panayotis" sort="Kevrekidis, Panayotis" uniqKey="Kevrekidis P" first="Panayotis" last="Kevrekidis">Panayotis Kevrekidis</name>
<name sortKey="Vainchtein, Anna" sort="Vainchtein, Anna" uniqKey="Vainchtein A" first="Anna" last="Vainchtein">Anna Vainchtein</name>
</country>
<country name="France"><region name="Auvergne-Rhône-Alpes"><name sortKey="James, Guillaume" sort="James, Guillaume" uniqKey="James G" first="Guillaume" last="James">Guillaume James</name>
</region>
</country>
</tree>
</affiliations>
</record>

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Breathers in a locally resonant granular chain with precompression

Breathers in a locally resonant granular chain with precompression

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