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LOCALIZATION OF HIGH-FREQUENCY WAVES PROPAGATING IN A LOCALLY PERIODIC MEDIUM

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dc.creatorLUIS ALBERTO FRIZ ROA
dc.date2010
dc.date.accessioned2025-01-10T14:43:52Z
dc.date.available2025-01-10T14:43:52Z
dc.date.issued2010
dc.description.abstractWE STUDY THE HOMOGENIZATION AND LOCALIZATION OF HIGH-FREQUENCY WAVES IN A LOCALLY PERIODIC MEDIA WITH PERIOD ?. WE CONSIDER INITIAL DATA THAT ARE LOCALIZED BLOCH-WAVE PACKETS, I.E. THAT ARE THE PRODUCT OF A FAST OSCILLATING BLOCH WAVE AT A GIVEN FREQUENCY ? AND OF A SMOOTH ENVELOPE FUNCTION WHOSE SUPPORT IS CONCENTRATED AT A POINT X WITH LENGTH SCALE . WE ASSUME THAT (?, X) IS A STATIONARY POINT IN THE PHASE SPACE OF THE HAMILTONIAN ?(?, X), I.E. OF THE CORRESPONDING BLOCH EIGENVALUE. UPON RESCALING AT SIZE WE PROVE THAT THE SOLUTION OF THE WAVE EQUATION IS APPROXIMATELY THE SUM OF TWO TERMS WITH OPPOSITE PHASES WHICH ARE THE PRODUCT OF THE OSCILLATING BLOCH WAVE AND OF TWO LIMIT ENVELOPE FUNCTIONS WHICH ARE THE SOLUTION OF TWO SCHRÖDINGER TYPE EQUATIONS WITH QUADRATIC POTENTIAL. FURTHERMORE, IF THE FULL HESSIAN OF THE HAMILTONIAN ?(?, X) IS POSITIVE DEFINITE, THEN LOCALIZATION TAKES PLACE IN THE SENSE THAT THE SPECTRUM OF EACH HOMOGENIZED SCHRÖDINGER EQUATION IS MADE OF A COUNTABLE SEQUENCE OF FINITE MULTIPLICITY EIGENVALUES WITH EXPONENTIALLY DECAYING EIGENFUNCTIONS.
dc.formatapplication/pdf
dc.identifier.doi10.1017/S0308210509000080
dc.identifier.issn1473-7124
dc.identifier.issn0308-2105
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/8719
dc.languagespa
dc.publisherPROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
dc.relation.uri10.1017/S0308210509000080
dc.rightsPUBLICADA
dc.titleLOCALIZATION OF HIGH-FREQUENCY WAVES PROPAGATING IN A LOCALLY PERIODIC MEDIUM
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE CIENCIAS BASICAS
ubb.SedeCHILLÁN
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