Wavelet-based spatial and temporal multiscaling: Bridging the atomistic and continuum space and time scales

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Abstract

A wavelet-based multiscale methodology is presented that naturally addresses time scaling in addition to spatial scaling. The method combines recently developed atomistic-continuum models and wavelet analysis. An atomistic one-dimensional harmonic crystal is coupled to a one-dimensional continuum. The methodology is illustrated through analysis of the dispersion relation, which is highly dispersive at small spatial scales and, as usual, nondispersive at large (continuum) scales. It is feasible to obtain the complete dispersion relation through the combination of the atomistic and the continuum analyses. Wavelet analysis in this work is not only used for bridging the atomistic and continuum scales but also for efficiently extracting the dispersion relation from the solution of wave propagation problems.

Original languageEnglish (US)
Article number024105
Pages (from-to)241051-241058
Number of pages8
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume68
Issue number2
StatePublished - Jul 2003

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Wavelet analysis
continuums
wavelet analysis
Wave propagation
methodology
scaling
Crystals
wave propagation
harmonics
crystals

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

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AB - A wavelet-based multiscale methodology is presented that naturally addresses time scaling in addition to spatial scaling. The method combines recently developed atomistic-continuum models and wavelet analysis. An atomistic one-dimensional harmonic crystal is coupled to a one-dimensional continuum. The methodology is illustrated through analysis of the dispersion relation, which is highly dispersive at small spatial scales and, as usual, nondispersive at large (continuum) scales. It is feasible to obtain the complete dispersion relation through the combination of the atomistic and the continuum analyses. Wavelet analysis in this work is not only used for bridging the atomistic and continuum scales but also for efficiently extracting the dispersion relation from the solution of wave propagation problems.

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