Matches in SemOpenAlex for { <https://semopenalex.org/work/W1987224062> ?p ?o ?g. }
- W1987224062 abstract "Localization of elastic waves in two-dimensional (2D) and three-dimensional (3D) media with random distributions of the Lam'e coefficients (the shear and bulk moduli) is studied, using extensive numerical simulations. We compute the frequency dependence of the minimum positive Lyapunov exponent $ensuremath{gamma}$ (the inverse of the localization length) using the transfer-matrix method, the density of states utilizing the force oscillator method, and the energy-level statistics of the media. The results indicate that all the states may be localized in the 2D media, up to the disorder width and the smallest frequencies considered, although the numerical results also hint at the possibility that there might be a small range of the allowed frequencies over which a mobility edge might exist. In the 3D media, however, most of the states are extended (with only a small part of the spectrum in the upper band tail that contains localized states) even if the Lam'e coefficients are randomly distributed. Thus, the 3D heterogeneous media still possess a mobility edge. If both the Lam'e coefficients vary spatially in the 3D medium, the localization length $ensuremath{Lambda}$ follows a power law near the mobility edge, $ensuremath{Lambda}ensuremath{sim}{(ensuremath{Omega}ensuremath{-}{ensuremath{Omega}}_{c})}^{ensuremath{-}ensuremath{nu}}$, where ${ensuremath{Omega}}_{c}$ is the critical frequency. The numerical estimate, $ensuremath{nu}ensuremath{simeq}1.89ifmmodepmelsetextpmfi{}0.17$, is significantly larger than the numerical estimate, $ensuremath{nu}ensuremath{simeq}1.57ifmmodepmelsetextpmfi{}0.01$, and $ensuremath{nu}=3/2$ (which was recently derived by a semiclassical theory for the 3D Anderson model of electron localization). If the shear modulus is constant but the bulk modulus varies spatially, the plane waves with transverse polarization propagate without any scattering---leading to a band of completely extended states, even in the 2D media. At the mobility edge of such media the localization length follows the same type of power law as $ensuremath{Lambda}$ but with an exponent ${ensuremath{nu}}_{T}ensuremath{simeq}1/2$ for both 2D and 3D media." @default.
- W1987224062 created "2016-06-24" @default.
- W1987224062 creator A5056001412 @default.
- W1987224062 creator A5087150520 @default.
- W1987224062 creator A5090718954 @default.
- W1987224062 date "2008-07-24" @default.
- W1987224062 modified "2023-10-16" @default.
- W1987224062 title "Numerical simulation of the localization of elastic waves in two- and three-dimensional heterogeneous media" @default.
- W1987224062 cites W1626579222 @default.
- W1987224062 cites W1662674546 @default.
- W1987224062 cites W1964392553 @default.
- W1987224062 cites W1968385832 @default.
- W1987224062 cites W1969306742 @default.
- W1987224062 cites W1969336240 @default.
- W1987224062 cites W1971489990 @default.
- W1987224062 cites W1984753804 @default.
- W1987224062 cites W1988628491 @default.
- W1987224062 cites W1989728915 @default.
- W1987224062 cites W1990001655 @default.
- W1987224062 cites W1990056747 @default.
- W1987224062 cites W1992637551 @default.
- W1987224062 cites W2018249891 @default.
- W1987224062 cites W2028925109 @default.
- W1987224062 cites W2031737699 @default.
- W1987224062 cites W2033759311 @default.
- W1987224062 cites W2044358302 @default.
- W1987224062 cites W2048449905 @default.
- W1987224062 cites W2049587182 @default.
- W1987224062 cites W2050675284 @default.
- W1987224062 cites W2051954300 @default.
- W1987224062 cites W2075690446 @default.
- W1987224062 cites W2084128468 @default.
- W1987224062 cites W2088376080 @default.
- W1987224062 cites W2088832670 @default.
- W1987224062 cites W2098781439 @default.
- W1987224062 cites W2104760713 @default.
- W1987224062 cites W2114497791 @default.
- W1987224062 cites W2264002775 @default.
- W1987224062 cites W3022099520 @default.
- W1987224062 cites W3098347892 @default.
- W1987224062 cites W4210545731 @default.
- W1987224062 cites W4237758070 @default.
- W1987224062 cites W4248383505 @default.
- W1987224062 cites W3103490625 @default.
- W1987224062 doi "https://doi.org/10.1103/physrevb.78.024207" @default.
- W1987224062 hasPublicationYear "2008" @default.
- W1987224062 type Work @default.
- W1987224062 sameAs 1987224062 @default.
- W1987224062 citedByCount "21" @default.
- W1987224062 countsByYear W19872240622012 @default.
- W1987224062 countsByYear W19872240622013 @default.
- W1987224062 countsByYear W19872240622014 @default.
- W1987224062 countsByYear W19872240622016 @default.
- W1987224062 countsByYear W19872240622017 @default.
- W1987224062 countsByYear W19872240622018 @default.
- W1987224062 countsByYear W19872240622020 @default.
- W1987224062 countsByYear W19872240622022 @default.
- W1987224062 crossrefType "journal-article" @default.
- W1987224062 hasAuthorship W1987224062A5056001412 @default.
- W1987224062 hasAuthorship W1987224062A5087150520 @default.
- W1987224062 hasAuthorship W1987224062A5090718954 @default.
- W1987224062 hasBestOaLocation W19872240622 @default.
- W1987224062 hasConcept C121332964 @default.
- W1987224062 hasConcept C138885662 @default.
- W1987224062 hasConcept C158622935 @default.
- W1987224062 hasConcept C191544260 @default.
- W1987224062 hasConcept C207467116 @default.
- W1987224062 hasConcept C2524010 @default.
- W1987224062 hasConcept C26873012 @default.
- W1987224062 hasConcept C2778113609 @default.
- W1987224062 hasConcept C2779557605 @default.
- W1987224062 hasConcept C2780388253 @default.
- W1987224062 hasConcept C33923547 @default.
- W1987224062 hasConcept C37914503 @default.
- W1987224062 hasConcept C41895202 @default.
- W1987224062 hasConcept C62520636 @default.
- W1987224062 hasConceptScore W1987224062C121332964 @default.
- W1987224062 hasConceptScore W1987224062C138885662 @default.
- W1987224062 hasConceptScore W1987224062C158622935 @default.
- W1987224062 hasConceptScore W1987224062C191544260 @default.
- W1987224062 hasConceptScore W1987224062C207467116 @default.
- W1987224062 hasConceptScore W1987224062C2524010 @default.
- W1987224062 hasConceptScore W1987224062C26873012 @default.
- W1987224062 hasConceptScore W1987224062C2778113609 @default.
- W1987224062 hasConceptScore W1987224062C2779557605 @default.
- W1987224062 hasConceptScore W1987224062C2780388253 @default.
- W1987224062 hasConceptScore W1987224062C33923547 @default.
- W1987224062 hasConceptScore W1987224062C37914503 @default.
- W1987224062 hasConceptScore W1987224062C41895202 @default.
- W1987224062 hasConceptScore W1987224062C62520636 @default.
- W1987224062 hasIssue "2" @default.
- W1987224062 hasLocation W19872240621 @default.
- W1987224062 hasLocation W19872240622 @default.
- W1987224062 hasLocation W19872240623 @default.
- W1987224062 hasOpenAccess W1987224062 @default.
- W1987224062 hasPrimaryLocation W19872240621 @default.
- W1987224062 hasRelatedWork W1513122110 @default.
- W1987224062 hasRelatedWork W1542602325 @default.
- W1987224062 hasRelatedWork W1998459108 @default.
- W1987224062 hasRelatedWork W2081858368 @default.