Resonant waves and localization phenomena in lattices

Sagdulla A. Abdukadirov; Mark V. Ayzenberg-Stepanenko; Gregory G. Osharovich

doi:10.1098/rsta.2019.0110

Resonant waves and localization phenomena in lattices

Sagdulla A. Abdukadirov, Mark V. Ayzenberg-Stepanenko, Gregory G. Osharovich

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Transient wave processes in mass-spring lattices excited by point oscillating sources are studied. Dispersion properties of uniform periodic threedimensional (3D) square-cell and two-dimensional (2D) hexagonal-cell lattices including revealed starshaped localization phenomena are analysed. The resonant-like waves and localization-like patterns in non-uniform lattices possessing predetermined and randomly distributed defects are numerically examined in order to identify the sensitivity of starshape forms to different types of defects.

Original language	English
Article number	20190110
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	377
Issue number	2156
DOIs	https://doi.org/10.1098/rsta.2019.0110
State	Published - 21 Oct 2019

Keywords

Computer modelling
Lattice dynamics
Localization patterns
Resonant waves

ASJC Scopus subject areas

General Mathematics
General Engineering
General Physics and Astronomy

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10.1098/rsta.2019.0110

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title = "Resonant waves and localization phenomena in lattices",

abstract = "Transient wave processes in mass-spring lattices excited by point oscillating sources are studied. Dispersion properties of uniform periodic threedimensional (3D) square-cell and two-dimensional (2D) hexagonal-cell lattices including revealed starshaped localization phenomena are analysed. The resonant-like waves and localization-like patterns in non-uniform lattices possessing predetermined and randomly distributed defects are numerically examined in order to identify the sensitivity of starshape forms to different types of defects.",

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AU - Abdukadirov, Sagdulla A.

AU - Ayzenberg-Stepanenko, Mark V.

AU - Osharovich, Gregory G.

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Y1 - 2019/10/21

N2 - Transient wave processes in mass-spring lattices excited by point oscillating sources are studied. Dispersion properties of uniform periodic threedimensional (3D) square-cell and two-dimensional (2D) hexagonal-cell lattices including revealed starshaped localization phenomena are analysed. The resonant-like waves and localization-like patterns in non-uniform lattices possessing predetermined and randomly distributed defects are numerically examined in order to identify the sensitivity of starshape forms to different types of defects.

AB - Transient wave processes in mass-spring lattices excited by point oscillating sources are studied. Dispersion properties of uniform periodic threedimensional (3D) square-cell and two-dimensional (2D) hexagonal-cell lattices including revealed starshaped localization phenomena are analysed. The resonant-like waves and localization-like patterns in non-uniform lattices possessing predetermined and randomly distributed defects are numerically examined in order to identify the sensitivity of starshape forms to different types of defects.

KW - Computer modelling

KW - Lattice dynamics

KW - Localization patterns

KW - Resonant waves

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JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

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IS - 2156

M1 - 20190110

ER -

Resonant waves and localization phenomena in lattices

Abstract

Keywords

ASJC Scopus subject areas

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