المؤلفون: ABLOWITZ, MARK J.¹ mark.ablowitz@colorado.edu, COLE, JUSTIN T.² jcole13@uccs.edu, NIXON, S. D.¹ Sean.D.Nixon@gmail.com

المصدر: SIAM Journal on Applied Mathematics. 2023, Vol. 83 Issue 4, p1623-1653. 31p.

مصطلحات موضوعية: *TOPOLOGICAL insulators, *ELECTROMAGNETIC wave propagation, *TOPOLOGICAL dynamics, *DYNAMICAL systems, *HONEYCOMB structures

مستخلص: A unified method for analyzing the dynamics and topological structure associated with a class of Floquet topological insulators is presented. The method is applied to a system that describes the propagation of electromagnetic waves through the bulk of a two-dimensional lattice that is helically driven in the direction of propagation. Tight-binding approximations are employed to derive reduced dynamical systems. Further asymptotic approximations, valid in the high-frequency driving regime, yield a time-averaged system which governs the leading order behavior of the wave. From this follows an analytic calculation of the Berry connection, curvature, and Chern number via analyzing the local behavior of the eigenfunctions near the critical points of the spectrum. Examples include honeycomb, Lieb, kagome, and 1/5-depleted lattices. In the nonlinear regime, novel equations governing slowly varying wave envelopes are derived. For the honeycomb lattice, numerical simulations show that for relatively small nonlinear effects a striking spiral pattern occurs; as nonlinearity increases, localized structures emerge, and for somewhat higher nonlinearity the waves appear to collapse. [ABSTRACT FROM AUTHOR]

المؤلفون: HONGJIE LI¹ hjli@math.cuhk.edu.hk, HONGYU LIU² hongyliu@cityu.edu.hk, JUN ZOU¹ zou@math.cuhk.edu.hk

المصدر: SIAM Journal on Applied Mathematics. Feb2022, Vol. 82 Issue 1, p119-141. 23p.

مصطلحات موضوعية: *ELASTIC wave propagation, *ACOUSTIC wave propagation, *RESONANCE, *ELASTIC waves, *ACOUSTIC resonance, *ACOUSTIC couplers, *BUBBLES

مستخلص: Minnaert resonance is a widely known acoustic phenomenon, and it has many important applications, in particular in the effective realization of acoustic metamaterials using bubbly media in recent years. In this paper, motivated by the Minnaert resonance in acoustics, we consider the low-frequency resonance for acoustic bubbles embedded in soft elastic materials. This is a hybrid physical process that couples the acoustic and elastic wave propagations. By delicately and subtly balancing the acoustic and elastic parameters as well as the geometry of the bubble, we show that Minnaert resonance can occur (at least approximately) for rather general constructions. Our study highlights the great potential for the effective realization of negative elastic materials by using bubbly elastic media. [ABSTRACT FROM AUTHOR]

المؤلفون: BORCEA, LILIANA¹ borcea@umich.edu, GARNIER, JOSSELIN² josselin.garnier@polytechnique.edu, SØLNA, KNUT³ ksolna@math.uci.edu

المصدر: SIAM Journal on Applied Mathematics. 2019, Vol. 79 Issue 6, p2663-2687. 25p.

مصطلحات موضوعية: *TURBULENCE, *ACOUSTIC wave propagation, *SOUND pressure, *RANDOM fields, *INVERSE problems, *SOUND waves, *WAVEGUIDES

مستخلص: We analyze sound propagation in a waveguide filled with a random medium modeled by small-amplitude spatial and temporal uctuations of the mass density and wave speed. The time dependence of the medium is due to a weakly turbulent flow. The analysis is based on a wave equation satisfied by the acoustic pressure, obtained by linearization of the uid dynamic equations about the flow. The acoustic pressure is decomposed into modes, which are propagating and evanescent time- harmonic waves with amplitudes that are random fields. These amplitudes model the randomization of the sound wave due to cumulative scattering over a long distance of propagation in the random medium. We obtain a detailed statistical characterization of the mode amplitudes and use the results to solve two inverse problems: The first problem estimates the mean ow velocity from measurements of the acoustic pressure at one end of the waveguide. The second problem seeks to determine, from the same measurements, if the flow is laminar or if there is a region of turbulent flow. [ABSTRACT FROM AUTHOR]

المؤلفون: GARNIER, JOSSELIN

المصدر: SIAM Journal on Applied Mathematics; 2021, Vol. 81 Issue 3, p814-833, 20p

مصطلحات موضوعية: SPECTRAL energy distribution, WIRELESS communications, NOISE, THEORY of wave motion, METAMATERIALS, GAUSSIAN channels, RADIO wave propagation

مستخلص: Motivated by applications to wireless communications, this paper addresses the propagation of waves transmitted by ambient noise sources and interacting with metamaterials. We discuss a generalized Helmholtz--Kirchhoff identity that is valid in dispersive media and characterize the statistical properties of the empirical cross spectral density of the wave field. We can then introduce and analyze an original communication scheme between two passive arrays that uses only ambient noise illumination. The passive transmitter array does not transmit anything, but it is a tunable metamaterial surface that can modulate its dispersive properties and encode a message in the modulation. The passive receiver array made of two receivers that are half a wavelength apart from each other can decode the message from the empirical cross spectral density of the wave field. [ABSTRACT FROM AUTHOR]

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المؤلفون: Papanicolaou, George, Ryzhik, Leonid, Sølna, Knut

المصدر: SIAM Journal on Applied Mathematics, 2004 Apr 01. 64(4), 1133-1155.

الوصول الحر: https://www.jstor.org/stable/4095974Test

المؤلفون: Fibich, G.

المصدر: SIAM Journal on Applied Mathematics, 2003 Jun 01. 63(5), 1718-1736.

الوصول الحر: https://www.jstor.org/stable/4096059Test

المؤلفون: Sølna, Knut

المصدر: SIAM Journal on Applied Mathematics, 2003 Jun 01. 63(5), 1764-1788.

الوصول الحر: https://www.jstor.org/stable/4096061Test

المؤلفون: Sølna, Knut, Milton, Graeme W.

المصدر: SIAM Journal on Applied Mathematics, 2002 Jul 01. 62(6), 2064-2091.

الوصول الحر: https://www.jstor.org/stable/3648752Test

المؤلفون: Magnanini, Rolando, Santosa, Fadil

المصدر: SIAM Journal on Applied Mathematics, 2000 Nov 01. 61(4), 1237-1252.

الوصول الحر: https://www.jstor.org/stable/3061826Test

المؤلفون: Grote, Marcus J., Keller, Joseph B.

المصدر: SIAM Journal on Applied Mathematics, 2000 Feb 01. 60(3), 803-819.

الوصول الحر: https://www.jstor.org/stable/118528Test