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Mathematics of nonlinear acoustics
Evolution Equations and Control Theory, 2015 The aim of this paper is to highlight some recent developments and outcomes in the mathematical analysis of partial differential equations describing nonlinear sound propagation.
Barbara Kaltenbacher
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Nonlinear Oscillatory Acoustic Vacuum
SIAM Journal on Applied Mathematics, 2014A finite chain of particles with next-neighbor interactions, undergoing in-plane nonlinear oscillations with fixed-fixed boundary conditions is considered. In the most significant limiting case of low-energy predominantly transverse particle oscillations, the geometric nonlinearity in the system generates a nonlinear acoustic vacuum, whereby the ...
Leonid I. Manevitch +1 more
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Nonlinear acoustics in studies of structural features of materials
MRS bulletin, 2019Linear elastic moduli of solids with similar chemical compositions usually vary fairly insignificantly. However, for a broad class of apparently similar materials, their higher-order (nonlinear) moduli may differ by many times or even by orders of ...
V. Zaitsev
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Nonlinear acoustics and the Acoustical Society of America
The Journal of the Acoustical Society of America, 2015The modern era of nonlinear underwater acoustics had its roots in a remarkable session at the 57th ASA meeting at Providence RI in June, 1960, chaired by Westervelt, of Brown University, who also presented his remarkable new theory of the parametric acoustic array. This conceptual “device” enables highly directive low frequency sound to be created from
Thomas G. Muir +2 more
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Nonlinear equations of acoustics, with application to parametric acoustic arrays
The Journal of the Acoustical Society of America, 1981The propagation and interaction of finite amplitude sound waves produced by a baffled piston source in a thermoviscous fluid are considered. Basic equations are derived and their ranges of validity established. This is used to relate some earlier works by others on nonlinear model equations in acoustics.
Tjotta, Jacqueline Naze, Tjotta, Sigve
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Doing Arithmetic With Nonlinear Acoustic Vortices
Physical Review Letters, 2008Phase singularities of wave-front-like screw dislocations or vortices possess a well-defined quantity that can only take integer value: the topological charge. In the nonlinear regime, it has been demonstrated that optical or acoustical vortices interact and the topological charge follows a conservation law.
Marchiano, R., Thomas, Jean-Louis
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Mathematical analysis in nonlinear acoustics
AIP Conference Proceedings, 2017A. Tani
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The status and future of nonlinear acoustics
The Journal of the Acoustical Society of America, 1973In addition to serving as an ideal discipline for introducing the concepts of quantum field theory and general relativity, nonlinear acoustics provides a new means for absorbing and generating sound. The many applications of this exciting subject are based in part on the fact that, in common with vector (electromagnetic and shear) and tensor ...
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Nonlinear Acoustics: Blackstock–Crighton Equations with a Periodic Forcing Term
Journal of Mathematical Fluid Mechanics, 2017Blackstock–Crighton equations describe the motion of a viscous, heat-conducting, compressible fluid. They are used as models for acoustic wave propagation in a medium in which both nonlinear and dissipative effects are taken into account. In this article,
A. Celik, M. Kyed
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