Influence of boundary conditions on wave localization characteristics in layered randomly inhomogeneous medium

1994 ◽  
Author(s):  
Michael A. Guzev ◽  
Valery I. Klyatskin ◽  
Gennadii V. Popov
Keyword(s):  
Boundary Conditions ◽  
Inhomogeneous Medium ◽  
Wave Localization

SOUND PROPAGATION THROUGH STRUCTURAL COMPONENTS UNDER CONDITIONS OF NON-RIGID CONTACT AT THE BOUNDARIES BETWEEN THEM

Akustika ◽  
2021 ◽  
Author(s):  
Konstantin Abbakumov ◽  
Anton Vagin ◽  
Alena Vjuginova
Keyword(s):  
Boundary Conditions ◽  
Inhomogeneous Medium ◽  
Dispersion Equation ◽  
Numerical Solutions ◽  
Sound Propagation ◽  
Structural Components ◽  
Frequency Range ◽  
Problem Statement ◽  
Ultrasonic Measurements ◽  
Rigid Contact

The report considers the problem statement, derivation and solution of the dispersion equation for sound propagation in a layered inhomogeneous medium with oriented fracturing, simulated by the presence of boundary conditions in the "linear slip" approximation. Numerical solutions are obtained and analyzed for the frequency range and values of the parameters of contact breaking, which is relevant in the problems of ultrasonic measurements

Uniform stabilization for the semilinear wave equation in an inhomogeneous medium with locally distributed nonlinear damping and dynamic Cauchy–Ventcel type boundary conditions

2019 ◽  
pp. 1950072
Author(s):  
A. F. Almeida ◽  
M. M. Cavalcanti ◽  
V. H. Gonzalez Martinez ◽  
J. P. Zanchetta
Keyword(s):  
Boundary Conditions ◽  
Inhomogeneous Medium ◽  
Linear Problem ◽  
Nonlinear Damping ◽  
Decay Rates ◽  
Geometric Control ◽  
Dynamic Boundary Conditions ◽  
Uniform Stabilization ◽  
Uniform Decay ◽  
Type Boundary

In this paper, we consider the Cauchy–Ventcel problem in an inhomogeneous medium with dynamic boundary conditions subject to a nonlinear damping distributed around a neighborhood [Formula: see text] of the boundary according to the Geometric Control Condition. Uniform decay rates of the associated energy are established and, in addition, the exact internal controllability for the linear problem is also proved. For this purpose, refined microlocal analysis arguments are considered by exploiting ideas due to Burq and Gérard [Contrôle Optimal des équations aux dérivées partielles. (2001); http://www.math.u-psud.fr/burq/articles/coursX.pdf ].

scholarly journals Phase Evolution of the Time- and Space-Like Peregrine Breather in a Laboratory

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 308
Author(s):  
Yuchen He ◽  
Pierre Suret ◽  
Amin Chabchoub
Keyword(s):  
Boundary Conditions ◽  
Phase Evolution ◽  
Wave Localization ◽  
Time And Space ◽  
Wave Groups ◽  
Phase Dynamics ◽  
Wave Flume ◽  
Coherent Wave ◽  
Intrinsic Shape ◽  
Peregrine Breather

Coherent wave groups are not only characterized by the intrinsic shape of the wave packet, but also by the underlying phase evolution during the propagation. Exact deterministic formulations of hydrodynamic or electromagnetic coherent wave groups can be obtained by solving the nonlinear Schrödinger equation (NLSE). When considering the NLSE, there are two asymptotically equivalent formulations, which can be used to describe the wave dynamics: the time- or space-like NLSE. These differences have been theoretically elaborated upon in the 2016 work of Chabchoub and Grimshaw. In this paper, we address fundamental characteristic differences beyond the shape of wave envelope, which arise in the phase evolution. We use the Peregrine breather as a referenced wave envelope model, whose dynamics is created and tracked in a wave flume using two boundary conditions, namely as defined by the time- and space-like NLSE. It is shown that whichever of the two boundary conditions is used, the corresponding local shape of wave localization is very close and almost identical during the evolution; however, the respective local phase evolution is different. The phase dynamics follows the prediction from the respective NLSE framework adopted in each case.

Stability for Semilinear Wave Equation in an Inhomogeneous Medium with Frictional Localized Damping and Acoustic Boundary Conditions

2020 ◽  
Vol 58 (4) ◽  
pp. 2411-2445
Author(s):  
Marcelo Moreira Cavalcanti ◽  
Valéria Neves Domingos Cavalcanti ◽  
Cícero Lopes Frota ◽  
André Vicente
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Inhomogeneous Medium ◽  
Acoustic Boundary Conditions ◽  
Semilinear Wave Equation ◽  
Localized Damping

Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

1970 ◽  
Vol 28 ◽  
pp. 360-361
Author(s):  
John W. Coleman
Keyword(s):  
Boundary Conditions ◽  
High Performance ◽  
Force Fields ◽  
Optical Design ◽  
Direct Conversion ◽  
Design Engineering ◽  
Design Data ◽  
Scalar Potentials ◽  
Geometric Elements ◽  
At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

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