A hybrid system of PDE’s arising in multi-structure interaction: coupling of wave equations in 𝑛 and 𝑛-1 space dimensions

So far, mathematical modelling of Lamb wave propagation under fluid-structure interaction (FSI) was limited to the case of rigid structure. We extend this concept to account for structural dynamics. Thereby, we provide a model that is suitable for the structural health monitoring (SHM) during the operation of the structure. The model we develop is referred to as the “eXtended Fluid-Structure Interaction” (eXFSI) problem, which is a one-directional coupling of typical FSI problem with an ultrasonic wave propagation in fluid-solid and their interface (WpFSI). Here, the strongly coupled problem of acoustic & elastic wave equations is denoted by WpFSI. Next, we explore the approach to the efficient numerical solution of the problem. We use a combination of Finite Element and Finite Difference methods and employ a dual-loop algorithm to balance the computational cost and quality of the numerical solution. To facilitate our solution algorithm, we rely upon the software library package DOpElib.

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Remarks on nonlinear elastic waves with null conditions

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2020039 ◽

2020 ◽

Vol 26 ◽

pp. 121

Author(s):

Dongbing Zha ◽

Weimin Peng

Keyword(s):

Initial Data ◽

Global Existence ◽

Elastic Waves ◽

Wave Equations ◽

Alternative Proof ◽

Classical Solutions ◽

Small Initial Data ◽

Hyperelastic Materials ◽

Variational Structure ◽

Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

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Kryothermie-Hybrid-System mit intern gasgekühltem Applikator zur Radiofrequenzablation

RöFo - Fortschritte auf dem Gebiet der Röntgenstrahlen und der bildgebenden Verfahren ◽

10.1055/s-2007-977319 ◽

2007 ◽

Vol 179 (S 1) ◽

Author(s):

H Rempp ◽

S Clasen ◽

M Voigtländer ◽

S Kempf ◽

A Weihusen ◽

...

Keyword(s):

Hybrid System

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On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

GUB Journal of Science and Engineering ◽

10.3329/gubjse.v5i1.47898 ◽

2018 ◽

Vol 5 (1) ◽

pp. 31-36

Author(s):

Md Monirul Islam ◽

Muztuba Ahbab ◽

Md Robiul Islam ◽

Md Humayun Kabir

Keyword(s):

Solitary Wave ◽

Acoustic Waves ◽

Water Waves ◽

Wave Equations ◽

Rectangular Channel ◽

Soliton Solutions ◽

Boussinesq Equations ◽

Travelling Wave ◽

Ion Acoustic Waves ◽

Analytical System

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

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Control of odor using an electrostatic precipitator andadsorption hybrid system in unregulated facilities

Journal of Odor and Indoor Environment ◽

10.15250/joie.2014.13.2.113 ◽

2014 ◽

Vol 13 (2) ◽

pp. 113-123 ◽

Cited By ~ 1

Author(s):

Hak-Song Jeon ◽

◽

Jong-Min Kim ◽

Kwang-Han Bae ◽

Tae-Oh Kim

Keyword(s):

Hybrid System ◽

Electrostatic Precipitator

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FLUID STRUCTURE INTERACTION OF ROWING BLADE FOR HYDRODYNAMIC PROPULSION TO ENHANCE ROWING PERFORMANCE

10.15282/mohe.2014.ses.025 ◽

2014 ◽

Author(s):

Abdul Aziz Mohd. Yusof ◽

◽

Ardiyansyah Syahrom ◽

M. N. Harun ◽

A. H. Omar

Keyword(s):

Fluid Structure Interaction ◽

Fluid Structure ◽

Structure Interaction ◽

Rowing Performance

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“Collective Redress” in European Competition Law

Zeitschrift für Wettbewerbsrecht ◽

10.15375/zwer-2016-0407 ◽

2016 ◽

Vol 14 (4) ◽

pp. 388-414

Author(s):

Alexandra P. Mikroulea

Keyword(s):

Hybrid System ◽

Competition Law ◽

Mixed System ◽

Basic Question ◽

Effective Implementation ◽

The United Kingdom ◽

Collective Redress ◽

Opt Out ◽

Private Autonomy ◽

European Competition Law

AbstractOpt-in or opt-out? That is the basic question to be answered. The decision to promote actions of “opt-in” type as opposed to those of the “opt-out” type, for the sake of private autonomy, does not ensure the effective application of european competition law. On the contrary, it may decrease the application’s intensity and effectiveness. Recent reforms among European state members such as in the United Kingdom, Belgium, the Netherlands, Denmark and Norway are powerful indications that the opt-out principle may result in the effective implementation of competition law. There is no doubt that a mixed system (hybrid system), providing the court with the power to decide in favour of either the opt-in or the opt-out system, will result in better implementation of competition law. At the present time there are two pending cases in England (Dorothy Gibson and Mastercard) for which the decision on opt-out or opt-in are highly anticipated. Should the court decide, in one or both of the cases, on an opt-out approach, this will bring a momentous reevaluation of the entire collective redress concept.

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