Acoustics, Mechanics, and the Related Topics of Mathematical Analysis: Proceedings of the International Conference to Celebrate Robert P Gilbert's 70th Birthday Caes Du Cnrs, Frejus, France 18 - 22 June 2002

by Wirgin, Armand

• ISBN13: 9789812382641
• ISBN10: 981238264X
• Format: Hardcover
• Copyright: 2003-04-01
• Publisher: World Scientific Pub Co Inc

Summary

This book concerns the mathematical analysis -- modeling physical concepts, existence, uniqueness, stability, asymptotics, computational schemes, etc. -- involved in predicting complex mechanical/acoustical behavior/response and identifying or optimizing mechanical/acoustical systems giving rise to phenomena that are either observed or aimed at. The forward problems consist in solving generally coupled, nonlinear systems of integral or partial (integer or fractional) differential equations with nonconstant coefficients. The identification/optimization of the latter, of the driving terms and/or of the boundary conditions, all of which are often affected by random perturbations, forms the class of related inverse or control problems.

Table of Contents

Preface
Paen R. P. Gilbert	p. 1
About Bob Gilbert	p. 4
Representation formulas in Clifford analysis	p. 8
Imaging methods in random media	p. 14
Resonances of an elastic plate in a duct, in the presence of a uniform flow	p. 21
First order asymptotic modeling of a nuclear waste repository	p. 28
Exact axisymmetric solution for temperature-dependent compressible Navier-Stokes Equations	p. 34
Recovery of the poroelastic parameters of cancellous bone using low frequency acoustic interrogation	p. 41
Mathematical model of the interaction problem between electromagnetic field and elastic body	p. 48
Bore evolution in inhomogeneous channels	p. 55
An inverse spectral problem for a Schrodinger operator with an unbounded potential	p. 64
Trapping regions for discontinuously coupled dynamic systems	p. 71
Differential calculi	p. 78
Reconstruction problem for a periodic boundary between two media	p. 85
A note on generalized Cesaro operators	p. 92
On the boundedness of functions from an anisotropic weighted space satisfying some integral inequalities	p. 100
Homogenizing a flow of an incompressible inviscid fluid through an elastic porous media	p. 108
Approximation of a dynamic unilateral contact problem for a cracked viscoelastic body	p. 116
Principles of signal based ray tracing for 2D and 3D complex tectonics	p. 123
Regularity up to the boundary for a class of solutions of a functional-differential system	p. 130
On the Hardy spaces of harmonic and monogenic functions in the unit ball of R[superscript M+1]	p. 137
Time domain wave equations for lossy media obeying a frequency power law: application to the porous materials	p. 143
A model for porous ductile viscoplastic solids including void shape effects	p. 150
Acoustic wave propagation in a composite of two different poroelastic materials with a very rough periodic interface: a homogenization approach	p. 157
Effective acoustic equations for a nonconsolidated medium with microstructure	p. 164
A domain decomposition method for the Helmholtz equation in an unbounded waveguide	p. 171
Support function method for inverse obstacle scattering problems	p. 178
Heat polynomial analogs	p. 185
Blow-up, shock formation, and acceleration waves in hyperelastic media	p. 192
Summability of solutions of Dirichlet problem	p. 199
On isophonic surfaces	p. 207
A survey of pointwise interpolation inequalities for integer and fractional derivatives	p. 212
Non-uniqueness in connection with methods for the reconstruction of the shape of cylindrical bodies from acoustic scattering data	p. 222
Dispersion identification using the Fourier analysis of resonances in elastic and viscoelastic rods	p. 229
Application of the likelihood method of the analysis of waves in elastic and viscoelastic rods	p. 236
On the controlled evolution of level sets and like methods: the shape and contrast reconstruction	p. 243
Recent progress in the theoretical and numerical modeling of thin-layer flow	p. 251
Seismic response in a city	p. 258
Transmission of ultrasonic waves in cancellous bone and evaluation of osteoporosis	p. 265
Hadamard singular integral equations for the Stokes problem and Hermite wavelets	p. 272
List of Communications	p. 281
Author Index	p. 285
Table of Contents provided by Blackwell. All Rights Reserved.