Paul A. Martin

Bio: Paul A. Martin is an academic researcher from Colorado School of Mines. The author has contributed to research in topics: Integral equation & Scattering. The author has an hindex of 36, co-authored 191 publications receiving 5225 citations. Previous affiliations of Paul A. Martin include University of Manchester & University of Delaware.

Acoustics of Wood

Abstract: Environmental Acoustics.- Acoustics of Forests and Acoustic Quality Control of Some Forest Products.- Wood and Wood-Based Materials in Architectural Acoustics.- Material Characterization.- Theory of and Experimental Methods for the Acoustic Characterization of Wood.- Elastic Constants of Wood Material.- Wood Structural Anisotropy and Ultrasonic Parameters.- Quality Assessment.- Wood Species for Musical Instruments.- Acoustic Methods as a Nondestructive Tool for Wood Quality Assessment.- Environmental Modifiers of Wood Structural Parameters Detected with Ultrasonic Waves.- Acoustic Emission.- Acousto-Ultrasonics.- High-Power Ultrasonic Treatment for Wood Processing.

Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles

Abstract: The interaction of waves with obstacles is an everyday phenomenon in science and engineering, arising for example in acoustics, electromagnetism, seismology and hydrodynamics. The mathematical theory and technology needed to understand the phenomenon is known as multiple scattering, and this book is the first devoted to the subject. The author covers a variety of techniques, describing first the single-obstacle methods and then extending them to the multiple-obstacle case. A key ingredient in many of these extensions is an appropriate addition theorem: a coherent, thorough exposition of these theorems is given, and computational and numerical issues around them are explored. The application of these methods to different types of problems is also explained; in particular, sound waves, electromagnetic radiation, waves in solids and water waves. A comprehensive bibliography of some 1400 items rounds off the book, which will be an essential reference on the topic for applied mathematicians, physicists and engineers.

The method of fundamental solutions for scattering and radiation problems

Abstract: The development of the method of fundamental solutions (MFS) and related methods for the numerical solution of scattering and radiation problems in fluids and solids is described and reviewed A brief review of the developments and applications in all areas of the MFS over the last five years is also given Future possible areas of applications in fields related to scattering and radiation problems are identified

Reflection and transmission from porous structures under oblique wave attack

Abstract: The linear theory for water waves impinging obliquely on a vertically sided porous structure is examined. For normal wave incidence, the reflection and transmission from a porous breakwater has been studied many times using eigenfunction expansions in the water region in front of the structure, within the porous medium, and behind the structure in the down-wave water region. For oblique wave incidence, the reflection and transmission coefficients are significantly altered and they are calculated here. Using a plane-wave assumption, which involves neglecting the evanescent eigenmodes that exist near the structure boundaries (to satisfy matching conditions), the problem can be reduced from a matrix problem to one which is analytic. The plane-wave approximation provides an adequate solution for the case where the damping within the structure is not too great. An important parameter in this problem is Γ 2 = ω 2 h ( s - i f )/ g , where ω is the wave angular frequency, h the constant water depth, g the acceleration due to gravity, and s and f are parameters describing the porous medium. As the friction in the porous medium, f , becomes non-zero, the eigenfunctions differ from those in the fluid regions, largely owing to the change in the modal wavenumbers, which depend on Γ 2 . For an infinite number of values of ΓF 2 , there are no eigenfunction expansions in the porous medium, owing to the coalescence of two of the wavenumbers. These cases are shown to result in a non-separable mathematical problem and the appropriate wave modes are determined. As the two wavenumbers approach the critical value of Γ 2 , it is shown that the wave modes can swap their identity.

On single integral equations for the transmission problem of acoustics

Abstract: The transmission problem, namely scattering of time-harmonic waves in a compressible fluid by a fluid inclusion with different material properties, is usually formulated as a pair of coupled boundary integral equations over the interface S between the inclusion and the exterior fluid. In this paper, however,we consider methods for solving the transmission problem using a single integral equation over S for a single unknown function. In fact, we derive four different integral equations, using a hybrid of the direct (Green’s theorem) and indirect (layer ansatz) methods, and give conditions for the unique-solvability of each and for the subsequent construction of the solution to the transmission problem. Some of our single integral equations are Fredholm integral equations of the second kind with weakly-singular kernels. Thus, these equations, all of which appear to be new, are attractive computationally.

Table Of Integrals Series And Products

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Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Quantum Inverse Scattering Method and Correlation Functions

Abstract: One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral models on a lattice Theory of scalar products Form factors Mean value of operator Q Assymptotics of correlation functions Temperature correlation functions Appendices References.