Francesco Mainardi

This book is a printed edition of the Special Issue "Fractional Calculus: Theory and Applications" that was published in Mathematics

Fractional Calculus: Theory and Applications

Dieter Guicking

Ardéshir Guran

Adrianus De Hoop

The interaction of acoustic fields with submerged elastic structures, both by propagation and scattering, is being investigated at various institutions and laboratories world-wide with ever-increasing sophistication of experiments and analysis. This book offers a collection of contributions from these research centers that represent the present state-of-the-art in the study of acoustic elastic interaction, being on the cutting edge of these investigations. This includes the description of acoustic scattering from submerged elastic objects and shells by the Resonance Scattering Theory of Flax, Dragonette and Überall, and the interaction of these phenomena in terms of interface waves. It also includes the use of this theory for the purpose of inverse scattering, i.e. the determination of the scattered objects properties from the received acoustic backscattered signals. The problem of acoustically excited waves in inhomogeneous and anisotropic materials, and of inhomogeneous propagating waves is considered. Vibrations and resonances of elastic shells, including shells with various kinds of internal attachments, are analyzed. Acoustic scattering experiments are described in the time domain, and on the basis of the Wigner–Ville distribution. Acoustic propagation in the water column over elastic boundaries is studied experimentally both in laboratory tanks, and in the field, and is analyzed theoretically. Ultrasonic nondestructive testing, including such aspects like probe modelling, scattering by various types of cracks, receiving probes and calibration by a side-drilled hole is also studied in details. A comprehensive picture of these complex phenomena and other aspects is presented in the book by researchers that are experts in each of these domains, giving up-to-date accounts of the field in all these aspects. Contents:Three Dimensional Underwater Sound Propagation Over Sloping Bottoms (S A L Glegg & J M Riley)Modeling of Sound Propagation Over a Shear-Supporting Sediment Layer and Substrate (J I Arvelo et al.)Propagation of Acoustic Pulses in Layered Media (P P Delsanto et al.)Response of a Vibrating Structure to a Turbulent Flow Wall Pressure: Fluid-Loaded Structure Modes Series and Boundary Element Method (P J T Filippi & D Mazzoni)Plane Evanescent Waves and Interface Waves (F Luppé et al.)Application of Wavelet Analysis to Inverse Scattering (W Tobocman)Application of Time-Frequency Analysis to the Characterization of Acoustical Scattering (M E Zakharia et al.)Acoustical Resonance Scattering Theory for Strongly Overlapping Resonances (H Peine & D Guicking)Inverse Scattering Based on the Resonances of the Target (P P Delsanto et al.)Modern Developments in the Theory and Application of Classical Scattering (M F Werby & N A Sidorovskaia)Modeling and Ultrasonic Measurements of Damage (A Gérard)Some Aspects of Nonlinear Wave Propagation (A Jeffrey) Readership: Nonlinear scientists. keywords: “… Überall's work in acoustic and electromagnetic scattering has evoked much interest, in the US as well as abroad, because of its possible practical applications, as well as the theoretical understanding. Many collaborators have been inspired by it, and have now contributed to this volume. The book is an excellent contribution to the literature of Acoustics and Wave Propagation. Professor Guran is to be congratulated for organizing and editing this volume.” Prof. Hans A Bethe Nobel Laureate Cornell University “This highly interesting collection of papers makes a valuable addition to the acoustics literature.” Applied Acoustics “… This is an impressive collection of 45 research and review chapters involving 78 authors. Taking into account the high educational quality and research value of this set of books, it is recommended for purchase by libraries that serves research programs involved with acoustic scattering related to underwater and ultrasonics.” Professor Philip Marston Journal of the Acoustical Society of America

Part III: Acoustic Propagation and Scattering, Wavelets and Time Frequency Analysis

Acoustic Interactions with Submerged Elastic Structures

This book is likely to be of interest to applied scientists and engineers. --Book Jacket.

An Introduction to Mathematical Models

Fractional Calculus and Waves in Linear Viscoelasticity

Rudolf Gorenflo

Anatoly A. Kilbas

Sergei V. Rogosin

As a result of researchers’ and scientists’ increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have recently caught the interest of the scientific community. Focusing on the theory of the Mittag-Leffler functions, the present volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to the applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular the Mittag-Leffler functions allow us to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and its successors. The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, theory of control and several other related areas.

Francesco Mainardi

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