Microstructured Materials: Inverse Problems - neues Buch

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ISBN/EAN: 9783642215841

ISBN - alternative Schreibweisen:
3-642-21584-X, 978-3-642-21584-1
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: engelbrecht, juri, janno, calisher charles
Titel des Buches: invers, engelbrecht, microstructure, microstructured

Daten vom Verlag:

Autor/in: Jaan Janno; Jüri Engelbrecht
Titel: Springer Monographs in Mathematics; Microstructured Materials: Inverse Problems
Verlag: Springer; Springer Berlin
162 Seiten
Erscheinungsjahr: 2011-08-27
Berlin; Heidelberg; DE
Gedruckt / Hergestellt in Niederlande.
Sprache: Englisch
53,49 € (DE)
55,00 € (AT)
59,00 CHF (CH)
Available
X, 162 p.

EA; E107; eBook; Nonbooks, PBS / Mathematik/Analysis; Differentialrechnung und -gleichungen; Verstehen; deformation waves; inverse problems; microstructured solids; nonlinearity; partial differential equations; B; Partial Differential Equations; Classical Mechanics; Solid Mechanics; Structural Materials; Differential Equations; Classical Mechanics; Solid Mechanics; Structural Materials; Mathematics and Statistics; Klassische Mechanik; Maschinenbau: Festkörpermechanik; Materialwissenschaft; BB

Complex, microstructured materials are widely used in industry and technology and include alloys, ceramics and composites. Focusing on non-destructive evaluation (NDE), this book explores in detail the mathematical modeling and inverse problems encountered when using ultrasound to investigate heterogeneous microstructured materials. The outstanding features of the text are firstly, a clear description of both linear and nonlinear mathematical models derived for modelling the propagation of ultrasonic deformation waves, and secondly, the provision of solutions to the corresponding inverse problems that determine the physical parameters of the models. The data are related to nonlinearities at both a macro- and micro- level, as well as to dispersion. 

The authors’ goal has been to construct algorithms that allow us to determine the parameters within which we are required to characterize microstructure. To achieve this, the authors not only use conventional harmonic waves, but also propose a novel methodology based on using solitary waves in NDE. The book analyzes the uniqueness and stability of the solutions, in addition to providing numerical examples.

Introduction.- 1 Inverse problems and non-destructive evaluation.- 2 Mathematical models of microstructured solids.- 3 Linear waves.- 4 Inverse problems for linear waves.- 5 Solitary waves in nonlinear models.- 6 Inverse problems for solitary waves.- 7 Summary.- References.- Index

From the reviews:

“The book is written by well-known specialists in the field of inverse problems and deals with the mathematical analysis of inverse problems arising in the study of complex microstructured materials, ceramics and composites. … The book can be useful for specialists in mechanics and mathematics, and for engineers who use mathematical methods for solving specific practical problems. It will also be useful for graduate students specializing in applied mathematics and mechanics.” (Viatcheslav I. Priĭmenko, Mathematical Reviews, January, 2014)

“The book is concerned with inverse problems of microstructured materials and is composed of 8 chapters. … The book is well written and could find many readers working in the area of microstructured materials.” (Hilmi Demiray, Zentralblatt MATH, Vol. 1235, 2012)

Complex, microstructured materials are widely used in industry and technology and include alloys, ceramics and composites. Focusing on non-destructive evaluation (NDE), this book explores in detail the mathematical modeling and inverse problems encountered when using ultrasound to investigate heterogeneous microstructured materials. The outstanding features of the text are firstly, a clear description of both linear and nonlinear mathematical models derived for modelling the propagation of ultrasonic deformation waves, and secondly, the provision of solutions to the corresponding inverse problems that determine the physical parameters of the models. The data are related to nonlinearities at both a macro- and micro- level, as well as to dispersion. 

The authors’ goal has been to construct algorithms that allow us to determine the parameters within which we are required to characterize microstructure. To achieve this, the authors not only use conventional harmonic waves, but also propose a novel methodology based on using solitary waves in NDE. The book analyzes the uniqueness and stability of the solutions, in addition to providing numerical examples.

Mathematical modelling is based on physical principles

Physical models are interwoven with inverse problems

A novel concept of using solitary waves for NDE is proposed

Includes supplementary material: sn.pub/extras