Microstructured Materials: Inverse Problems [electronic resource] /by Jaan Janno, Jüri Engelbrecht.
by Janno, Jaan [author.]; Engelbrecht, Jüri [author.]; SpringerLink (Online service).
Material type:
BookSeries: Springer Monographs in Mathematics: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.Description: X, 162 p. online resource.ISBN: 9783642215841.Subject(s): Mathematics | Differential equations, partial | Mechanics | Materials | Mathematics | Partial Differential Equations | Mechanics | Continuum Mechanics and Mechanics of Materials | Structural MaterialsDDC classification: 515.353 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
| MAIN LIBRARY | QA370-380 (Browse shelf) | Available |
Browsing MAIN LIBRARY Shelves Close shelf browser
| QA75.5-76.95 Advances in Self-Organizing Maps | TA1637-1638 Mathematical Morphology and Its Applications to Image and Signal Processing | K7000-7720.22 Reconstituting the Constitution | QA370-380 Microstructured Materials: Inverse Problems | TA1637-1638 Pattern Recognition | TA1637-1638 Image Analysis and Recognition | TA1637-1638 Image Analysis and Recognition |
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.
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.
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