Springer Microstructured Materials: Inverse Problems (Springer Monographs in Mathematics)

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. Review 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) From the Back Cover 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.