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The Cahn–Hilliard Equation: Recent Advances and Applications

2019-09-09 Mathematics
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Release : 2019-09-09
Genre : Mathematics
Kind : eBook
Book Rating : 921/5 ( reviews)

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Book Synopsis The Cahn–Hilliard Equation: Recent Advances and Applications by : Alain Miranville

Download or read book The Cahn–Hilliard Equation: Recent Advances and Applications written by Alain Miranville. This book was released on 2019-09-09. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn–Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn–Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the Cahn–Hilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.

Recent Advances in Numerical Methods for Partial Differential Equations and Applications

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 70X/5 ( reviews)

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Book Synopsis Recent Advances in Numerical Methods for Partial Differential Equations and Applications by : Xiaobing Feng

Download or read book Recent Advances in Numerical Methods for Partial Differential Equations and Applications written by Xiaobing Feng. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: This book is derived from lectures presented at the 2001 John H. Barrett Memorial Lectures at the University of Tennessee, Knoxville. The topic was computational mathematics, focusing on parallel numerical algorithms for partial differential equations, their implementation and applications in fluid mechanics and material science. Compiled here are articles from six of nine speakers. Each of them is a leading researcher in the field of computational mathematics and its applications. A vast area that has been coming into its own over the past 15 years, computational mathematics has experienced major developments in both algorithmic advances and applications to other fields. These developments have had profound implications in mathematics, science, engineering and industry. With the aid of powerful high performance computers, numerical simulation of physical phenomena is the only feasible method for analyzing many types of important phenomena, joining experimentation and theoretical analysis as the third method of scientific investigation. The three aspects: applications, theory, and computer implementation comprise a comprehensive overview of the topic. Leading lecturers were Mary Wheeler on applications, Jinchao Xu on theory, and David Keyes on computer implementation. Following the tradition of the Barrett Lectures, these in-depth articles and expository discussions make this book a useful reference for graduate students as well as the many groups of researchers working in advanced computations, including engineering and computer scientists.

Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems

2019-11-06 Mathematics
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Release : 2019-11-06
Genre : Mathematics
Kind : eBook
Book Rating : 905/5 ( reviews)

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Book Synopsis Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems by : Luis Rodrigues

Download or read book Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems written by Luis Rodrigues . This book was released on 2019-11-06. Available in PDF, EPUB and Kindle. Book excerpt: Engineering systems operate through actuators, most of which will exhibit phenomena such as saturation or zones of no operation, commonly known as dead zones. These are examples of piecewise-affine characteristics, and they can have a considerable impact on the stability and performance of engineering systems. This book targets controller design for piecewise affine systems, fulfilling both stability and performance requirements. The authors present a unified computational methodology for the analysis and synthesis of piecewise affine controllers, taking an approach that is capable of handling sliding modes, sampled-data, and networked systems. They introduce algorithms that will be applicable to nonlinear systems approximated by piecewise affine systems, and they feature several examples from areas such as switching electronic circuits, autonomous vehicles, neural networks, and aerospace applications. Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems is intended for graduate students, advanced senior undergraduate students, and researchers in academia and industry. It is also appropriate for engineers working on applications where switched linear and affine models are important.

Advances and Trends in Optimization with Engineering Applications

2017-04-26 Mathematics
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Release : 2017-04-26
Genre : Mathematics
Kind : eBook
Book Rating : 674/5 ( reviews)

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Book Synopsis Advances and Trends in Optimization with Engineering Applications by : Tamas Terlaky

Download or read book Advances and Trends in Optimization with Engineering Applications written by Tamas Terlaky. This book was released on 2017-04-26. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is of critical importance in engineering. Engineers constantly strive for the best possible solutions, the most economical use of limited resources, and the greatest efficiency. As system complexity increases, these goals mandate the use of state-of-the-art optimization techniques. In recent years, the theory and methodology of optimization have seen revolutionary improvements. Moreover, the exponential growth in computational power, along with the availability of multicore computing with virtually unlimited memory and storage capacity, has fundamentally changed what engineers can do to optimize their designs. This is a two-way process: engineers benefit from developments in optimization methodology, and challenging new classes of optimization problems arise from novel engineering applications. Advances and Trends in Optimization with Engineering Applications reviews 10 major areas of optimization and related engineering applications, providing a broad summary of state-of-the-art optimization techniques most important to engineering practice. Each part provides a clear overview of a specific area and discusses a range of real-world problems. The book provides a solid foundation for engineers and mathematical optimizers alike who want to understand the importance of optimization methods to engineering and the capabilities of these methods.

Steady States of the One-dimensional Cahn-Hilliard Equation

1992
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Release : 1992
Genre :
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Book Synopsis Steady States of the One-dimensional Cahn-Hilliard Equation by : University of Minnesota. Institute for Mathematics and Its Applications

Download or read book Steady States of the One-dimensional Cahn-Hilliard Equation written by University of Minnesota. Institute for Mathematics and Its Applications. This book was released on 1992. Available in PDF, EPUB and Kindle. Book excerpt:

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