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Rate-Independent Systems

2015-10-21 Mathematics
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Release : 2015-10-21
Genre : Mathematics
Kind : eBook
Book Rating : 06X/5 ( reviews)

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Book Synopsis Rate-Independent Systems by : Alexander Mielke

Download or read book Rate-Independent Systems written by Alexander Mielke. This book was released on 2015-10-21. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides both an introduction to and a thorough exposition of the theory of rate-independent systems, which the authors have been working on with a lot of collaborators over 15 years. The focus is mostly on fully rate-independent systems, first on an abstract level either with or even without a linear structure, discussing various concepts of solutions with full mathematical rigor. Then, usefulness of the abstract concepts is demonstrated on the level of various applications primarily in continuum mechanics of solids, including suitable approximation strategies with guaranteed numerical stability and convergence. Particular applications concern inelastic processes such as plasticity, damage, phase transformations, or adhesive-type contacts both at small strains and at finite strains. A few other physical systems, e.g. magnetic or ferroelectric materials, and couplings to rate-dependent thermodynamic models are considered as well. Selected applications are accompanied by numerical simulations illustrating both the models and the efficiency of computational algorithms. In this book, the mathematical framework for a rigorous mathematical treatment of "rate-independent systems" is presented in a comprehensive form for the first time. Researchers and graduate students in applied mathematics, engineering, and computational physics will find this timely and well written book useful.

Rate-Independent Systems

2015
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Release : 2015
Genre :
Kind : eBook
Book Rating : 074/5 ( reviews)

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Book Synopsis Rate-Independent Systems by : Alexander Mielke

Download or read book Rate-Independent Systems written by Alexander Mielke. This book was released on 2015. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides both an introduction to and a thorough exposition of the theory of rate-independent systems, which the authors have worked on with a number of collaborators over many years. The focus is mostly on fully rate-independent systems, first on an abstract level with or without a linear structure, discussing various concepts of solutions with full mathematical rigor. The usefulness of the abstract concepts is then demonstrated on the level of various applications primarily in continuum mechanics of solids, including suitable approximation strategies with guaranteed numerical stability and convergence. Particular applications concern inelastic processes such as plasticity, damage, phase transformations, or adhesive-type contacts both at small strains and at finite strains. Other physical systems such as magnetic or ferroelectric materials, and couplings to rate-dependent thermodynamic models are also considered. Selected applications are accompanied by numerical simulations illustrating both the models and the efficiency of computational algorithms. This book presents the mathematical framework for a rigorous mathematical treatment of rate-independent systems in a comprehensive form for the first time. Researchers and graduate students in applied mathematics, engineering, and computational physics will find this timely and well-written book useful.

Evolution of Rate-independent Systems

2004
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Release : 2004
Genre :
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Book Synopsis Evolution of Rate-independent Systems by : Alexander Mielke

Download or read book Evolution of Rate-independent Systems written by Alexander Mielke. This book was released on 2004. Available in PDF, EPUB and Kindle. Book excerpt:

Non-Smooth and Complementarity-Based Distributed Parameter Systems

2022-02-18 Mathematics
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Release : 2022-02-18
Genre : Mathematics
Kind : eBook
Book Rating : 931/5 ( reviews)

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Book Synopsis Non-Smooth and Complementarity-Based Distributed Parameter Systems by : Michael Hintermüller

Download or read book Non-Smooth and Complementarity-Based Distributed Parameter Systems written by Michael Hintermüller. This book was released on 2022-02-18. Available in PDF, EPUB and Kindle. Book excerpt: Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks. Chapters are written by leading researchers and present results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2016 to 2019.

Nonlinear PDE’s and Applications

2011-07-30 Mathematics
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Release : 2011-07-30
Genre : Mathematics
Kind : eBook
Book Rating : 184/5 ( reviews)

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Book Synopsis Nonlinear PDE’s and Applications by : Stefano Bianchini

Download or read book Nonlinear PDE’s and Applications written by Stefano Bianchini. This book was released on 2011-07-30. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects the notes of the CIME course "Nonlinear PDE’s and applications" held in Cetraro (Italy) on June 23–28, 2008. It consists of four series of lectures, delivered by Stefano Bianchini (SISSA, Trieste), Eric A. Carlen (Rutgers University), Alexander Mielke (WIAS, Berlin), and Cédric Villani (Ecole Normale Superieure de Lyon). They presented a broad overview of far-reaching findings and exciting new developments concerning, in particular, optimal transport theory, nonlinear evolution equations, functional inequalities, and differential geometry. A sampling of the main topics considered here includes optimal transport, Hamilton-Jacobi equations, Riemannian geometry, and their links with sharp geometric/functional inequalities, variational methods for studying nonlinear evolution equations and their scaling properties, and the metric/energetic theory of gradient flows and of rate-independent evolution problems. The book explores the fundamental connections between all of these topics and points to new research directions in contributions by leading experts in these fields.

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