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Rate-Independent Systems

Alexander Mielke,Tomáš Roubíček
Rate Independent Systems Book PDF

Author : Alexander Mielke,Tomáš Roubíček
Publisher : Springer
Page : 660 pages
File Size : 47,9 Mb
Release : 2015-10-21
Category : Mathematics
ISBN : 9781493927067

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Rate-Independent Systems by Alexander Mielke,Tomáš Roubíček Pdf

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

Alexander Mielke,Tomáš Roubíček
Rate Independent Systems Book PDF

Author : Alexander Mielke,Tomáš Roubíček
Publisher : Unknown
Page : 128 pages
File Size : 54,5 Mb
Release : 2015
Category : Electronic
ISBN : 1493927078

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Rate-Independent Systems by Alexander Mielke,Tomáš Roubíček Pdf

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.

Non-Smooth and Complementarity-Based Distributed Parameter Systems

Michael Hintermüller,Roland Herzog,Christian Kanzow,Michael Ulbrich,Stefan Ulbrich
Non Smooth and Complementarity Based Distributed Parameter Systems Book PDF

Author : Michael Hintermüller,Roland Herzog,Christian Kanzow,Michael Ulbrich,Stefan Ulbrich
Publisher : Springer Nature
Page : 518 pages
File Size : 41,9 Mb
Release : 2022-02-18
Category : Mathematics
ISBN : 9783030793937

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Non-Smooth and Complementarity-Based Distributed Parameter Systems by Michael Hintermüller,Roland Herzog,Christian Kanzow,Michael Ulbrich,Stefan Ulbrich Pdf

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.

Handbook of Differential Equations: Evolutionary Equations

C.M. Dafermos,Eduard Feireisl
Handbook of Differential Equations Evolutionary Equations Book PDF

Author : C.M. Dafermos,Eduard Feireisl
Publisher : Elsevier
Page : 677 pages
File Size : 50,6 Mb
Release : 2005-10-05
Category : Mathematics
ISBN : 9780080461380

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Handbook of Differential Equations: Evolutionary Equations by C.M. Dafermos,Eduard Feireisl Pdf

The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today. . Volume I of this Handbook does focus on the abstract theory of evolutionary equations. . Volume 2 considers more concrete problems relating to specific applications. . Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.

Self-dual Partial Differential Systems and Their Variational Principles

Nassif Ghoussoub
Self dual Partial Differential Systems and Their Variational Principles Book PDF

Author : Nassif Ghoussoub
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 54,5 Mb
Release : 2008-10-08
Category : Mathematics
ISBN : 9780387848976

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Self-dual Partial Differential Systems and Their Variational Principles by Nassif Ghoussoub Pdf

This text is intended for a beginning graduate course on convexity methods for PDEs. The generality chosen by the author puts this under the classification of "functional analysis". The book contains new results and plenty of examples and exercises.

Non-standard Discretisation Methods in Solid Mechanics

Jörg Schröder,Peter Wriggers
Non standard Discretisation Methods in Solid Mechanics Book PDF

Author : Jörg Schröder,Peter Wriggers
Publisher : Springer Nature
Page : 561 pages
File Size : 52,5 Mb
Release : 2022-04-14
Category : Technology & Engineering
ISBN : 9783030926724

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Non-standard Discretisation Methods in Solid Mechanics by Jörg Schröder,Peter Wriggers Pdf

This edited volume summarizes research being pursued within the DFG Priority Programme 1748: "Reliable Simulation Methods in Solid Mechanics. Development of non-standard discretisation methods, mechanical and mathematical analysis", the aim of which was to develop novel discretisation methods based e.g. on mixed finite element methods, isogeometric approaches as well as discontinuous Galerkin formulations, including a sound mathematical analysis for geometrically as well as physically nonlinear problems. The Priority Programme has established an international framework for mechanical and applied mathematical research to pursue open challenges on an inter-disciplinary level. The compiled results can be understood as state of the art in the research field and show promising ways of further research in the respective areas. The book is intended for doctoral and post-doctoral students in civil engineering, mechanical engineering, applied mathematics and physics, as well as industrial researchers interested in the field.

Nonlinear PDE’s and Applications

Stefano Bianchini
Nonlinear PDE s and Applications Book PDF

Author : Stefano Bianchini
Publisher : Springer Science & Business Media
Page : 237 pages
File Size : 52,7 Mb
Release : 2011-07-30
Category : Mathematics
ISBN : 9783642217180

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Nonlinear PDE’s and Applications by Stefano Bianchini Pdf

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.

Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs

Pierluigi Colli,Angelo Favini,Elisabetta Rocca,Giulio Schimperna,Jürgen Sprekels
Solvability Regularity and Optimal Control of Boundary Value Problems for PDEs Book PDF

Author : Pierluigi Colli,Angelo Favini,Elisabetta Rocca,Giulio Schimperna,Jürgen Sprekels
Publisher : Springer
Page : 571 pages
File Size : 42,9 Mb
Release : 2017-11-03
Category : Mathematics
ISBN : 9783319644899

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Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs by Pierluigi Colli,Angelo Favini,Elisabetta Rocca,Giulio Schimperna,Jürgen Sprekels Pdf

This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.

Nonlinear Dynamics of Structures, Systems and Devices

Walter Lacarbonara,Balakumar Balachandran,Jun Ma,J. A. Tenreiro Machado,Gabor Stepan
Nonlinear Dynamics of Structures Systems and Devices Book PDF

Author : Walter Lacarbonara,Balakumar Balachandran,Jun Ma,J. A. Tenreiro Machado,Gabor Stepan
Publisher : Springer Nature
Page : 592 pages
File Size : 42,6 Mb
Release : 2020-01-29
Category : Science
ISBN : 9783030347130

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Nonlinear Dynamics of Structures, Systems and Devices by Walter Lacarbonara,Balakumar Balachandran,Jun Ma,J. A. Tenreiro Machado,Gabor Stepan Pdf

This first of three volumes from the inaugural NODYCON, held at the University of Rome, in February of 2019, presents papers devoted to Nonlinear Dynamics of Structures, Systems and Devices. The collection features both well-established streams of research as well as novel areas and emerging fields of investigation. Topics in Volume I include multi-scale dynamics: coexistence of multiple time/space scales, large system dynamics; dynamics of structures/industrial machines/equipment/facilities (e.g., cable transportation systems, suspension bridges, cranes, vehicles); nonlinear interactions: parametric vibrations with single/multi-frequency excitations, multiple external and autoparametric resonances in multi-dof systems; nonlinear system identification: parametric/nonparametric identification, data-driven identification; experimental dynamics: benchmark experiments, experimental methods, instrumentation techniques, measurements in harsh environments, experimental validation of nonlinear models; wave propagation, solitons, kinks, breathers; solution methods for pdes: Lie groups, Hirota’s method, perturbation methods, etc; nonlinear waves in media (granular materials, porous materials, materials with memory); composite structures: multi-layer, functionally graded, thermal loading; fluid/structure interaction; nonsmooth and retarded dynamics: systems with impacts, free play, stick-slip, friction hysteresis; nonlinear systems with time and/or space delays; stability of delay differential equations, differential-algebraic equations; space/time reduced-order modeling: enhanced discretization methods, center manifold reduction, nonlinear normal modes, normal forms; fractional-order systems; computational techniques: efficient algorithms, use of symbolic manipulators, integration of symbolic manipulation and numerical methods, use of parallel processors; and multibody dynamics: rigid and flexible multibody system dynamics, impact and contact mechanics, tire modeling, railroad vehicle dynamics, computational multibody dynamics.

Stability of Discrete Non-conservative Systems

Jean Lerbet,Noel Challamel,Francois Nicot,Felix Darve
Stability of Discrete Non conservative Systems Book PDF

Author : Jean Lerbet,Noel Challamel,Francois Nicot,Felix Darve
Publisher : Elsevier
Page : 291 pages
File Size : 52,7 Mb
Release : 2020-11-27
Category : Technology & Engineering
ISBN : 9780081027653

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Stability of Discrete Non-conservative Systems by Jean Lerbet,Noel Challamel,Francois Nicot,Felix Darve Pdf

Stability of Discrete Non-conservative Systems first exposes the general concepts and results concerning stability issues. It then presents an approach of stability that is different from Lyapunov which leads to the second order work criterion. Thanks to the new concept of Kinematic Structural Stability, a complete equivalence between two approaches of stability is obtained for a divergent type of stability. Extensions to flutter instability, to continuous systems, and to the dual questions concerning the measure of non-conservativeness provides a full, fresh look at these fundamental questions. A special chapter is devoted to applications for granular systems. Presents a structured review on stability questions Provides analytical methods and key concepts that may be used in non-conservative frameworks like hypoelasticity

Media Production, Delivery and Interaction for Platform Independent Systems

Oliver Schreer,Jean-François Macq,Omar Aziz Niamut,Javier Ruiz-Hidalgo,Ben Shirley,Georg Thallinger,Graham Thomas
Media Production Delivery and Interaction for Platform Independent Systems Book PDF

Author : Oliver Schreer,Jean-François Macq,Omar Aziz Niamut,Javier Ruiz-Hidalgo,Ben Shirley,Georg Thallinger,Graham Thomas
Publisher : John Wiley & Sons
Page : 369 pages
File Size : 51,6 Mb
Release : 2013-12-06
Category : Technology & Engineering
ISBN : 9781118706336

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Media Production, Delivery and Interaction for Platform Independent Systems by Oliver Schreer,Jean-François Macq,Omar Aziz Niamut,Javier Ruiz-Hidalgo,Ben Shirley,Georg Thallinger,Graham Thomas Pdf

Presents current trends and potential future developments by leading researchers in immersive media production, delivery, rendering and interaction The underlying audio and video processing technology that is discussed in the book relates to areas such as 3D object extraction, audio event detection; 3D sound rendering and face detection, gesture analysis and tracking using video and depth information. The book will give an insight into current trends and developments of future media production, delivery and reproduction. Consideration of the complete production, processing and distribution chain will allow for a full picture to be presented to the reader. Production developments covered will include integrated workflows developed by researchers and industry practitioners as well as capture of ultra-high resolution panoramic video and 3D object based audio across a range of programme genres. Distribution developments will include script based format agnostic network delivery to a full range of devices from large scale public panoramic displays with wavefield synthesis and ambisonic audio reproduction to ’small screen’ mobile devices. Key developments at the consumer end of the chain apply to both passive and interactive viewing modes and will incorporate user interfaces such as gesture recognition and ‘second screen’ devices to allow manipulation of the audio visual content. Presents current trends and potential future developments by leading researchers in immersive media production, delivery, rendering and interaction. Considers the complete production, processing and distribution chain illustrating the dependencies and the relationship between different components. Proposes that a format-agnostic approach to the production and delivery of broadcast programmes will overcome the problems faced with the steadily growing number of production and delivery formats. Explains the fundamentals of media production in addition to the complete production chain, beyond current-state-of-the-art through to presenting novel approaches and technologies for future media production. Focuses on the technologies that will allow for the realization of an E2E media platform that supports flexible content representations and interactivity for users. An essential read for Researchers and developers of audio-visual technology in industry and academia, such as engineers in broadcast technology companies and students working toward a career in the rapidly changing area of broadcast both from a production and an engineering perspective.

Mathematical Analysis of Continuum Mechanics and Industrial Applications II

Patrick van Meurs,Masato Kimura,Hirofumi Notsu
Mathematical Analysis of Continuum Mechanics and Industrial Applications II Book PDF

Author : Patrick van Meurs,Masato Kimura,Hirofumi Notsu
Publisher : Springer
Page : 193 pages
File Size : 44,5 Mb
Release : 2017-11-16
Category : Science
ISBN : 9789811062834

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Mathematical Analysis of Continuum Mechanics and Industrial Applications II by Patrick van Meurs,Masato Kimura,Hirofumi Notsu Pdf

As the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS15), the proceedings of CoMFoS16 present further advances and new topics in mathematical theory and numerical simulations related to various aspects of continuum mechanics. These include fracture mechanics, shape optimization, modeling of earthquakes, material structure, interface dynamics and complex systems.. The authors are leading researchers with a profound knowledge of mathematical analysis from the fields of applied mathematics, physics, seismology, engineering, and industry. The book helps readers to understand how mathematical theory can be applied to various industrial problems, and conversely, how industrial problems lead to new mathematical challenges.

Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs

Emanuel Indrei,Diego Marcon,Levon Nurbekyan
Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs Book PDF

Author : Emanuel Indrei,Diego Marcon,Levon Nurbekyan
Publisher : American Mathematical Society
Page : 148 pages
File Size : 49,5 Mb
Release : 2023-01-09
Category : Mathematics
ISBN : 9781470466527

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Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs by Emanuel Indrei,Diego Marcon,Levon Nurbekyan Pdf

This volume contains the proceedings of the virtual conference on Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs, held from February 28–March 1, 2021, and hosted by Purdue University, West Lafayette, IN. The mathematical content of this volume is at the intersection of viscosity theory, Fourier analysis, mass transport theory, fractional elliptic theory, and geometric analysis. The reader will encounter, among others, the following topics: the principal-agent problem; Maxwell's equations; Liouville-type theorems for fully nonlinear elliptic equations; a doubly monotone flow for constant width bodies; and the edge dislocations problem for crystals that describes the equilibrium configurations by a nonlocal fractional Laplacian equation.

Mathematical Methods And Models In Composites (Second Edition)

Vladislav Mantic
Mathematical Methods And Models In Composites Second Edition Book PDF

Author : Vladislav Mantic
Publisher : World Scientific
Page : 731 pages
File Size : 40,7 Mb
Release : 2023-03-10
Category : Mathematics
ISBN : 9781800611894

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Mathematical Methods And Models In Composites (Second Edition) by Vladislav Mantic Pdf

Mathematical Methods and Models in Composites (Second Edition) provides an in-depth treatment of modern and rigorous mathematical methods and models applied to composites modeling on the micro-, meso-, and macro scale. There has been a steady growth in the diversity of such methods and models that are used in the analysis and characterization of composites, their behavior, and their associated phenomena and processes. This second edition expands upon the success of the first edition, and has been substantially revised and updated.Written by well-known experts in different areas of applied mathematics, physics, and composite engineering, this book is mainly focused on continuous fiber reinforced composites and their ever increasing range of applications (for example, in the aerospace industry), though it also covers other kind of composites. The chapters cover a range of topics including, but not limited to: scaling and homogenization procedures in composites, thin plate and wave solutions in anisotropic materials, laminated structures, fiber-reinforced nonlinearly elastic solids, buckling and postbuckling, fracture and damage analysis of composites, and highly efficient methods for simulation of composites manufacturing such as resin transfer molding. The results presented are useful for the design, fabrication, testing and industrial applications of composite components and structures.This book is an essential reference for graduate and doctoral students, as well as researchers in mathematics, physics and composite engineering. Explanations and references in the book are sufficiently detailed so as to provide the necessary background to further investigate the fascinating subject of composites modeling and explore relevant research literature. It is also suitable for non-experts who wish to have an overview of the mathematical methods and models used for composites, and of the open problems in this area that require further research.

Trends in Applications of Mathematics to Mechanics

Elisabetta Rocca,Ulisse Stefanelli,Lev Truskinovsky,Augusto Visintin
Trends in Applications of Mathematics to Mechanics Book PDF

Author : Elisabetta Rocca,Ulisse Stefanelli,Lev Truskinovsky,Augusto Visintin
Publisher : Springer
Page : 373 pages
File Size : 40,6 Mb
Release : 2018-04-27
Category : Mathematics
ISBN : 9783319759401

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Trends in Applications of Mathematics to Mechanics by Elisabetta Rocca,Ulisse Stefanelli,Lev Truskinovsky,Augusto Visintin Pdf

This volume originates from the INDAM Symposium on Trends on Applications of Mathematics to Mechanics (STAMM), which was held at the INDAM headquarters in Rome on 5–9 September 2016. It brings together original contributions at the interface of Mathematics and Mechanics. The focus is on mathematical models of phenomena issued from various applications. These include thermomechanics of solids and gases, nematic shells, thin films, dry friction, delamination, damage, and phase-field dynamics. The papers in the volume present novel results and identify possible future developments. The book is addressed to researchers involved in Mathematics and its applications to Mechanics.