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Electrorheological Fluids: Modeling and Mathematical Theory

Author : Michael Ruzicka

Publisher : Springer

Page : 186 pages

File Size : 21,7 MB

Release : 2007-05-06

Category : Technology & Engineering

ISBN : 3540444270

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Book Description

This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.





The Wulff Crystal in Ising and Percolation Models

Author : Raphaël Cerf

Publisher : Springer

Page : 267 pages

File Size : 20,82 MB

Release : 2006-08-29

Category : Mathematics

ISBN : 3540348069

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Book Description

This volume is a synopsis of recent works aiming at a mathematically rigorous justification of the phase coexistence phenomenon, starting from a microscopic model. It is intended to be self-contained. Those proofs that can be found only in research papers have been included, whereas results for which the proofs can be found in classical textbooks are only quoted.



Generalized Models and Non-classical Approaches in Complex Materials 1

Author : Holm Altenbach

Publisher : Springer

Page : 799 pages

File Size : 17,16 MB

Release : 2018-03-24

Category : Science

ISBN : 3319724401

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Book Description

This book is the first of 2 special volumes dedicated to the memory of Gérard Maugin. Including 40 papers that reflect his vast field of scientific activity, the contributions discuss non-standard methods (generalized model) to demonstrate the wide range of subjects that were covered by this exceptional scientific leader. The topics range from micromechanical basics to engineering applications, focusing on new models and applications of well-known models to new problems. They include micro–macro aspects, computational endeavors, options for identifying constitutive equations, and old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.



Current Trends in Mathematical Analysis and Its Interdisciplinary Applications

Author : Hemen Dutta

Publisher : Springer Nature

Page : 912 pages

File Size : 36,21 MB

Release : 2019-08-23

Category : Mathematics

ISBN : 3030152421

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Book Description

This book explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research. Each of the 23 carefully reviewed chapters was written by experienced expert(s) in respective field, and will enrich readers’ understanding of the respective research problems, providing them with sufficient background to understand the theories, methods and applications discussed. The book’s main goal is to highlight the latest trends and advances, equipping interested readers to pursue further research of their own. Given its scope, the book will especially benefit graduate and PhD students, researchers in the applied sciences, educators, and engineers with an interest in recent developments in the interdisciplinary applications of mathematical analysis.



Weighted Littlewood-Paley Theory and Exponential-Square Integrability

Author : Michael Wilson

Publisher : Springer Science & Business Media

Page : 233 pages

File Size : 18,86 MB

Release : 2008

Category : Mathematics

ISBN : 3540745823

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Book Description

Littlewood-Paley theory is an essential tool of Fourier analysis, with applications and connections to PDEs, signal processing, and probability. It extends some of the benefits of orthogonality to situations where orthogonality doesn’t really make sense. It does so by letting us control certain oscillatory infinite series of functions in terms of infinite series of non-negative functions. Beginning in the 1980s, it was discovered that this control could be made much sharper than was previously suspected. The present book tries to give a gentle, well-motivated introduction to those discoveries, the methods behind them, their consequences, and some of their applications.



Representation Theory and Complex Analysis

Author : Michael Cowling

Publisher : Springer

Page : 400 pages

File Size : 35,85 MB

Release : 2008-02-22

Category : Mathematics

ISBN : 3540768920

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Book Description

Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability. They further illustrate how representation theory is related to quantum computing; and much more. Taken together, this volume provides both a solid reference and deep insights on current research activity.



Lectures on Probability Theory and Statistics

Author : Amir Dembo

Publisher : Springer Science & Business Media

Page : 300 pages

File Size : 38,54 MB

Release : 2005-11-03

Category : Mathematics

ISBN : 9783540260691

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Book Description

This volume contains two of the three lectures that were given at the 33rd Probability Summer School in Saint-Flour (July 6-23, 2003). Amir Dembo’s course is devoted to recent studies of the fractal nature of random sets, focusing on some fine properties of the sample path of random walk and Brownian motion. In particular, the cover time for Markov chains, the dimension of discrete limsup random fractals, the multi-scale truncated second moment and the Ciesielski-Taylor identities are explored. Tadahisa Funaki’s course reviews recent developments of the mathematical theory on stochastic interface models, mostly on the so-called \nabla \varphi interface model. The results are formulated as classical limit theorems in probability theory, and the text serves with good applications of basic probability techniques.



Nonlinear and Optimal Control Theory

Author : Andrei A. Agrachev

Publisher : Springer

Page : 368 pages

File Size : 37,99 MB

Release : 2008-06-24

Category : Science

ISBN : 3540776532

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Book Description

The lectures gathered in this volume present some of the different aspects of Mathematical Control Theory. Adopting the point of view of Geometric Control Theory and of Nonlinear Control Theory, the lectures focus on some aspects of the Optimization and Control of nonlinear, not necessarily smooth, dynamical systems. Specifically, three of the five lectures discuss respectively: logic-based switching control, sliding mode control and the input to the state stability paradigm for the control and stability of nonlinear systems. The remaining two lectures are devoted to Optimal Control: one investigates the connections between Optimal Control Theory, Dynamical Systems and Differential Geometry, while the second presents a very general version, in a non-smooth context, of the Pontryagin Maximum Principle. The arguments of the whole volume are self-contained and are directed to everyone working in Control Theory. They offer a sound presentation of the methods employed in the control and optimization of nonlinear dynamical systems.