Homogenization In Time Of Singularly Perturbed Mechanical Systems
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Homogenization In Time Of Singularly Perturbed Mechanical Systems
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Author : Folkmar Bornemann
language : en
Publisher: Springer
Release Date : 2006-11-15
Homogenization In Time Of Singularly Perturbed Mechanical Systems written by Folkmar Bornemann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
This book is about the explicit elimination of fast oscillatory scales in dynamical systems, which is important for efficient computer-simulations and our understanding of model hierarchies. The author presents his new direct method, homogenization in time, based on energy principles and weak convergence techniques. How to use this method is shown in several general cases taken from classical and quantum mechanics. The results are applied to special problems from plasma physics, molecular dynamics and quantum chemistry. Background material from functional analysis is provided and explained to make this book accessible for a general audience of graduate students and researchers.
Homogenization In Time Of Singularly Perturbed Conservative Mechanical Systems
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Author : Folkmar A. Bornemann
language : en
Publisher:
Release Date : 1997
Homogenization In Time Of Singularly Perturbed Conservative Mechanical Systems written by Folkmar A. Bornemann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Homogenization (Differential equations) categories.
Second Order Transitions In Quantum Classical Molecular Dynamics
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Author : Peter Nettesheim
language : en
Publisher:
Release Date : 1998
Second Order Transitions In Quantum Classical Molecular Dynamics written by Peter Nettesheim and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Molecular dynamics categories.
Abstract: "Mixed quantum-classical models have attracted considerable interest due to the expectation that they correctly describe non-adiabatic processes of full quantum dynamics. One of these models, the so-called QCMD model, represents most degrees of freedom of the molecular system by the means of classical mechanics but an important, small portion of the system is modeled by a quantum wavefunction: the wavefunction is nonlinearly coupled to the classical motion via a singularly perturbed Schrödinger equation. In extension to the analysis given by F.A. Bornemann [Homogenization in Time of Singularly Perturbed Mechanical Systems, Lecture Notes in Mathematics, no. 1687, 1998, Springer, Berlin], the article presents an asymptotic expansion up to second order in the perturbation parameter. This result allows for the construction of new models and numerical integration schemes."
Adiabatic Perturbation Theory In Quantum Dynamics
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Author : Stefan Teufel
language : en
Publisher: Springer Science & Business Media
Release Date : 2003
Adiabatic Perturbation Theory In Quantum Dynamics written by Stefan Teufel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Perturbation (Quantum dynamics) categories.
Nonsmooth Mechanics
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Author : Bernard Brogliato
language : en
Publisher: Springer
Release Date : 2016-02-29
Nonsmooth Mechanics written by Bernard Brogliato and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-29 with Technology & Engineering categories.
Now in its third edition, this standard reference is a comprehensive treatment of nonsmooth mechanical systems refocused to give more prominence to issues connected with control and modelling. It covers Lagrangian and Newton–Euler systems, detailing mathematical tools such as convex analysis and complementarity theory. The ways in which nonsmooth mechanics influence and are influenced by well-posedness analysis, numerical analysis and simulation, modelling and control are explained. Contact/impact laws, stability theory and trajectory-tracking control are given detailed exposition connected by a mathematical framework formed from complementarity systems and measure-differential inclusions. Links are established with electrical circuits with set-valued nonsmooth elements as well as with other nonsmooth dynamical systems like impulsive and piecewise linear systems. Nonsmooth Mechanics (third edition) retains the topical structure familiar from its predecessors but has been substantially rewritten, edited and updated to account for the significant body of results that have emerged in the twenty-first century—including developments in: the existence and uniqueness of solutions; impact models; extension of the Lagrange–Dirichlet theorem and trajectory tracking; and well-posedness of contact complementarity problems with and without friction. Many figures (both new and redrawn to improve the clarity of the presentation) and examples are used to illustrate the theoretical developments. Material introducing the mathematics of nonsmooth mechanics has been improved to reflect the broad range of applications interest that has developed since publication of the second edition. The detail of some mathematical essentials is provided in four appendices. With its improved bibliography of over 1,300 references and wide-ranging coverage, Nonsmooth Mechanics (third edition) is sure to be an invaluable resource for researchers and postgraduates studying the control of mechanical systems, robotics, granular matter and relevant fields of applied mathematics. “The book’s two best features, in my view are its detailed survey of the literature... and its detailed presentation of many examples illustrating both the techniques and their limitations... For readers interested in the field, this book will serve as an excellent introductory survey.” Andrew Lewis in Automatica “It is written with clarity, contains the latest research results in the area of impact problems for rigid bodies and is recommended for both applied mathematicians and engineers.” Panagiotis D. Panagiotopoulos in Mathematical Reviews “The presentation is excellent in combining rigorous mathematics with a great number of examples... allowing the reader to understand the basic concepts.” Hans Troger in Mathematical Abstracts “/i>
Analysis Modeling And Simulation Of Multiscale Problems
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Author : Alexander Mielke
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-10-14
Analysis Modeling And Simulation Of Multiscale Problems written by Alexander Mielke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-14 with Mathematics categories.
This book reports recent mathematical developments in the Programme "Analysis, Modeling and Simulation of Multiscale Problems", which started as a German research initiative in 2006. Multiscale problems occur in many fields of science, such as microstructures in materials, sharp-interface models, many-particle systems and motions on different spatial and temporal scales in quantum mechanics or in molecular dynamics. The book presents current mathematical foundations of modeling, and proposes efficient numerical treatment.
Extended Abstracts Spring 2016
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Author : Alessandro Colombo
language : en
Publisher: Birkhäuser
Release Date : 2017-05-24
Extended Abstracts Spring 2016 written by Alessandro Colombo and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-24 with Science categories.
This volume contains extended abstracts outlining selected talks and other selected presentations given by participants throughout the "Intensive Research Program on Advances in Nonsmooth Dynamics 2016", held at the Centre de Recerca Matemàtica (CRM) in Barcelona from February 1st to April 29th, 2016. They include brief research articles reporting new results, descriptions of preliminary work or open problems, and outlines of prominent discussion sessions. The articles are all the result of direct collaborations initiated during the research program. The topic is the theory and applications of Nonsmooth Dynamics. This includes systems involving elements of: impacting, switching, on/off control, hybrid discrete-continuous dynamics, jumps in physical properties, and many others. Applications include: electronics, climate modeling, life sciences, mechanics, ecology, and more. Numerous new results are reported concerning the dimensionality and robustness of nonsmooth models, shadowing variables, numbers of limit cycles, discontinuity-induced bifurcations and chaos, determinacy-breaking, stability criteria, and the classification of attractors and other singularities. This material offers a variety of new exciting problems to mathematicians, but also a diverse range of new tools and insights for scientists and engineers making use of mathematical modeling and analysis. The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.
Scientific Computing In Chemical Engineering Ii
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Author : Frerich Keil
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Scientific Computing In Chemical Engineering Ii written by Frerich Keil and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The application of modern methods in numerical mathematics on problems in chemical engineering is essential for designing, analyzing and running chemical processes and even entire plants. Scientific Computing in Chemical Engineering II gives the state of the art from the point of view of numerical mathematicians as well as that of engineers. The present volume as part of a two-volume edition covers topics such as the simulation of reactive flows, reaction engineering, reaction diffusion problems, and molecular properties. The volume is aimed at scientists, practitioners and graduate students in chemical engineering, industrial engineering and numerical mathematics.
The Red Book Of Varieties And Schemes
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Author : David Mumford
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-09-17
The Red Book Of Varieties And Schemes written by David Mumford and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-17 with Mathematics categories.
Mumford's famous "Red Book" gives a simple, readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduates or mathematicians in other fields wishing to quickly learn aboutalgebraic geometry. This new edition includes an appendix that gives an overview of the theory of curves, their moduli spaces and their Jacobians -- one of the most exciting fields within algebraic geometry.
Quantum Theory From Small To Large Scales
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Author : Jürg Frohlich
language : en
Publisher: Oxford University Press
Release Date : 2012-05-24
Quantum Theory From Small To Large Scales written by Jürg Frohlich and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Science categories.
This book collects lecture courses and seminars given at the Les Houches Summer School 2010 on "Quantum Theory: From Small to Large Scales". Fundamental quantum phenomena appear on all scales, from microscopic to macroscopic. Some of the pertinent questions include the onset of decoherence, the dynamics of collective modes, the influence of external randomness and the emergence of dissipative behaviour. Our understanding of such phenomena has been advanced by the study of model systems and by the derivation and analysis of effective dynamics for large systems and over long times. In this field, research in mathematical physics has regularly contributed results that were recognized as essential in the physics community. During the last few years, the key questions have been sharpened and progress on answering them has been particularly strong. This book reviews the state-of-the-art developments in this field and provides the necessary background for future studies. All chapters are written from a pedagogical perspective, making the book accessible to master and PhD students and researchers willing to enter this field.