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Molecular Dynamics
This book describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods. Molecular dynamics is one of the most versatile and powerful methods of modern computational science and engineering and is used widely in chemistry, physics, materials science and biology. Understanding the foundations of numerical methods means knowing how to select the best one for a given problem (from the wide range of techniques on offer) and how to create new, efficient methods to address particular challenges as they arise in complex applications. Aimed at a broad audience, this book presents the basic theory of Hamiltonian mechanics and stochastic differential equations, as well as topics including symplectic numerical methods, the handling of constraints and rigid bodies, the efficient treatment of Langevin dynamics, thermostats to control the molecular ensemble, multiple time-stepping, and the dissipative particle dynamics method.
The Mathematical Foundations of Mixing
Mixing processes occur in many technological and natural applications, with length and time scales ranging from the very small to the very large. The diversity of problems can give rise to a diversity of approaches. Are there concepts that are central to all of them? Are there tools that allow for prediction and quantification? The authors show how a variety of flows in very different settings possess the characteristic of streamline crossing. This notion can be placed on firm mathematical footing via Linked Twist Maps (LTMs), which is the central organizing principle of this book. The authors discuss the definition and construction of LTMs, provide examples of specific mixers that can be analyzed in the LTM framework and introduce a number of mathematical techniques which are then brought to bear on the problem of fluid mixing. In a final chapter, they present a number of open problems and new directions.
Understanding Molecular Simulation
Understanding Molecular Simulation explains molecular simulation from a chemical-physics and statistical-mechanics perspective. It highlights how physical concepts are used to develop better algorithms and expand the range of applicability of simulations. Understanding Molecular Simulation is equally relevant for those who develop new code and those who use existing packages. Both groups are continuously confronted with the question of which computational technique best suits a given application. Understanding Molecular Simulation provides readers with the foundational knowledge they need to learn about, select and apply the most appropriate of these tools to their own work. The implementati...
Topology for Computing
The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.
Current and Future Directions in Applied Mathematics
Mark Alber, Bei Hu and Joachim Rosenthal ... ... vii Part I Some Remarks on Applied Mathematics Roger Brockett ... ... ... ... ... 1 Mathematics is a Profession Christopher 1. Byrnes ... ... ... ... . 4 Comments on Applied Mathematics Avner Friedman ... ... ... ... . . 9 Towards an Applied Mathematics for Computer Science Jeremy Gunawardena ... ... ... ... . 11 Infomercial for Applied Mathematics Darryl Holm ... ... ... ... ... 15 On Research in Mathematical Economics M. Ali Khan ... ... ... ... ... 21 Applied Mathematics in the Computer and Communications Industry Brian Marcus ... ... ... ... ... 25 'frends in Applied Mathematics Jerrold E. Marsden ... ... ... ... 28 Applied Mathematics as ...
Continuous System Simulation
Highly computer-oriented text, introducing numerical methods and algorithms along with the applications and conceptual tools. Includes homework problems, suggestions for research projects, and open-ended questions at the end of each chapter. Written by our successful author who also wrote Continuous System Modeling, a best-selling Springer book first published in the 1991 (sold about 1500 copies).
Dynamics of Algorithms
The articles collected in this volume represent the contributions presented at the IMA workshop on "Dynamics of Algorithms" which took place in November 1997. The workshop was an integral part of the 1997 -98 IMA program on "Emerging Applications of Dynamical Systems." The interaction between algorithms and dynamical systems is mutually beneficial since dynamical methods can be used to study algorithms that are applied repeatedly. Convergence, asymptotic rates are indeed dynamical properties. On the other hand, the study of dynamical systems benefits enormously from having efficient algorithms to compute dynamical objects.
Surveys in Differential-Algebraic Equations IV
The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs) which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - History of DAEs - DAE aspects of mechanical multibody systems - Model reduction of DAEs - Observability for DAEs - Numerical Analysis for DAEs The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.
Simulation And Control Of Chaotic Nonequilibrium Systems: With A Foreword By Julien Clinton Sprott
This book aims to provide a lively working knowledge of the thermodynamic control of microscopic simulations, while summarizing the historical development of the subject, along with some personal reminiscences. Many computational examples are described so that they are well-suited to learning by doing. The contents enhance the current understanding of the reversibility paradox and are accessible to advanced undergraduates and researchers in physics, computation, and irreversible thermodynamics.
Multiscale Methods in Science and Engineering
Multiscale problems naturally pose severe challenges for computational science and engineering. The smaller scales must be well resolved over the range of the larger scales. Challenging multiscale problems are very common and are found in e.g. materials science, fluid mechanics, electrical and mechanical engineering. Homogenization, subgrid modelling, heterogeneous multiscale methods, multigrid, multipole, and adaptive algorithms are examples of methods to tackle these problems. This volume is an overview of current mathematical and computational methods for problems with multiple scales with applications in chemistry, physics and engineering.
