George M. Zaslavsky, Department of Physics and Courant Institute of Mathematical Sciences, New York University, USA

Hamiltonian Chaos and Fractional Dynamics

0-19-852604-0
Publication date: November 2004
320 pages, 181 b/w line figs; 4 b/w halftones, 234mm x 156mm

Written in a pedagogical style, richly illustrated, plenty of applications, examples, and problem sets
Presents some of the most complex and important features of Hamiltonian chaos
Comprehensive discussion of space-time fractality of chaotic dynamics
Includes detailed analysis of the foundations of statistical mechanics and Maxwell's demon
Includes unique material on non-KAM systems, symmetry of plane tilings, erasing of chaos, and cooling of particles

Description

This books gives a realistic contemporary image of Hamiltonian dynamics, dealing with the basic principles of the Hamiltonian theory of chaos in addition to very recent and unusual applications of nonlinear dynamics and the fractality of dynamics.

Readership: Graduate students, researchers and professionals working in physics, applied mathematics and engineering.

Contents

Chaotic Dynamics
1 Hamiltonian dynamics
2 Examples of Hamiltonian dynamics
3 Perturbed dynamics
4 Chaotic dynamics
5 Physical models of chaos
6 Separatrix chaos
7 Chaos and symmetry
8 Beyond the KAM-theory
9 Phase space of chaos
Fractality of chaos
10 Fractals and chaos
11 Poincare recurrences
12 Dynamical traps
13 Fractal time
Kinetics
14 General principles of kinetics
15 Levy processes and levy flights
16 Fractional kinetic equation (FKE)
17 Renormalization group of kinetics (RGK)
18 Fractional kinetics equation solutions and modifications
19 Pseudochaos
Applications
20 Complexity and entropy of dynamics
21 Complexity and entropy functions
22 Chaos and foundation of statistical mechanics
23 Chaotic advection (dynamics of tracers)
24 Advection by point vortices
25 Appendix 1
26 Appendix 2
27 Appendix 3
28 Appendix 4
29 Notes
30 Problems

Dan C. Marinescu/ Gabriela M. Marinescu

Approaching Quantum Computing

ISBN: 0-13-145224-X

Copyright: 2005
Format: Cloth; 400 pp

Description

For one-semester first courses in Quantum Computing. An introduction to the subject for undergraduate and graduate students in computer and electrical engineering, computer science, mathematics, and chemistry.

With a clear writing style and matter-of-fact approach, this rigorous yet accessible introduction is designed for students with a solid mathematical background but limited knowledge of physics and quantum mechanics. It introduces the quantum circuit model comprehensively?including the mathematical formalism required for quantum computing?using a methodical approach and an abundance of worked examples.

Table of Contents

1 Preface
2 Introduction
3 Quantum Mechanics, a Mathematical Model of the Physical World
4 Qubits and Their Physical Realization
5 Quantum Gates and Quantum Circuits
6 Quantum Algorithms
7 The "Entanglement" of Computing and Communication with Quantum Mechanics. Reversible Computations
8 Appendix I: Algebraic Structures
9 Appendix II: Modular Arithmetic
10 Appendix III: Welsh-Hadamard Transform
11 Appendix IV: Fourier Transform and Fourier Series
12 Glossary

Bernardini, Carlo; Bonolis, Luisa (Eds.)

Enrico Fermi: His Work and Legacy

2004, XII, 410 p., Hardcover
ISBN: 3-540-22141-7

About this book

Enrico Fermifs scientific work, noted for its originality and breadth, has had lasting consequences throughout modern science. Written by close colleagues as well as scientists whose fields were profoundly influenced by Fermi, the papers collected here constitute a tribute to him and his scientific legacy. They were commissioned on the occasion of his 100th birthday by the Italian Physical Society and confirm that Fermi was a rare combination of theorist, experimentalist, teacher, and inspiring colleague. The book is organized into three parts: three biographical overviews by close colleagues, replete with personal insights; fourteen analyses of Fermi's impact by specialists in their fields, spanning physics, chemistry, mathematics, and engineering; and a year-by-year chronology of Fermifs scientific endeavors. Written for a general scientific audience, Enrico Fermi: His Work and Legacy offers a highly readable source on the life of one of the 20th century's most distinguished scientists and a must for everybody interested in the history of modern science.

Table of contents

Commemoration of Enrico Fermi (Edoardo Amaldi).- Commemoration of Enrico Fermi (Enrico Persico).- Enrico Fermi and Italian physics (Franco Rasetti).- Enrico Fermi and solid state physics (Franco Bassani).- Fermi's statistics (Giorgio Parisi).- Classical mechanics and the quantum revolution in Fermi's early works (Giovanni Gallavotti).- On the adiabatic invariants (Tullio Levi-Civita).- Fermi's coordinates and the principle of equivalence (Bruno Bertotti).- Fermi and quantum electrodynamics (Marcello Cini).-Weak interactions (Nicola Cabibbo).- Nuclear physics from the nineteen thirties to the present day (Ugo Amaldi).- The birth of nuclear energy: Fermi's pile (Carlo Salvetti).- From the Chicago Pile 1 to the next-generation reactors (Augusto Gandini).- Reactors and nuclear technology: development in the world (Maurizio Cumo).- The scientific legacy of Fermi in particle physics (Maurice Jacob and Luciano Maiani).- Enrico Fermi's contributions to non-linear systems: the influence of an unpublished article (Massimo Falcioni and Angelo Vulpiani).- Fermi's last lessons (Renato Angelo Ricci).- Enrico Fermi's scientific work (Lisa Bonolis).- Bibliography.- Index.

Favre, Charles, Jonsson, Mattias

The Valuative Tree

Series : Lecture Notes in Mathematics , Vol. 1853

2004, XV, 234 p., Softcover
ISBN: 3-540-22984-1

About this book

This volume is devoted to a beautiful object, called the valuative tree and designed as a powerful tool for the study of singularities in two complex dimensions. Its intricate yet manageable structure can be analyzed by both algebraic and geometric means. Many types of singularities, including those of curves, ideals, and plurisubharmonic functions, can be encoded in terms of positive measures on the valuative tree. The construction of these measures uses a natural tree Laplace operator of independent interest.

Table of contents


Saeki, Osamu

Topology of Singular Fibers of Differentiable Maps

Series : Lecture Notes in Mathematics , Vol. 1854
2004, X, 145 p., Softcover
ISBN: 3-540-23021-1

About this book

The volume develops a thorough theory of singular fibers of generic differentiable maps. This is the first work that establishes the foundational framework of the global study of singular differentiable maps of negative codimension from the viewpoint of differential topology. The book contains not only a general theory, but also some explicit examples together with a number of very concrete applications. This is a very interesting subject in differential topology, since it shows a beautiful interplay between the usual theory of singularities of differentiable maps and the geometric topology of manifolds.

Table of Contents



Da Prato, G., Kunstmann, P.C., Lasiecka, I., Lunardi, A., Schnaubelt, R., Weis, L.
Iannelli, Mimmo; Nagel, Rainer; Piazzera, Susanna (Eds.)

Functional Analytic Methods for Evolution Equations

Series : Lecture Notes in Mathematics , Vol. 1855
2004, VIII, 472 p., Softcover
ISBN: 3-540-23030-0

About this book

This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.

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Capasso, Vincenzo; Periaux, Jaques (Eds.)

Multidisciplinary Methods for Analysis,
Optimization and Control of Complex Systems

Series : Mathematics in Industry
Subseries : The European Consortium for Mathematics in Industry , Vol. 6

2004, XVI, 312 p., Hardcover
ISBN: 3-540-22310-X

About this book

This book consists of lecture notes of a summer school named after the late Jacques Louis Lions. The summer school was designed to alert both Academia and Industry to the increasing role of multidisciplinary methods and tools for the design of complex products in various areas of socio-economic interest. This volume offers the reader a rare opportunity of being exposed to the presentation of real industrial and societal problems together with the relevant innovative methods used.

Table of contents

Part I Lectures: A computational fluid-structure interaction analysis of a fiber-reinforced stentless aortic valve, J. De Hart, G.W.M. Peters, P.J.G. Schreurs, F.P.T. Baaijens; Nonlinear Inverse Problems: Theoretical Aspects and Some Industrial Applications, Heinz W. Engl, Philipp Kugler; Numerical Methods for the Simulation of Incompressible Viscous Flow: An Introduction, Roland Glowinski, Tsorng-Whay, Pan, L. Hector Juarez V. Edward Dean.- Part II Speakers: Data assimilation methods for an oceanographic problem, Didier Auroux, Jacques Blum; Ant colonies: a nature inspired paradigm for the mathematical modelling of self-organizing systems, Vincenzo Capasso, Daniela Morale; Distribution Theoretic Approach to Multi-phase Flow, Hideo Kawarada, E. Baba, M. Okada, H. Suito ; An Ant System Heuristic for the Two-Dimensional Finite Bin Packing Problem: preliminary results, Marco A. Boschetti, Vittorio Maniezzo; Distributed Multidisciplinary Design Optimisation in Aeronautics using Evolutionary Algorithms, Game Theory and Hierarchy, Eric J. Whitney, Luis F. Gonzalez, Jacques Periaux; Distributed Multidisciplinary Design Optimisation in Aeronautics using Evolutionary Algorithms, Game Theory and Hierarchy, Eric J. Whitney, Luis F. Gonzalez, Jacques Periaux.