Books in Mathematical methods in physics

Books Journals

Transmutation, Scattering Theory and Special Functions

1st Edition
Volume 69
August 18, 2011
R. Carroll
English
eBook
9 7 8 0 0 8 0 8 7 1 8 0 6

Transmutation Theory and Applications

1st Edition
Volume 117
August 18, 2011
R. Carroll
English
eBook
9 7 8 0 0 8 0 8 7 2 2 8 5

Exploring Monte Carlo Methods

1st Edition
April 6, 2011
William L. Dunn + 1 more
English
Hardback
9 7 8 0 4 4 4 5 1 5 7 5 9
eBook
9 7 8 0 0 8 0 9 3 0 6 1 9

Exploring Monte Carlo Methods is a basic text that describes the numerical methods that have come to be known as "Monte Carlo." The book treats the subject generically through the first eight chapters and, thus, should be of use to anyone who wants to learn to use Monte Carlo. The next two chapters focus on applications in nuclear engineering, which are illustrative of uses in other fields. Five appendices are included, which provide useful information on probability distributions, general-purpose Monte Carlo codes for radiation transport, and other matters. The famous "Buffon’s needle problem" provides a unifying theme as it is repeatedly used to illustrate many features of Monte Carlo methods. This book provides the basic detail necessary to learn how to apply Monte Carlo methods and thus should be useful as a text book for undergraduate or graduate courses in numerical methods. It is written so that interested readers with only an understanding of calculus and differential equations can learn Monte Carlo on their own. Coverage of topics such as variance reduction, pseudo-random number generation, Markov chain Monte Carlo, inverse Monte Carlo, and linear operator equations will make the book useful even to experienced Monte Carlo practitioners.

Guide to Essential Math

1st Edition
April 24, 2008
Sy M. Blinder
English
eBook
9 7 8 0 0 8 0 5 5 9 6 7 4

This book reminds students in junior, senior and graduate level courses in physics, chemistry and engineering of the math they may have forgotten (or learned imperfectly) which is needed to succeed in science courses. The focus is on math actually used in physics, chemistry and engineering, and the approach to mathematics begins with 12 examples of increasing complexity, designed to hone the student's ability to think in mathematical terms and to apply quantitative methods to scientific problems. By the author's design, no problems are included in the text, to allow the students to focus on their science course assignments.

The Synchronized Dynamics of Complex Systems

1st Edition
Volume 6
February 5, 2008
Stefano Boccaletti
Albert C.J. Luo + 1 more
English
eBook
9 7 8 0 0 8 0 5 6 0 4 2 7

The origin of the word synchronization is a greek root, meaning "to share the common time". The original meaning of synchronization has been maintained up to now in the colloquial use of this word, as agreement or correlation in time of different processes. Historically, the analysis of synchronization phenomena in the evolution of dynamical systems has been a subject of active investigation since the earlier days of physics. Recently, the search for synchronization has moved to chaotic systems. In this latter framework, the appearance of collective (synchronized) dynamics is, in general, not trivial. Indeed, a dynamical system is called chaotic whenever its evolution sensitively depends on the initial conditions. The above said implies that two trajectories emerging from two different closeby initial conditions separate exponentially in the course of the time. As a result, chaotic systems intrinsically defy synchronization, because even two identical systems starting from slightly different initial conditions would evolve in time in a unsynchronized manner (the differences in the systems' states would grow exponentially). This is a relevant practical problem, insofar as experimental initial conditions are never known perfectly. The setting of some collective (synchronized) behavior in coupled chaotic systems has therefore a great importance and interest.The subject of the present book is to summarize the recent discoveries involving the study of synchronization in coupled chaotic systems.Not always the word synchronization is taken as having the same colloquial meaning, and one needs to specify what synchrony means in all particular contexts in which we will describe its emergence.The book describes the complete synchronization phenomenon, both for low and for high dimensional situations, and illustrates possible applications in the field of communicating with chaos.Furthermore, the book summarizes the concepts of phase synchronization, lag synchronization, imperfect phase synchronization, and generalized synchronization, describing a general transition scenario between a hierarchy of different types of synchronization for chaotic oscillators.These concepts are extended to the case of structurally different systems, of uncoupled systems subjected to a common external source, of space extended nonlinearly evolving fields, and of dynamical units networking via a complex wiring of connections, giving thus a summary of all possible situations that are encountered in real life and in technology.

Neutron Fluctuations

1st Edition
October 5, 2007
Imre Pazsit + 1 more
English
Hardback
9 7 8 0 0 8 0 4 5 0 6 4 3
eBook
9 7 8 0 0 8 0 5 5 0 4 3 5

The transport of neutrons in a multiplying system is an area of branching processes with a clear formalism. Neutron Fluctuations presents an account of the mathematical tools used in describing branching processes, which are then used to derive a large number of properties of the neutron distribution in multiplying systems with or without an external source. In the second part of the book, the theory is applied to the description of the neutron fluctuations in nuclear reactor cores as well as in small samples of fissile material. The question of how to extract information about the system under study is discussed. In particular the measurement of the reactivity of subcritical cores, driven with various Poisson and non-Poisson (pulsed) sources, and the identification of fissile material samples, is illustrated. The book gives pragmatic information for those planning and executing and evaluating experiments on such systems.

Handbook of Mathematical Fluid Dynamics

1st Edition
Volume 4
April 4, 2007
S. Friedlander + 1 more
English
eBook
9 7 8 0 0 8 0 4 7 8 3 0 2

This is the fourth volume in a series of survey articles covering many aspects of mathematical fluid dynamics, a vital source of open mathematical problems and exciting physics.

Singularity and Dynamics on Discontinuous Vector Fields

1st Edition
Volume 3
July 7, 2006
Albert C.J. Luo
English
eBook
9 7 8 0 0 8 0 4 8 0 9 3 0

This book discussed fundamental problems in dynamics, which extensively exist in engineering, natural and social sciences. The book presented a basic theory for the interactions among many dynamical systems and for a system whose motions are constrained naturally or artificially. The methodology and techniques presented in this book are applicable to discontinuous dynamical systems in physics, engineering and control. In addition, they may provide useful tools to solve non-traditional dynamics in biology, stock market and internet network et al, which cannot be easily solved by the traditional Newton mechanics. The new ideas and concepts will stimulate ones’ thought and creativities in corresponding subjects. The author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in dynamics.

Bifurcation and Chaos in Complex Systems

1st Edition
Volume 1
June 30, 2006
Jian-Qiao Sun + 1 more
English
Hardback
9 7 8 0 4 4 4 5 2 2 2 9 0
eBook
9 7 8 0 0 8 0 4 6 2 6 6 0

The book presents the recent achievements on bifurcation studies of nonlinear dynamical systems. The contributing authors of the book are all distinguished researchers in this interesting subject area. The first two chapters deal with the fundamental theoretical issues of bifurcation analysis in smooth and non-smooth dynamical systems. The cell mapping methods are presented for global bifurcations in stochastic and deterministic, nonlinear dynamical systems in the third chapter. The fourth chapter studies bifurcations and chaos in time-varying, parametrically excited nonlinear dynamical systems. The fifth chapter presents bifurcation analyses of modal interactions in distributed, nonlinear, dynamical systems of circular thin von Karman plates. The theories, methods and results presented in this book are of great interest to scientists and engineers in a wide range of disciplines. This book can be adopted as references for mathematicians, scientists, engineers and graduate students conducting research in nonlinear dynamical systems.

Mathematical Statistical Physics

1st Edition
Volume 83
June 27, 2006
Anton Bovier + 4 more
English
Hardback
9 7 8 0 4 4 4 5 2 8 1 3 1
eBook
9 7 8 0 0 8 0 4 7 9 2 3 1

The proceedings of the 2005 les Houches summer school on Mathematical Statistical Physics give and broad and clear overview on this fast developing area of interest to both physicists and mathematicians.

Life Sciences

Physical Sciences & Engineering

Social Sciences & Humanities

Health