Series:De Gruyter Studies in Mathematical Physics 51
The Phase Field Crystal (PFC) model incorporates microscopic structural details into a mesoscopic continuum theory. Methods for fast propagation of PFC interfaces are discussed in this book. They can handle a wide range of thermal gradients, supersaturations and supercoolings, including applications such as selective laser melting. The reader will find theoretical treatment in the first half, while the latter half discusses numerical models.
xii, 123 pages
Language: English
Type of Publication: Monograph
Chemistry > Physical Chemistry
Materials Sciences > Thin Films, Surfaces and Interfaces
Materials Sciences > Modeling and Simulations
Physics > Condensed Matter Physics
Oxford Studies in Probability
Hardback
Published: 28 February 2019 (Estimated)
496 Pages
234x156mm
ISBN: 9780198826941
Gives the tools for dealing with dependent structures to obtain normal approximations, and applies them to various examples
Presents the state-of-the-art and new progress concerning the analysis of stochastic processes, and exhibits the importance of these different structures through a large variety of examples
Tools to analyse a variety of models are clearly and elegantly provided, allowing for broad discipline application and ease of dissemination
The different notions of dependence are well separated in the book through clearly identified chapters
1: Introduction to Stochastic Processes
2: Moment Inequalities and Gaussian Approximation for Martingales
3: Moment Inequalities via Martingale Methods
4: Gaussian Approximation via Martingale Methods
5: Dependence coefficients for sequences
6: Moment Inequalities and Gaussian Approximation for Mixing Sequences
7: Weakly associated random variables : L2-bounds and approximation by independent structures
8: Maximal moment inequalities for weakly negatively dependent variables
9: Gaussian approximation under asymptotic negative dependence
10: Examples of Stationary Sequences with Approximate Negative Dependence
11: Stationary Sequences in a Random Time Scenery
12: Linear Processes
13: Random walk in random scenery
14: Reversible Markov chains
15: Functional central limit theorem for empirical processes
16: Application to the uniform laws of large numbers for dependent processes
17: Examples and Counterexamples
Published: 20 February 2019 (Estimated)
256 Pages
246x171mm
ISBN: 9780198836285
Provides a unique pedagogical introduction to clifford algebras with a focus on spinors
Bridges a gap between physics and mathematics
Merges both applications and the formal approach
Includes various worked examples throughout
An in depth exploration of how Clifford algebras and spinors have been sparking collaboration and bridging the gap between Physics and Mathematics. This collaboration has been the consequence of a growing awareness of the importance of algebraic and geometric properties in many physical phenomena, and of the discovery of common ground through various touch points: relating Clifford algebras and the arising geometry to so-called spinors, and to their three definitions (both from the mathematical and physical viewpoint). The main points of contact are the representations of Clifford algebras and the periodicity theorems. Clifford algebras also constitute a highly intuitive formalism, having an intimate relationship to quantum field theory. The text strives to seamlessly combine these various viewpoints and is devoted to a wider audience of both physicists and mathematicians. Among the existing approaches to Clifford algebras and spinors this book is unique in that it provides a didactical presentation of the topic and is accessible to both students and researchers. It emphasizes the formal character and the deep algebraic and geometric completeness, and merges them with the physical applications.
1: Preliminaries
2: Exterior Algebra and Grassmann Algebra
3: Geometric or Clifford Algebra
4: Classification and Representation of the Clifford Algebras
5: Clifford Algebras and Associated Groups
6: Spinors
Appendix: The Standard 2-Component Spinor Formalism
Hardcover
ISBN 9780691155791
864 pp. 7 x 10
87 b/w illus. 12 tables.
forthcoming April 2019
The essential introduction to modern string theory?now fully expanded and revised
String Theory in a Nutshell is the definitive introduction to modern string theory. Written by one of the world’s leading authorities on the subject, this concise and accessible book starts with basic definitions and guides readers from classic topics to the most exciting frontiers of research today. It covers perturbative string theory, the unity of string interactions, black holes and their microscopic entropy, the AdS/CFT correspondence and its applications, matrix model tools for string theory, and more. It also includes 600 exercises and serves as a self-contained guide to the literature.
This fully updated edition features an entirely new chapter on flux compactifications in string theory, and the chapter on AdS/CFT has been substantially expanded by adding many applications to diverse topics. In addition, the discussion of conformal field theory has been extensively revised to make it more student-friendly.
The essential one-volume reference for students and researchers in theoretical high-energy physics
Now fully expanded and revised
Provides expanded coverage of AdS/CFT and its applications, namely the holographic renormalization group, holographic theories for Yang-Mills and QCD, nonequilibrium thermal physics, finite density physics, and entanglement entropy
Ideal for mathematicians and physicists specializing in theoretical cosmology, QCD, and novel approaches to condensed matter systems
An online illustration package is available to professors
Elias Kiritsis is director of research at the French National Center for Scientific Research and professor of physics at the University of Crete.
Hardcover
ISBN 9780691181301
232 pp. 6 1/8 x 9 1/4
79 b/w illus.
forthcoming May 2019
An essential introduction to the analysis and verification of control systems software
The verification of control systems software is critical to a host of technologies and industries, from aeronautics and medical technology to the cars we drive?the failure of controller software can cost people their lives. In this authoritative and accessible book, Pierre-Loic Garoche provides control engineers and computer scientists with an indispensable introduction to the formal techniques for analyzing and verifying this important class of software.
Too often, control engineers are unaware of the issues surrounding the verification of software, while computer scientists tend to be unfamiliar with the specificities of controller software. Garoche provides a unified approach especially geared to graduate students in both fields, covering formal verification methods as well as the design and verification of controllers. He presents a wealth of new verification techniques for performing exhaustive analysis of controller software. These include new means to compute nonlinear invariants, the use of convex optimization tools, and methods for dealing with numerical imprecisions such as floating point computations occurring in the analyzed software.
As the autonomy of these systems continues to increase?such as in autonomous cars, drones, and satellites and landers?the numerical functions in critical systems are growing ever more advanced. The techniques presented here are essential to support the formal analysis of the controller software being used in these new and emerging technologies.
Pierre-Loic Garoche is senior research scientist at ONERA, France’s national aerospace research center.
Paperback
ISBN 9780691161525
280 pp. 5 1/2 x 8 1/2
84 b/w illus.
forthcoming August 2019
Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, an important and exciting area that has shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview.
In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder.
Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.
David P. Feldman is professor of physics and mathematics at the College of the Atlantic. He is the author of Chaos and Fractals: An Elementary Introduction.