Part of Cambridge Monographs on Mathematical Physics
Publication planned for: December 2018
availability: Not yet published - available from December 2018
format: Hardback
isbn: 9781107107328
During the past two decades the gravitational asymptotic safety scenario has undergone a major transition from an exotic possibility to a serious contender for a realistic theory of quantum gravity. It aims at a mathematically consistent quantum description of the gravitational interaction and the geometry of spacetime within the realm of quantum field theory, which keeps its predictive power at the highest energies. This volume provides a self-contained pedagogical introduction to asymptotic safety, and introduces the functional renormalization group techniques used in its investigation, along with the requisite computational techniques. The foundational chapters are followed by an accessible summary of the results obtained so far. It is the first detailed exposition of asymptotic safety, providing a unique introduction to quantum gravity and it assumes no previous familiarity with the renormalization group. It serves as an important resource for both practising researchers and graduate students entering this maturing field.
Part of Cambridge Studies in Advanced Mathematics
Publication planned for: October 2018
availability: Not yet published - available from October 2018
format: Hardback
isbn: 9781108473842
This is Volume 2 of a two-volume book that provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. The two-volume book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. Volume 2 features critical results, which are proven carefully and in detail, including automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics. Volume 1 features discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automorphic forms, and also as a resource for researchers working in automorphic forms, analytic number theory, and related fields.
Part of Cambridge Texts in Applied Mathematics
Publication planned for: October 2018
format: Hardback
isbn: 9781107024649
format: Paperback
isbn: 9781107695931
dimensions: 247 x 174 mm
contains: 57 b/w illus. 75 exercises
availability: Not yet published - available from October 2018
This is an introduction to the dynamics of fluids at small scales, the physical and mathematical underpinnings of Brownian motion, and the application of these subjects to the dynamics and flow of complex fluids such as colloidal suspensions and polymer solutions. It brings together continuum mechanics, statistical mechanics, polymer and colloid science, and various branches of applied mathematics, in a self-contained and integrated treatment that provides a foundation for understanding complex fluids, with a strong emphasis on fluid dynamics. Students and researchers will find that this book is extensively cross-referenced to illustrate connections between different aspects of the field. Its focus on fundamental principles and theoretical approaches provides the necessary groundwork for research in the dynamics of flowing complex fluids.
November 8, 2017 by Chapman and Hall/CRC
Reference - 248 Pages - 40 B/W Illustrations
ISBN 9781498782098 - CAT# K30027
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Provides a comprehensive modelling guide to wave propagation in elastic metamaterials
Brings novel insights into the dynamic response of solids, which include multi-scale resonators. The book is based on the results of original research.
Addresses the very rare topic of the dynamic response of "disintegrating solids", using advanced tools of singular perturbation analysis
Includes a step-by-step explanation of dynamic anisotropy and directional localisation for structured solids. This also includes analysis of so-called stop-band Greenfs functions
Presents cloaking as a method of channelling of waves around obstacles. Special attention is also given to methods of cloaking for flexural waves in elastic plates.
Mathematical Modelling of Waves in Multi-Scale Structured Media presents novel analytical and numerical models of waves in structured elastic media, with emphasis on the asymptotic analysis of phenomena such as dynamic anisotropy, localisation, filtering and polarisation as well as on the modelling of photonic, phononic, and platonic crystals.
September 11, 2018 Forthcoming by CRC Press
Reference - 456 Pages
ISBN 9781138332294 - CAT# K393112
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Provides an essential background in multivalued analysis
Suitable for an advanced or seminar course as well as a standalone research source
Develops ideas such as the Vietoris topology, a variety of fixed point theorems including those of Kakutani, Fan, Leray and Schauder
Covers related topics on systems of impulsive differential equations
Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis.