Mathematical physics Books

Materials sciences relate the macroscopic properties of materials to their microscopic structure and postulate the need for holistic multiscale research. The investigation of shape memory alloys is a prime example in this regard. This particular class of...

Central to this thesis is the characterisation and exploitation of electromagnetic properties of light in imaging and measurement systems. To this end an information theoretic approach is used to formulate a hitherto lacking, quantitative definition of...

Local Dynamics: Piecewise Isometries of A Square.- Symbolic Dynamics.- Global Dynamics.- Model of Hamiltonian Round-off.

Conformal invariance has been a spectacularly successful tool in advancing our understanding of the two-dimensional phase transitions found in classical systems at equilibrium. This volume sharpens our picture of the applications of conformal invariance,...

Quarks are the main constituents of protons and neutrons and hence are important building blocks of all the matter that surrounds us. However, quarks have the intriguing property that they never appear as isolated single particles but only in bound...

The production of heavy quarks in high-energy experiments offers a rich field to study, both experimentally and theoretically. Due to the additional quark mass, the description of these processes in the framework of perturbative QCD is much more...

This work addresses time-delay in complex nonlinear systems and, in particular, its applications in complex networks; its role in control theory and nonlinear optics are also investigated. Delays arise naturally in networks of coupled systems due to...

At extremely low temperatures, clouds of bosonic atoms form what is known as a Bose-Einstein condensate. Recently, it has become clear that many different types of condensates -- so called fragmented condensates -- exist. In order to tell whether...

Density functional theory (DFT) has become the standard workhorse for quantum mechanical simulations as it offers a good compromise between accuracy and computational cost. However, there are many important systems for which DFT performs very poorly,...

This book is a snapshot of current research in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and multiphysics models...

This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure-the Schrödinger-Virasoro algebra. Just as Poincaré invariance or conformal (Virasoro) invariance play a key rôle in...

Commencing with a self-contained overview of atomic collision theory, this monograph presents recent developments of R-matrix theory and its applications to a wide-range of atomic molecular and optical processes. These developments include the electron...

This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians". This new edition will appear in two volumes, the present first volume presents the basic results and...

The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2009), and provides an overview of the depth and breadth of the activities within this...

This volume contains the extended version of selected talks given at the international research workshop "Coping with Complexity: Model Reduction and Data Analysis", Ambleside, UK, August 31 - September 4, 2009. The book is deliberately broad in scope...

This is a book describing electronic structure theory and application within the framework of a methodology implemented in the computer code RSPt. In 1986, when the code that was to become RSPt was developed enough to be useful, it was one of the ?rst...

Resonances: Models and Captures.- The Lyapunov Characteristic Exponents and Their Computation.- Asteroid Dynamical Families.- An Introduction to the Dynamics of Trojan Asteroids.- The Physics of Asteroids and Their Junction with Dynamics.- The Gaia...

Ever since the historical discovery of the now-famous Lorenz system in 1963, a large number of nonlinear systems that can produce chaos have been - served,constructedandanalyzed. Infact,chaostheoryhasbecomeindispe- able for...

Modern techniques from quantum field theory are applied in this work to the description of ultracold quantum gases. This leads to a unified description of many phenomena including superfluidity for bosons and fermions, classical and quantum phase...

Simulation of materials at the atomistic level is an important tool in studying microscopic structures and processes. The atomic interactions necessary for the simulations are correctly described by Quantum Mechanics, but the...

This book contains contributions by some of the leading researchers in the area of grey systems theory and applications. All the papers included in this volume are selected from the contributions physically presented at the...

General circulation models (GCMs), which define the fundamental dynamics of atmospheric circulation, are nowadays used in various fields of atmospheric science such as weather forecasting, climate predictions and environmental...

This research addresses delay effects in nonlinear systems, which are ubiquitous in various fields of physics, chemistry, biology, engineering, and even in social and economic systems. They may arise as a result of processing...

Part I An ABC on Compositionality.- Part II Manifestations of Linearity.- Part III More Example Applications.- Part IV Informatic Geometry.- Part V. Spatio-Temporal Geometry.- Part VI Geometry and Topology in Computation.

Throughout my whole career including student time I have had a feeling that leaning and teaching electromagnetism, especially macroscopic Maxwell equations (M-eqs) is dif?cult. In order to make a good use of these equations, it seemed necessary to be...

The interest in the field of active flow control (AFC) is steadily increasing. In - cent years the number of conferences and special sessions devoted to AFC org- ized by various institutions around the world continuously rises...

Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry,...

These are the proceedings of the 19th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linear or nonlinear systems of algebraic...

Over last decades low-dimensional materials are in focus of physics and chemistry as well as of material and other natural sciences. Like Vitaly Ginzburg has foreseen 30 years ago, low dimensionality offers physical phenomena...

Preface "In aircraft design, efficiency is determined by the ability to accurately and rel- bly predict the occurrence of, and to model the development of, turbulent flows. Hence, the main objective in industrial computational...

In 2003 the German Research Foundation established a new priority programme on the subject of "Imaging Measurement Methods for Flow Analysis" (SPP 1147). This research programme was based on the fact that experimental ?ow...

Materials Properties.- Computer Simulation Studies in Condensed Matter Physics: An Introduction.- Accelerated Molecular-Dynamics Simulation of Thin Film Growth.- Simulating the Interaction of High Intensity Optical Pulses with Nanostructured Optical...

Nonrelativistic Collisions.- First Order Considerations.- Considerations Beyond First Order Perturbation Theory.- Relativistic Collisions.- to Relativistic Collisions.- Descriptions of Collisions Within the First Order Approximation in the...

Integrable Hamiltonian Hierarchies: Spectral Methods.- The Lax Representation and the AKNS Approach.- The Direct Scattering Problem for theZakharov-Shabat System.- The Inverse Scattering Problem for the Zakharov-Shabat System.- The Generalized Fourier...

Fundamentals.- Multiscale Computational Materials Science.- Mathematical and Physical Prerequisites.- Fundamentals of Numerical Simulation.- Computational Methods on Multiscales.- Computational Methods on Electronic/Atomistic Scale.- Computational...

The Concept of Symmetry.- Science Is Founded on Symmetry.- Symmetry in Physics.- The Symmetry Principle.- Application of Symmetry.- Approximate Symmetry, Spontaneous Symmetry Breaking.- Cosmic Considerations.- The Mathematics of Symmetry: Group Theory.-...

This book contains papers presented at the fifth and sixth Teraflop Workshop. It presents the state-of-the-art in high performance computing and simulation on modern supercomputer architectures. It covers trends in hardware and...

In June of 2002, over 500 professors, students and researchers met in Boston, Massachusetts for the Fourth International Conference on Complex Systems. The attendees represented a remarkably diverse collection of fields:...

Experimental evidence in humans and other mammalians indicates that complex neurodynamics is crucial for the emergence of higher-level intelligence. Dynamical neural systems with encoding in limit cycle and non-convergent...

Generalities and methods.- A Few Illustrative Examples of CFD-based Optimization.- Mathematical Aspects of CFD-based Optimization.- Adjoint Methods for Shape Optimization.- Specific Applications of CFD-based Optimization to Engineering Problems.-...

Manifolds.- Topology of Riemann Surfaces.- Analytic Structure.- Diffierentials and Integration.- Tori and Jacobians.- Projective Varieties.- Moduli Spaces of Curves.- Vector Bundles, Sheaves and Cohomology.- The Theorem of Riemann-Roch for Line Bundles.-...

to FPU.- Dynamics of Oscillator Chains.- Role of Chaos for the Validity of Statistical Mechanics Laws: Diffusion and Conduction.- The Fermi-Pasta-Ulam Problem and the Metastability Perspective.- Resonance, Metastability and Blow up in FPU.- Center...

This novel approach is presented for the first time in book form. The author demonstrates that fundamental concepts and methods from phenomenological particle physics can be derived rigorously from well-defined general...

has been in the of a Symmetry major ingredient development quantum perturba tion and it is a basic of the of theory, ingredient theory integrable (Hamiltonian and of the the use in context of non Hamiltonian) systems; yet,...

This book offers the first comprehensive account of the new method of density matrix renormalization. Recent years have seen enormous progress in the numerical treatment of low-dimensional quantum sytems. With this new...

This book explores two important aspects of the optimal control of oscillatory systems: the initiation of optimal oscillatory regimes and control possibilities for random disturbances. The main content of the book is based upon...