Kategoria BISAC: Science >> Physics - Mathematical & Computational

Dr. Charles Legendy's Circuits in the Brain: A Model of Shape Processing in the Primary Visual Cortex is published at a time marked by unprecedented advances in experimental brain research which are, however, not matched by similar advances in theoretical insight. For this reason, the timing is ideal for the appearance of Dr. Legendy's book, which undertakes to derive certain global features of the brain directly from the neurons.

Circuits in the Brain, with its "relational firing" model of shape processing, includes a step-by-step development of a set of...

Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a...

This book presents the state-of-the-art in simulation on supercomputers. Leading researchers present results achieved on systems of the Stuttgart High Performance Computing Center in 2007. The reports cover all fields of computational science and engineering, with emphasis on industrially relevant applications. Presenting results for both vector-based and microprocessor-based systems, the book allows comparison between performance levels and usability of various architectures.

Form Symmetries and Reduction of Order in Difference Equations presents a new approach to the formulation and analysis of difference equations in which the underlying space is typically an algebraic group. In some problems and applications, an additional algebraic or topological structure is assumed in order to define equations and obtain significant results about them. Reflecting the author s past research experience, the majority of examples involve equations in finite dimensional Euclidean spaces.

The book first introduces difference equations on groups,...

The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell's inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of...

Ten years after a 1989 meeting of number theorists and physicists at the Centre de Physique des Houches, a second event focused on the broader interface of number theory, geometry, and physics. This book is the first of two volumes resulting from that meeting. Broken into three parts, it covers Conformal Field Theories, Discrete Groups, and Renormalization, offering extended versions of the lecture courses and shorter texts on special topics.

The LES-method is rapidly developing in many practical applications in engineering

The mathematical background is presented here for the first time in book form by one of the leaders in the field

The relation between mathematics and physics has a long history, in which the role of number theory and of other more abstract parts of mathematics has recently become more prominent. More than 10 years after a first meeting between number theorists and physicists at the Centre de Physique des Houches, a second two-week event focused on the broader interface of number theory, geometry, and physics. This book collects the material presented at this meeting.

Soft matter science is nowadays an acronym for an increasingly important class of materials, which ranges from polymers, liquid crystals, colloids up to complex macromolecular assemblies, covering sizes from the nanoscale up the microscale. Computer simulations have proven as an indispensable, if not the most powerful, tool to understand properties of these materials and link theoretical models to experiments. In this first volume of a small series recognized leaders of the field review advanced topics and provide critical insight into the state-of-the-art methods and scientific questions...

This third edition includes the corrections made by the late C. Truesdell in his personal copy. It is annotated by S. Antman who describes the monographs genesis and the impact it has made on the modern development of mechanics. Originally published as Volume III/3 of the famous Encyclopedia of Physics in 1965, this book describes and summarizes "everything that was both known and worth knowing in the field at the time." It also has greatly contributed to the unification and standardization of the concepts, terms and notations in the field.

The main aim of this book is to develop the methods of Global Analysis and of Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as quite distant from each other and requiring different methods of investigation. Among those areas we mention classical mechanics on non-linear configuration spaces, some problems of statistical and quantum physics, hydrodynamics, etc. The idea, yielding the unification of these topics, is based on the use of a geometrically invariant form of...

The book project was launched to access the latest research related to chaos applications in intelligent computing where researchers from all over the world provide the necessary coverage of the mentioned field. The primary objective of this project was to assemble as much research coverage as possible related to the field by defining the latest innovative technologies and providing the most comprehensive list of research references. The coverage of this book provides strength to this reference resource for both researchers and also decision makers in obtaining a greater understanding of...