Kategoria BISAC: Science >> Physics - Mathematical & Computational

This book provides an advanced introduction to extended theories of quantum field theory and algebraic topology, including Hamiltonian quantization associated with some geometrical constraints, symplectic embedding and Hamilton-Jacobi quantization and Becci-Rouet-Stora-Tyutin (BRST) symmetry, as well as de Rham cohomology. It offers a critical overview of the research in this area and unifies the existing literature, employing a consistent notation.

Although the results presented apply in principle to all alternative quantization schemes, special emphasis is placed on the BRST...

This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations.The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks and a comprehensive introduction to...

This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its...

This book covers classical and modern aerodynamics, theories and related numerical methods, for senior and first-year graduate engineering students, including:
-The classical potential (incompressible) flow theories for low speed aerodynamics of thin airfoils and high and low aspect ratio wings.
- The linearized theories for compressible subsonic and supersonic aerodynamics.
- The nonlinear transonic small disturbance potential flow theory, including supercritical wing sections, the extended transonic area rule with lift effect, transonic lifting line and swept or oblique wings...

This book covers the major problems of turbulence and turbulent processes, including physical phenomena, their modeling and their simulation.

After a general introduction in Chapter 1 illustrating many aspects dealing with turbulent flows, averaged equations and kinetic energy budgets are provided in Chapter 2. The concept of turbulent viscosity as a closure of the Reynolds stress is also introduced. Wall-bounded flows are presented in Chapter 3 and aspects specific to boundary layers and channel or pipe flows are also pointed out. Free shear flows, namely free jets and wakes, are...

The book is dedicated to the construction of particular solutions of systems of ordinary differential equations in the form of series that are analogous to those used in Lyapunov's first method. A prominent place is given to asymptotic solutions that tend to an equilibrium position, especially in the strongly nonlinear case, where the existence of such solutions can't be inferred on the basis of the first approximation alone.

The book is illustrated with a large number of concrete examples of systems in which the presence of a particular solution of a certain class is related...

The goal of this book is to describe the most powerful methods for evaluating multiloop Feynman integrals that are currently used in practice. This book supersedes the author's previous Springer book "Evaluating Feynman Integrals" and its textbook version "Feynman Integral Calculus." Since the publication of these two books, powerful new methods have arisen and conventional methods have been improved on in essential ways. A further qualitative change is the fact that most of the methods and the corresponding algorithms have now been implemented in computer codes which are often...

Dieses bekannte Lehrbuch stellt zunachst die fur die Elektrodynamik benotigten mathematischen Grundlagen bereit, um die Vermischung mathematischer Schwierigkeiten mit Problemen physikalischer Natur zu vermeiden. Es folgt eine sorgfaltige Einfuhrung in die physikalischen Grundgesetze der Elektrodynamik bis hin zu den vollen Maxwell-Gleichungen. In den weiteren Kapiteln werden, allmahlich vom Leichteren zum Schwereren fortschreitend, unter anderem die Konsequenzen der Maxwell-Gleichungen aufgezeigt und die Theorie elektromagnetischer Wellen behandelt. Das Buch ist auf die Bedurfnisse von...

This textbook explores both the theoretical foundation of the Finite Volume Method (FVM) and its applications in Computational Fluid Dynamics (CFD). Readers will discover a thorough explanation of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, along with a detailed examination of the components needed for the development of a collocated unstructured pressure-based CFD solver. Two particular CFD codes are explored. The first is uFVM, a three-dimensional unstructured pressure-based finite volume academic CFD code, implemented within...