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From Hyperbolic Systems to Kinetic Theory : A Personalized Quest
Equations of state are not always effective in continuum mechanics. Maxwell and Boltzmann created a kinetic theory of gases, using classical mechanics. How could they derive the irreversible Boltzmann equation from a reversible Hamiltonian framework? By using probabilities, which destroy physical reality! Forces at distance are non-physical as we know from Poincaré's theory of relativity. Yet Maxwell and Boltzmann only used trajectories like hyperbolas, reasonable for rarefied gases, but wrong without bound trajectories if the "mean free path between collisions" tends to 0. Tartar relies on his H-measures, a tool created for homogenization, to explain some of the weaknesses, e.g. from quantum mechanics: there are no "particles", so the Boltzmann equation and the second principle, can not apply. He examines modes used by energy, proves which equation governs each mode, and conjectures that the result will not look like the Boltzmann equation, and there will be more modes than those indexed by velocity!
From Geometry to quantum mechanics : In Honor of Hideki Omori
This volume is composed of invited expository articles by well-known mathematicians in differential geometry and mathematical physics that have been arranged in celebration of Hideki Omori's recent retirement from Tokyo University of Science and in honor of his fundamental contributions to these areas.The papers focus on recent trends and future directions in symplectic and Poisson geometry, global analysis, infinite-dimensional Lie group theory, quantizations and noncommutative geometry, as well as applications of partial differential equations and variational methods to geometry.
Free Surface Flows under Compensated Gravity Conditions
Considers the behavior of fluids in a low-gravity environment with special emphasis on application in PMD (propellant management device) systems . This book treats three different flow problems with analytical, numerical and experimental means: the transient contour change between two static surface configurations (free surface oscillations), the capillary rise in tubes (capillary rise), and the flow through open capillary channels (choking).
Free Energy and Self-Interacting Particles
This book examines a system of parabolic-elliptic partial differential eq- tions proposed in mathematical biology, statistical mechanics, and chemical kinetics. In the context of biology, this system of equations describes the chemotactic feature of cellular slime molds and also the capillary formation of blood vessels in angiogenesis. There are several methods to derive this system. One is the biased random walk of the individual, and another is the reinforced random walk of one particle modelled on the cellular automaton. In the context of statistical mechanics or chemical kinetics, this system of equations describes the motion of a mean field of many particles, interacting under the gravitational inner force or the chemical reaction
Free Boundary Problems : Theory and Applications
This book gathersa collection of refereed articles containing original result srepo- ing the recent originalcontributions of the lectures and communications presented at the Free Boundary Problems (FBP2005) Conference that took place at the University of Coimbra, Portugal, from 7 to 12 of June 2005. They deal with the Mathematics of a broad class of models and problems involving nonlinear partial diferentialequationsarising inPhysics, Engineering, Biology and Finance. Among the main topics, the talks considered free boundary problems in biomedicine, in porous media, in thermodynamic modeling.
Fracture of Nano and Engineering Materials and Structures; Proceedings of the 16th European Conference of Fracture, Alexandroupolis, Greece, July 3-7, 2006
The 16th European Conference of Fracture (ECF16) was held in Greece, July, 2006. Emphasis was given to the failure of nanostructured materials and nanostructures including micro- and nano-electromechanical systems (MEMS and NEMS).
Fracture Mechanics of Ceramics ; Active Materials, Nanoscale Materials, Composites, Glass, and Fundamentals
The 8th International Symposium on fracture mechanics of ceramics was held in on the campus of the University of Houston, Houston, TX, USA, on February 25-28, 2003. With the natural maturing of the fields of structural ceramics, this symposium focused on nano-scale materials, composites, thin films and coatings as well as glass. The symposium also addressed new issues on fundamentals of fracture mechanics and contact mechanics, and a session on reliability and standardization.
Fracture Mechanics ; Vol.123 : An Introduction
The second edition of the book contains four new chapters in addition to the ten chapters of the first edition. The fourteen chapters of the book cover the basic principles and traditional applications, as well as the latest developments of fracture mechanics as applied to problems of composite materials, thin films, nanoindentation and cementitious materials. Thus the book provides an introductory coverage of the traditional and contemporary applications of fracture mechanics in problems of utmost technological importance.
Fracture Mechanics : With an Introduction to Micromechanics
Concerned with the fundamental concepts and methods of fracture mechanics and micromechanics, Fracture Mechanics primarily focuses on the mechanical description of fracture processes; however, material specific aspects are also discussed. The presentation of continuum mechanical and phenomenological foundations is followed by an introduction into classical failure hypotheses. A major part of the book is devoted to linear elastic and elastic-plastic fracture mechanics. Further subjects are creep fracture, dynamic fracture mechanics, damage mechanics, probabilistic fracture mechanics, failure of thin films and fracture of piezoelectric materials. The book also contains an extensive introduction into micromechanics.
Fracture Mechanics : Inverse Problems and Solutions
This book presents, in a unified manner, a variety of topics in Continuum and Fracture Mechanics: energy methods, conservation laws, mathematical methods to solve two-dimensional and three-dimensional crack problems.
Foundations of Quantum Theory : From Classical Concepts to Operator Algebras
This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory.
Foundations of Quantum Physics
Intended to be used as a textbook for an introductory course in quantum mechanics at the undergraduate level, Foundations of Quantum Physics is also meant to be retained by the student for later use as a reference. The presentation begins with the solution of some basic quantum mechanical problems. The emphasis is on those features of the solutions that are unique to quantum physics. It is only after these aspects of quantum physics are thoroughly discussed that the mathematical formalism of quantum mechanics is presented and related to the previous chapters. Throughout the book, the emphasis is on understanding the concepts and relating them to known phenomena.
Foundations of plasma physics for physicists and mathematicians
Foundations of Plasma Physics for Physicists and Mathematicians covers the basic physics underlying plasmas and describes the methodology and techniques used in both plasma research and other disciplines such as optics and fluid mechanics.
Formulas of Acoustics
This collection of formulas has been written by applied scientists and industrial engineers for design professionals and students who work in engineering acoustics. It is subdivided into the most important fields of applied acoustics, each dealing with a well-defined type of problem.
Football Traumatology : Current Concepts : From Prevention to Treatment
Lesions associated with football are on the increase and their typology has also changed over the years. Football, like many other sports, has undergone major changes: the increase in the intensity and speed of the game, the modern training methodologies, the technical and tactical innovations are all factors contributing to increased risks of traumatic injury. The footballers, the trainers, the sport's medical staff are asking for greater information and knowledge on the traumatic lesions associated with this sport. The primary role of those who are concerned with the health of footballers is to enforce preventive measures to reduce wherever possible the risks of trauma.
Fluid-structure interaction : Modelling, simulation, optimisation
Fluid-structure interactions (FSI), that is interactions of some movable or deformable structure with an internal or surrounding fluid flow, are among the most important and, with respect to both modelling and computational issues, the most challenging multi-physics problems. The variety of FSI occurrences is abundant and ranges from tent-roofs to micropumps, from parachutes via airbags to blood flow in arteries.
Fluid Mechanics of Flow Metering
This book addresses two major fluid mechanical problems in flow metering: the analysis of signal generation in turbulent pipe flow, which explains the function of the meter beyond a simple calibration, and the possible use of a meter in non-developed flows. These problems are investigated with reference to, and examples from, a variety of meters, e.g. ultrasound cross-correlation meters, vortex meters, and turbine meters. Studying these problems requires consideration of specific phenomena in turbulent non-developed pipe flow, as caused by installations, and finding special solutions with signal processing, both of which are included in the book.
Fluid Mechanics : With Problems and Solutions, and an Aerodynamics Laboratory
This textbook introduces the major branches of fluid mechanics of incompressible and compressible media, the basic laws governing their flow, and gasdynamics. "Fluid Mechanics" demonstrates how flows can be classified and how specific engineering problems can be identified, formulated and solved, using the methods of applied mathematics. The material is elaborated in special applications sections by more than 200 exercises and separately listed solutions. The final section comprises the Aerodynamics Laboratory, an introduction to experimental methods treating eleven flow experiments. This class-tested textbook offers a unique combination of introduction to the major fundamentals, many exercises, and a detailed description of experiments.
Fluid Mechanics : An Introduction to the Theory of Fluid Flows
Advancements of fluid flow measuring techniques and of computational methods have led to new ways to treat laminar and turbulent flows. These methods are extensively used these days in research and engineering practise. This also requires new ways to teach the subject to students at higher educational institutions in an introductory manner. The book provides the knowledge to students in engineering and natural science needed to enter fluid mechanics applications in various fields. Analytical treatments are provided, based on the Navier-Stokes equations. Introductions are also given into numerical and experimental methods applied to flows. The main benefit the reader will derive from the book is a sound introduction into all aspects of fluid mechanics covering all relevant subfields.
Fluid Mechanics
This successful textbook emphasizes the unified nature of all the disciplines of Fluid Mechanics as they emerge from the general principles of continuum mechanics. The different branches of Fluid Mechanics, always originating from simplifying assumptions, are developed according to the basic rule: from the general to the specific.
