Quasi-Gas Dynamic Equations


Book Description

The monograph is devoted to modern mathematical models and numerical methods for solving gas- and ?uid-dynamic problems based on them. Two interconnected mathematical models generalizing the Navier–Stokes system are presented; they differ from the Navier–Stokes system by additional dissipative terms with a small parameter as a coef?cient. The new models are called the quasi-gas-dynamic and quasi-hydrodynamic equations. Based on these equations, effective ?nite-difference algorithms for calculating viscous nonstationary ?ows are constructed and examples of numerical computations are presented. The universality, the ef?ciency, and the exactness of the algorithms constructed are ensured by the ful?llment of integral conservation laws and the theorem on entropy balance for them. The book is a course of lectures and is intended for scientists and engineers who deal with constructing numerical algorithms and performing practical calculations of gas and ?uid ?ows and also for students and postgraduate students who specialize in numerical gas and ?uid dynamics.




From Particle Systems to Partial Differential Equations II


Book Description

This book focuses on mathematical problems concerning different applications in physics, engineering, chemistry and biology. It covers topics ranging from interacting particle systems to partial differential equations (PDEs), statistical mechanics and dynamical systems. The purpose of the second meeting on Particle Systems and PDEs was to bring together renowned researchers working actively in the respective fields, to discuss their topics of expertise and to present recent scientific results in both areas. Further, the meeting was intended to present the subject of interacting particle systems, its roots in and impacts on the field of physics and its relation with PDEs to a vast and varied public, including young researchers. The book also includes the notes from two mini-courses presented at the conference, allowing readers who are less familiar with these areas of mathematics to more easily approach them. The contributions will be of interest to mathematicians, theoretical physicists and other researchers interested in interacting particle systems, partial differential equations, statistical mechanics, stochastic processes, kinetic theory, dynamical systems and mathematical modeling aspects.




Rarefied Gas Dynamics


Book Description

This volume is concerned with the properties and flows of rarefied gases and with the interactions of these gases with solid surfaces and force fields. Topics include: low density aerodynamics, jets, plumes, and propulsion clusters, aerosols, and internal flows and vacuum systems.







From Particle Systems to Partial Differential Equations


Book Description

"This book addresses mathematical problems motivated by various applications in physics, engineering, chemistry and biology. It gathers the lecture notes from the mini-course presented by Jean-Christophe Mourrat on the construction of the various stochastic “basic” terms involved in the formulation of the dynamic Ö4 theory in three space dimensions, as well as selected contributions presented at the fourth meeting on Particle Systems and PDEs, which was held at the University of Minho’s Centre of Mathematics in December 2015. The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations, offering them a forum to present their recent results and discuss their topics of expertise. The meeting was also intended to present to a vast and varied public, including young researchers, the area of interacting particle systems, its underlying motivation, and its relation to partial differential equations. The book will be of great interest to probabilists, analysts, and all mathematicians whose work focuses on topics in mathematical physics, stochastic processes and differential equations in general, as well as physicists working in statistical mechanics and kinetic theory.”




Adiabatic Waves in Liquid-Vapor Systems


Book Description

The planning for the IUTAM Symposium on Adiabatic Waves in Liquid-Vapor Systems began in May of 1986 in G5ttingen. The Symposium was held in August of 1989 in the Max-Planck-Institut fUr Str5mungsforschung. The invitations to participants suggested that the written papers concern Fast Adiabatic Phase Changes in Fluids and Related Phenomena. Particular topics suggested were: Liquefaction shockwaves and Shock splitting; Evaporation waves; Condensation in Laval nozzles and turbines; Stability in multiphase shocks; Non-equilibrium and near-critical phenomena; Nucleation in dynamic systems; Structure of transition layers; Acoustic phenomena in two phase systems and Cavitation waves. All of these topics should have been treated with emphasis on physical results, new phenomena and theoretical models. Participants from fourteen nations took part in the Symposium and presented papers which were within the range of suggested topics. The organization and execution of the Symposium was performed by the Max-Planck-Institut fUr Str5mungsforschung in G5ttingen. In particular, the meeting has been promoted under the leadership of Professor Dr. E.-A. MUller, who has for many years given his support for international exchanges in science. The detailed work of organization up to and during the Symposium was in large part due to Dr. T. Kowalewski, who served as Symposium Secretary.




Shock Waves - Proceedings Of The 20th International Symposium (In 2 Volumes)


Book Description

The symposia take place every two years. They are the forum at which scientists concerned with shock waves present their research. They USE shock waves for chemical kinetics studies, for materials studies, and smashing kidney stones; they STUDY the phenomena associated with flows involving shock waves, such as supersonic flow, explosions, detonations, volcanic eruptions, and, in this symposium, even such with-it topics as impact of Shoemaker-Levy on Jupiter and blast waves in the World Trade Center. They also discover new, bigger and better ways of generating flows at hypervelocity speeds and develop their technological tools further.The international exchange of information is documented in the proceedings volumes, which have become a storehouse of information on the subject, documenting the history of this peculiar branch of science that involves chemists, physicists, engineers, geophysicists, material scientists and biologists.




Rarefied Gas Dynamics


Book Description




Introduction to Molecular Beams Gas Dynamics


Book Description

Introduction to Molecular Beams Gas Dynamics is devoted to the theory and phenomenology of supersonic molecular beams. The book describes the main physical idea and mathematical methods of the gas dynamics of molecular beams, while the detailed derivation of results and equations is accompanied by an explanation of their physical meaning. Many of the applications of supersonic molecular beams are discussed, including their application to molecular spectroscopy, and the study of surface phonons by monoatomic and monokinetic beams, and the study of intermolecular potentials and the onset of condensation. The phenomenology of supersonic beams can appear complex to those not experienced in supersonic gas dynamics and, as a result, the few existing reviews on the topic generally assume a limited level of knowledge. The book begins with a quantitative description of the fundamental laws of gas dynamics and goes on to explain such phenomena. It analyzes the evolution of the gas jet from the continuum to the regime of almost free collisions between molecules, and includes numerous figures, illustrations, tables and references.




Material Substructures in Complex Bodies


Book Description

Stringent industrial requirements of sophisticated performances and of circumstantial control for micro-devices or nanotechnology manufactures, and other types of machinery at multiple scales, can be satisfied often only by resort to or allowance for complex materials. The adjective 'complex' beckons to the fact that the substructure influences gross mechanical behaviour in a prominent way and interactions due to substructural changes are represented directly. The description of the mechanical behaviour of complex bodies proposes a wide class of challenging problems from macroscopic-to-nano-world. The collection of chapters composing this book aims to explore some aspects of these problems, proposing also new matter of discussion together with specific solutions. Contributors are Carlo Cercignani, Gianfranco Capriz, Pierre Degond, Antonio Fasano, Harley T. Johnson, Sukky Jun, Krishna Kannan, Wing Kam Liu, Alberto Mancini, Paolo Maria Mariano, Ingo Müller, Kumbakonan R. Rajagopal, Jan Jerzy Slawianowski. The book can be a useful tool for Scholars and PhD students addressing their research activity toward basic mathematical and physical problems accruing from the mechanics of materials.