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This is a unique collection of lectures on integrability, intended for graduate students or anyone who would like to master the subject from scratch, and written by leading experts in the field including Fields Medallist Serge Novikov. Since integrable systems have found a wide range of applications in modern theoretical and mathematical physics, it is important to recognise integrable models and, ideally, to obtain a global picture of the integrable world. The main aims of the book are to present a variety of views on the definition of integrable systems; to develop methods and tests for integrability based on these definitions; and to uncover beautiful hidden structures associated with integrable equations.

Integral equations --- Mathematical physics --- Applied Physics --- Engineering & Applied Sciences --- Mathematical physics. --- Integral equations. --- Equations, Integral --- Physical mathematics --- Physics --- Mathematics --- Physics. --- Mechanics. --- Fluids. --- Theoretical, Mathematical and Computational Physics. --- Fluid- and Aerodynamics. --- Functional equations --- Functional analysis --- Classical Mechanics. --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Hydraulics --- Mechanics --- Hydrostatics --- Permeability

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The monograph is devoted to modern mathematical models and numerical methods for solving gas- and fluid-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 coefficient. The new models are called the quasi-gas-dynamic and quasi-hydrodynamic equations. Based on these equations, effective finite-difference algorithms for calculating viscous non-stationary flows are constructed and examples of numerical computations are presented. The universality, the efficiency, and the exactness of the algorithms constructed are ensured by the fulfillment 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 fluid flows and also for students and post-graduated students who specialize in numerical gas and liquid dynamics.

Fluid dynamics -- Mathematical models. --- Gas dynamics -- Mathematical models. --- Gas dynamics --- Fluid dynamics --- Applied Mathematics --- Engineering & Applied Sciences --- Mathematical models --- Fluid dynamics. --- Gas dynamics. --- Navier-Stokes equations --- Numerical solutions. --- Gasdynamics --- Engineering. --- Computer mathematics. --- Fluids. --- Fluid mechanics. --- Engineering Fluid Dynamics. --- Fluid- and Aerodynamics. --- Computational Science and Engineering. --- Numerical analysis --- Thermodynamics --- Dynamics --- Fluid mechanics --- Hydraulic engineering. --- Computer science. --- Informatics --- Science --- Engineering, Hydraulic --- Engineering --- Hydraulics --- Shore protection --- Computer mathematics --- Electronic data processing --- Mathematics --- Mechanics --- Physics --- Hydrostatics --- Permeability --- Hydromechanics --- Continuum mechanics

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This edited volume consists of twelve contributions related to the EU Marie Curie Transfer of Knowledge Project Cooperation of Estonian and Norwegian Scienti c Centres within Mathematics and its Applications, CENS-CMA (2005-2009), - der contract MTKD-CT-2004-013909, which ?nanced exchange visits to and from CENS, the Centre for Nonlinear Studies at the Institute of Cybernetics of Tallinn University of Technology in Estonia. Seven contributions describe research highlights of CENS members, two the work of members of CMA, the Centre of Mathematics for Applications,Univ- sity of Oslo, Norway, as the partner institution of CENS in the Marie Curie project, and three the ?eld of work of foreign research fellows, who visited CENS as part of theproject. Thestructureofthebookre?ectsthedistributionofthetopicsaddressed: Part I Waves in Solids Part II Mesoscopic Theory Part III Exploiting the Dissipation Inequality Part IV Waves in Fluids Part V Mathematical Methods The papers are written in a tutorial style, intended for non-specialist researchers and students, where the authors communicate their own experiences in tackling a problem that is currently of interest in the scienti?c community. The goal was to produce a book, which highlights the importance of applied mathematics and which can be used for educational purposes, such as material for a course or a seminar. To ensure the scienti?c quality of the contributions, each paper was carefully - viewed by two international experts. Special thanks go to all authors and referees, without whom making this book would not have been possible.

Fluids -- Mathematics. --- Nonlinear waves. --- Solids -- Mathematics. --- Wave-motion, Theory of. --- Wave-motion, Theory of --- Nonlinear waves --- Solids --- Fluids --- Calculus --- Applied Mathematics --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Mathematics. --- Undulatory theory --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Numerical analysis. --- Physics. --- Acoustics. --- Optics. --- Electrodynamics. --- Partial Differential Equations. --- Applications of Mathematics. --- Numerical Analysis. --- Optics and Electrodynamics. --- Mathematical Methods in Physics. --- Mechanics --- Solid state physics --- Transparent solids --- Nonlinear theories --- Waves --- Hydraulics --- Physics --- Hydrostatics --- Permeability

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The International Conference on Computational Fluid Dynamics (ICCFD) is the merger of the International Conference on Numerical Methods in Fluid Dynamics, ICNMFD (since 1969) and International Symposium on Computational Fluid Dynamics, ISCFD (since 1985). It is held every two years and brings together physicists, mathematicians and engineers to review and share recent advances in mathematical and computational techniques for modeling fluid dynamics. The proceedings of the 2006 conference (ICCFD4) held in Gent, Belgium, contain a selection of refereed contributions and are meant to serve as a source of reference for all those interested in the state of the art in computational fluid mechanics.

Fluid dynamics --- Physics. --- Data processing --- Engineering. --- Computer mathematics. --- Fluids. --- Applied mathematics. --- Engineering mathematics. --- Fluid mechanics. --- Engineering Fluid Dynamics. --- Fluid- and Aerodynamics. --- Appl.Mathematics/Computational Methods of Engineering. --- Computational Science and Engineering. --- Hydromechanics --- Continuum mechanics --- Engineering --- Engineering analysis --- Mathematical analysis --- Hydraulics --- Mechanics --- Physics --- Hydrostatics --- Permeability --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Construction --- Industrial arts --- Technology --- Mathematics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Fluid mechanics --- Hydraulic engineering. --- Computer science. --- Mathematical and Computational Engineering. --- Informatics --- Science --- Engineering, Hydraulic --- Shore protection --- Computational fluid dynamics --- Numerische Strömungssimulation.

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This volume contains seven keynote lectures of the TI 2006 conference that was held in Porquerolles, May 29-June 2, 2006. These lectures address the latest developments in direct numerical simulations, large eddy simulations, compressible turbulence, coherent structures, bubbly channel flows, combustion. The keynote lectures are extended manuscripts that were not published in the special issues of the journals "Computers and Fluids" and "Flow, Turbulence and Combustion". The present monograph is a snapshot of the state-of-the-art in the field of turbulence with a view on theory, experiments and numerical simulations.

Fluid dynamics --Congresses. --- Turbulence --Congresses. --- Turbulence --- Fluid dynamics --- Civil Engineering --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Engineering. --- Applied mathematics. --- Engineering mathematics. --- Continuum physics. --- Fluids. --- Statistical physics. --- Dynamical systems. --- Complexity, Computational. --- Fluid mechanics. --- Engineering Fluid Dynamics. --- Classical Continuum Physics. --- Applications of Mathematics. --- Complexity. --- Fluid- and Aerodynamics. --- Statistical Physics, Dynamical Systems and Complexity. --- Hydraulic engineering. --- Mathematics. --- Classical and Continuum Physics. --- Complex Systems. --- Construction --- Industrial arts --- Technology --- Math --- Science --- Engineering, Hydraulic --- Engineering --- Fluid mechanics --- Hydraulics --- Shore protection --- Computational complexity. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Mathematical statistics --- Hydrostatics --- Permeability --- Complexity, Computational --- Electronic data processing --- Machine theory --- Engineering analysis --- Mathematical analysis --- Classical field theory --- Continuum physics --- Continuum mechanics --- Hydromechanics --- Statistical methods