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Mixing may be thought of as the operation by which a system evolves from one state of simplicity (initial segregation) to another state of simplicity (complete uniformity). Between these two extremes, complex patterns emerge and die. Questions naturally arise- how can the geometry of complex patterns be characterised, what is the time scale of the process, what structures are involved in the flow? This volume, comprising the proceedings of the NATO ASI on Mixing, attempts to address these questions from the approaches of geometry, kinetics and structure. The ASI which brought together diverse communities with a common interest in the problem of mixing, now provides us with a comprehensive work on the problem of mixing.

Mixing --- Congresses --- Continuum physics. --- Condensed matter. --- Mathematical physics. --- Geometry. --- Classical and Continuum Physics. --- Condensed Matter Physics. --- Theoretical, Mathematical and Computational Physics. --- Mathematics --- Euclid's Elements --- Physical mathematics --- Physics --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Classical field theory --- Continuum physics --- Continuum mechanics --- Mixing. --- Blending --- Chemical engineering --- Fluid dynamics --- Hydrodynamics --- Chaos (dynamical) --- Process engineering --- Turbulence --- Atmosphere (earth)

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Award-winning monograph of the Ferran Sunyer i Balaguer Prize 1998.This book is devoted to the relation between two different concepts of integrability: the complete integrability of complex analytical Hamiltonian systems and the integrability of complex analytical linear differential equations. For linear differential equations, integrability is made precise within the framework of differential Galois theory. The connection of these two integrability notions is given by the variational equation (i.e. linearized equation) along a particular integral curve of the Hamiltonian system. The underlying heuristic idea, which motivated the main results presented in this monograph, is that a necessary condition for the integrability of a Hamiltonian system is the integrability of the variational equation along any of its particular integral curves. This idea led to the algebraic non-integrability criteria for Hamiltonian systems. These criteria can be considered as generalizations of classical non-integrability results by Poincaré and Liapunov, as well as more recent results by Ziglin and Yoshida. Thus, by means of the differential Galois theory it is not only possible to understand all these approaches in a unified way but also to improve them. Several important applications are also included: homogeneous potentials, Bianchi IX cosmological model, three-body problem, Hénon-Heiles system, etc.The book is based on the original joint research of the author with J.M. Peris, J.P. Ramis and C. Simó, but an effort was made to present these achievements in their logical order rather than their historical one. The necessary background on differential Galois theory and Hamiltonian systems is included, and several new problems and conjectures which open new lines of research are proposed.

Differential algebra. --- Galois theory --- Hamiltonian systems. --- Galois theory. --- Mathematics. --- Algebra. --- Field theory (Physics). --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Differential equations. --- Ordinary Differential Equations. --- Global Analysis and Analysis on Manifolds. --- Field Theory and Polynomials. --- 517.91 Differential equations --- Differential equations --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Mathematics --- Mathematical analysis --- Math --- Science

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Preferred finite difference schemes in one, two, and three space dimensions are described for solving the three fundamental equations of mechanics (conservation of mass, conservation of momentum, and conservation of energy). Models of the behavior of materials provide the closure to the three fundamentals equations for applications to problems in compressible fluid flow and solid mechanics. The use of Lagrange coordinates permits the history of mass elements to be followed where the integrated effects of plasticity and external loads change the material physical properties. Models of fracture, including size effects, are described. The detonation of explosives is modelled following the Chapman--Jouget theory with equations of state for the detonation products derived from experiments. An equation-of-state library for solids and explosives is presented with theoretical models that incorporate experimental data from the open literature. The versatility of the simulation programs is demonstrated by applications to the calculations of surface waves from an earthquake to the shock waves from supersonic flow and other examples.

Artificial intelligence. Robotics. Simulation. Graphics --- Classical mechanics. Field theory --- Hydrodynamics --- Gas dynamics --- Elastoplasticity --- Computer simulation. --- Mathematical physics. --- Continuum physics. --- Condensed matter. --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Theoretical, Mathematical and Computational Physics. --- Classical and Continuum Physics. --- Simulation and Modeling. --- Condensed Matter Physics. --- Mathematical and Computational Engineering. --- Computational Science and Engineering. --- Computer mathematics --- Electronic data processing --- Mathematics --- Engineering --- Engineering analysis --- Mathematical analysis --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Physical mathematics --- Hydrodynamics - Computer simulation. --- Gas dynamics - Computer simulation. --- Elastoplasticity - Computer simulation.