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This invaluable book studies synchronization of coupled chaotic circuits and systems, as well as its applications. It shows how one can use stability results in nonlinear control to derive synchronization criteria for coupled chaotic circuits and systems. It also discusses the use of Lyapunov exponents in deriving synchronization criteria. Both the case of two coupled systems and the case of arbitrarily coupled arrays of systems are considered. The book examines how synchronization properties in arrays of coupled systems are dependent on graph-theoretical properties of the underlying coupling

Electronic circuits. --- Chaotic behavior in systems. --- Coupled mode theory.

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Solid-liquid interfaces. --- Coupled mode theory. --- Elastic solids. --- Navier-Stokes equations.

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Numerical solutions of differential equations --- Solid-liquid interfaces. --- Coupled mode theory. --- Elastic solids. --- Navier-Stokes equations. --- Interfaces solide-liquide --- Modes couplés, Théorie des --- Solides élastiques --- Navier-Stokes, Equations de --- 51 <082.1> --- Mathematics--Series --- Modes couplés, Théorie des --- Solides élastiques --- Coupled mode theory --- Elastic solids --- Navier-Stokes equations --- Solid-liquid interfaces --- Liquid-solid interfaces --- Interfaces (Physical sciences) --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow --- Continuum mechanics --- Mechanics --- Solids --- Statics --- Coupled modes, Theory of --- Coupled systems --- Oscillations --- Vibration --- Wave-motion, Theory of

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Strongly coupled (or cross-diffusion) systems of parabolic and elliptic partial differential equations appear in many physical applications. This book presents a new approach to the solvability of general strongly coupled systems, a much more difficult problem in contrast to the scalar case, by unifying, elucidating and extending breakthrough results obtained by the author, and providing solutions to many open fundamental questions in the theory. Several examples in mathematical biology and ecology are also included. Contents Interpolation Gagliardo-Nirenberg inequalities The parabolic systems The elliptic systems Cross-diffusion systems of porous media type Nontrivial steady-state solutions The duality RBMO(μ)-H1(μ)| Some algebraic inequalities Partial regularity

Control theory. --- Coupled mode theory. --- Differential equations, Partial. --- Differential equations, Parabolic. --- Differential equations, Elliptic. --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear --- Differential equations, Partial --- Parabolic differential equations --- Parabolic partial differential equations --- Partial differential equations --- Coupled modes, Theory of --- Coupled systems --- Oscillations --- Vibration --- Wave-motion, Theory of --- Dynamics --- Machine theory

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The concepts of the Jahn-Teller effect and vibronic coupling are being applied to more and more systems in both chemistry and physics. Aspects of structural chemistry such as the distortion of the nuclear framework to a lower-symmetry conformation have received an increasing attention, as well as the dynamics on the coupled potential energy surfaces.   The Jahn-Teller intersections are now recognized as prototype cases of conical intersections where the nuclear motion is known to be inherently nonadiabatic in nature and interchanges freely between the different potential energy surfaces. In the condensed phase especially, the significance of the Jahn-Teller effect has been increasingly appreciated, following the discovery of superconductivity in the fullerides and of very large ("colossal") magnetoresistance in the manganite perovskites. Indeed, these materials are particularly challenging since the Jahn-Teller interaction competes with electronic correlation effects.     Vibronic Interactions and the Jahn-Teller Effect: Theory and Applications provides an in-depth discussion of the Jahn-Teller effect and vibronic interactions as reflected by the contributions presented at the XX International Conference on the Jahn-Teller effect, Fribourg, Switzerland, 2010. The following topics have been treated in a clear and concise way:   - Complex topologies of Jahn-Teller effect and conical intersections - Multi-state vibronic interactions on strongly coupled potential energy surfaces - Interplay of vibronic and spin-orbit coupling - Strain in Jahn-Teller systems and cooperative Jahn-Teller effect - Orbital ordering and its relation to ferromagnetism, ferroelectricity and molecular magnets - The Jahn-Teller effect in icosahedral systems - The Jahn-Teller effect and high temperature superconductivity   This book is of interest to a wide audience including academic and industrial theoretical and experimental physicists, chemists, spectroscopists, and crystallographers.

Chemistry. --- Jahn-Teller effect. --- Vibration. --- Jahn-Teller effect --- Vibration --- Chemistry --- Physical Sciences & Mathematics --- Physical & Theoretical Chemistry --- Teller-Jahn effect --- Chemistry, Physical and theoretical. --- Condensed matter. --- Theoretical and Computational Chemistry. --- Condensed Matter Physics. --- Cycles --- Mechanics --- Sound --- Coupled mode theory --- Crystal field theory --- Energy levels (Quantum mechanics) --- Physical sciences --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids --- Chemistry, Theoretical --- Physical chemistry --- Theoretical chemistry