Topics Nonlinear Physics Proceedings (18 results)

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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - Nonlinear Problems in Physics.- Nonlinear Problems in Physics.- The Nonlinear Field Theories in Mechanics.- 1. Thermodynamics of Homogeneous Processes.- Temperature and Heat.- Homogeneous Processes.- The Thermodynamic State.- Thermodynamic Processes.- Histories.- Thermodynamic Constitutive Equations.- Example 1. The Classical Caloric Equations of State.- 2. Kinematics. Changes of Frame.- Geometry.- Primitive Elements of Thermomechanics.- Bodies, Configurations, Motions.- Mass Density.- Reference Configuration.- Deformation Gradient.- Change of Reference Configuration.- Current Configuration as Reference.- Stretch and Rotation.- Stretching and Spin.- Changes of Frame.- 3. Force and Work, Laws of Motion.- Physical Principles of Mechanics.- Forces and Moments in Continuum Mechanics.- Momentum and Moment of Momentum.- The Euler-Cauchy Stress Principle.- Energy and Heat Work.- Equations of Balance.- Differential Equations of Continuum Mechanics.- 4. Constitutive Equations. Simple Materials.- Nature of Constitutive Equations.- Equivalent Processes.- Constitutive Equations.- Axioms for Constitutive Equations.- Simple Materials.- Exercise 4.1 (Zaremba-Noll Theorem).- Reduction for Material Frame-Indifference.- Internal Constraints.- 5. The Isotropy Group.- Isotropy Group.- Orthogonal Part of the Isotropy Group.- Change of Reference Configuration.- 6. Solids, Isotropic Materials, Fluids, Fluid Crystals.- Main Properties of the Isotropy Group.- Isotropic Materials.- Solids.- Fluids.- Fluid Crystals.- 7. Motions with Constant Stretch History.- Definition.- Noll¿s Theorem.- Determination of the Deformation History from the First Three Rivlin-Ericksen Tensors.- Equivalence of Simple Materials with Rivlin-Ericksen Materials in Motions with Constant Stretch History.- Classification of Motions with Constant Stretch History.- 8. The Stress System in Viscometric Flows of Incompressible Fluids.- Recapitulation.- Functional Equations for the Response Function.- Illustration by Means of Shearing Flow.- Consequences of Invariance Under Reflections.- The Viscometric Functions. Normal-Stress Effects.- Position of the Classical Theory.- 9. Dynamical Conditions in Viscometric Flows.- Recapitulation.- Dynamic Compatibility.- Shearing Flow.- Channel Flow.- Helical Flows.- Flow Between Rotating Cylinders.- Flow in a Circular Pipe.- Other Viscometric Flows.- 10. Impossibility of Rectilinear Plow in Pipes.- Problem.- Explicit Constitutive Equation.- Dynamical Equation.- Compatibility.- 11. Elastic Materials.- Statics of Simple Materials.- Reduction for Frame-Indifference.- Elastic Fluids.- Natural States.- Isotropic Elastic Materials.- Unconstrained Bodies.- Incompressible Bodies.- Remarks.- 12. Non-Homogeneous Universal Solutions for Incompressible Elastic Bodies.- Universal Solutions.- List of the Universal Solutions.- Inflation or Eversion, Torsion, and Extension of a Cylinder.- Torsion and Tension of a Solid Cylinder.- Eversion.- Remarks on Method.- 13. Hyperelastic Materials.- The Piola-Kirchhoff Stress Tensor.- Definition of a Hyperelastic Material.- The Two Isotropy Groups.- Minimum of the Stored-Energy Function.- Need for an A Priori Inequality.- Coleman and Noll¿s Inequality.- 14. Work Theorems in Hyperelasticity.- Nonsense About Perpetual Motion.- Virtual Work of the Traction on the Boundary.- Homogeneous Processes in Homogeneous Bodies.- The First Work Theorem.- The Second Work Theorem.- The Third Work Theorem.- 15. Thermomechanics. Equipresence.- Fading Memory.- Thermodynamics and Continuum Mechanics Reviewed.- General Principles of the Thermomechanics of Continua.- Thermodynamic Process.- Constitutive Equations. Equipresence.- The Clausius-Duhem Inequality.- The Reduced Dissipation Inequality.- Simple Thermodynamic Materials.- 16. Thermodynamics of Simple Materials with Fading Memory.- Quasi-Elastic Response. Fading Memory.- Dissipation and Quasi-Elastic Response.- Applications.- A Final Remark on the Stored-Energy Function in Elasticity.- 17. Wave Motions. Compatibility.- The Nature of Wave Motions.- Hadamard¿s Lemma.- Singular Surfaces.- Singular Surfaces for a Motion.- Compatibility Conditions for Second-Order Singular Surfaces.- Equation of Balance at a Singular Surface.- Acceleration Waves in Elasticity.- Weak Singular Surfaces in General.- 18. Wave Propagation in Dissipative Materials.- The ¿Smoothing¿ Effect of Dissipation.- Waves and Quasi-Elastic Response.- Relation Between the Homo-thermal and Homentropic Acoustic Tensors.- Waves in Non-Conductors.- Waves in Definite Conductors.- Closure.- to Nonequilibrium Statistical Physics.- 1. Introduction.- References.- 2. Phenomenological Approach ¿ Thermodynamics of Irreversible Processes.- References.- 3. Statistical Mechanics ¿ General Method.- a) Introduction.- b) Liouville Equation.- c) Free Particles.- d) Potential Scattering.- e) General Theory.- f) General Evolution Equation.- g) Transformation Theory of the Kinetic Equation.- h) Correlations.- References.- 4. Boltzmann Situations.- a) Anharmonlc Solids.- b) Brownlan Motion.- References.- 5. Generalized Boltzmann Situations.- a) The Three-Body Problem.- b) Strongly Coupled Systems.- c) The RenormallzatIon Program.- Strongly Coupled Anharmonlc Oscillators.- d) Pl¿n Production in Baryon-Pion Scattering with a p-Meson in the Intermediate Stage.- e) Relation with S-Matrix Theory.- References.- 6. NonBoltzmann Situations.- a) General Remarks.- b) Harmonic Lattices.- c) Heisenberg Spin Systems.- d) Gravitational Plasmas.- References.- 7. Irreversibility.- a) Introduction.- b) Discussion of Zermelo¿s Paradox.- c) Discussion of Loschmidt¿s Paradox.- d) Meaning of Irreversibility.- References.- 8. Entropy.- a) Thermodynamic Entropy and Statistical Mechanics.- b) Entropy in Strongly Coupled Anharmonic Oscillators -Disorder and Entropy.- c) Canonical Entropy and Resonance Effects.- d) Numerical Calculations.- References.- 9. Concluding Remarks.- References.…

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