UID:
almahu_9949697315902882
Umfang:
1 online resource (623 p.)
ISBN:
1-281-76765-4
,
9786611767655
,
0-08-087399-5
Serie:
Pure and applied mathematics, a series of monographs and textbooks ; 83
Inhalt:
Fundamentals of MaxwellÆs kinetic theory of a simple monatomic gas
Anmerkung:
Description based upon print version of record.
,
Front Cover; Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas; Copyright Page; Contents; Prologue; Acknowledgments; Notation; List of Special Symbols; Part A: Continuum Thermomechanics; Chapter I. Continuum Theories of Fluids; (i) Basic concepts. Field equations; (ii) Constitutive relations. The Navier-Stokes-Fourier theory of viscous fluids; (iii) Thermodynamic quantities. The Maxwell number and the caloric; (iv) More general constitutive assumptions and principles; (v) Thermodynamics: The Clausius-Duhem inequality and its special cases and generalizations
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Chapter II. The Stokes-Kirchhoff Gas, Some of Its Peculiarities, and Some of Its Flows(i) The Stokes-Kirchhoff and Euler-Hadamard theories of ideal gases; (ii) Some parameters that control dynamical similarity; (iii) The caloric of an ideal gas; (iv) Equilibrium; (v) Some particular homo-energetic flows: dilatation, affine flow, simple shearing, extension; Part B: Basic Structures of the Kinetic Theory; Chapter III. The Molecular Density, the Definitions of Gross Fields, and the Equation of Evolution; (i) The molecular density and the number density
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(ii) Expectations. The thirteen basic fields(iii) The higher moments; (iv) The retrogressors; (v) The equation of evolution; Chapter IV. Some Limits of Agreement between Kinetic Theories and Classical Fluid Mechanics; (i) Failure of constitutive relations in the sense of continuum mechanics; (ii) Limitations on the shear viscosity; (iii) Vanishing of the bulk viscosity; (iv) Disagreement between the kinetic theory and the Stokes-Kirchhoff theory for flows in which T 〉= 1; Chapter V. The Differential Operators of the Kinetic Theory; (i) The retrogressor and the retrogression reviewed
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(ii) Differentiation along a trajectory. Mild and strong derivatives(iii) Local forms of the equation of evolution; (iv) Moments of the strong derivative of a function; Chapter VI. The Dynamics of Molecular Encounters; (i) Binary encounters; (ii) Summational invariants and the Boltzmann-Gronwall theorem; (iii) The encounter problem and its solutions; (iv) The encounter operator and its properties; Appendix A Proof of the lemma; Chapter VII. The Maxwell Collisions Operator. Kinetic Constitutive Relations. The Total Collisions Operator and Bilinear Form; (i) The collisions operator
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(ii) Kinetic constitutive quantities(iii) Alternative forms of the collisions operator; (iv) The bilinear form; (v) Orthogonal invariance of the collisions operator and the bilinear form; (vi) Inconsistency of Maxwell's kinetic theory with Newtonian mechanics; Chapter VIII. Boltzmann's Monotonicity Theorem. The Maxwellian Density. Analogues of the Caloric and Its Flux; (i) The Boltzmann monotonicity theorem; (ii) Properties of the Maxwellian density; (iii) Degree to which a Maxwellian expectation approximates a general one; (iv) The caloric of a kinetic gas: Boltzmann's field h
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(v) Bounds for h and for its flux s
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English
Weitere Ausg.:
ISBN 0-12-701350-4
Sprache:
Englisch
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