Titlebook: Mathematical Methods in Kinetic Theory; Carlo Cercignani Book 1969 Springer Science+Business Media New York 1969 kinetic theory.Mathematic

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Basic Principles,t number of particles, such as the number of molecules contained in a lump of matter of macroscopic dimensions. The aim of statistical mechanics is to explain the macroscopic behavior of matter in terms of the mechanical behavior of the constituent molecules, i.e., in terms of motions and interactio

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The Linearized Collision Operator,he only known exact solution [another solution is due to Ikenberry and Truesdell (see ref. 1) but is interesting only for illustrative purposes]. The meaning of the Maxwellian distribution is clear : it describes equilibrium states (or slight generalizations of them), characterized by the fact that

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Model Equations,ersion, Eq. (1.1) of Chapter II, and the linearized form, Eq. (2.2) of Chapter III. It is therefore not surprising that alternative, simpler expressions have been proposed for the collision term; they are known as collision models, and any Boltzmann-like equation where the Boltzmann collision integr

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The Linearized Boltzmann Equation,n number ; other procedures based on the assumption of a large Knudsen number will briefly be described later (Chapter VIII, Section 3). The above two procedures are valid in the so-called near-continuum (or slip) regime (Kn → 0) and in nearly-free regime (Kn → ∞). They are both based upon a specifi

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Analytical Methods of Solution,he features of its solutions can be retained by using model equations. We can say more, that practically all the features are retained by a properly chosen model. The advantages offered by the models consist essentially in simplifying both the analytical and numerical procedures for solving boundary

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https://doi.org/10.1007/978-1-4899-5409-1kinetic theory; Mathematica; mathematical method; mathematics

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