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Titlebook: Analytical Methods for Problems of Molecular Transport; I. N. Ivchenko,S. K. Loyalka,R. V. Tompson Textbook 2007 Springer Science+Business

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The Collision Operator,efined by [1]: . where dN is the number of molecules deflected per unit time by the central force field in dΣ. Since the incident molecules scattered into dΣ must primarily pass through that portion of the annular differential element represented by dS = bdbdε, dN may be expressed in the form:
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Politik und Gesellschaft des Nahen Ostenson of v. For the time interval, ., the position of this phase element will change from (v,r) to (v + . + vdt). It is important to note that the magnitude of this volume element is unaltered in accordance with the Liouville theorem of classical mechanics [.].
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The Boltzmann Equation,on of v. For the time interval, ., the position of this phase element will change from (v,r) to (v + . + vdt). It is important to note that the magnitude of this volume element is unaltered in accordance with the Liouville theorem of classical mechanics [.].
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The Free-Molecular Regime,s may be derived by using the Chapman-Enskog method of solution of the Boltzmann equation. It is very important in the continuum regime that such gas characteristics as the viscosity and thermal conductivity coefficients be determined independently of the boundary conditions.
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