The Maxwell-Boltzmann Equation as a Constitutive Equation of Continuum Mechanics
While speculations that gross matter is a vast assembly of tiny grains of a few distinct kinds are of great age, the first mathematical theories sufficient to yield quantities rather than pictures are those of NAVIER, POISSON, and CAUCHY, in which fluids and solids are represented as static or nearly static arrays of point centers of force. Although correct if somewhat special equations were drawn from such hypotheses by those mathematicians, physicists later rejected the molecular models on which they rest, entirely in the case of fluids, and with such qualifications for solids as to bury the starting point. Scientists should use these theories as examples to show that one man’s molecules may be another man’s poison.
KeywordsConstitutive Equation Stream Velocity Collision Operator Pressure Tensor Molecular Density
Unable to display preview. Download preview PDF.
- T. CARLEMAN’ Problemés Mathématiques dans la Thérie Cinétique des Gaz, Uppsala, Almqvist & Wiskell, 1957.Google Scholar
- H. GRAD, “Principles of the kineic theory of gases” in FLÜGGE’SHandbuch der Physik, page 205–294 of Volume XII, Berlin etc., Springer-Verlag, 1958.Google Scholar
- H. GRAD “The mechanical foundations of elasticity and fluid dynamics”Journal of Rational Mechanics and Analysis1 (1952): 125–300.Google Scholar