Statistical foundations of liquid-crystal theory: II: Macroscopic balance laws.
ABSTRACT Working on a state space determined by considering a discrete system of rigid rods, we use nonequilibrium statistical mechanics to derive macroscopic balance laws for liquid crystals. A probability function that satisfies the Liouville equation serves as the starting point for deriving each macroscopic balance. The terms appearing in the derived balances are interpreted as expected values and explicit formulas for these terms are obtained. Among the list of derived balances appear two, the tensor moment of inertia balance and the mesofluctuation balance, that are not standard in previously proposed macroscopic theories for liquid crystals but which have precedents in other theories for structured media.
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ABSTRACT: The equations of hydrodynamics—continuity equation, equation of motion, and equation of energy transport—are derived by means of the classical statistical mechanics. Thereby, expressions are obtained for the stress tensor and heat current density in terms of molecular variables. In addition to the familiar terms occurring in the kinetic theory of gases, there are terms depending upon intermolecular force. The contributions of intermolecular force to the stress tensor and heat current density are expressed, respectively, as quadratures of the density and current density in the configuration space of a pair of molecules.The Journal of Chemical Physics 05/1950; 18(6):817-829. · 3.16 Impact Factor
Article: On ephemeral continuaPhysical Mesomechanics - PHYS MESOMECH. 01/2008; 11(5):285-298.
- Archive for Rational Mechanics and Analysis 01/1991; 113:97-120. · 2.29 Impact Factor