Seguin Brian, Fried Eliot
Department of Mathematics and Statistics, 805 Sherbrooke Street West, Montreal, QC H3A 2K6, Tel.: 514-398-2998, ,
Arch Ration Mech Anal. 2012 Dec 1;206(3):1039-1072. doi: 10.1007/s00205-012-0550-3.
We develop a mechanical theory for systems of rod-like particles. Central to our approach is the assumption that the external power expenditure for any subsystem of rods is independent of the underlying frame of reference. This assumption is used to derive the basic balance laws for forces and torques. By considering inertial forces on par with other forces, these laws hold relative to any frame of reference, inertial or noninertial. Finally, we introduce a simple set of constitutive relations to govern the interactions between rods and find restrictions necessary and sufficient for these laws to be consistent with thermodynamics. Our framework provides a foundation for a statistical mechanical derivation of the macroscopic balance laws governing liquid crystals.
我们为棒状粒子系统建立了一个力学理论。我们方法的核心假设是，任何棒状子系统的外部功率消耗与基础参考系无关。该假设用于推导力和扭矩的基本平衡定律。通过将惯性力与其他力同等考虑，这些定律相对于任何参考系（惯性或非惯性）都成立。最后，我们引入了一组简单的本构关系来控制棒之间的相互作用，并找出这些定律与热力学一致所必需且充分的限制条件。我们的框架为支配液晶的宏观平衡定律的统计力学推导提供了基础。
