Papenfuss Christina, Muschik Wolfgang
Department of Engineering 2, Hochschule für Technik und Wirtschaft Berlin, 12459 Berlin, Germany.
Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany.
Entropy (Basel). 2018 Jan 22;20(1):81. doi: 10.3390/e20010081.
Internal and mesoscopic variables differ fundamentally from each other: both are state space variables, but mesoscopic variables are additionally equipped with a distribution function introducing a statistical item into consideration which is missing in connection with internal variables. Thus, the alignment tensor of the liquid crystal theory can be introduced as an internal variable or as one generated by a mesoscopic background using the microscopic director as a mesoscopic variable. Because the mesoscopic variable is part of the state space, the corresponding balance equations change into mesoscopic balances, and additionally an evolution equation of the mesoscopic distribution function appears. The flexibility of the mesoscopic concept is not only demonstrated for liquid crystals, but is also discussed for dipolar media and flexible fibers.
二者均为状态空间变量，但介观变量还配备有一个分布函数，该函数引入了一个统计项以供考虑，而这一统计项在涉及内变量时是不存在的。因此，液晶理论的取向张量既可以作为一个内变量引入，也可以通过将微观指向矢用作介观变量，由介观背景生成。由于介观变量是状态空间的一部分，相应的平衡方程转变为介观平衡，此外还出现了介观分布函数的演化方程。介观概念的灵活性不仅在液晶中得到了体现，在偶极介质和柔性纤维中也有所讨论。
