Takashi Uneyama, Tatsuma Oishi, Takato Ishida, Y. Doi, Yuichi Masubuchi
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Stress Tensor of Single Rigid Dumbbell by Virtual Work Method
We derive the stress tensor of a rigid dumbbell by using the virtual work method. In the virtual work method, we virtually apply a small deformation to the system, and relate the change of the energy to the work done by the stress tensor. A rigid dumbbell consists of two particles connected by a rigid bond of which length is constant (the rigid constraint). The energy of the rigid dumbbell consists only on the kinetic energy. Also, only the deformations which do not violate the rigid constraint are allowed. Thus we need the dynamic equations which is consistent with the rigid constraint to apply the virtual deformation. We rewrite the dynamic equations for the underdamped SLLOD-type dynamic equations into the forms which are consistent with the rigid constraint. Then we apply the virtual deformation to a rigid dumbbell based on the obtained dynamic equations. We derive the stress tensor for the rigid dumbbell model from the change of the kinetic energy. Finally, we take the overdamped limit and derive the stress tensor and the dynamic equation for the overdamped rigid dumbbell. We show that the Green-Kubo type linear response formula can be reproduced by combining the stress tensor and the dynamic equation at the overdamped limit.
期刊介绍:
For the communication among the members, the journal of the Society of Rheology Japan, NIHON REOROJI GAKKAISHI (5 issues per year), was established in 1973 and it is the oldest journal on rheology in Asia. The journal contains original and review articles on rheology and related topics, information for all SRJ events, and reports of domestic/overseas meetings. Articles in Japanese as well as in English are considered for publication, not only from the members but also from the researchers outside. Papers from new emerging areas of the field are particularly welcome. The electronic version of the articles is available via the internet with an open access policy.