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Short lecture in the Univ. Tokyo

I went to the University of Tokyo on Sep/21/2016 to deliver a lecture on simulations of polymers to the member of Prof. Yamashita‘s group. Professor Yamashita is the leader of SIP project dedicated to the development of simulations for thermoset polymers. I am in his team and the budget for Ankita comes from this project. In this sense, he is the boss. Nevertheless, he is an expert of large-scale molecular dynamics simulations and his main interest is simulation of proteins. More specifically, his research is for drug discovery.

I was asked by Prof. Yamashita for the lecture because they are not familiar with the coarse-graining in the simulation of polymers.

Although molecular dynamics simulation is basically capable of any kind of problems in which dynamics of molecules is of importance, for polymers the conventional molecular dynamics is not that quite useful because the dynamics of polymers is very very …. very slow. The relaxation time of polymers is too much long to be traced by the molecular dynamics simulations.

To overcome this problem, we employ theoretical technique so called “coarse-graining”. In this framework, we have to chose a small number of degrees of freedom in the system. The chosen degrees of freedom should dominate the slow dynamics of the system, and actually they are called as “slow variables”. The rest of the degrees of freedom is averaged out, and their effects are embedded into the parameters in the kinetic equations for the slow variables.

The coarse-graining is very powerful to move the time domain of calculation toward the long time region. The main benefit is the smearing of fast valuables. For the fast motion the numerical integration should be made with a small time step otherwise the fast motion (e.g. collisions between atoms) cannot be traced. On the other hand, if the slow variables are correctly chosen and the effects of fast motions are pre-averaged, then the time step for the integration can be elongated drastically. Of course, the drawback is that the fast dynamics cannot be observed in the coarse-grained calculations. (Thus, we cannot enlarge the time domain for the calculation. The coarse-graining just moves the time domain to the long time side.) Although there has been theoretical frameworks for coarse-graining, in reality systematic coarse-graining is very difficult. For instance, the choice of slow valuables is just a matter of intuition.

For polymers, the coarse-graining is frequently used owing to the strong support of experimental results on the universality of polymers. The remarkable success of the hypothetical models (proposed by brilliant peoples in the past) also pushes this direction. However, without the knowledge of these earlier works, coarse-graining of polymers (i.e., the modeling of polymers) is not straightforward. When I was a JST-PRESTO fellow (‘Sakigake’ in Japanese), the project manager was a professor who is an expert of solid-state physics and who does not know about polymers. For such a person, the idea of coarse-graining is totally silly. The coarse-graining assumes that the fast dynamics (and the phenomena in small length scale) is not significant, and such details can be averaged out. I had a very difficult time during Sakigake, and I recognized that the use of coarse-graining is of danger, if it is used without a sufficient explanation of the background.

I am not quite sure that the things above were conveyed or not. But I saw that nobody in the room got to sleep. The talk seems reasonably interesting for the audience ;->. Nevertheless, I thank Prof. Yamashita for giving me the opportunity.

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