Name	Shinya Saka
	Department	Department of Physics, School of Fundamental Science and Technology
	Research Fields	Polymer Physics

Extension of the Relaxation Mode Analysis to Nonequilibrium Systems and Its Application to Knotted Ring Polymers Using Computer Simulations
One of the purposes of the polymer physics is discovering the universal characters not depending on the chemical details by using the statistical mechanics. The effects of topological constraints caused by the entanglement of polymers on properties of polymer systems have attracted much attention. In the case of a single knotted ring polymer, which is one of the self-entangled systems, the topological constraints are determined by the knot type and do not change with time. Therefore, a single ring polymer system can be considered as an idealized system for the study of topological effects. The investigation of knots in this system is expected to provide a basis for further understanding of topological effects in polymer system.
In the polymer physics, the relaxation phenomena have been studied systematically in term of the relaxation modes and rates. For ideal systems, the relaxation mode is approximally given as the normal coordinate of the linear Langevin equation. In recent years, for complex systems, the relaxation modes and rates are estimated numerically by solving a generalized eigenvalue problem for the time correlation matrices obtained from simulation data. This method is called the relaxation mode analysis (RMA).
In our study, the relaxation of a single ring polymer with the trefoil knot is studied by the Brownian dynamics simulation. From the behavior of the relaxation rate obtained form the RMA, it is found that the structure changes from a ``uniform’’ state for short polymer length N, where the knotted part is expanded widely along the ring polymer, to a ``segregated’’ state for long N, where the knotted part is localized to a part of the ring polymer and the rest of the ring polymer behaves like a ring polymer with the trivial knot. Thus, the topological constraint affect on the relaxation rate distribution and the localization of knotted part depends on the polymer length.
In the COE program, our purpose is the extension of the relaxation mode analysis to nonlinear nonequilibrium systems, which is far from the equilibrium. Especially, the relaxation of the topological constraint after cutting a knotted ring polymer will be studied.