Fluctuating Elastic Rings: Statics and Dynamics

摘要

We study the effects of thermal fluctuations on elastic rings. Analyticalexpressions are derived for correlation functions of Euler angles, mean squaredistance between points on the ring contour, radius of gyration, andprobability distribution of writhe fluctuations. Since fluctuation amplitudesdiverge in the limit of vanishing twist rigidity, twist elasticity is essentialfor the description of fluctuating rings. We find a crossover from a smallscale regime in which the filament behaves as a straight rod, to a large scaleregime in which spontaneous curvature is important and twist rigidity affectsthe spatial configurations of the ring. The fluctuation-dissipation relationbetween correlation functions of Euler angles and response functions, is usedto study the deformation of the ring by external forces. The effects of inertiaand dissipation on the relaxation of temporal correlations of writhefluctuations, are analyzed using Langevin dynamics.