| In Part I, we study the effects of random fluctuations included in microscopic models for phase transitions, to macroscopic interface flows. We first derive asymptotically a stochastic mean curvature evolution law from the stochastic Ginzburg-Landau model and develop a corresponding level set formulation. Secondly we demonstrate numerically, using stochastic Ginzburg-Landau and Ising algorithms, that microscopic random perturbations resolve geometric and numerical instabilities in the event of non-uniqueness in the corresponding deterministic flow. In Part II, we analyze the effects of random local linker length variability on the global morphology of a very long, linear, homogeneous chromatin fiber that is modelled as a diffusion process which is parametrized by arclength under a suitable spatial re-scaling. We obtain a Fokker-Planck equation for the process whose solution, a probability density function describes the folding. |
