Multi-scale analysis for microscopic models in materials science and cell biology

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