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.
| Identifer | oai:union.ndltd.org:UMASS/oai:scholarworks.umass.edu:dissertations-3362 |
| Date | 01 January 2000 |
| Creators | Kho, Alvin Thong-Juak |
| Publisher | ScholarWorks@UMass Amherst |
| Source Sets | University of Massachusetts, Amherst |
| Language | English |
| Detected Language | English |
| Type | text |
| Source | Doctoral Dissertations Available from Proquest |
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