Abstract/Details

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


2000 2000

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Abstract (summary)

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.

Indexing (details)


Subject
Mathematics;
Materials science;
Cellular biology
Classification
0405: Mathematics
0794: Materials science
0379: Cellular biology
Identifier / keyword
Applied sciences; Pure sciences; Biological sciences; Microscopic; Phase transitions; Random perturbations
Title
Multi-scale analysis for microscopic models in materials science and cell biology
Author
Kho, Alvin Thong-Juak
Number of pages
89
Publication year
2000
Degree date
2000
School code
0118
Source
DAI-B 61/07, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780599844636, 0599844639
Advisor
Katsoulakis, Markos A.; Whitaker, Nathaniel
University/institution
University of Massachusetts Amherst
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9978515
ProQuest document ID
304604811
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304604811
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