Abstract/Details

Some applications of computational mathematics: Tumor angiogenesis & Bose-Einstein condensates


2007 2007

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Abstract (summary)

This diploma thesis studies the application of computational mathematics to two different fields of research: tumor angiogenesis and Bose-Einstein condensates (BECs).

In Chapter 2, a minimal model for describing the effect of an angiogenic inhibitor upon tumor-induced angiogenesis is examined. Simulations of the model will make use of the Deterministic Cellular Automata technique developed by Dr. Sandy Anderson.

Chapter 3 examines steady states and their dynamics for four different scenarios related to Bose-Einstein condensates. The first two scenarios address the possibility of manipulating a condensate via the use of a laser in the form of either a localized inhomogeneity or optical lattice. A system of linearly coupled, discrete nonlinear Schrödinger equations is the subject of the third scenario, which can be used to describe the behavior of two different BECs contained within a strong optical lattice and subject to an external microwave or radio-frequency field. The final scenario expands upon previous research into radial BEC solutions by including numerical simulations achieved through the use of spectral methods.

Both of these problems provide interesting systems for study and draw upon different aspects of computational mathematics, along with other areas of analytical mathematics, including bifurcation and perturbation theory.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences, Bose-Einstein condensation, Computational mathematics, Tumor angiogenesis
Title
Some applications of computational mathematics: Tumor angiogenesis & Bose-Einstein condensates
Author
Herring, Gregory J.
Number of pages
102
Publication year
2007
Degree date
2007
School code
0118
Source
DAI-B 68/11, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780549330622
Advisor
Kevrekidis, Panayotis G.
Committee member
Johnston, Hans; Mountziaris, T. J.; Whitaker, Nathaniel
University/institution
University of Massachusetts Amherst
Department
Mathematics
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3289253
ProQuest document ID
304838912
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304838912
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