This is an archive of the LaTeX source and necessary scripts used to make my Ph.D. dissertation. It was submitted and approved in late 2007.
If you’re interested in reading this work, please download it from the University of Michigan Library System.
If you’re interested in creating a PDF copy from this source (perhaps to then modify it to write your own dissertation):
- Fetch a copy of this repository from GitHub.
- Make sure you have a reasonable LaTeX stack installed on your machine.
- Run
makein the folder you fetched the repository to.
(c) Harish Narayanan, 2007
This dissertation presents a continuum treatment of growth in biological tissue developed within the context of modern mixture theory. The crux of this work is a careful examination of the assumptions underlying continuum thermodynamics under the condition that multiple interacting species occupy a region of Euclidean space simultaneously. The formal axiomatic treatment presented derives from these assumptions, and provides insight into the sequence of interactions among tissue mechanics, mass transport and biochemical reactions. A computational formulation built upon the theory is used to solve a broad class of numerical examples demonstrating several biophysical aspects of tissue growth.
Continuum Thermodynamics, Mixture Theory, Biological Growth, Numerical Methods