Date of Award
Doctor of Philosophy
Network thermodynamics is a method of representing thermodynamic systems as equivalent electrical circuits which allows the application of well-developed techniques of network analysis to thermodynamic problems (Oster, G. F., Perelson, A. S. and Katchalsky, A. 1973, "Network Thermodynamics: Dynamical Modelling of Biophysical Systems." Q. Rev. Biophys., 6, 1-134). This dissertation covers four aspects. First, the relevant graph theory, circuit theory including normal tree analysis, and systems theory are summarized to provide a context and working vocabulary for the subsequent sections. Next, a systematic approach is presented for representing thermodynamic systems as equivalent circuits based on dynamical, dimensional, topological and mathematical similarities. Its use is demonstrated by designing an equivalent circuit to represent a primitive autocatalytic reaction-diffusion system (based on the Brusselator) capable of evolving stable asymmetries in the distribution of reactants. This is an example of a morphogenetic system, that is a dynamical chemical system capable of evolving stable changes in structure over time. The resulting equivalent circuit is analyzed using a general circuit simulation language Spice (Dowell, R., Newton, A. R. and Pederson, D. O. 1976. "Spice VAX Version 2X.x User's Guide." Department of Electrical Engineering and Computer Sciences, University of California, Berkeley). Using several different sets of boundary conditions, initial system states and system topologies as examples, the versatility of the equivalent circuit method is demonstrated. When the most asymmetrical topology and open boundary conditions are used, and a non-linear positive feedback loop is used to represent the autocatalytic step, the circuit response shows stable potential differences between distributed subcircuit regions. The final section is a note outlining a method for the sequential synthesis and analysis of a morphogenetic automaton based on network thermodynamics.
Marin, Jeanne Kay, "Network Thermodynamics And Morphogenesis" (1982). Digitized Theses. 1161.