Geometric methods for optimizing ramified flow networks

Using geometrically based approaches, optimal characteristics of nonlinear flow networks were examined. The first model studied was that of a fractal-like desalination plant. Solving the equations of diffusion by analogy to electrostatics, desalination graphs superimposed on the diffusion gradients were optimized to produce maximal water flow. Graphs were generated while varying branching angles and ratios to determine optimal morphologies. Three different boundary conditions are discussed, those of constant pressure difference, constant water flow rate, and constant absorber salinity. Another type of flow network, that of the perceptron, was analyzed from the point of view of its attractors in order to determine which patterns resonated with the network. Using the definition of resonance as learning rapidity, convergence rates were studied by calculating the mean paths to convergence for perceptron weights. Polynomial expressions were given for the mean and variance steps to convergence, which depended upon two dimensionless geometric parameters.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Singleton, Martin S.

Contributors dc:contributor

• Hubler, Alfred W.
• Oono, Yoshitsugu
• Weissman, Michael B.
• Stack, John D.

• nonlinear networks
• flow networks
• ramified networks
• neural networks
• constructal theory
• perceptrons
• optimization
• fractal networks
• smart materials

Statement dc:rights

• Copyright 2010 by Martin S. Singleton. All rights reserved.

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/24117

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/24117