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Geometric methods for optimizing ramified flow networks

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Title: Geometric methods for optimizing ramified flow networks
Author(s): Singleton, Martin S.
Director of Research: Hubler, Alfred
Doctoral Committee Chair(s): Oono, Yoshi
Doctoral Committee Member(s): Hubler, Alfred; Weissman, Mike; Stack, John
Department / Program: Physics
Discipline: Physics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): nonlinear networks flow networks ramified networks neural networks constructal theory perceptrons optimization fractal networks smart materials
Abstract: 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.
Issue Date: 2011-05-25
URI: http://hdl.handle.net/2142/24117
Rights Information: Copyright 2010 by Martin S. Singleton. All rights reserved.
Date Available in IDEALS: 2011-05-25
Date Deposited: 2011-05
 

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