A Study of Conductance for a Random, Hierarchically-Structured Material

Salvador, Daniel (2017) A Study of Conductance for a Random, Hierarchically-Structured Material. Undergraduate thesis, under the direction of Jeremy Clark from Mathematics, The University of Mississippi.

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Abstract

I consider a mathematical model for the conductance of a system formed by a hi- erarchical network of random bonds. My simulations show that the net conductance converges to a fixed number γ ≈ 0.35337 when the conductances of the bonds are num- bers selected uniformly at random from the interval (0,1). By linearly approximating the model around γ, I derive a new simplified model which I then study in rigorous mathematical detail. I prove a generalized central limit theorem for the new linearized system.

Item Type: Thesis (Undergraduate)
Creators: Salvador, Daniel
Student's Degree Program(s): B.S. in Mathematics
Thesis Advisor: Jeremy Clark
Thesis Advisor's Department: Mathematics
Institution: The University of Mississippi
Subjects: Q Science > QA Mathematics
Depositing User: Daniel Salvador
Date Deposited: 12 May 2017 15:17
Last Modified: 08 Jun 2017 13:47
URI: http://thesis.honors.olemiss.edu/id/eprint/892

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