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

Author

Daniel Salvador, University of Mississippi. Sally McDonnell Barksdale Honors College

Date of Award

2017

Document Type

Undergraduate Thesis

Department

Mathematics

First Advisor

Jeremy Clark

Relational Format

Dissertation/Thesis

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.

Recommended Citation

Salvador, Daniel, "A Study of Conductance for a Random, Hierarchically-Structured Material" (2017). Honors Theses. 245.
https://egrove.olemiss.edu/hon_thesis/245

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