Abstract:
Metal flow analysis, a discipline in industrial ecology, describes the manner in
which metals propagate throughout a coupled ecological and industrial system. The
current models in industrial ecology are static representations that provide analysts with
only a qualitative understanding of the dynamics at play. As such, many industry metrics
are difficult to ascertain, such as recyclability and loss rates, future metal demand, and
sustainability thresholds. The discipline can be expanded for its current state to a more
quantitative framework where reliance on mathematical modeling is central. The intent of
this thesis is to provide a fundamental framework for the mathematical modeling of metal
flows.
A seamless transition is made from the static models to mathematical
representations by incorporating dependence (independent or random variables) to the
existing models and studying the rate at which metal flows throughout a system. Due to
the composition of the static metal flow models (disjoint domains and adherence to
conservation of mass), compartmental modeling that has been used for over a century in
epidemiology to study the spread of infectious diseases is utilized. Deterministic models
consisting of ordinary differential equations are constructed and analyzed. Parameter
optimization techniques using the Levenberg-Marquardt algorithm and numerical
schemes for the acquisition of approximation solutions to the models are constructed and
programmed in the Matlab language. In attempts to provide users with the ability to
interface with the models—analyze and solve the models based on various parameters—
standalone graphical user interfaces written in Matlab are constructed. To provide insight
into the modification and improvement of the models, economic principles are introduced
into the ordinary differential equation models, a pricing independent variable is included
into the models producing systems of reaction-diffusion equations, and economic
fluctuations and volatility are modeled using stochastic differential equations.
