Computational and Applied Analysis

Topics and Advisors

Topic Area	Faculty Advisor(s)
Calculus of Variations	C. Larsen, K. Lurie, U. Mosco, M. Sarkis, B.Vernescu, D. Volkov
Chemical Reaction Models	P. W. Davis, W. Farr
Composite Materials	C. Larsen, K. Lurie, B. Vernescu
Fluid Mechanics	M. Humi, D. Tang, S. Weekes
Mathematical Biology	R. Lui, D. Tang
Mathematical Physics	M. Humi, C. Larsen, D. Volkov
Numerical Methods for Differential Equations/Scientific Computation	W. Farr, J. D. Fehribach, M. Humi, M. Sarkis, D. Tang, H. Walker, S. Weekes
Optimal Control/Stochastic Control	A. C. Heinricher, D. Vermes

Numerical Methods for Neutral Coated Inclusions Conductivity: Student: Murphy, Ethan K.
Advisor: SARKIS-MARTINS, M. (MA)
This project used finite element method to obtain neutral coated inclusions shapes for a thermal conductivity problem. Such an inclusion when inserted in a homogeneous matrix has the property that it does not disturb the uniform heat flow outside the inclusion. A free-boundary problem was formed and Newton's Method was used to handle the nonlinearity of the system. Dynamic mesh refinements were implemented to increase accuracy in certain areas. Iterations of the method yielded the desired neutrally coated shapes.
Mathematical Modeling of Metal Bioremediation: Student: Vega, Nicole Marie
Advisor: WEEKES, S. L. (MA)
A model for metal bioremediation in groundwater is constructed. The mathematical model accounts for (i) the chemical processes that eventually render biomass inactive (ii) the toxicity of metal to biomass, and (iii) transport by groundwater. Numerical simulations of the reaction-convection-diffusion equations are carried out via an operator splitting method. The results of the model are compared to a structurally similar model for organic bioremediation. We find that metal cleanup differs significantly from organic cleanup due to the unique mechanisms involved.

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Last modified: March 04, 2009 13:43:21