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Home > Benito Chen-Charpentier
November 12, 2015
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Specialty in Mathematical Modeling and Numerical Analysis
I have a Bachelor of Science degree in Physics from the National University of Mexico and a Ph.D. in Applied Mathematics from the California Institute of Technology. My areas of specialization are Mathematical Modeling and Numerical Analysis, but have also worked in perturbation methods, dynamical systems, optimization, calculus of variations and optimal control. My main applications are mathematical biology and flow in porous media. Among the problems in mathematical biology that I worked are biofilm modeling, epidemics, bone remodeling, pollution control, and the carbon cycle. I have also been involved in problems in related areas such as spread of information, spread of criminal behavior and optimization of benefit in harvesting of beetle infected forests. In the area of flow in porous media I have worked in simulation of pollution in aquifers, of pollution caused by coal bed methane and soli consolidation. Most of the models are described in terms of differential equations, both ordinary and partial, but some are given by difference equations and integro-differential equations. Some of the processes modeled involve delays so it is necessary to deal with delayed differential equations. Other models involved uncertainty, errors and other unknowns that have been included by using random and stochastic differential equations. In particular I have researched the use of polynomial chaos in formulating and solving equations with random coefficients. In the Numerical Analysis part, I have worked with nonstandard methods for differential equations. These methods are constructed to preserve certain properties of the solutions of the differential equations such as positivity and boundedness. Related to sustainability I am working with a student in an epidemic type model to simulate how recyclers and non-recyclers can be influenced by peer pressure and by advertising and availability of recycling options. Also related to sustainability is my work on the carbon cycle, especially on soil carbon models and how to increase the storage capacity of carbon in soils.
I have taught a wide variety of mathematical courses from College Algebra, Calculus to graduate Analysis and Special Topics. I have participated in research sponsored by NSF, DOE, EPA and other sources.