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Course Information
Donald A French
Professor
611C Old Chemistry Building
513-556-4039
donald.french@uc.edu
http://math.uc.edu/~french
Professional Summary
Born Syracuse, NY 1958. B.A.'s in Math and Physics at SUNY Oswego 1980. PhD Applied Mathematics Cornell University 1985 (Thesis on Finite Element Error Analysis -- Advisor Lars B. Wahlbin). Visiting Assistant Professor at Purdue University (1985-7). Assistant Professor at Carnegie Mellon (1987-90). Permanent Position at University of Cincinnati since 1990.
Education
PhD, Cornell University, 1985.
Research Interests
Recent work has been on mathematical modeling in Cellular Physiology with emphasis on problems in Neuroscience. Past research has been on error analysis for finite element methods for partial differential equations and primarily time-dependent problems arising in applications such as phase transitions, viscoelasticity, and thermoelasticity. Investigations into the development of time discretizations using finite element techniques have led to various energy preserving schemes. Have also worked in Industrial Mathematics.
Peer Reviewed Publications
French, D.A., Edwards, D., Badamdorj, D., & Kleene, S.J. (2008). Analysis of the dynamics of CNG and Cl(Ca) ion channels in olfactory cilia. Math. Meth. Appl. Sci., 31, 1860-1873.
French, D.A., & Groetsch, C. (2007). Numerical Approximation of Solutions of a Constrained Integral Equation Arising in Olfaction Experimentation. J. of Physics: Conference Series, 73, 1-10.
French, D.A., & Edwards, D. (2007). Perturbation derivation of ligand-gated ion channel distributions arising in olfaction experimentation. J. Math. Biology, 55, 745-765.
French, Donald, & Oh, J. (2006). Error Analysis of a Specialized Numerical Method for Differential Equation Models in Neuroscience. Appl. Math. Comput., 172, 491-507.
Flannery, R., French, Donald, Groetsch, C., Krantz, W., & Kleene, S. (2006). Identification of CNG channel distributions in frog olfactory cilia. Math. Comp. Modelling, 43, 945-956.
Flannery, R., French, Donald, & Kleene, S.J. (2006). Clustering of CNG channels in the cilia of frog olfactory receptor neurons. Biophys. J., 91, 179-188.
French, Donald, & Gruenstein, E. (2006). An Integrate-and-Fire Model for Synchronized Bursting in a Network of Cultured Cortical Neurons. J. Comp. Neurosci, 21, 227-241.
Copetti, M.I.M., & French, Donald (2005). A posteriori error estimates for low order continuous and discontinuous Galerkin methods for a thermoelastic contact problem. Appl. Num. Math., 55, 439-457.
Copetti, M.I.N., & French, Donald (2004). Numerical studies of thermoelastic contact problem. Applied Mathematica lModeling, 28, 323-332.
French, Donald (2004). Identification of a free energy functional in an integro-differential equation model for neuronal activity. Appl. Math. Lett., 17, 1047-1051.
Copetti, M.I.M., & French, Donald (2003). Numerical solution of a thermoviscoelastic contact problem by a penalty method. SIAM J. Num. Anal., 41, 1487-1504.
French, Donald (2003). Analysis of the convergence behavior of the localized nonlinear approximation for electromagnetic scattering. J. Comp. Appl. Math., 161, 27-39.
French, Donald, Larsson, S., & Nochetto, R. (2001). A posteriori error estimates for a finite element approximation of the obstacle problem in L1. Computational Methods in Applied Mathematics, 1, 18-38.
Albert, S., Cockburn, B., French, Donald, & Peterson, T. (2001). A posteriori error estimates for general numerical methods for the Hamilton-Jacobi equation. Math. Comp., 71, 49-76.
Other Publications
French, Donald (1992). Analysis and computation of solutions to an evolution problem in nonlinear viscoelasticity. Proceedings of the Ninth Army Conference on Applied Mathematics and Computing, 92-1, 107-113.
French, Donald (1993). Long time behavior of a numerical approximation to a nonlinear evolution problem in viscoelasticity. Proceedings of the Tenth Army Conference on Applied Mathematics and Computing, 93-1, 23-28.
French, Donald (1994). Analysis and computation of approximate solutions to a simple model of shear band formation in one and two dimensions. Proceedings of the Eleventh Army Conference on Applied Mathematics and Computing, 94-1, 287-298.
Abbot, J.S., French, Donald, & et al. (1995). Determining index data and refracted/diffracted rays. Proceedings of the Eleventh Workshop on Mathematical Problems in Industry, Los Alamos National Laboratory Technical Report LA-UR 95-4038.
Hendricks, F. et al. (1997). The design of hard drive slider bearings. Proceedings of the Twelfth Workshop on Mathematical Problems in Industry 47-60.
Hector, Jr., L.G. et al. (1999). Thermomechanical models of air gap nucleation during pure metal solidification on moving molds with periodic surface topographies. Proceedings of the Fourteenth Workshop on Mathematical Problems in Industry.
Mauk, M. et al. (2000). A mathematical model for epitaxial semiconductor crystal growth from a vapor phase masked substrate. Proceedings of the Fifteenth Workshop on Mathematical Problems in Industry.
Lectures
(10-2006). Identification of ion channel distributions in olfactory cilia. AMS Sectional Meeting, Cincinnati, OH.
(04/06/2006). Numerical approximation of solutions of a nonlinear inverse problem arising in olfaction experimentation. University of California at Davis .
(2006). Identification of ion channel distributions in olfactory cilia. SIAM Annual Meeting, Raleigh, NC.
(10/27/2005). Numerical approximation of solutions of a nonlinear inverse problem arising in olfaction experimentation. University of Delaware.
(07-2005). Numerical approximation of solutions of a nonlinear inverse problem arising in olfaction experimentation. SIAM Annual Meeting, New Orleans, LA.
(05-2005). Numerical approximation of solutions of a nonlinear inverse problem arising in olfaction experimentation. Midwest Numerical Analysis Conference, University of Iowa.
(11/14/2000). Time discretizations for evolution problems derived with finite element techniques. University of Kentucky.
(06/15/2000). The evaluation of option prices on baskets via a perturbation approach. Mathematical Problems in Industry Workshop, University of Delaware.
