Ph.D. Applied Mathematics, University of Pittsburgh, 2004
M.Sc. Applied Mathematics, University of Kaiserslautern, 2000
M.Sc. Mathematics, Institute for Advanced Studies in Sciences of Zanjan, 1996
B.A. Mathematics, Sharif University of Technology, 1993
Research Interests and Innovations
My research is in the area of Computational Mathematics with a particular interest in Sensitivity Analysis that has applications in different branches of science (Biology, Physics, and Finance) as well as engineering. The main focus of my research is the development and implementation of Sensitivity Equation Methods for models in Ordinary and Partial Differential Equations which primarily involves the areas of Numerical Analysis and Scientific Computing.
Generally speaking sensitivity describes how small changes in a parameter affect the behavior of a given physical system. There are parameters appearing in the mathematical models as equation coefficients, initial and boundary conditions, or the shape of the domain describing a physical property, physical shape or position, etc. Sensitivities have the important application of utilizing the parameter prioritization in model analysis, and of quantifying the parameter uncertainty in models.
I have used the Parameter Sensitivity Analysis in the following areas:
- Parameter Sensitivity Analysis in Models of Fluid Dynamics
- Parameter Sensitivity Analysis of Biology Models
- Parameter Sensitivity Analysis as an Undergraduate Research Project
Teaching Interests and courses taught
I am particularly interested in teaching topics that covers Ordinary Differential Equations, Partial Differential Equations, and Numerical Analysis.
Courses taught includes: Math 110, Math 140/140B, Math 141/141B, Math 230, Math 231.
S. Liu, F. Pahlevani, K. Pawelek and L. Rong, A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data, Journal of Mathematical Biosciences, Vol. 235 (2012), pp. 98-109.
L. Davis and F. Pahlevani, Parameter Sensitivity of an Eddy Viscosity Model: Analysis, Computation and Its Application to Quantifying Model Reliability, To appear in International Journal for Uncertainty Quantification, (2012).
L. Davis and F. Pahlevani, Semi-Implicit Schemes for Transient Navier-Stokes Equations and Eddy Viscosity Models, International Journal of Numerical Methods for Partial Differential Equations, Vol. 25 (2009), pp. 212-231.
F. Pahlevani, Sensitivity Computations of Eddy Viscosity Models with an Application in Drag Computation, International Journal for Numerical Methods in Fluids, Vol. 52 (2006), pp. 381-392.
M. Anitescu, F. Pahlevani and W. Layton, Implicit for Local Effects and Explicit for Nonlocal Effects is Unconditionally Stable, Electronic Transaction on Numerical Analysis, Vol. 18 (2004), pp. 178-183.
Selected Awards, Grants, Patents, other Honors
The Pennsylvania State University, Research Collaboration Fellowship; Summer 2012; Award: $10000.
PSC-CUNY grant #60107-37 38; Academic year 2007-2008; Award: $4,016.
Medgar Evers College Presidential Research Award, in collaboration with Dr. Christina Mouser; Academic year 2007-2008; Award: $5,000.