Applied Mathematics
Chaitan Gupta
A summary of my research is as follows: “It is well-known that the function 
cannot be expressed in terms of well-known functions, like polynomials, trigonometric functions, exponential functions or logarithmic functions. However, it is a very useful function and is used extensively in mathematics. The problem of finding the function F(x) can be posed as an initial value problem
exp (x^2) with y(0) = 0.
In view of the above remarks, we say that a solution to this problem exists even though we cannot express it in terms of well-known functions. What we have here is usually called an “existence theorem” for this initial value problem.
My current research consists in proving existence of solutions of non-linear boundary value problems for ordinary differential equations. The methods involve using non-linear functional analysis techniques and clever use of differential and integral calculus methods.”
Eric Olson
I study Navier-Stokes equations, dynamical systems, fractal dimensions and turbulence. Techniques used include functional analysis and large scale numerical simulation. I am currently working on the normal form of the Navier-Stokes equations, the Langrangian averaged Navier-Stokes alpha model of turbulence, numerically determining modes, the Bouligand dimension and the bioremediation of contaminated soil.
Mark Pinsky
My research centers on the modeling, simulation and control of complex nonlinear systems, multiscale computing, integration of asymptotic and numerical techniques, abstraction and reduction techniques for large nonlinear models, modeling and control of bifurcation and chaos phenomena, and robust, impulsive and observation control of nonlinear systems.
Specific current projects include a) Multiscale modeling and simulation of molecule systems, b) Modeling and simulation of flow of magnetized nanoparticles in blood vessels, c) fast algorithms for modeling of atmospheric chemistry phenomena, d) Image tracking and processing algorithms, e) Stability bounds for partially uncertain nonlinear systems, and f) Robust control of bifurcation phenomena.
Aleksey Telyakovskiy
My research interests include numerical analysis, approximate solution techniques, mathematical modeling, and mechanics of flows through porous media. Some specific applications in these topics are contaminant transport, modeling of underground flows in enhanced oil recovery and saltwater intrusion. In some cases analytical or approximate analytical solutions can be constructed as a result important qualitative information on nature of solutions can be obtained, but in general equations are solved numerically. There are many numerical methods that can be used for analysis, such as, finite differences, mixed finite elements and Eulerian-Lagrangian methods. In modeling of flows through porous media multiple physical phenomena occur that complicate the numerical solution. Here are some of the difficulties: sharp fronts, which traditional upwind numerical schemes do not resolve due to the excessive numerical diffusion; a grid orientation effect; equations may include chemical reactions, consequently nonlinear thermodynamic constraints must be solved taking significant computational time. All these make these problems interesting and challenging.