Research Projects

The common theme underlying my research may be broadly defined as Interactions of Particles with Matter. More specifically, I study a variety of processes occurring when accelerated beams of electrons or atomic, molecular and cluster ions interact with the bulk or surface regions of solid and plasma targets, as well as with nano-meter sized matter. Such processes have found many technological applications in areas such as catalysis, materials science, fusion technology, fabrication of micro-electronic devices, radiation medicine, and environmental studies. Moreover, many interesting new applications are emerging from contemporary experimental research. Here are some intriguing examples.
  1. Fast cluster ions may be used to achieve controllable structural and chemical modifications in microscopic volumes of solid material, or to accomplish very efficient energy deposition in fusion reactors.
  2. The so-called Coulomb explosion of deuterium clusters, driven by a strong and short laser pulse, may give rise to a significant rate of nuclear fusion, allowing one to speculate about prospects for table-top fusion reactors.
  3. Fluctuations of electrostatic fields above solid surfaces with structural and chemical irregularities impart strong influences on the electron transmission through the nano-meter-scale electronic circuits designed on such surfaces.
  4. The so-called dusty plasma, occurring in the conventional plasma processing of micro-electronic devices, exhibits crystallization of the micron-sized dust grains, which may be controlled by ion flow.
  5. The newly-discovered carbon structures in the form of nano-meter wide cylindrical tubules may be used as microscopic "wave-guides", or accelerators, for beams of particles such as electrons and ions.
  6. My latest research topic within carbon nanostructires involves the immensely popular graphene, where I am interested in its applications in Plasmonics and bio-chamical sensors. This latter direction brings me to an anterface with Electrochemistry.
My research focuses on the theoretical description of such processes, with the goals of understanding observed phenomena and delineating possibilities for new applications.

In my work, I often use stochastic methods. In near future, I plan to extend the focus of my research to applications of Stochastic Processes in new areas, such as Biology.

Student Training

Funding is available for one graduate student (Master's or PhD degree), who is interested in any aspects of the research problems, described here.

From the methodological point of view, my research encompasses theoretical models from a variety of scientific disciplines, such as solid state physics, plasma physics, collision theory, kinetic theory, and stochastic processes. Mathematical challenges arising in my research require skillful use of many techniques from vector calculus, complex analysis, ordinary and partial differential equations, integral equations, calculus of variations, probability and statistics, numerical analysis, and symbolic computation.

Both graduate and undergraduate students in Applied Mathematics and Physics programs will benefit from involvement in the research described here in several ways. Each student will acquire the following essential skills of a problem-solver: effective and critical use of the information available from various resources, ability to formulate mathematical model for a real-world problem, resourcefulness in using analytical and numerical methods to solve the problem at hand, and competence in presenting and interpreting the results in scientific terms.