Dmitriy Melnikov

Biography

Dr. Dmitriy Melnikov presently working as a Professor in the Deparment of Computer Science, at Clarkson University.

Research Interest

"I am interested in the properties of large networks occurring in everyday life (social networks of contact, the Internet and the WWW, networks of flight connections, of neurons in the brain, etc.) and I use tools from statistical physics for their analysis. The study of networks has numerous applications, from devising more efficient networks of transportation, to improving the resilience of the Internet to random breakdown or to intentional attack, to finding strategies for arresting the spread of epidemics that propagate by social interaction. I am also interested in diffusion-limited kinetics, that is, the way reaction processes evolve when the reactants take a much longer time to encounter each other (by diffusion) than to undergo reaction. The situation is dominated by fluctuations at all length scales and gives rise to anomalous kinetics -- quite different from reaction-limited kinetics (where the reaction time is very large), which can be analyzed by classical rate equations. At a more fundamental level, I study diffusion and random walks in fractals and disordered media. In all regular lattices, regardless of dimensionality (e.g., square, triangular, cubic, etc.) diffusion follows a universal scaling law: the mean square displacement increases linearly with time. However, in fractals and disordered media diffusion is anomalous - the mean square displacement grows slower than linearly with time. Other interests of mine include nonequilibrium kinetics and kinetics phase transitions, heterogeneous catalysis (catalytic reactions occurring on surfaces, or the interface of different media), and self avoiding walks (a model for linear polymers). I am also interested in various aspects of biological physics, such as the structure and motility of proteins (normal modes analysis), actin filaments in muscle and the scaffolding of cells, and the role of diffusion in signal transduction. "