Areas of Research

• Traffic flow Modelling

• In traffic flow modeling, we are interested in developing realistic models (Micro as well as Macro) to discover many interesting phenomenon of traffic dynamics in a network. The proposed models are analyzed and investigated theoretically and simulation is performed to test the analytical findings. These models plays a crucial role in understanding the complex mechanism of traffic congestion (jam) which is one of the serious problem for developed as well as developing countries nowadays.

• Multi - Channel Exclusion Process

• There exist a large number of systems in real world namely vehicular traffic and kinesin's motion along parallel mictrotubules, which comprise of particles moving in more than one channel. Therefore, in order to understand the dynamical aspect of many-particle systems more adequately, it becomes important to analyze multi-channel transport systems which we study using discrete lattice gas models namely asymmetric simple exclusion process (ASEP). Given the complexity involved in the dynamics of multi-channel systems due to the inter as well as intra-channel interactions, one needs to develop new theoretical as well as computational techniques to analyze such systems.

• Cellular Automata

• Cellular automata (CA) is a modelling technique giving due consideration to individual properties and raising spatial and time discrete models of dynamical systems. CA are simple models to imitate many physical, biological or environmental complex phenomena. Typically, a two-dimensional CA comprise of two-dimensional array of identical objects called cells, having one of the possible finite states which changes in discrete time steps according to state update function.

• Ribosome Flow Model (RFM)

• Dynamical systems play a pivotal role in comprehending the diverse biophysical facets of complex transport phenomena. Within biological systems, intracellular transport stands as a fundamental process ubiquitous to all cells, thus requiring thorough investigation into its dynamics. Various mathematical models have been suggested based on a different paradigm, for example, Petri nets, probabilistic Boolean networks, and Kinetics-based ordinary differential equations. One such important model is the ribosome flow model (RFM) which is a deterministic model obtained via a mean-field approximation of ASEP. We extend the RFM by incorporating more intricate features to enhance our understanding of transport processes. We are also interested in modelling various physical phenomena under consideration involve stochastic or partial differential equations, like stock market movement and traffic flow. The aim is to augment the physics behind such systems with machine learning and generate a predictive model that learns the evolution of these systems.

• Machine learning approaches to mathematical modeling

• We are also interested in modelling various physical phenomena under consideration involve stochastic or partial differential equations, like stock market movement and traffic flow. The aim is to augment the physics behind such systems with machine learning and generate a predictive model that learns the evolution of these systems.