Research Projects

The search strategies are ubiquitous in nature and attracted tremendous attention over the past few years. The searcher spends some time trying to locate the desired object; after an unsuccessful and haphazard effort, the searcher goes back to the starting point and starts all over again. In this proposed project, we will consider a Brownian particle that is diffusing in a space with absorbing endpoints in one dimension and investigate what happens when such motion is stopped and then resumed from the same initial configuration in an underdamped limit considering the velocity-dependent force. We offer a thorough analysis of this trapping phenomenon's first-passage features. We will calculate the mean first passage time (MFPT) and determine the condition by which restarting the process always speeds up the completion of the underlying task. To calculate the MFPT, we will use the probability distribution function for the position of the Brownian particle. Furthermore, we will explore the memory effect on this resetting dynamics. To corroborate our analytical findings, numerical studies will be offered. In the second part of the project, we will establish a connection between the stochastic resetting mechanism and the kinetic proofreading in the biological copying process. Recasting the framework of kinetic proofreading in the same language as the stochastic resetting mechanism, we will compute the effectiveness of proofreading or optimal properties such as speed, error, or dissipation. The outcome of the proposed project will be immensely helpful in understanding the effect of velocity-dependent force and, more importantly, the non-Markovian dynamics on the first passage properties under the resetting mechanism. The ability to link stochastic resetting with kinetic proofreading opens the door toward the intelligent design of "Michaelian filters."