We investigate the persistence probability p(t) of the position of a passive and active Brownian particle with shape asymmetry in two dimensions. The persistence probability is defined as the probability that a stochastic variable has not changed its sign in the given time interval. We explicitly consider two cases—diffusion of a free particle and that of a harmonically trapped particle. The latter is particularly relevant in experiments that use trapping and tracking techniques to measure the displacements. We provide analytical expressions of p(t) for both the scenarios and show that in the absence of the shape asymmetry, the results reduce to the case of an isotropic particle. The analytical expressions of p(t) are further validated against numerical simulation of the underlying overdamped dynamics. We also illustrate that p(t) can be a measure to determine the shape asymmetry of a colloid and the translational and rotational diffusivities can be estimated from the measured persistence probability. The advantage of this method is that it does not require the tracking of the orientation of the particle.
The dynamical evolution of the surface height is controlled by either a linear or a nonlinear Langevin equation, depending on the underlying microscopic dynamics, and is often done theoretically using stochastic coarse-grained growth equations. The persistence probability p(t) of stochastic models of surface growth that are constrained by a finite system size is examined in this work. We focus on the linear Edwards-Wilkinson model (EW) and the nonlinear Kardar-Parisi-Zhang (KPZ) model, two specific models of surface growth. The persistence exponents in the continuum version of these two models have been widely investigated. Krug et al.[Phys. Rev. E , 56:2702-2712, (1997)] and Kallabis et al. [EPL (Europhysics Letters) , 45(1):20, 1999] had shown that, the steady-state persistence exponents for both these models are related to the growth exponent β as θ = 1−β. It is numerically found that the values of persistence exponents for both these models are close to the analytically predicted values. While the results of the continuum equations of the surface growth are well known, we focus to study the persistence probability expressions for discrete models with a finite size effect. In our work, we have investigated the persistence probabilities for the linear Edwards-Wilkinson (EW) model and for the non-linear Kardar-Parisi-Zhang (KPZ) model of surface growth on a finite one-dimensional lattice. The interesting phenomena which is found in this case is, the known scenario of p(t) of following algebraic decay vanishes as we introduce finite system size.
Presently I am working on binary mixture using vision based sensing model where active particle is allowed to create a vision cone and interact with the neighboring particles residing in that vision cone. Using the model we are investigating the transport dynamics and phase separation of the active particle system.
I am also working on the statistics of Cover time in stochastic search processes of Random walk and RTP particles. Until now, the primary metrics for assessing the effectiveness of such search processes have typically been articulated in relation to the duration required for the searcher to reach a solitary target, commonly referred to as the first-passage time. Yet, when the task involves locating multiple targets—a scenario frequently encountered in chemistry, ecology, or robotics—the pertinent measure shifts to the time required to reach a portion of the domain’s sites. The most comprehensive form of these exhaustive searches, where every site within a domain must be visited, defines what’s known as the cover time. This metric is particularly significant as it signifies the time required to definitively locate all targets within a domain. Determining the cover time has been a persistent challenge in the realm of random walk theory.
We study the dynamical behavior of an anisotropic active Brownian particle subjected to various stochastic resetting protocols in two dimensions. The motion of shape-asymmetric active Brownian particles in two dimensions leads to anisotropic diffusion at short times, whereas rotational diffusion causes the transport to become isotropic at longer times. We have considered three different resetting protocols: (a) complete resetting, when both position and orientation are reset to their initial states, (b) only position is reset to its initial state, (c) only orientation is reset to its initial state. We reveal that orientational resetting sustains anisotropy even at late times. When both the spatial position and orientation are subject to resetting, a complex position probability distribution forms in the steady state.