Extension and dynamical phases in random walkers depositing and following chemical trails. (1st November 2022)

• Record Type: Journal Article
• Authors: Khuntia, Subhashree Subhrasmita; Chaudhuri, Abhishek; Chaudhuri, Debasish
• Is Part Of: Europhysics letters. Volume 140:Number 3(2022)
• Publication Date: 2022-11-01
• Subjects: Physics -- Periodicals; Electronic journals; 530.05
• DOI: 10.1209/0295-5075/ac9b87
• Languages: English
• ISSNs: 0295-5075

Abstract

Abstract: Active walker models have proved to be extremely effective in understanding the evolution of a large class of systems in biology like ant trail formation and pedestrian trails. We propose a simple model of a random walker which modifies its local environment that in turn influences the motion of the walker at a later time. We perform direct numerical simulations of the walker in a discrete lattice with the walker actively depositing a chemical which attracts the walker trajectory and also evaporates in time. We propose a method to look at the structural transitions of the trajectory using radius of gyration for finite time walks. The extension over a definite time window shows a non-monotonic change with the deposition rate characteristic of a coil-globule transition. At certain regions of the parameter space of the chemical deposition and evaporation rates, the extensions of the walker shows a re-entrant behavior. The dynamics, characterised by the mean-squared displacement, shows deviation from diffusive scaling at intermediate time scales, returning to diffusive behavior asymptotically. A mean-field theory captures the variation of the asymptotic diffusivity.