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We study the dynamics of a single inertial run-and-tumble particle on a straight line. The motion of this particle is characterized by two intrinsic time-scales, namely, an inertial and an active time-scale. We show that interplay of these…

Statistical Mechanics · Physics 2025-05-21 Debraj Dutta , Anupam Kundu , Urna Basu

We study the non-stationary Feller process with time varying coefficients. We obtain the exact probability distribution exemplified by its characteristic function and cumulants. In some particular cases we exactly invert the distribution…

Statistical Mechanics · Physics 2016-02-17 Jaume Masoliver

In this paper we present a new model for modeling the diffusion and relative dispersion of particles in homogeneous isotropic turbulence. We use an Heisenberg-like Hamiltonian to incorporate spatial correlations between fluid particles,…

Fluid Dynamics · Physics 2012-12-18 Thomas Burgener , Dirk Kadau , Hans Jürgen Herrmann

We consider a run-and-tumble particle whose speed and tumbling rate are space-dependent on an infinite line. Unlike most of the previous work on such models, here we make the physical assumption that at large distances, these rates saturate…

Statistical Mechanics · Physics 2024-12-10 Kavita Jain , Sakuntala Chatterjee

The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…

Statistical Mechanics · Physics 2017-10-11 A. Kamińska , T. Srokowski

We consider an active run-and-tumble particle (RTP) in $d$ dimensions and compute exactly the probability $S(t)$ that the $x$-component of the position of the RTP does not change sign up to time $t$. When the tumblings occur at a constant…

Statistical Mechanics · Physics 2020-03-03 Francesco Mori , Pierre Le Doussal , Satya N. Majumdar , Gregory Schehr

We study the long-time behaviour of a run and tumble model which is a kinetic-transport equation describing bacterial movement under the effect of a chemical stimulus. The experiments suggest that the non-uniform tumbling kernels are…

Analysis of PDEs · Mathematics 2024-04-30 Josephine Evans , Havva Yoldaş

We present a general framework to study the distribution of the flux through the origin up to time $t$, in a non-interacting one-dimensional system of particles with a step initial condition with a fixed density $\rho$ of particles to the…

Statistical Mechanics · Physics 2020-05-06 Tirthankar Banerjee , Satya N. Majumdar , Alberto Rosso , Gregory Schehr

The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…

Quantum Physics · Physics 2013-05-29 Alex D. Gottlieb

The phenomenology of turbulent relative dispersion is revisited. A heuristic scenario is proposed, in which pairs of tracers undergo a succession of independent ballistic separations during time intervals whose lengths fluctuate. This…

Fluid Dynamics · Physics 2015-06-19 Simon Thalabard , Giorgio Krstulovic , Jeremie Bec

We consider the moving particle process in Rd which is defined in the following way. There are two independent sequences (Tk) and (dk) of random variables. The variables Tk are non negative and form an increasing sequence, while variables…

Probability · Mathematics 2016-09-27 Youri Davydov , Valentin Konakov

We study a set of Run-and-tumble particle (RTP) dynamics in two spatial dimensions. In the first case of the orientation {\theta} of the particle can assume a set of n possible discrete values while in the second case {\theta} is a…

Statistical Mechanics · Physics 2020-06-17 Ion Santra , Urna Basu , Sanjib Sabhapandit

We study interacting particle systems on the real line which generalize the Hammersley process [D. Aldous and P. Diaconis, Prob. Theory Relat. Fields 103, 199-213 (1995)]. Particles jump to the right to a randomly chosen point between their…

Statistical Mechanics · Physics 2011-05-20 J. Krug , J. Garcia

This paper introduces a run-and-tumble model with self-reinforcing directionality and rests. We derive a single governing hyperbolic partial differential equation for the probability density of random walk position, from which we obtain the…

Quantitative Methods · Quantitative Biology 2022-02-09 Sergei Fedotov , Daniel Han , Alexey O Ivanov , Marco A A da Silva

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model,…

Statistical Mechanics · Physics 2014-03-20 Long Shi , Zuguo Yu , Zhi Mao , Aiguo Xiao

We derive the fully time-dependent solution to a run-and-tumble model for a particle which has tumbling restricted to the boundaries of a one-dimensional interval. This is achieved through a field-theoretic perturbative framework by…

Statistical Mechanics · Physics 2025-08-06 Connor Roberts , Gunnar Pruessner

We consider a one-dimensional run-and-tumble particle, or persistent random walk, in the presence of an absorbing boundary located at the origin. After each tumbling event, which occurs at a constant rate $\gamma$, the (new) velocity of the…

Statistical Mechanics · Physics 2021-05-31 Benjamin De Bruyne , Satya N. Majumdar , Gregory Schehr

We study a model of interacting run-and-tumble random walkers operating under mutual hardcore exclusion on a one-dimensional lattice with periodic boundary conditions. We incorporate a finite, Poisson-distributed, tumble duration so that a…

Statistical Mechanics · Physics 2017-08-18 A. B. Slowman , M. R. Evans , R. A. Blythe

We study persistent random walk with time dependent velocity reversal probabilities and identify a criterion for a non-equilibrium dynamical transition. As a representative example, we consider a power law reversal probability $p(t)\sim…

Statistical Mechanics · Physics 2026-05-20 Amit Pradhan , Reshmi Roy , Purusattam Ray

We study the steady-state distribution function of a run-and-tumble particle evolving around a repulsive hard spherical obstacle. We show that the well-documented activity-induced attraction translates into a delta peak accumulation at the…

Statistical Mechanics · Physics 2023-09-01 Thibaut Arnoulx de Pirey , Frédéric van Wijland