First-passage time of run-and-tumble particles with noninstantaneous resetting

Optimal resetting strategies for search processes in heterogeneous environments

“…We have focused on providing a minimal model, for which the novel first passage properties stemming from the disorder could be obtained in an exact way. However, there are many aspects still to be explored, as a consequence of the distributed target position: (i) the latter can be interpreted as a quenched disorder, and a search process in a quenched vs annealed case can be investigated in the framework of disordered systems [18,36,37]; (ii) the problem of finding an optimal resetting rate α(x) for a given target distribution p T (x T ) in 1d processes is still open [1,33], and our work represents a first step in this direction; (iii) our results may be generalised to higher-dimensional systems, where we conjecture that the MFPT performance may increase significantly [38]; (iv) prior information about the target distribution leads to more efficient search strategies; in the context of stochastic thermodynamics [39][40][41], it would be interesting to address the role of fluctuation relations and the entropy of information in resetting systems [42][43][44]-in analogy with the situation found in feedback controlled systems [45][46][47]; (v) it is tempting to associate this information to an active particle exploring the environment with a persistent self-propulsion [48,49], following recent approaches in resetting dynamics [50,51]. (s|x 0 ) yields…”

Striking universalities in stochastic resetting processes

“…There are two interesting consequences of resetting: i) the resetting drives the system into a nonequilibrium stationary state where the distribution of the position of the particle becomes independent of time and is typically non-Gaussian, ii) the mean first-passage time (MFPT) to a target located at a distance R from the origin becomes finite and, moreover, as a function of the resetting rate r, the MFPT exhibits a minimum indicating the existence of an optimal resetting rate r * [4][5][6]. These two features have been found in numerous theoretical models, going beyond simple diffusion: random walk on a lattice with resetting [7], continuous-time random walks [8][9][10][11] and Lévy flights with resetting [12,13], Brownian particle in a confining potential [14], active run-and-tumble particles under resetting [15][16][17], non-Poissonian resetting [18,19], Poissonian resetting with a site-dependent (a) E-mail: schehr@lpthe.jussieu.fr (corresponding author) resetting rate [20,21], resetting with memory [22,23], etc. Moreover, these two features have been verified in recent experiments using optical tweezers, both in one [24,25] and two dimensions [26].…”

One-dimensional run-and-tumble motions with generic boundary conditions

“…Table 1. Different types of boundaries and the corresponding expressions of the gw function, appearing in boundary conditions ( 15) and ( 16), obtained for particular choices of the parameters values λw and αw in the general expression (24) given in the text. See figure 1 for the meaning of the different parameters.…”

“…Totally absorbing/reflecting boundaries are considered in [11,15,16]; the case of partial absorption has been investigated in [17,18]; sticky boundaries, allowing particles accumulation, are analyzed in [19]. There are also many studies that deal with the boundary problem for RT particles in a variety of contexts, as, for example, considering resetting processes [20][21][22][23][24], diffusion terms in kinetic equations [25], space-dependent speed [26], confining potentials [27,28], ratchet effects [29,30], extremal statistics [31], fractional equations [32], encounter-based absorption [33,34]. While previous work provides a fairly clear picture of the possible cases of boundary conditions, a thorough discussion of their role and a comprehensive treatment is still lacking.…”