arXiv subjects

T. V. Mendes

Publications and source records attributed to T. V. Mendes.

3 recordsLinked to original sources

arXiv2026

Optimization of multisite reactions in complex compartmentalized media

In complex media, transport and geometric properties deeply influence the kinetics of random encounters between reactants. Here, we consider the situation where a random walker, moving in a regularly diffusing medium, has to reach and activate a target located inside a compartment characterized by fractal (obstructed) sub-diffusion. We focus on dual-site reactions, which end when two activation events occur within a given time window. Each activation event happens with a finite probability whenever the random walker visits the target. For weakly reactive targets, we demonstrate that the reaction time can be minimized for an optimal compartment size and can even be accelerated when compared to the same system without compartment. Our analytical predictions are validated through simulations of a random walker on a cubic lattice, where some sites inside the compartment are obstructed at the critical percolation threshold. Our theory illustrates the fact that adding a crowded compartment around a target, even if it slows down the motion in its vicinity, can accelerate the kinetics of complex reactions, especially for weakly reactive targets.

cond-mat.stat-mech↗

arXiv2025

Evidence and quantification of memory effects in competitive first passage events

Splitting probabilities quantify the likelihood of a given outcome out of competitive events. This key observable of random walk theory, historically introduced as the gambler's ruin problem, is well understood for memoryless (Markovian) processes. However, in complex systems such as polymer fluids, the motion of a particle should typically be described as a process with memory, for which splitting probabilities are much less characterized analytically. Here, we introduce an analytical approach that provides the splitting probabilities for one-dimensional isotropic non-Markovian Gaussian processes with stationary increments, in the case of two targets. This analysis shows that splitting probabilities are controlled by the out of equilibrium trajectories observed after the first passage. This is directly evidenced in a prototypical experimental reaction scheme in viscoelastic fluids. These results are extended to $d$-dimensional processes in large confining volumes, opening a path towards the study of competitive events in complex media.

cond-mat.stat-mech↗

arXiv2022

Everlasting impact of initial perturbations on first-passage times of non-Markovian random walks

Persistence, defined as the probability that a fluctuating signal has not reached a threshold up to a given observation time, plays a crucial role in the theory of random processes. It quantifies the kinetics of processes as varied as phase ordering, reaction diffusion or interface relaxation dynamics. The fact that persistence can decay algebraically with time with non trivial exponents has triggered a number of experimental and theoretical studies. However, general analytical methods to calculate persistence exponents cannot be applied to the ubiquitous case of non-Markovian systems relaxing transiently after an imposed initial perturbation. Here, we introduce a theoretical framework that enables the non perturbative determination of persistence exponents of $d$-dimensional Gaussian non-Markovian processes with general non stationary dynamics relaxing to a steady state after an initial perturbation. Two prototypical classes of situations are analyzed: either the system is subjected to a temperature quench at initial time, or its past trajectory is assumed to have been observed and thus known. Altogether, our results reveal and quantify, on the basis of Gaussian processes, the deep impact of initial perturbations on first-passage statistics of non-Markovian processes. Our theory covers the case of spatial dimension higher than one, opening the way to characterize non-trivial reaction kinetics for complex systems with non-equilibrium initial conditions.

cond-mat.stat-mech↗