arXiv subjects

Denis Boyer

Publications and source records attributed to Denis Boyer.

At least 37 records · Page 2Linked to original sources

arXiv2024

Optimizing the random search of a finite-lived target by a Lévy flight

In many random search processes of interest in chemistry, biology or during rescue operations, an entity must find a specific target site before the latter becomes inactive, no longer available for reaction or lost. We present exact results on a minimal model system, a one-dimensional searcher performing a discrete time random walk or Lévy flight. In contrast with the case of a permanent target, the capture probability and the conditional mean first passage time can be optimized. The optimal Lévy index takes a non-trivial value, even in the long lifetime limit, and exhibits an abrupt transition as the initial distance to the target is varied. Depending on the target lifetime, this transition is discontinuous or continuous, separated by a non-conventional tricritical point. These results pave the way to the optimization of search processes under time constraints.

cond-mat.stat-mech↗

arXiv2023

Diffusion limited aggregation, resetting and large deviations of Brownian motion

Models of fractal growth commonly consider particles diffusing in a medium and that stick irreversibly to the forming aggregate when making contact for the first time. As shown by the well-known diffusion limited aggregation (DLA) model and its generalisations, the fractal dimension is sensitive to the nature of the stochastic motion of the particles. Here, we study the structures formed by finite-lived Brownian particles, i.e., particles constrained to find the aggregate within a prescribed time, and which are removed otherwise. This motion can be modelled by diffusion with stochastic resetting, a class of processes which has been widely studied in recent years. In the short lifetime limit, a very small fraction of the particles manage to reach the aggregate. Hence, growth is controlled by atypical Brownian trajectories, that move nearly in straight line according to a large deviation principle. In $d$ dimensions, the resulting fractal dimension of the aggregate decreases from the DLA value and tends to 1, instead of increasing to $d$ as expected from ballistic aggregation. In the zero lifetime limit one recovers the non-trivial model of "aggregation by the tips" proposed long ago by R. Jullien [J. Phys. A: Math. Gen. 19, 2129 (1986)].

cond-mat.stat-mech↗

arXiv2022

Fick-Jacobs description and first passage dynamics for diffusion in a channel under stochastic resetting

Transport of particles through channels is of paramount importance in physics, chemistry and surface science due to its broad real world applications. Much insights can be gained by observing the transition paths of a particle through a channel and collecting statistics on the lifetimes in the channel or the escape probabilities from the channel. In this paper, we consider the diffusive transport through a narrow conical channel of a Brownian particle subject to intermittent dynamics, namely, stochastic resetting. As such, resetting brings the particle back to a desired location from where it resumes its diffusive phase. To this end, we extend the Fick-Jacobs theory of channel-facilitated diffusive transport to resetting-induced transport. Exact expressions for the conditional mean first passage times, escape probabilities and the total average lifetime in the channel are obtained, and their behaviour as a function of the resetting rate are highlighted. It is shown that resetting can expedite the transport through the channel -- rigorous constraints for such conditions are then illustrated. Furthermore, we observe that a carefully chosen resetting rate can render the average lifetime of the particle inside the channel minimal. Interestingly, the optimal rate undergoes continuous and discontinuous transitions as some relevant system parameters are varied. The validity of our one-dimensional analysis and the corresponding theoretical predictions are supported by three-dimensional Brownian dynamics simulations. We thus believe that resetting can be useful to facilitate particle transport across biological membranes -- a phenomena that can spearhead further theoretical and experimental studies.

cond-mat.stat-mech↗

arXiv2022

Reducing mean first passage times with intermittent confining potentials: a realization of resetting processes

During a random search, resetting the searcher's position from time to time to the starting point often reduces the mean completion time of the process. Although many different resetting models have been studied over the past ten years, only a few can be physically implemented. Here we study theoretically a protocol that can be realised experimentally and which exhibits unusual optimization properties. A Brownian particle is subject to an arbitrary confining potential $v(x)$ which is switched on and off intermittently at fixed rates. Motion is constrained between an absorbing wall located at the origin and a reflective wall. When the walls are sufficiently far apart, the interplay between free diffusion during the "off" phases and attraction toward the potential minimum during the "on" phases gives rise to rich behaviours, not observed in ideal resetting models. For potentials of the form $v(x)=k|x-x_0|^n/n$, with $n>0$, the switch-on and switch-off rates that minimise the mean first passage time (MFPT) to the origin undergo a continuous phase transition as the potential stiffness $k$ is varied. When $k$ is above a critical value $k_c$, potential intermittency enhances target encounter: the minimal MFPT is lower than the Kramer's time and is attained for a non-vanishing pair of switching rates. We focus on the harmonic case $n=2$, extending previous results for the piecewise linear potential ($n=1$) in unbounded domains. We also study the non-equilibrium stationary states emerging in this process.

cond-mat.stat-mech↗

arXiv2022

Freezing transitions of Brownian particles in confining potentials

We study the mean first passage time (MFPT) to an absorbing target of a one-dimensional Brownian particle subject to an external potential $v(x)$ in a finite domain. We focus on the cases in which the external potential is confining, of the form $v(x)=k|x-x_0|^n/n$, and where the particle's initial position coincides with $x_0$. We first consider a particle between an absorbing target at $x=0$ and a reflective wall at $x=c$. At fixed $x_0$, we show that when the target distance $c$ exceeds a critical value, there exists a nonzero optimal stiffness $k_{\rm opt}$ that minimizes the MFPT to the target. However, when $c$ lies below the critical value, the optimal stiffness $k_{\rm opt}$ vanishes. Hence, for any value of $n$, the optimal potential stiffness undergoes a continuous "freezing" transition as the domain size is varied. On the other hand, when the reflective wall is replaced by a second absorbing target, the freezing transition in $k_{\rm opt}$ becomes discontinuous. The phase diagram in the $(x_0,n)$-plane then exhibits three dynamical phases and metastability, with a "triple" point at $(x_0/c\simeq 0.17185$, $n\simeq 0.39539)$. For harmonic or higher order potentials $(n\ge 2)$, the MFPT always increases with $k$ at small $k$, for any $x_0$ or domain size. These results are contrasted with problems of diffusion under optimal resetting in bounded domains.

cond-mat.stat-mech↗

arXiv2022

First passage time and information of a one-dimensional Brownian particle with stochastic resetting to random positions

We explore the effects of stochastic resetting to random positions of a Brownian particle on first passage times and Shannon's entropy. We explore the different entropy regimes, namely, the \textit{externally-driven}, the \textit{zero-entropy} and the \textit{Maxwell demon} regimes. We show that the mean first passage time (MPFT) minimum can be found in any of these regimes. We provide a novel analytical method to compute the MFPT, the mean first passage number of resets (MFPNR) and mean first passage entropy (MFPE) in the case where the Brownian particle resets to random positions sampled from a set of distributions known \textit{a priori}. We show the interplay between the reset position distribution's second moment and the reset rate, and the effect it has on the MFPT and MFPE. We further propose a mechanism whereby the entropy per reset can be either in the Maxwell demon or the externally driven regime, yet the overall mean first passage entropy corresponds to the zero-entropy regime. Additionally, we find an overlap between the dynamic phase space and the entropy phase space. We use this method in a generalized version of the Evans-Majumdar model by assuming the reset position is random and sampled from a Gaussian distribution. We then consider the \textit{toggling reset} whereby the Brownian particle resets to a random position sampled from a distribution dependent on the reset parity. All our results are compared to and in agreement with numerical simulations.

cond-mat.soft↗

arXiv2022

Discrete-time random walks and Lévy flights on arbitrary networks: when resetting becomes advantageous?

The spectral theory of random walks on networks of arbitrary topology can be readily extended to study random walks and Lévy flights subject to resetting on these structures. When a discrete-time process is stochastically brought back from time to time to its starting node, the mean search time needed to reach another node of the network may be significantly decreased. In other cases, however, resetting is detrimental to search. Using the eigenvalues and eigenvectors of the transition matrix defining the process without resetting, we derive a general criterion for finite networks that establishes when there exists a non-zero resetting probability that minimizes the mean first passage time at a target node. Right at optimality, the coefficient of variation of the first passage time is not unity, unlike in continuous time processes with instantaneous resetting, but above 1 and depends on the minimal mean first passage time. The approach is general and applicable to the study of different discrete-time ergodic Markov processes such as Lévy flights, where the long-range dynamics is introduced in terms of the fractional Laplacian of the graph. We apply these results to the study of optimal transport on rings and Cayley trees.

cond-mat.stat-mech↗

arXiv2021

Search of stochastically gated targets with diffusive particles under resetting

The effects of Poissonian resetting at a constant rate $r$ on the reaction time between a Brownian particle and a stochastically gated target are studied. The target switches between a reactive state and a non-reactive one. We calculate the mean time at which the particle subject to resetting hits the target for the first time, while the latter is in the reactive state. The search time is minimum at a resetting rate that depends on the target transition rates. When the target relaxation rate is much larger than both the resetting rate and the inverse diffusion time, the system becomes equivalent to a partially absorbing boundary problem. In other cases, however, the optimal resetting rate can be a non-monotonic function of the target rates, a feature not observed in partial absorption. We compute the relative fluctuations of the first hitting time around its mean and compare our results with the ungated case. The usual universal behavior of these fluctuations for resetting processes at their optimum breaks down due to the target internal dynamics.

cond-mat.stat-mech↗

arXiv2021

Diffusive transport on networks with stochastic resetting to multiple nodes

We study the diffusive transport of Markovian random walks on arbitrary networks with stochastic resetting to multiple nodes. We deduce analytical expressions for the stationary occupation probability and for the mean and global first passage times. This general approach allows us to characterize the effect of resetting on the capacity of random walk strategies to reach a particular target or to explore the network. Our formalism holds for ergodic random walks and can be implemented from the spectral properties of the random walk without resetting, providing a tool to analyze the efficiency of search strategies with resetting to multiple nodes. We apply the methods developed here to the dynamics with two reset nodes and derive analytical results for normal random walks and Lévy flights on rings. We also explore the effect of resetting to multiple nodes on a comb graph, Lévy flights that visit specific locations in a continuous space, and the Google random walk strategy on regular networks.

cond-mat.stat-mech↗

arXiv2021

First hitting times between a run-and-tumble particle and a stochastically-gated target

We study the first hitting time statistics between a one-dimensional run-and-tumble particle and a target site that switches intermittently between visible and invisible phases. The two-state dynamics of the target is independent of the motion of the particle, which can be absorbed by the target only in its visible phase. We obtain the mean first hitting time when the motion takes place in a finite domain with reflecting boundaries. Considering the turning rate of the particle as a tuning parameter, we find that ballistic motion represents the best strategy to minimize the mean first hitting time. However, the relative fluctuations of the first hitting time are large and exhibit non-monotonous behaviours with respect to the turning rate or the target transition rates. Paradoxically, these fluctuations can be the largest for targets that are visible most of the time, and not for those that are mostly invisible or rapidly transiting between the two states. On the infinite line, the classical asymptotic behaviour $\propto t^{-3/2}$ of the first hitting time distribution is typically preceded, due to target intermittency, by an intermediate scaling regime varying as $t^{-1/2}$. The extent of this transient regime becomes very long when the target is most of the time invisible, especially at low turning rates. In both finite and infinite geometries, we draw analogies with partial absorption problems.

cond-mat.stat-mech↗

arXiv2020

Intermittent resetting potentials

We study the non-equilibrium steady states and first passage properties of a Brownian particle with position $X$ subject to an external confining potential of the form $V(X)=μ|X|$, and that is switched on and off stochastically. Applying the potential intermittently generates a physically realistic diffusion process with stochastic resetting toward the origin, a topic which has recently attracted a considerable interest in a variety of theoretical contexts but has remained challenging to implement in lab experiments. The present system exhibits rich features, not observed in previous resetting models. The mean time needed by a particle starting from the potential minimum to reach an absorbing target located at a certain distance can be minimized with respect to the switch-on and switch-off rates. The optimal rates undergo continuous or discontinuous transitions as the potential strength $μ$ is varied across non-trivial values. A discontinuous transition with metastable behavior is also observed for the optimal strength at fixed rates.

cond-mat.stat-mech↗

arXiv2020

Random walks on networks with stochastic resetting

We study random walks with stochastic resetting to the initial position on arbitrary networks. We obtain the stationary probability distribution as well as the mean and global first passage times, which allow us to characterize the effect of resetting on the capacity of a random walker to reach a particular target or to explore a finite network. We apply the results to rings, Cayley trees, random and complex networks. Our formalism holds for undirected networks and can be implemented from the spectral properties of the random walk without resetting, providing a tool to analyze the search efficiency in different structures with the small-world property or communities. In this way, we extend the study of resetting processes to the domain of networks.

cond-mat.stat-mech↗

arXiv2020

Using posterior predictive distributions to analyse epidemic models: COVID-19 in Mexico City

Epidemiological models contain a set of parameters that must be adjusted based on available observations. Once a model has been calibrated, it can be used as a forecasting tool to make predictions and to evaluate contingency plans. It is customary to employ only point estimators for such predictions. However, some models may fit the same data reasonably well for a broad range of parameter values, and this flexibility means that predictions stemming from such models will vary widely, depending on the particular parameter values employed within the range that give a good fit. When data are poor or incomplete, model uncertainty widens further. A way to circumvent this problem is to use Bayesian statistics to incorporate observations and use the full range of parameter estimates contained in the posterior distribution to adjust for uncertainties in model predictions. Specifically, given the epidemiological model and a probability distribution for observations, we use the posterior distribution of model parameters to generate all possible epidemiological curves via the posterior predictive distribution. From the envelope of all curves one can extract the worst-case scenario and study the impact of implementing contingency plans according to this assessment. We apply this approach to the potential evolution of COVID-19 in Mexico City and assess whether contingency plans are being successful and whether the epidemiological curve has flattened.

q-bio.PE↗

arXiv2020

Anderson-like localization transition of random walks with resetting

We study several lattice random walk models with stochastic resetting to previously visited sites which exhibit a phase transition between an anomalous diffusive regime and a localization regime where diffusion is suppressed. The localized phase settles above a critical resetting rate, or rate of memory use, and the probability density asymptotically adopts in this regime a non-equilibrium steady state similar to that of the well known problem of diffusion with resetting to the origin. The transition occurs because of the presence of a single impurity site where the resetting rate is lower than on other sites, and around which the walker spontaneously localizes. Near criticality, the localization length diverges with a critical exponent that falls in the same class as the self-consistent theory of Anderson localization of waves in random media. The critical dimensions are also the same in both problems. Our study provides analytically tractable examples of localization transitions in path-dependent, reinforced stochastic processes, which can be also useful for understanding spatial learning by living organisms.

cond-mat.stat-mech↗

arXiv2020

First hitting times to intermittent targets

In noisy environments such as the cell, many processes involve target sites that are often hidden or inactive, and thus not always available for reaction with diffusing entities. To understand reaction kinetics in these situations, we study the first hitting time statistics of a Brownian particle searching for a target site that switches stochastically between visible and hidden phases. At high crypticity, an unexpected rate limited power-law regime emerges for the first hitting time density, which markedly differs from the classic $t^{-3/2}$ scaling for steady targets. Our problem admits an asymptotic mapping onto a mixed, or Robin, boundary condition. Similar results are obtained with non-Markov targets and particles diffusing anomalously.

cond-mat.stat-mech↗

arXiv2019

Predator-prey dynamics: Chasing by stochastic resetting

We analyze predator-prey dynamics in one dimension in which a Brownian predator adopts a chasing strategy that consists in stochastically resetting its current position to locations previously visited by a diffusive prey. We study three different chasing strategies, namely, active, uniform and passive which lead to different diffusive behaviors of the predator in the absence of capture. When capture is considered, regardless of the chasing strategy, the mean first-encounter time is finite and decreases with the resetting rate. This model illustrates how the use of cues significantly improves the efficiency of random searches. We compare numerical simulations with analytical calculations and find excellent agreement.

cond-mat.dis-nn↗

arXiv2019

Collective learning from individual experiences and information transfer during group foraging

Living in groups brings benefits to many animals, such as a protection against predators and an improved capacity for sensing and making decisions while searching for resources in uncertain environments. A body of studies has shown how collective behaviors within animal groups on the move can be useful for pooling information about the current state of the environment. The effects of interactions on collective motion have been mostly studied in models of agents with no memory. Thus, whether coordinated behaviors can emerge from individuals with memory and different foraging experiences is still poorly understood. By means of an agent based model, we quantify how individual memory and information fluxes can contribute to improving the foraging success of a group in complex environments. In this context, we define collective learning as a coordinated change of behavior within a group resulting from individual experiences and information transfer. We show that an initially scattered population of foragers visiting dispersed resources can gradually achieve cohesion and become selectively localized in space around the most salient resource sites. Coordination is lost when memory or information transfer among individuals is suppressed. The present modelling framework provides predictions for empirical studies of collective learning and could also find applications in swarm robotics and motivate new search algorithms based on reinforcement.

q-bio.PE↗

arXiv2018

Contribution of social network analysis and collective phenomena to understanding social complexity and cognition

The social brain hypothesis postulates the increasing complexity of social interactions as a driving force for the evolution of cognitive abilities. Whereas dyadic and triadic relations play a basic role in defining social behaviours and pose many challenges for the social brain, individuals in animal societies typically belong to relatively large networks. How the structure and dynamics of these networks also contribute to the evolution of cognition, and vice versa, is less understood. Here we review how collective phenomena can occur in systems where social agents do not require sophisticated cognitive skills, and how complex networks can grow from simple probabilistic rules, or even emerge from the interaction between agents and their environment, without explicit social factors. We further show that the analysis of social networks can be used to develop good indicators of social complexity beyond the individual or dyadic level. We also discuss the types of challenges that the social brain must cope with in structured groups, such as higher information fluxes, originating from individuals playing different roles in the network, or dyadic contacts of widely varying durations and frequencies. We discuss the relevance of these ideas for primates and other animals societies.

q-bio.NC↗