arXiv subjects

Michele Caraglio

Publications and source records attributed to Michele Caraglio.

At least 19 recordsLinked to original sources

arXiv2026

Two-Dimensional Active Brownian Particles Crossing a Parabolic Barrier: Transition-Path Times, Survival Probability, and First-Passage Time

We derive an analytical expression for the propagator and the transition path time distribution of a two-dimensional active Brownian particle crossing a parabolic barrier with absorbing boundary conditions at both sides. By taking those of a passive Brownian particle as basis states and dealing with the activity as a perturbation, our solution is expressed in terms of the perturbed eigenfunctions and eigenvalues of the associated Fokker-Planck equation once the latter is reduced by taking into account only the coordinate along the direction of the barrier and the self-propulsion angle. We show that transition path times are typically shortened by the self-propulsion of the particle. Our solution also allows us to obtain the survival probability and the first-passage times distribution, which display a strong dependence on the particle's activity, while the rotational diffusivity influences them to a minor extent.

cond-mat.stat-mech↗

arXiv2026

Two-Dimensional Active Brownian Particles Crossing a Parabolic Barrier: Finite Rectangular Domain with Absorbing Boundary Conditions

We solve the time-dependent Fokker-Planck equation for a two-dimensional active Brownian particle exploring a rectangular domain with absorbing boundary and in the presence of a parabolic barrier along one direction. By taking those of a passive Brownian particle as basis states and dealing with the activity as a perturbation, we provide a matrix representation of the Fokker-Planck operator and express the propagator in terms of the perturbed eigenvalues and eigenfunctions. Our solution also allows us to obtain the survival probability and the first-passage-time distribution. The non-equilibrium character of the dynamics induces a strong dependence of the latter quantities on the particle's activity, while the rotational diffusivity influences them to a minor extent.

cond-mat.stat-mech↗

arXiv2025

Glass transition in colloidal monolayers controlled by light-induced caging

We theoretically investigate the glass-transition problem for a quasi-two-dimensional colloidal dense suspension modulated by a one-dimensional periodic external potential as imposed by interfering laser beams. Relying on a mode-coupling approach, we examine the nonequilibrium state diagram for hard disks as a function of the density and the period of the modulation for various potential strengths. The competition between the local packing and the distortion of the cages induced by the potential leads to a striking nonmonotonic behavior of the glass-transition line which allows melting of a glass state merely by changing the external fields. In particular, we find regions in the non-equilibrium state diagram where a moderate periodic modulation stabilizes the liquid state.

cond-mat.soft↗

arXiv2025

Mode-coupling theory of the glass transition for a liquid in a periodic potential

We derive a microscopic theory for the structural dynamics in the vicinity of the glass transition for a liquid exposed to a one-dimensional periodic potential. The periodic potential breaks translational invariance, in particular, the density exhibits a periodic modulation. Using techniques familiar from solid-state theory, we define generalized intermediate scattering functions from fluctuating densities in wave-vector space. Exact equations of motion are derived within the Mori-Zwanzig projection-operator formalism reflecting the residual lattice symmetries. Due to the lack of rotational symmetry it is necessary to split the currents into components parallel and perpendicular to the modulation. We provide a closure of the equations in terms of a mode-coupling approximation for the force kernel. The theory reflects the usual analytic properties of correlation functions and encodes all phenomena known for mode-coupling theories. We prove that the theory reduces to the conventional mode-coupling theory in the case of vanishing amplitude of the modulation.

cond-mat.soft↗

arXiv2025

Run-and-Tumble Particles Learning Chemotaxis

Through evolution, bacteria have developed the ability to perform chemotactic motion in order to find nourishment. By adopting a machine learning approach, we aim to understand how this behavior arises. We consider run-and-tumble agents able to tune the instantaneous probability of switching between the run and the tumble phase. When such agents are navigating in an environment characterized by a concentration field pointing towards a circular target, we investigate how a chemotactic strategy may be learned starting from unbiased run-and-tumble dynamics. We compare the learning performances of agents that sense only the instantaneous concentration with those of agents having a short-term memory that allows them to perform temporal comparisons. While both types of learning agents develop successful target-search policies, we demonstrate that those achieved by agents endowed with temporal comparison abilities are significantly more efficient, particularly when the initial distance from the target is large. Finally, we also show that when an additional length scale is imposed, for example by fixing the initial distance to the target, the learning agents can leverage this information to further improve their efficiency in locating the target.

cond-mat.soft↗

arXiv2025

Learning to reset in target search problems

Target search problems are central to a wide range of fields, from biological foraging to the optimization algorithms. Recently, the ability to reset the search has been shown to significantly improve the searcher's efficiency. However, the optimal resetting strategy depends on the specific properties of the search problem and can often be challenging to determine. In this work, we propose a reinforcement learning (RL)-based framework to train agents capable of optimizing their search efficiency in environments by learning how to reset. First, we validate the approach in a well-established benchmark: the Brownian search with resetting. There, RL agents consistently recover strategies closely resembling the sharp resetting distribution, known to be optimal in this scenario. We then extend the framework by allowing agents to control not only when to reset, but also their spatial dynamics through turning actions. In this more complex setting, the agents discover strategies that adapt both resetting and turning to the properties of the environment, outperforming the proposed benchmarks. These results demonstrate how reinforcement learning can serve both as an optimization tool and a mechanism for uncovering new, interpretable strategies in stochastic search processes with resetting.

cond-mat.stat-mech↗

arXiv2024

Transition-path sampling for Run-and-Tumble particles

We elaborate and validate a generalization of the renowned transition-path-sampling algorithm for a paradigmatic model of active particles, namely the Run-and-Tumble particles. Notwithstanding the non-equilibrium character of these particles, we show how the consequent lack of the microscopical reversibility property, which is usually required by transition-path sampling, can be circumvented by identifying reasonable backward dynamics with a well-defined path-probability density. Our method is then applied to characterize the structure and kinetics of rare transition pathways undergone by Run-and-Tumble particles having to cross a potential barrier in order to find a target.

cond-mat.soft↗

arXiv2023

Learning how to find targets in the micro-world: The case of intermittent active Brownian particles

Finding the best strategy to minimize the time needed to find a given target is a crucial task both in nature and in reaching decisive technological advances. By considering learning agents able to switch their dynamics between standard and active Brownian motion, here we focus on developing effective target-search behavioral policies for microswimmers navigating a homogeneous environment and searching for targets of unknown position. We exploit Projective Simulation, a reinforcement learning algorithm, to acquire an efficient stochastic policy represented by the probability of switching the phase, i.e. the navigation mode, in response to the type and the duration of the current phase. Our findings reveal that the target-search efficiency increases with the particle's self-propulsion during the active phase and that, while the optimal duration of the passive case decreases monotonically with the activity, the optimal duration of the active phase displays a non-monotonic behavior.

cond-mat.soft↗

arXiv2023

Adaptive active Brownian particles searching for targets of unknown positions

Developing behavioral policies designed to efficiently solve target-search problems is a crucial issue both in nature and in the nanotechnology of the 21st century. Here, we characterize the target-search strategies of simple microswimmers in a homogeneous environment containing sparse targets of unknown positions. The microswimmers are capable of controlling their dynamics by switching between Brownian motion and an active Brownian particle and by selecting the time duration of each of the two phases. The specific conduct of a single microswimmer depends on an internal decision-making process determined by a simple neural network associated with the agent itself. Starting from a population of individuals with random behavior, we exploit the genetic algorithm NeuroEvolution of Augmenting Topologies to show how an evolutionary pressure based on the target-search performances of single individuals helps to find the optimal duration of the two different phases. Our findings reveal that the optimal policy strongly depends on the magnitude of the particle's self-propulsion during the active phase and that a broad spectrum of network topology solutions exists, differing in the number of connections and hidden nodes.

cond-mat.soft↗

arXiv2023

Active Brownian Particles in a Circular Disk with an Absorbing Boundary

We solve the time-dependent Fokker-Planck equation for a two-dimensional active Brownian particle exploring a circular region with an absorbing boundary. Using the passive Brownian particle as basis states and dealing with the activity as a perturbation, we provide a matrix representation of the Fokker-Planck operator and we express the propagator in terms of the perturbed eigenvalues and eigenfunctions. Alternatively, we show that the propagator can be expressed as a combination of the equilibrium eigenstates with weights depending only on time and on the initial conditions, and obeying exact iterative relations. Our solution allows also obtaining the survival probability and the first-passage time distribution. These latter quantities exhibit peculiarities induced by the non-equilibrium character of the dynamics, in particular, they display a strong dependence on the activity of the particle and, to a less extent, also on its rotational diffusivity.

cond-mat.stat-mech↗

arXiv2022

Analytic Solution of an Active Brownian Particle in a Harmonic Well

We provide an analytical solution for the time-dependent Fokker-Planck equation for a two-dimensional active Brownian particle trapped in an isotropic harmonic potential. Using the passive Brownian particle as basis states we show that the Fokker-Planck operator becomes lower diagonal, implying that the eigenvalues are unaffected by the activity. The propagator is then expressed as a combination of the equilibrium eigenstates with weights obeying exact iterative relations. We show that for the low-order correlation functions, such as the positional autocorrelation function, the recursion terminates at finite order in the Péclet number allowing us to generate exact compact expressions and derive the velocity autocorrelation function and the time-dependent diffusion coefficient. The nonmonotonic behavior of latter quantities serves as a fingerprint of the non-equilibrium dynamics.

cond-mat.soft↗

arXiv2022

Geometric Predictors of Knotted and Linked Arcs

Inspired by how certain proteins "sense" knots and entanglements in DNA molecules, here we ask if there exist local geometric features that may be used as a read-out of the underlying topology of generic polymers. We perform molecular simulations of knotted and linked semiflexbile polymers and study four geometric measures to predict topological entanglements: local curvature, local density, local 1D writhe and non-local 3D writhe. We discover that local curvature is a poor predictor of entanglements. In contrast, segments with maximum local density or writhe correlate as much as 90% of the time with the shortest knotted and linked arcs. We find that this accuracy is preserved across different knot types and also under significant spherical confinement, which is known to delocalise essential crossings in knotted polymers. We further discover that non-local 3D writhe is the best geometric read-out of knot location. Finally, we discuss how these geometric features may be used to computationally analyse entanglements in generic polymer melts and gels.

cond-mat.soft↗

arXiv2021

Tagged-particle motion in quasi-confined colloidal hard-sphere liquids

We investigate the tagged-particle motion in a strongly interacting quasi-confined liquid using periodic boundary conditions along the confining direction. Within a mode-coupling theory of the glass transition (MCT) we calculate the self-nonergodicity parameters and the self-intermediate scattering function and compare them with event-driven molecular dynamics simulations. We observe non-monotonic behavior for the in-plane mean-square displacement and further correlation functions which refer to higher mode indices encoding information about the perpendicular motion. The in-plane velocity-autocorrelation function reveals persistent anti-correlations with a negative algebraic power-law decay $t^{-2}$ at all packing fractions.

cond-mat.soft↗

arXiv2021

Optimal navigation strategy of active Brownian particles in target-search problems

We investigate exploration patterns of a microswimmer, modeled as an active Brownian particle, searching for a target region located in a well of an energy landscape and separated from the initial position of the particle by high barriers. We find that the microswimmer can enhance its success rate in finding the target by tuning its activity and its persistence in response to features of the environment. The target-search patterns of active Brownian particles are counterintuitive and display characteristics robust to changes of the energy landscape. On the contrary, the transition rates and transition-path times are sensitive to the details of the specific energy landscape. In striking contrast to the passive case, the presence of additional local minima does not significantly slow down the active target-search dynamics.

cond-mat.soft↗

arXiv2021

Emergence of effective temperatures in an out-of-equilibrium model of biopolymer folding

We investigate the possibility of extending the notion of temperature in a stochastic model for the RNA/protein folding driven out of equilibrium. We simulate the dynamics of a small RNA hairpin subject to an external pulling force, which is time-dependent. First, we consider a fluctuation-dissipation relation (FDR) whereby we verify that various effective temperatures can be obtained for different observables, only when the slowest intrinsic relaxation timescale of the system regulates the dynamics of the system. Then, we introduce a different nonequilibrium temperature, which is defined from the rate of heat exchanged with a weakly-interacting thermal bath. Notably, this 'kinetic' temperature can be defined for any frequency of the external switching force. We also discuss and compare the behavior of these two emerging parameters, by discriminating the time-delayed nature of the FDR temperature from the instantaneous character of the kinetic temperature. The validity of our numerics are corroborated by a simple 4-state Markov model which describes the long-time behaviour of the RNA molecule.

cond-mat.stat-mech↗

arXiv2021

Entropic measure unveils country competitiveness and product specialization in the World trade web

We show how the Shannon entropy function can be used as a basis to set up complexity measures weighting the economic efficiency of countries and the specialization of products beyond bare diversification. This entropy function guarantees the existence of a fixed point which is rapidly reached by an iterative scheme converging to our self-consistent measures. Our approach naturally allows to decompose into inter-sectorial and intra-sectorial contributions the country competitivity measure if products are partitioned into larger categories. Besides outlining the technical features and advantages of the method, we describe a wide range of results arising from the analysis of the obtained rankings and we benchmark these observations against those established with other economical parameters. These comparisons allow to partition countries and products into various main typologies, with well-revealed characterizing features. Our methods have wide applicability to general problems of ranking in bipartite networks.

physics.soc-ph↗

arXiv2021

Target search of active agents crossing high energy barriers

Target search by active agents in rugged energy landscapes has remained a challenge because standard enhanced sampling methods do not apply to irreversible dynamics. We overcome this non-equilibrium rare-event problem by developing an algorithm generalizing transition-path sampling to active Brownian dynamics. This method is exemplified and benchmarked for a paradigmatic two-dimensional potential with a high barrier. We find that even in such a simple landscape the structure and kinetics of the ensemble of transition paths change drastically in the presence of activity. Indeed, active Brownian particles reach the target more frequently than passive Brownian particles, following longer and counterintuitive search patterns.

cond-mat.soft↗

arXiv2020

Topological disentanglement of linear polymers under tension

We develop a theoretical description of the topological disentanglement occurring when torus knots reach the ends of a semi-flexible polymer under tension. These include decays into simpler knots and total unknotting. The minimal number of crossings and the minimal knot contour length are the topological invariants playing a key role in the model. The crossings behave as particles diffusing along the chain and the application of appropriate boundary conditions at the ends of the chain accounts for the knot disentanglement. Starting from the number of particles and their positions, suitable rules allow reconstructing the type and location of the knot moving on the chain. Our theory is extensively benchmarked with corresponding Molecular Dynamics simulations and the results show a remarkable agreement between the simulations and the theoretical predictions of the model.

cond-mat.stat-mech↗