arXiv subjects

Olivier Pierre-Louis

Publications and source records attributed to Olivier Pierre-Louis.

At least 19 recordsLinked to original sources

arXiv2026

Optimal Navigation in Stochastic and Disordered Gridworlds

Navigation in complex and noisy environments is a key issue in diverse fields from biology to engineering. Despite extensive progress in numerical optimization methods for computing navigation policies, insights into how disorder reshapes optimal navigation remain elusive. To address this question, we investigate the navigation of a Brownian particle in a disordered energy landscape, modeled as a lattice with randomly distributed traps. Using dynamic programming, we compute the optimal navigation policies that minimize the mean first-passage time to a target site. To quantify the impact of disorder, we introduce a density of change from a Kullback-Leibler divergence, which captures how the optimal policy is reshaped by either the presence of disorder or the knowledge of its configuration. Our results reveal a non-monotonic dependence of the change of the policy on trap concentration, with a pronounced maximum. In the fluctuation-dominated regime where the navigation bias is weak, we derive an analytical expression for the density of change, and demonstrate that the maximum occurs unexpectedly at low trap concentrations.

cond-mat.stat-mech↗

arXiv2025

Learning Kinetic Monte Carlo stochastic dynamics with Deep Generative Adversarial Networks

We show that Generative Adversarial Networks (GANs) may be fruitfully exploited to learn stochastic dynamics, surrogating traditional models while capturing thermal fluctuations. Specifically, we showcase the application to a two-dimensional, many-particle system, focusing on surface-step fluctuations and on the related time-dependent roughness. After the construction of a dataset based on Kinetic Monte Carlo simulations, a conditional GAN is trained to propagate stochastically the state of the system in time, allowing the generation of new sequences with a reduced computational cost. Modifications with respect to standard GANs, which facilitate convergence and increase accuracy, are discussed. The trained network is demonstrated to quantitatively reproduce equilibrium and kinetic properties, including scaling laws, with deviations of a few percent from the exact value. Extrapolation limits and future perspectives are critically discussed.

cond-mat.stat-mech↗

arXiv2024

Extreme time extrapolation capabilities and thermodynamic consistency of physics-inspired Neural Networks for the 3D microstructure evolution of materials via Cahn-Hilliard flow

A Convolutional Recurrent Neural Network (CRNN) is trained to reproduce the evolution of the spinodal decomposition process in three dimensions as described by the Cahn-Hilliard equation. A specialized, physics-inspired architecture is proven to provide close accordance between the predicted evolutions and the ground truth ones obtained via conventional integration schemes. The method can accurately reproduce the evolution of microstructures not represented in the training set at a fraction of the computational costs. Extremely long-time extrapolation capabilities are achieved, up to reaching the theoretically expected equilibrium state of the system, consisting of a layered, phase-separated morphology, despite the training set containing only relatively-short, initial phases of the evolution. Quantitative accordance with the decay rate of the Free energy is also demonstrated up to the late coarsening stages, proving that this class of Machine Learning approaches can become a new and powerful tool for the long timescale and high throughput simulation of materials, while retaining thermodynamic consistency and high-accuracy.

cond-mat.mes-hall↗

arXiv2023

Reinforcement Learning with thermal fluctuations at the nano-scale

Reinforcement Learning offers a framework to learn to choose actions in order to achieve some goal. However, at the nano-scale, thermal fluctuations hamper the learning process. We analyze this regime using the general framework of Markov Decision Processes, which applies to a wide variety of problems from nano-navigation to nano-machine actuation. We show that at the nan-oscale, while optimal actions should bring an improvement proportional to the small ratio of the applied force times a length-scale over the temperature, the learned improvement is smaller and proportional to the square of this small ratio. Consequently, the efficiency of learning, which compares the learning improvement to the theoretical optimal improvement, drops to zero. Nevertheless, these limitations can be circumvented by using actions learned at a lower temperature. These results are illustrated with simulations of the control of the shape of small particle clusters.

cond-mat.stat-mech↗

arXiv2023

Accurate generation of stochastic dynamics based on multi-model Generative Adversarial Networks

Generative Adversarial Networks (GANs) have shown immense potential in fields such as text and image generation. Only very recently attempts to exploit GANs to statistical-mechanics models have been reported. Here we quantitatively test this approach by applying it to a prototypical stochastic process on a lattice. By suitably adding noise to the original data we succeed in bringing both the Generator and the Discriminator loss functions close to their ideal value. Importantly, the discreteness of the model is retained despite the noise. As typical for adversarial approaches, oscillations around the convergence limit persist also at large epochs. This undermines model selection and the quality of the generated trajectories. We demonstrate that a simple multi-model procedure where stochastic trajectories are advanced at each step upon randomly selecting a Generator leads to a remarkable increase in accuracy. This is illustrated by quantitative analysis of both the predicted equilibrium probability distribution and of the escape-time distribution. Based on the reported findings, we believe that GANs are a promising tool to tackle complex statistical dynamics by machine learning techniques

cond-mat.stat-mech↗

arXiv2023

Domain convexification: a simple model for invasion processes

We propose an invasion model where domains grow up to their convex hulls and merge when they overlap. This model can be seen as a continuum and isotropic counterpart of bootstrap percolation models. From numerical investigations of the model starting with randomly scattered discs in two dimensions, we find an invasion transition that occurs via macroscopic avalanches. The disc concentration threshold and the sharpness of the transition are found to decrease as the system size is increased. Our results are consistent with a vanishing threshold in the limit of infinitely large system sizes. However this limit could not be investigated by simulations. For finite initial concentrations of discs, the cluster size distribution presents a power-law tail characterized by an exponent that varies approximately linearly with the initial concentration of discs. These results at finite initial concentration open novel directions for the understanding of the transition in systems of finite size. Furthermore, we find that the domain area distribution has oscillations with discontinuities. In addition, the deviation from circularity of large domains is constant. Finally, we compare our results to experimental observations on de-adhesion of graphene induced by the intercalation of nanoparticles.

cond-mat.stat-mech↗

arXiv2022

Temperature transitions and degeneracy in the control of small clusters with a macroscopic field

We present a numerical investigation of the control of few-particle fluctuating clusters with a macroscopic field. Our goal is to reach a given target cluster shape is minimum time. This question is formulated as a first passage problem in the space of cluster configurations. We find the optimal policy to set the macroscopic field as a function of the observed shape using dynamic programming. Our results show that the optimal policy is non-unique, and its degeneracy is mainly related to symmetries shared by the initial shape, the force and the target shape. The total fraction of shapes for which optimal choice of the force is non-unique vanishes as the cluster size increases. Furthermore, the optimal policy exhibits a discrete set of transitions when the temperature is varied. Each transition leads to a discontinuity in the derivative of the time to reach with target with respect to temperature. As the size of the cluster increases, the change in the policy due to temperature transitions grows like the total number of configurations and a continuum limit emerges.

cond-mat.stat-mech↗

arXiv2022

Equilibrium return times of small fluctuating clusters and vacancies

The expected return time of a fluctuating two-dimensional cluster or vacancy to a given configuration is studied in thermodynamic equilibrium. We define a family of bond-breaking models that preserve the number of particles. This family includes edge diffusion and surface diffusion inside vacancies in the limit of fast particle diffusion and slow attachment-detachment kinetics. Within the frame of these bond-breaking models, the expected return time is found to depend on the energies of the configurations and on the energies of the excited states formed by removing a single particle from the cluster. High and low temperature regimes are studied. We clarify the conditions under which the return time is a non-monotonous function of temperature: a minimum is found when the energy obtained by the average over the excited states of the configuration weighted by their attachment probabilities is lower than the energy averaged over all states. In addition, we show that the optimal temperature at which the return time is minimum is shifted to a higher temperature as compared to the temperature at which the equilibrium probability is maximum. This shift is influenced by the average curvature of the cluster edge, and is therefore larger for vacancies.

cond-mat.stat-mech↗

arXiv2022

Controlling the shape of small clusters with and without macroscopic fields

Despite major advances in the understanding of the formation and dynamics of nano-clusters in the past decades, theoretical bases for the control of their shape are still lacking. We investigate strategies for driving fluctuating few-particle clusters to an arbitrary target shape in minimum time with or without an external field. This question is recast into a first passage problem, solved numerically, and discussed within a high temperature expansion. Without field, large-enough low-energy target shapes exhibit an optimal temperature at which they are reached in minimum time. We then compute the optimal way to set an external field to minimize the time to reach the target, leading to a gain of time that grows when increasing cluster size or decreasing temperature. This gain can shift the optimal temperature or even create one. Our results could apply to clusters of atoms at equilibrium, and colloidal or nanoparticle clusters under thermo- or electrophoresis.

cond-mat.stat-mech↗

arXiv2022

Interface collisions with diffusive mass transport

We report on a linear Langevin model that describes the evolution of the roughness of two interfaces that move towards each other and are coupled by a diffusion field. This model aims at describing the closing of the gap between two two-dimensional material domains during growth, and the subsequent formation of a rough grain boundary. We assume that deposition occurs in the gap between the two domains and that the growth units diffuse and may attach to the edges of the domains. These units can also detach from edges, diffuse, and re-attach elsewhere. For slow growth, the edge roughness increases monotonously and then saturates at some equilibrium value. For fast growth, the roughness exhibits a maximum just before the collision between the two interfaces, which is followed by a minimum. The peak of the roughness can be dominated by statistical fluctuations or by edge instabilities. A phase diagram with three regimes is obtained: slow growth without peak, peak dominated by statistical fluctuations, and peak dominated by instabilities. These results reproduce the main features observed in Kinetic Monte Carlo simulations.

cond-mat.mtrl-sci↗

arXiv2022

Growth at high substrate coverage can decrease the grain boundary roughness of 2D materials

Grain boundary roughness can affect electronic and mechanical properties of two-dimensional materials. This roughness depends crucially on the growth process by which the two-dimensional material is formed. To investigate the key mechanisms that govern the roughness, we have performed kinetic Monte Carlo simulations of a simple model that includes particle attachment, detachment, and diffusion. We have studied the closure of the gap between two flakes during growth, and the subsequent formation of the grain boundary (GB) for a broad range of model parameters. The well known near-equilibrium (attachment-limited) and unstable (diffusion-limited) growth regimes are identified, but we also observe a third regime when the precursor flux is sufficiently high to fully cover the gap between the edges. This high coverage regime forms GBs with spatially uncorrelated roughness, which quickly relax to smoother configurations. Extrapolating the numerical results (with support from a theoretical approach) to edge lengths and gap widths of some micrometers, we confirm the advantage of this regime to produce GBs with minimal roughness faster than near-equilibrium conditions. This suggests an unexpected route towards efficient growth of two-dimensional materials with smooth GBs.

cond-mat.mtrl-sci↗

arXiv2022

Crystal growth in confinement

The growth of crystals confined in porous or cellular materials is ubiquitous in Nature and industry. Confinement affects the formation of biominerals in living organisms, of minerals in the Earth's crust and of salt crystals damaging porous limestone monuments, and is also used to control the growth of artificial crystals. However, the mechanisms by which confinement alters crystal shapes and growth rates are still not elucidated. Based on novel \textit{in situ} optical observations of (001) surfaces of NaClO$_3$ and CaCO$_3$ crystals at nanometric distances from a glass substrate, we demonstrate that new molecular layers can nucleate homogeneously and propagate without interruption even when in contact with other solids, raising the macroscopic crystal above them. Confined growth is governed by the peculiar dynamics of these molecular layers controlled by the two-dimensional transport of mass through the liquid film from the edges to the center of the contact, with distinctive features such as skewed dislocation spirals, kinetic localization of nucleation in the vicinity of the contact edge, and directed instabilities. Confined growth morphologies can be predicted from the values of three main dimensionless parameters.

cond-mat.mtrl-sci↗

arXiv2021

Controlling anisotropy in 2D microscopic models of growth

The quantitative knowledge of interface anisotropy in lattice models is a major issue, both for the parametrization of continuum interface models, and for the analysis of experimental observations. In this paper, we focus on the anisotropy of line tension and stiffness, which plays a major role both in equilibrium shapes and fluctuations, and in the selection of nonequilibrium growth patterns. We consider a 2D Ising Hamiltonian on a square lattice with first and second-nearest-neighbor interactions. The surface stiffness and line tension are calculated by means of a broken-bond model for arbitrary orientations. The analysis of the interface energy allows us to determine the conditions under which stiffness anisotropy is minimal. These results are supported by a quantitative comparison with kinetic Monte Carlo simulations, based on the coupling of a field of mobile atoms to a condensed phase. Furthermore, we introduce a generic smoothing parameter which allows one to mimic the finite resolution of experimental microscopy techniques. Our results provide a method to fine-tune the interface energy in models of nanoscale non-equilibrium processes, where anisotropy and fluctuations combine and give rise to non-trivial morphologies.

cond-mat.stat-mech↗

arXiv2021

Shear dynamics of confined membranes

We model the nonlinear response of a lubricated contact composed of a two-dimensional lipid membrane immersed in a simple fluid between two parallel flat and porous walls under shear. The nonlinear dynamics of the membrane gives rise to a rich dynamical behavior depending on the shear velocity. In quiescent conditions (i.e., absence of shear), the membrane freezes into a disordered labyrinthine wrinkle pattern. In the presence of shear, we find four different regimes depending on the shear rate. Regime I. For small shear, the labyrinthine pattern is still frozen, but exhibits a small drift which is mainly along the shear direction. In this regime, the tangential forces on the walls due to the presence of the membrane increase linearly with the shear rate. Regime II. When the shear rate is increased above a critical value, the membrane rearranges, and wrinkles start to align along the shear direction. This regime is accompanied by a sharp drop of the tangential forces on the wall. Regime III. For larger shear rates, the wrinkles align strongly along the shear direction, with a set of dislocation defects which assemble in pairs. The tangential forces are then controlled by the number of dislocations, and by the number of wrinkles between the two dislocations within each dislocation pairs. In this dislocation-dominated regime, the tangential forces in the transverse direction most often exceed those in the shear direction. Regime IV. For even larger shear, the membrane organizes into a perfect array of parallel stripes with no defects. The wavelength of the wrinkles is still identical to the wavelength in the absence of shear. In this final regime, the tangential forces due to the membrane vanish. These behaviors give rise to a non-linear rheological behavior of lubricated contacts containing membranes.

cond-mat.soft↗

arXiv2019

The Nonequilibrium Crystallization Force

The forces exerted by growing crystals on the surrounding materials play a major role in many geological processes, from diagenetic replacement to rock weathering and uplifting of rocks and soils. Although crystallization is a nonequilibrium process, the available theoretical prediction for these forces are based on equilibrium thermodynamics. Here we show that nonequilibrium effects can lead to a drop of the crystallization force in large pores where the crystal surface dissociates from the surrounding walls during growth. The critical pore size above which such detachment can be observed depends only on the ratio of kinetic coefficients and cannot be predicted from thermodynamics. Our conclusions are based on a physical model which accounts for the nonequilibrium kinetics of mass transport, and disjoining pressure effects within the thin liquid film separating the crystal and the surrounding walls. Our results suggest that the maximum size of the pores that can sustain crystallization forces close to the equilibrium prediction ranges from micrometers for salts to a millimetre for low solubility minerals such as calcite. These results are discussed in the light of recent experimental observations of the growth of confined salt crystals.

cond-mat.soft↗

arXiv2019

Interface Collisions

We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short range interactions between them. Due to their roughness, the collision events spread in time and form rough domain boundaries, which defines collision interfaces in time and space. We show that statistical properties of such interfaces depend on the kinetics of the growing interfaces before collision, but are independent of the details of their interaction and of their fluctuations during the collision. Those properties exhibit dynamic scaling with exponents related to the growth kinetics, but their distributions may be non-universal. These results are supported by simulations of lattice models with irreversible dynamics and local interactions. Relations to first passage processes are discussed and a possible application to grain boundary formation in two-dimensional materials is suggested.

cond-mat.stat-mech↗

arXiv2019

Confined Growth with slow surface kinetics: a Thin Film Model approach

Recent experimental and theoretical investigations of crystal growth from solution in the vicinity of an impermeable wall have shown that: (i) growth can be maintained within the contact region when a liquid film is present between the crystal and the substrate; (ii) a cavity can form in the center of the contact region due to insufficient supply of mass through the liquid film. Here, we investigate the influence of surface kinetics on these phenomena using a thin film model. First, we determine the growth rate within the confined region in the absence of a cavity. Growth within the contact induces a drift of the crystal away from the substrate. Our results suggest novel strategies to measure surface kinetic coefficients based on the observation of this drift. For the specific case where growth is controlled by surface kinetics outside the contact, we show that the total displacement of the crystal due to the growth in the contact is finite. As a consequence, the growth shape approaches asymptotically the free growth shape truncated by a plane passing through the center of the crystal. Second, we investigate the conditions under which a cavity forms. The critical supersaturation above which the cavity forms is found to be larger for slower surface kinetics. In addition, the critical supersaturation decays as a power law of the contact size. The asymptotic value of the critical supersaturation and the exponent of the decay are found to be different for attractive and repulsive disjoining pressures. Finally, our previous representation of the transition within a morphology diagram appears to be uninformative in the limit of slow surface kinetics.

cond-mat.soft↗

arXiv2018

Adhesion dynamics of confined membranes

We report on the modeling of the dynamics of confined lipid membranes. We derive a thin film model in the lubrication limit which describes an inextensible liquid membrane with bending rigidity confined between two adhesive walls. The resulting equations share similarities with the Swift-Hohenberg model. However, inextensibility is enforced by a time-dependent nonlocal tension. Depending on the excess membrane area available in the system, three different dynamical regimes, denoted as A, B and C, are found from the numerical solution of the model. In regime A, membranes with small excess area form flat adhesion domains and freeze. Such freezing is interpreted by means of an effective model for curvature-driven domain wall motion. The nonlocal membrane tension tends to a negative value corresponding to the linear stability threshold of flat domain walls in the Swift-Hohenberg equation. In regime B, membranes with intermediate excess areas exhibit endless coarsening with coexistence of flat adhesion domains and wrinkle domains. The tension tends to the nonlinear stability threshold of flat domain walls in the Swift-Hohenberg equation. The fraction of the system covered by the wrinkle phase increases linearly with the excess area in regime B. In regime C, membranes with large excess area are completely covered by a frozen labyrinthine pattern of wrinkles. As the excess area is increased, the tension increases and the wavelength of the wrinkles decreases. For large membrane area, there is a crossover to a regime where the extrema of the wrinkles are in contact with the walls. In all regimes after an initial transient, robust localised structures form, leading to an exact conservation of the number of adhesion domains.

cond-mat.soft↗