arXiv subjects

Alejandro B. Kolton

Publications and source records attributed to Alejandro B. Kolton.

At least 19 recordsLinked to original sources

arXiv2026

Geometric flow of planar domain-wall loops

We investigate the geometric evolution of elastic domain-wall loops in two dimensions. Assuming an instantaneous, isotropic, and homogeneous arc-velocity response of the domain wall to external pressure and local signed curvature, we derive closed dynamical equations linking the enclosed area and loop perimeter for both linear and nonlinear arc-velocity response functions. This reduced description enables predictions for the dynamics of both spontaneous and externally driven domains-subjected to constant or alternating fields-within the time-dependent Ginzburg-Landau scalar $ϕ^4$ model. In the linear response regime, where a non-crossing principle holds in the absence of external driving, we obtain exact results. In particular, we demonstrate that the relaxation rate of the total spontaneous magnetization becomes quantized for arbitrary initial conditions involving multiple, possibly nested, loops, with discrete jumps corresponding to individual loop collapse events. Under external driving, the avoidance principle breaks down due to sparse interactions between interfaces-either within a single loop or between multiple loops-leading to coalescence or splitting events that change the number of loops. A quantized geometrical observable involving the total area and perimeter is identified in this case as well, exhibiting discrete jumps both at interface interaction events and at individual loop collapses. We further use approximate area-perimeter relations to estimate the spontaneous collapse lifetimes of compact magnetic domains, as well as their dynamics under alternating-field-assisted collapse in disordered ultrathin magnetic films. Our predictions are compared with experimental observations in such systems.

cond-mat.dis-nn↗

arXiv2026

Roughening of active nonlinear interfaces with broken tilt symmetry

We study the roughening of an interface with nonlinear elasticity driven by temporally correlated noise, which breaks statistical tilt symmetry. Using scaling arguments and a self-consistent Hartree approximation, we derive the crossover diagram and the steady-state structure factor. We identify three scaling regimes associated with the Larkin, anharmonic Larkin, and Edwards--Wilkinson universality classes, and obtain the crossover lengths separating them. Numerical simulations of large systems confirm the analytical predictions over the full parameter range. Our results provide a unified description of finite-size and crossover effects in a minimal nonlinear-elastic Ornstein--Uhlenbeck active interface.

cond-mat.dis-nn↗

arXiv2026

Data-Driven Modelling to predict forest fire spread in the Patagonian region in Argentina

Wildfires are among the most severe disturbances affecting forest ecosystems, with over 50,000 hectares burned in Patagonia, Argentina, during 2025 alone. This study implements a Reaction-Diffusion-Convection (RDC) model to simulate wildfire spread in the Steffen and Martin Lakes area, a region severely impacted by fires. By integrating high-resolution maps of slope, wind velocity, and vegetation, we conducted three computational experiments of increasing complexity to simulate fire propagation across heterogeneous landscapes. We employed a Genetic Algorithm (GA) to recover reference model parameters by maximizing the spatial overlap between simulated and reference burned areas. Subsequently, parameter estimates were refined using XGBoost to improve accuracy. Results demonstrate that the GA accurately recovers reference parameters across all scenarios, while the XGBoost fine-tuning significantly enhances accuracy in simpler cases. This integrated framework offers a systematic approach for estimating difficult-to-measure wildfire parameters, demonstrating the potential of hybrid computational methods for wildfire modeling and forest management.

cond-mat.dis-nn↗

arXiv2026

Activation and Avalanche Length Scales in the Finite-Temperature Creep of an Elastic Interface

We investigate the creep dynamics of a driven elastic line at finite temperature, well below the depinning threshold. We show that creep is governed by two distinct length scales. The first, $\ell_{\mathrm{opt}}$, corresponds to the optimal activated rearrangements that control the dynamics' bottleneck and remains essentially temperature-independent. The second, $\ell_{\mathrm{av}}$, characterizes the spatial extent of thermally activated avalanches and grows as temperature decreases. By combining structural and dynamical observables, we show that $\ell_{\mathrm{av}}$ governs both the crossover in the structure factor and the growth of the four-point dynamical susceptibility, while the relaxation time remains controlled by activation over large barriers associated with $\ell_{\mathrm{opt}}$. We find that the avalanche scale follows $\ell_{\mathrm{av}}(T)\sim T^{-ν_{\mathrm{dep}}}$, thereby selecting a unique scenario among competing theoretical predictions. These results establish a unified picture of finite-temperature creep in which activation controls temporal scales while depinning criticality governs spatial correlations.

cond-mat.stat-mech↗

arXiv2024

Infection fronts in randomly varying transmission-rate media

We numerically investigate the geometry and transport properties of infection fronts within the spatial SIR model in two dimensions. The model incorporates short-range correlated quenched random transmission rates. Our findings reveal that the critical average transmission rate for the steady-state propagation of the infection is overestimated by the naive mean-field homogenization. Furthermore, we observe that the velocity, profile, and harmfulness of the fronts, given a specific average transmission, are sensitive to the details of randomness. In particular, we find that the harmfulness of the front is larger the more uniform the transmission-rate is, suggesting potential optimization in vaccination strategies under constraints like fixed average-transmission-rates or limited vaccine resources. The large-scale geometry of the advancing fronts presents nevertheless robust universal features and, for a statistically isotropic and short-range correlated disorder, we get a roughness exponent $α\approx 0.42 \pm 0.10$ and a dynamical exponent $z\approx 1.6 \pm 0.10$, which are roughly compatible with the one-dimensional Kardar-Parisi-Zhang (KPZ) universality class. We find that the KPZ term and the disorder-induced effective noise are present and have a kinematic origin.

cond-mat.dis-nn↗

arXiv2023

Depinning free of the elastic approximation

We model the isotropic depinning transition of a domain-wall using a two dimensional Ginzburg-Landau scalar field instead of a directed elastic string in a random media. An exact algorithm accurately targets both the critical depinning field and the critical configuration for each sample. For random bond disorder of weak strength $Δ$, the critical field scales as $Δ^{4/3}$ in agreement with the predictions for the quenched Edwards-Wilkinson elastic model. However, critical configurations display overhangs beyond a characteristic length $l_{\tt 0} \sim Δ^{-α}$, with $α\approx 2.2$, indicating a finite-size crossover. At the large scales, overhangs recover the orientational symmetry which is broken by directed elastic interfaces. We obtain quenched Edwards-Wilkinson exponents below $l_{\tt 0}$ and invasion percolation depinning exponents above $l_{\tt 0}$. A full picture of domain wall isotropic depinning in two dimensions is hence proposed.

cond-mat.dis-nn↗

arXiv2022

Driven particle dispersion in narrow disordered racetracks

We study the disorder-induced deterministic dispersion of particles uniformly driven in an array of narrow tracks. For different toy models with quenched disorder we obtain exact analytical expressions for the steady-state mean velocity $v$ and the dispersion constant $D$ for any driving force $f$ above a putative depinning threshold. For short-range correlated pinning forces we find that at large drives $D\sim 1/v$ for random-field type of disorder while $D \sim 1/v^3$ for the random-bond type. We show numerically that these results are robust: the same scaling holds for models of massive damped particles, soft particles, particles in quasi-one dimensional or two dimensional tracks, and for a model of a magnetic domain wall with two degrees of freedom driven either by electrical current or magnetic field. Crossover and finite temperature effects are discussed. The universal features we identify may be relevant for describing the fluctuating dynamics of stable localized objects such solitons, superconducting vortices, magnetic domain walls and skyrmions, and colloids driven in quasi one-dimensional track arrays. In particular, the drive dependence of $D$ appears as a sensitive tool for characterizing and assessing the nature of disorder in the host materials.

cond-mat.dis-nn↗

arXiv2022

Hyperuniformity in Type-II Superconductors with Point and Planar Defects

We use vortex matter in type-II superconductors as a playground to study how different types of disorder affect the long wavelength density fluctuations of the system. We find that irrespective of the vortex-vortex interaction, in the case of samples with weak and dense point defects the system presents the hidden order of hyperuniformity characterized by an algebraic suppression of density fluctuations when increasing the system size. We also reveal that, on the contrary, for samples with planar defects hyperuniformity is suppressed since density fluctuations have a tendency to unboundedness on increasing the system size. Although some of these results were known from previous works, this paper makes the fundamental discovery that the ability of planar disorder to suppress hyperuniformity grows on increasing the softness of the structure for more diluted systems.

cond-mat.supr-con↗

arXiv2022

Anisotropic suppression of hyperuniformity of elastic systems in media with planar disorder

Disordered hyperuniform materials with vanishing long-wavelength density fluctuations are attracting attention due to their unique physical properties. In these systems, the large-scale density fluctuations are strongly suppressed as in a perfect crystal, even though the system can be disordered like a liquid. Yet, hyperuniformity can be affected by the different types of quenched disorder unavoidably present in the host medium where constituents are nucleated. Here, we use vortex matter in superconductors as a model elastic system to study how planar correlated disorder impacts the otherwise hyperuniform structure nucleated in samples with weak point disorder. Planes of defects suppress hyperuniformity in an anisotropic fashion: While in the transverse direction to defects the long-wavelength density fluctuations are non-vanishing, in the longitudinal direction they are smaller and the system can eventually recover hyperuniformity for sufficiently thick samples. Our findings stress the need of considering the nature of disorder and thickness-dependent dimensional crossovers in the search for novel hyperuniform materials.

cond-mat.supr-con↗

arXiv2022

Depinning and flow of a vortex line in an uniaxial random medium

We study numerically and analytically the dynamics of a single directed elastic string driven through a 3-dimensional disordered medium. In the quasistatic limit the string is super-rough in the driving direction, with roughness exponent $ζ_{\parallel} = 1.25\pm 0.01$, dynamic exponent $z_{\parallel}= 1.43 \pm 0.01$, correlation-length exponent $ν= 1.33 \pm 0.02$, depinning exponent $β= 0.24\pm 0.01$, and avalanche-size exponent $τ_{\parallel} = 1.09 \pm 0.03$. In the transverse direction we find $ζ_{\perp} = 0.5 \pm 0.01$, $z_{\perp} = 2.27 \pm 0.05$, and $τ_{\perp} =1.17\pm 0.06$. We show that transverse fluctuations do not alter the critical exponents in the driving direction, as predicted by the planar approximation (PA) proposed in 1996 by Ertas and Kardar (EK). We check the PA for the force-force correlator, comparing to the functional renormalization group and simulations. Both Random-Bond (RB) and Random-Field (RF) disorder yield a single universality class, indistinguishable from the one of an elastic string in a 2-dimensional random medium. While $z_{\perp}=z_{\parallel}+1/ν$ and $ν=1/(2-ζ_{\parallel})$ of EK are satisfied, the transversal movement is that of a Brownian, with a clock set locally by the forward movement. This implies $ζ_\perp = (2-d)/2$, distinct from EK. At small driving velocities the distribution of local parallel displacements has a negative skewness, while in the transverse direction it is a Gaussian. For large scales, the system can be described by anisotropic effective temperatures. In the fast-flow regime the local displacement distributions become Gaussian in both directions and the effective temperatures vanish as $T^{\perp}_{\tt eff}\sim 1/v$ and $T^{\parallel}_{\tt eff}\sim 1/v^3$ for RB and as $T^{\perp}_{\tt eff} \approx T^{\parallel}_{\tt eff} \sim 1/v$ for RF.

cond-mat.dis-nn↗

arXiv2021

The yielding of amorphous solids at finite temperatures

We analyze the effect of temperature on the yielding transition of amorphous solids using different coarse-grained model approaches. On one hand we use an elasto-plastic model, with temperature introduced in the form of an Arrhenius activation law over energy barriers. On the other hand, we implement a Hamiltonian model with a relaxational dynamics, where temperature is introduced in the form of a Langevin stochastic force. In both cases, temperature transforms the sharp transition of the athermal case in a smooth crossover. We show that this thermally smoothed transition follows a simple scaling form that can be fully explained using a one-particle system driven in a potential under the combined action of a mechanical and a thermal noise, the stochastically-driven Prandtl-Tomlinson model. Our work harmonizes the results of simple models for amorphous solids with the phenomenological $\sim T^{2/3}$ law proposed by Johnson and Samwer [Phys. Rev. Lett. 95, 195501 (2005)] in the framework of experimental metallic glasses yield observations, and extend it to a generic case. Finally, our results strengthen the interpretation of the yielding transition as an effective mean-field phenomenon.

cond-mat.dis-nn↗

arXiv2021

Universal Critical Exponents of the Magnetic Domain Wall Depinning Transition

Magnetic field driven domain wall dynamics in a ferrimagnetic GdFeCo thin film with perpendicular magnetic anisotropy is studied using low temperature magneto-optical Kerr microscopy. Measurements performed in a practically athermal condition allow for the direct experimental determination of the velocity ($ β= 0.30 \pm 0.03 $) and correlation length ($ ν= 1.3 \pm 0.3 $) exponents of the depinning transition. The whole family of exponents characterizing the transition is deduced, providing evidence that the depinning of magnetic domain walls is better described by the quenched Edwards-Wilkinson universality class.

cond-mat.mtrl-sci↗

arXiv2020

Hysteretic depinning of a particle in a periodic potential: Phase diagram and criticality

We consider a massive particle driven with a constant force in a periodic potential and subjected to a dissipative friction. As a function of the drive and damping, the phase diagram of this paradigmatic model is well known to present a pinned, a sliding, and a bistable regime separated by three distinct bifurcation lines. In physical terms, the average velocity $v$ of the particle is nonzero only if either (i) the driving force is large enough to remove any stable point, forcing the particle to slide, or (ii) there are local minima but the damping is small enough, below a critical damping, for the inertia to allow the particle to cross barriers and follow a limit cycle; this regime is bistable and whether $v > 0$ or $v = 0$ depends on the initial state. In this paper, we focus on the asymptotes of the critical line separating the bistable and the pinned regimes. First, we study its behavior near the "triple point" where the pinned, the bistable, and the sliding dynamical regimes meet. Just below the critical damping we uncover a critical regime, where the line approaches the triple point following a power-law behavior. We show that its exponent is controlled by the normal form of the tilted potential close to its critical force. Second, in the opposite regime of very low damping, we revisit existing results by providing a simple method to determine analytically the exact behavior of the line in the case of a generic potential. The analytical estimates, accurately confirmed numerically, are obtained by exploiting exact soliton solutions describing the orbit in a modified tilted potential which can be mapped to the original tilted washboard potential. Our methods and results are particularly useful for an accurate description of underdamped nonuniform oscillators driven near their triple point.

cond-mat.stat-mech↗

arXiv2020

Non-Gaussian tail in the force distribution: A hallmark of correlated disorder in the host media of elastic objects

Inferring the nature of disorder in the media where elastic objects are nucleated is of crucial importance for many applications but remains a challenging basic-science problem. Here we propose a method to discern whether weak-point or strong-correlated disorder dominates based on characterizing the distribution of the interaction forces between objects mapped in large fields-of-view. We illustrate our proposal with the case-study system of vortex structures nucleated in type-II superconductors with different pinning landscapes. Interaction force distributions are computed from individual vortex positions imaged in thousands-vortices fields-of-view in a two-orders-of-magnitude-wide vortex-density range. Vortex structures nucleated in point-disordered media present Gaussian distributions of the interaction force components. In contrast, if the media have dilute and randomly-distributed correlated disorder, these distributions present non-Gaussian algebraically-decaying tails for large force magnitudes. We propose that detecting this deviation from the Gaussian behavior is a fingerprint of strong disorder, in our case originated from a dilute distribution of correlated pinning centers.

cond-mat.supr-con↗

arXiv2020

Creep motion of elastic interfaces driven in a disordered landscape

The thermally activated creep motion of an elastic interface weakly driven on a disordered landscape is one of the best examples of glassy universal dynamics. Its understanding has evolved over the last 30 years thanks to a fruitful interplay between elegant scaling arguments, sophisticated analytical calculations, efficient optimization algorithms and creative experiments. In this article, starting from the pioneer arguments, we review the main theoretical and experimental results that lead to the current physical picture of the creep regime. In particular, we discuss recent works unveiling the collective nature of such ultra-slow motion in terms of elementary activated events. We show that these events control the mean velocity of the interface and cluster into "creep avalanches" statistically similar to the deterministic avalanches observed at the depinning critical threshold. The associated spatio-temporal patterns of activated events have been recently observed in experiments with magnetic domain walls. The emergent physical picture is expected to be relevant for a large family of disordered systems presenting thermally activated dynamics.

cond-mat.dis-nn↗

arXiv2019

Hyperuniform vortex patterns at the surface of type-II superconductors

A many-particle system must posses long-range interactions in order to be hyperuniform at thermal equilibrium. Hydrodynamic arguments and numerical simulations show, nevertheless, that a three-dimensional elastic-line array with short-ranged repulsive interactions, such as vortex matter in a type-II superconductor, forms at equilibrium a class-II hyperuniform two-dimensional point pattern for any constant-$z$ cross section. In this case, density fluctuations vanish isotropically as $\sim q^α$ at small wave-vectors $q$, with $α=1$. This prediction includes the solid and liquid vortex phases in the ideal clean case, and the liquid in presence of weak uncorrelated disorder. We also show that the three-dimensional Bragg glass phase is marginally hyperuniform, while the Bose glass and the liquid phase with correlated disorder are expected to be non-hyperuniform at equilibrium. Furthermore, we compare these predictions with experimental results on the large-wavelength vortex density fluctuations of magnetically decorated vortex structures nucleated in pristine, electron-irradiated and heavy-ion irradiated superconducting BiSCCO samples in the mixed state. For most cases we find hyperuniform two-dimensional point patterns at the superconductor surface with an effective exponent $α_{\text{eff}} \approx 1$. We interpret these results in terms of a large-scale memory of the high-temperature line-liquid phase retained in the glassy dynamics when field-cooling the vortex structures into the solid phase. We also discuss the crossovers expected from the dispersivity of the elastic constants at intermediate length-scales, and the lack of hyperuniformity in the $x\,-y$ plane for lengths $q^{-1}$ larger than the sample thickness due to finite-size effects in the $z$-direction.

cond-mat.dis-nn↗

arXiv2019

Unveiling the vortex glass phase in the surface and volume of a type-II superconductor

Order-disorder transitions between glassy phases are quite common in nature and yet a comprehensive survey of the microscopic structural changes remains elusive since the scale of the constituents is tiny and in most cases few of them take part in the transformation. Vortex matter in type-II superconductors is a model system where some of the experimental challenges inherent to this general question can be tackled by adequately choosing the host superconducting sample. For instance, Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8 + δ}$ is a type-II superconductor with weak point disorder that presents a transition between two glassy phases on increasing the constituents' (vortices) density. At low vortex densities, the impact of disorder produces the nucleation of a glassy yet quasi-crystalline phase, the Bragg glass. For high vortex densities the stable phase, coined as $\textit{vortex glass}$, was proposed to be disordered, but its structural properties have remained elusive up to now. Here we answer this question by combining surface and bulk vortex imaging techniques, and show that the vortex glass is neither a messy nor a hexatic phase: in the plane of vortices it presents large crystallites with positional correlations growing algebraically and short-ranged orientational order. However, no dramatic change in the correlation length along the direction of vortices is observed on traversing the order-disorder transformation.

cond-mat.supr-con↗

arXiv2019

Distribution of velocities in an avalanche, and related quantities: Theory and numerical verification

We study several probability distributions relevant to the avalanche dynamics of elastic interfaces driven on a random substrate: The distribution of size, duration, lateral extension or area, as well as velocities. Results from the functional renormalization group and scaling relations involving two independent exponents, roughness $ζ$, and dynamics $z$, are confronted to high-precision numerical simulations of an elastic line with short-range elasticity, i.e. of internal dimension $d=1$. The latter are based on a novel stochastic algorithm which generates its disorder on the fly. Its precision grows linearly in the time-discretization step, and it is parallelizable. Our results show good agreement between theory and numerics, both for the critical exponents as for the scaling functions. In particular, the prediction ${\sf a} = 2 - \frac{2}{d+ ζ- z}$ for the velocity exponent is confirmed with good accuracy.

cond-mat.dis-nn↗