arXiv subjects

Renan A. L. Almeida

Publications and source records attributed to Renan A. L. Almeida.

8 recordsLinked to original sources

arXiv2026

Universal Coarsening and Giant-Cluster Formation in Growing Interfaces

Clusters formed by fluctuations of two-dimensional (2D) directed interfaces around a threshold level have been extensively studied at equilibrium and in nonequilibrium steady states, but their coarsening dynamics remain poorly understood. Here, we numerically investigate this unexplored coarsening of clusters in 2D growing interfaces believed to belong to the Kardar-Parisi-Zhang universality class. Using a two-point spatial correlator, we demonstrate statistical time invariance of the evolving configurations and identify scaling forms shared across distinct models. We reveal a pronounced asymmetry in the growth of the largest clusters: one cluster emerges as a giant structure whose characteristic length exceeds the correlation length. Population-dependent scaling forms for the number densities of cluster areas are uncovered. These findings highlight new universal aspects of growing interfaces and suggest avenues for experimental verification.

cond-mat.stat-mech↗

arXiv2025

Critical clusters in liquid crystals: Fractal geometry and conformal invariance

We study the two-dimensional domain morphology of twisted nematic liquid crystals during their phase-ordering kinetics [R. A. L. Almeida, Phys. Rev. Lett. 131 (2023) 268101], which is a physical candidate to self-generate critical clusters in the percolation universality class. Here we present experimental evidence that large clusters and their hulls are indeed both fractals with dimensions of the corresponding figures in critical percolation models. The asymptotic decay of a crossing probability, from a region in the vicinity of the origin to the boundary of disks, is described by the Lawler-Schramm-Werner theorem provided that a microscopic length in the original formulation is replaced by the coarsening length of the liquid crystal. Furthermore, the behavior for the winding angle of large loops is, at certain scales, compatible with that of Schramm-Loewner evolution curves with diffusivity $κ= 6$. These results show an experimental realization of critical clusters in phase ordering.

cond-mat.soft↗

arXiv2024

Effects of the growth kinetics on solute diffusion in porous films

For the development of porous materials with improved transport properties, a key missing ingredient is to determine the relations between growth kinetics, structure, and transport parameters. Here, we address these relations by studying solute diffusion through three-dimensional porous films produced by simple deposition models with controlled thickness and porosity. We simulate growing films with competitive aggregation rules that incorporate lateral aggregation (relative rate proportional to $p$), which leads to pore formation, and surface relaxation ($1-p$) that favors compaction. By connecting a solute source at the basis and a drain at the top outer surface of the films, we extract the effective diffusion coefficients from steady-state simulations. We find that for a given film thickness, the larger the $p$, the larger the effective porosity and diffusivity, but the smaller the tortuosity. Keeping constant growth conditions (i.e., same $p$), the increase of thickness always leads to an increase of effective porosity, but a nontrivial behavior in the diffusivity occurs: for $p\leq 0.7$, the diffusion coefficient is larger in thicker films; this is accompanied by a decrease of the tortuosity with the thickness, thus indicating that growth continuously improves pore structure for diffusion. Microscopically, such a result is associated with narrower distributions of local solute currents at higher points of films. Particularly for $p\geq 0.9$, in which film porosity is $\sim 0.65-0.7$, the tortuosity is between $1.3$ and $2$, increases with the thickness, and has maximal changes near $25\%$. Pairs of values of porosity and tortuosity that we obtain here, for the thickest films, agree with those experimentally measured in some porous electrodes. Noteworthy, the increase of film thickness is generally favorable for diffusion in their pores, and exceptions have small losses in tortuosity.

cond-mat.stat-mech↗

arXiv2024

Phase-ordering kinetics in the Allen-Cahn (Model A) class: universal aspects elucidated by electrically-induced transition in liquid crystals

The two-dimensional (2d) Ising model is the statistical physics textbook example for phase transitions and their kinetics. Quenched through the Curie point with Glauber rates, the late-time description of the ferromagnetic domain coarsening finds its place at the scalar sector of the Allen-Cahn (Model A) class. Resisting exact results sought since Lifshitz's account in 1962, central quantities in 2d Model A $-$ most scaling exponents and correlation functions $-$ remain known up to approximate theories whose disparate outcomes urge experimental assessment. Here, we perform such assessment from a comprehensive study of the coarsening of 2d twisted nematic liquid crystals whose kinetics is induced by a super-fast switching from a spatiotemporally chaotic state to a two-phase concurrent, equilibrium one. Tracking the dynamics via optical microscopy, we firstly show the sharp evidence of well-established Model A aspects, such as the dynamic exponent $z=2$ and the dynamic scaling hypothesis, to then move forward. We confirm the Bray-Humayun theory for Porod's regime describing intradomain length scales of spatial correlators, and show that their nontrivial decay beyond that regime is captured in a free-from-parameter fashion by Gaussian theories. These paradigmatic theories, however, do not perform well for time-related Model A statistics. We reveal that the collapsed form of two-time correlators is best accounted for by the local scaling invariance theory, along with the Fisher-Huse conjecture. We also suggest the true value for the local persistence exponent, in disfavour of Gaussian models, and extract a universal fractal dimension for the morphology of persistence clusters that is notably close to the golden ratio. Given its accuracy and possibilities, this experimental setup may work as a prototype to address universality issues in the realm of nonequilibrium systems.

cond-mat.stat-mech↗

arXiv2023

Critical percolation in the ordering kinetics of twisted nematic phases

I report on the experimental confirmation that critical percolation statistics underlie the ordering kinetics of twisted nematic phases in the Allen-Cahn universality class. Soon after the ordering starts from a homogeneous disordered phase and proceeds towards a broken $\mathbb{Z}_2$-symmetry phase, the system seems to be attracted to the random percolation fixed point at a special timescale $t_{\textrm{p}}$. At this time, exact formulae for crossing probabilities in percolation theory agree with the corresponding probabilities in the experimental data. The ensuing evolution for the number density of hull-enclosed areas is described by an exact expression derived from a percolation model endowed with curvature-driven interface motion. Scaling relation for hull-enclosed areas versus perimeters reveals that the fractal percolation geometry is progressively morphed into a regular geometry up to the order of the classical coarsening length. In view of its universality and experimental possibilities, the study opens a path for exploring percolation keystones in the realm of nonequilibrium, phase-ordering systems.

cond-mat.stat-mech↗

arXiv2022

Energy-lowering and constant-energy spin flips: Emergence of the percolating cluster in the kinetic Ising model

After a sudden quench from the disordered high-temperature $T_0\to\infty$ phase to a final temperature below the critical point $T_F \ll T_c$, the non-conserved order parameter dynamics of the two-dimensional ferromagnetic Ising model on a square lattice (2dIM) initially approaches the critical percolation state before entering the coarsening regime. This approach involves two timescales associated with the first appearance (at time $t_{{\rm p}_1}>0$) and stabilization (at time $t_{\rm p}>t_{{\rm p}_1}$) of a giant percolation cluster, as previously reported. However, the microscopic mechanisms that control such timescales are not yet fully understood. In this paper, in order to study their role on each time regime after the quench ($T_F=0$), we distinguish between spin flips that decrease the total energy of the system from those that keep it constant, the latter being parametrized by the probability $p$. We show that the cluster size heterogeneity $H(t,p)$ and the typical domain size $\ell (t,p)$ have no dependence on $p$ in the first time regime up to $t_{{\rm p}_1}$. On the other hand, the time for stabilizing a percolating cluster is controlled by the acceptance probability of constant-energy flips: $t_{\rm p}(p) \sim p^{-1}$ for $p\ll 1$ (at $p=0$, the dynamics gets stuck in a metastable state). These flips are also the relevant ones in the later coarsening regime where dynamical scaling takes place. Because the phenomenology on the approach to the percolation point seems to be shared by many 2d systems with a non-conserved order parameter dynamics (and certain cases of conserved ones as well), our results may suggest a simple and effective way to set, through the dynamics itself, $t_{{\rm p}_1}$ and $t_{\rm p}$ in such systems.

cond-mat.stat-mech↗

arXiv2021

Roughness and Correlations in the Transition from Island to Film Growth: Simulations and Application to CdTe Deposition

Using kinetic Monte Carlo simulations, we develop a framework to relate morphological properties and microscopic dynamics during island growth, coalescence, and initial formation of continuous heteroepitaxial films. The average island width is controlled by adatom mobility on the substrate. Subsequent evolution strongly depends on the Ehrlich-Schwöebel energy barrier $E_{ES}$ of the deposited material. As $E_{ES}$ decreases, islands becomes taller and their coalescence is delayed. For small islands and large $E_{ES}$, the global roughness increases as $W\sim{\text{thickness}}^{1/2}$ and the local roughness increases at short scales (apparent anomalous scaling) before and after island coalescence. If the islands are wide, $W$ may have a plateau for large $E_{ES}$ and has a maximum for small $E_{ES}$ when the islands coalesce. This framework is applied to atomic-force microscopy data of the initial stages of CdTe deposition on Kapton: a maximum of $W$ during island coalescence indicates negligible ES barrier, consistently with scaling properties of much thicker films, and the diffusion coefficient ${10}^{-7}{\text{--}}{10}^{-5}{\text{cm}}^2/{\text s}$ on the Kapton surface at $150\,^{\circ}\mathrm{C}$ is estimated. Applications of the framework to other materials are suggested, in which the expected roles of ES barriers are highlighted.

cond-mat.mtrl-sci↗

arXiv2015

Kardar-Parisi-Zhang Universality, Anomalous Scaling and Crossover Effects in the Growth of Cdte Thin Films

We report on the growth dynamic of CdTe thin films for deposition temperatures ($T$) in the range of $150\,^{\circ}\mathrm{C}$ to $300\,^{\circ}\mathrm{C}$. A relation between mound evolution and large-wavelength fluctuations at CdTe surface has been established. One finds that short-length scales are dictated by an interplay between the effects of the formation of defects at boundaries of neighbouring grains and a relaxation process which stems from the diffusion and deposition of particles (CdTe molecules) torward these regions. A Kinetic Monte Carlo model corroborates these reasonings. As $T$ is increased, the competition gives rise to different scenarios in the roughening scaling such as: uncorrelated growth, a crossover from random to correlated growth and transient anomalous scaling. In particular, for $T = 250\,^{\circ}\mathrm{C}$, one shows that surface fluctuations are described by the celebrated Kardar-Parisi-Zhang (KPZ) equation, in the meantime that, the universality of height, local roughness and maximal height distributions for the KPZ class is, finally, experimentally demonstrated. The dynamic of fluctuations at the CdTe surface for other temperatures still is described by the KPZ equation, but with different values for the superficial tension ($ν$) and excess of velocity ($λ$). Namely, for $T = 150\,^{\circ}\mathrm{C}$ one finds a Poissonian growth that indicates $ν= λ= 0$. For $T = 200\,^{\circ}\mathrm{C}$, however, a Random-to-KPZ crossover is found, with $λ> 0$ in the second regime. Finally, for films grown at $T = 300\,^{\circ}\mathrm{C}$, one demonstrates that a KPZ growth with $λ< 0$ takes place. We discuss the different mechanisms leading to KPZ scaling which depend on $T$, and conjecture the behavior of the phenomenological parameter $λ$ as function of the deposition temperature.

cond-mat.stat-mech↗