arXiv subjects

M. F. Torres

Publications and source records attributed to M. F. Torres.

4 recordsLinked to original sources

arXiv2021

KPZ models: height-gradient fluctuations and the tilt method

When a growing interface belonging to the KPZ universality class is tilted with average slope $m$, its average velocity increases in $\fracΛ{2}\,m^2$, where $Λ$ is related to the nonlinear coefficient $λ$ of the KPZ equation. Nevertheless, a necessary condition for this association to hold true is that the mean square height-gradient increases in $b\, m^2$ when the interface is tilted. For the continuous KPZ equation $b = 1$ and the relation $Λ=λ$ is achieved. In this work, we study the local fluctuations of the height gradient through an analysis of the values of $b$. We show that, for 1-dimensional discrete KPZ models, $b$ has a power-law dependence with the discretization step $s$ chosen to calculate the height gradient and $b$ goes to $1$ as $s$ increases. Its power-law exponent $γ_b$ matches the exponent associated with the finite-size corrections of the interface average velocity, $\textit{i.e.}$ $γ_b=2(ζ-1)$, where $ζ$ is the global roughness exponent. We also show how, for restricted (unrestricted) growth models, the value of $b$ goes to $1$ from below (above) as $s$ increases.

cond-mat.stat-mech↗

arXiv2017

Numerical integration of KPZ equation with restrictions

In this paper, we introduce a novel integration method of Kardar-Parisi-Zhang (KPZ) equation. It has always been known that if during the discrete integration of the KPZ equation the nearest-neighbor height-difference exceeds a critical value, an instability appears and the integration diverges. One way to avoid these instabilities is to replace the KPZ nonlinear-term by a function of the same term that depends on a single adjustable parameter which is able to control pillars or grooves growing on the interface. Here, we propose a different integration method which consists of directly limiting the value taken by the KPZ nonlinearity, thereby imposing a restriction rule that is applied in each integration time-step, as if it were the growth rule of a restricted discrete model, e.g. restricted-solid-on-solid (RSOS). Taking the discrete KPZ equation with restrictions to its dimensionless version, the integration depends on three parameters: the coupling constant $g$, the inverse of the time-step $k$, and the restriction constant $\varepsilon$ which is chosen to eliminate divergences while keeping all the properties of the continuous KPZ equation. We study in detail the conditions in the parameters' space that avoids divergences in the 1-dimensional integration and reproduce the scaling properties of the continuous KPZ with a particular parameter set. We apply the tested methodology to the $d$-dimensional case ($d = 3,4$) with the purpose of obtaining the growth exponent $β$, by establishing the conditions of the coupling constant $g$ under which we recover known values reached by other authors, in particular for the RSOS model. This method allows us to infer that $d = 4$ is not the critical dimension of the KPZ universality class, where the strong-coupling phase dissapears.

cond-mat.stat-mech↗

arXiv2016

Synchronization in interacting Scale Free Networks

We study the fluctuations of the interface, in the steady state, of the Surface Relaxation Model (SRM) in two scale free interacting networks where a fraction $q$ of nodes in both networks interact one to one through external connections. We find that as $q$ increases the fluctuations on both networks decrease and thus the synchronization reaches an improvement of nearly $40\%$ when $q=1$. The decrease of the fluctuations on both networks is due mainly to the diffusion through external connections which allows to reducing the load in nodes by sending their excess mostly to low-degree nodes, which we report have the lowest heights. This effect enhances the matching of the heights of low-and high-degree nodes as $q$ increases reducing the fluctuations. This effect is almost independent of the degree distribution of the networks which means that the interconnection governs the behavior of the process over its topology.

physics.soc-ph↗

arXiv2012

Intrinsic anomalous scaling in a ferromagnetic thin film model

Recently, the interest on theoretical and experimental studies of dynamic properties of the magnetic domain wall (MDW) of ferromagnetic thin films with disorder placed in an external magnetic field has increased. In order to study global and local measurable observables, we consider the $(1+1)$-dimensional model introduced by Buceta and Muraca [Physica A 390 (2011) 4192], based on rules of evolution that describe the MDW avalanches. From the values of the roughness exponents, global $ζ$, local $ζ_\text{loc}$, and spectral $ζ_s$, obtained from the global interface width, hight-difference correlation function and structure function, respectively, recent works have concluded that the universality classes should be analyzed in the context of the anomalous scaling theory. We show that the model is included in the group of systems with intrinsic anomalous scaling ($ζ\simeq 1.5 $, $ζ_\text{loc}=ζ_s\simeq 0.5 $), and that the surface of the MDW is multi-affine. With these results, we hope to establish in short term the scaling relations that verify the critical exponents of the model, including the dynamic exponent $z$, the exponents of the distributions of avalanche-size $τ$ and -duration $α$, among others.

cond-mat.stat-mech↗