Spatial Patterns Induced Purely by Dichotomous Disorder

We study conditions under which spatially extended systems with coupling a la Swift-Hohenberg exhibit spatial patterns induced purely by the presence of quenched dichotomous disorder. Complementing the theoretical results based on a generalized mean-field approximation, we also present numerical simulations of particular dynamical systems that exhibit the proposed phenomenology

Growing interfaces: A brief review on the tilt method

The tilt method applied to models of growing interfaces is a useful tool to characterize the nonlinearities of their associated equation. Growing interfaces with average slope $m$, in models and equations belonging to Kardar-Parisi-Zhang (KPZ) universality class, have average saturation velocity $\mathcal{V}_\mathrm{sat}=\Upsilon+\frac{1}{2}\Lambda\,m^2$ when $|m|\ll 1$. This property is sufficient to ensure that there is a nonlinearity type square height-gradient. Usually, the constant $\Lambda$ is considered equal to the nonlinear coefficient $\lambda$ of the KPZ equation. In this paper, we show that the mean square height-gradient $\langle |\nabla h|^2\rangle=a+b \,m^2$, where $b=1$ for the continuous KPZ equation and $b\neq 1$ otherwise, e.g. ballistic deposition (BD) and restricted-solid-on-solid (RSOS) models. In order to find the nonlinear coefficient $\lambda$ associated to each system, we establish the relationship $\Lambda=b\,\lambda$ and we test it through the discrete integration of the KPZ equation. We conclude that height-gradient fluctuations as function of $m^2$ are constant for continuous KPZ equation and increasing or decreasing in other systems, such as BD or RSOS models, respectively.Comment: 11 pages, 4 figure

Scaling properties of a ferromagnetic thin film model at the depinning transition

In this paper, we perform a detailed study of the scaling properties of a ferromagnetic thin film model. Recently, interest has increased in the scaling properties of the magnetic domain wall (MDW) motion in disordered media when an external driving field is present. We consider a (1+1)-dimensional model, based on evolution rules, able to describe the MDW avalanches. The global interface width of this model shows Family-Vicsek scaling with roughness exponent $\zeta\simeq 1.585$ and growth exponent $\beta\simeq 0.975$. In contrast, this model shows scaling anomalies in the interface local properties characteristic of other systems with depinning transition of the MDW, e.g. quenched Edwards-Wilkinson (QEW) equation and random-field Ising model (RFIM) with driving. We show that, at the depinning transition, the saturated average velocity $v_\mathrm{sat}\sim f^\theta$ vanished very slowly (with $\theta\simeq 0.037$) when the reduced force $f=p/p_\mathrm{c}-1\to 0^{+}$. The simulation results show that this model verifies all accepted scaling relations which relate the global exponents and the correlation length (or time) exponents, valid in systems with depinning transition. Using the interface tilting method, we show that the model, close to the depinning transition, exhibits a nonlinearity similar to the one included in the Kardar-Parisi-Zhang (KPZ) equation. The nonlinear coefficient $\lambda\sim f^{-\phi}$ with $\phi\simeq -1.118$, which implies that $\lambda\to 0$ as the depinning transition is approached, a similar qualitatively behaviour to the driven RFIM. We conclude this work by discussing the main features of the model and the prospects opened by it.Comment: 10 pages, 5 figures, 1 tabl

Generation of dynamic structures in nonequilibrium reactive bilayers

We present a nonequlibrium approach for the study of a flexible bilayer whose two components induce distinct curvatures. In turn, the two components are interconverted by an externally promoted reaction. Phase separation of the two species in the surface results in the growth of domains characterized by different local composition and curvature modulations. This domain growth is limited by the effective mixing due to the interconversion reaction, leading to a finite characteristic domain size. In addition to these effects, first introduced in our earlier work [Phys. Rev. E {\bf 71}, 051906 (2005)], the important new feature is the assumption that the reactive process actively affects the local curvature of the bilayer. Specifically, we suggest that a force energetically activated by external sources causes a modification of the shape of the membrane at the reaction site. Our results show the appearance of a rich and robust dynamical phenomenology that includes the generation of traveling and/or oscillatory patterns. Linear stability analysis, amplitude equations and numerical simulations of the model kinetic equations confirm the occurrence of these spatiotemporal behaviors in nonequilibrium reactive bilayers.Comment: To appear in Phys. Rev.

Revisiting random deposition with surface relaxation: approaches from growth rules to Edwards-Wilkinson equation

We present several approaches for deriving the coarse-grained continuous Langevin equation (or Edwards-Wilkinson equation) from a random deposition with surface relaxation (RDSR) model. First we introduce a novel procedure to divide the first transition moment into the three fundamental processes involved: deposition, diffusion and volume conservation. We show how the diffusion process is related to antisymmetric contribution and the volume conservation process is related to symmetric contribution, which renormalizes to zero in the coarse-grained limit. In another approach, we find the coefficients of the continuous Langevin equation, by regularizing the discrete Langevin equation. Finally, in a third approach, we derive these coefficients from the set of test functions supported by the stationary probability density function (SPDF) of the discrete model. The applicability of the used approaches to other discrete random deposition models with instantaneous relaxation to a neighboring site is discussed.Comment: 12 pages, 4 figure

Multidisciplinary approaches towards compartmentalization in development: Dorsoventral boundary formation of the Drosophila wing disc as a case of study

Els límits de restricció dels llinatges estableixen barreres durant el creixement tissular que compartimentalitzen els primordis i promouen el seu patró. Aquest descobriment va suposar un gran avenç en la biologia moderna, gràcies a les seves poderoses implicacions conceptuals sobre el pla de desenvolupament dels vertebrats i dels invertebrats, que és el tema d'aquesta breu revisió. Com a leitmotiv, utilitzem les nostres contribucions més recents al problema de la formació del límit dorsiventral del disc imaginal de l'ala de Drosophila, tot posant especial atenció en enfocaments multidisciplinaris recents que han aclarit la biomecànica i les interaccions gèniques reguladores subjacents al procés de compartimentalització.Lineage restriction boundaries set stable barriers during tissue growth that compartmentalize the primordia and promote their patterning. This discovery was a major breakthrough in modern biology because of its powerful conceptual implications regarding the developmental plan in both vertebrates and invertebrates, the subject of this short review. As a leitmotif, we focus on our own recent contributions to the problem of dorsoventral boundary formation in the wing disc of Drosophila, paying special attention to recent multidisciplinary approaches that have shed light on the gene regulatory interactions and biomechanics underlying the compartmentalization process

Coarse grained approach for volume conserving models

Volume conserving surface (VCS) models without deposition and evaporation, as well as ideal molecular-beam epitaxy models, are prototypes to study the symmetries of conserved dynamics. In this work we study two similar VCS models with conserved noise, which differ from each other by the axial symmetry of their dynamic hopping rules. We use a coarse-grained approach to analyze the models and show how to determine the coefficients of their corresponding continuous stochastic differential equation (SDE) within the same universality class. The employed method makes use of small translations in a test space which contains the stationary probability density function (SPDF). In case of the symmetric model we calculate all the coarse-grained coefficients of the related conserved Kardar-Parisi-Zhang (KPZ) equation. With respect to the symmetric model, the asymmetric model adds new terms which have to be analyzed, first of all the diffusion term, whose coarse-grained coefficient can be determined by the same method. In contrast to other methods, the used formalism allows to calculate all coefficients of the SDE theoretically and within limits numerically. Above all, the used approach connects the coefficients of the SDE with the SPDF and hence gives them a precise physical meaning.Comment: 11 pages, 2 figures, 2 table