Effective Edwards-Wilkinson equation for single-file diffusion

In this work, we present an effective discrete Edwards-Wilkinson equation aimed to describe the single-file diffusion process. The key physical properties of the system are captured defining an effective elasticity, which is proportional to the single particle diffusion coefficient and to the inverse squared mean separation between particles. The effective equation gives a description of single-file diffusion using the global roughness of the system of particles, which presents three characteristic regimes, namely normal diffusion, subdiffusion and saturation, separated by two crossover times. We show how these regimes scale with the parameters of the original system. Additional repulsive interaction terms are also considered and we analyze how the crossover times depend on the intensity of the additional terms. Finally, we show that the roughness distribution can be well characterized by the Edwards-Wilkinson universal form for the different single-file diffusion processes studied here.Comment: 9 pages, 9 figure

Parameter free scaling relation for nonequilibrium growth processes

We discuss a parameter free scaling relation that yields a complete data collapse for large classes of nonequilibrium growth processes. We illustrate the power of this new scaling relation through various growth models, as for example the competitive growth model RD/RDSR (random deposition/random deposition with surface diffusion) and the RSOS (restricted solid-on-solid) model with different nearest-neighbor height differences, as well as through a new deposition model with temperature dependent diffusion. The new scaling relation is compared to the familiar Family-Vicsek relation and the limitations of the latter are highlighted.Comment: 4 pages, 4 figures, to appear in Physical Review

Wavelet transforms in a critical interface model for Barkhausen noise

We discuss the application of wavelet transforms to a critical interface model, which is known to provide a good description of Barkhausen noise in soft ferromagnets. The two-dimensional version of the model (one-dimensional interface) is considered, mainly in the adiabatic limit of very slow driving. On length scales shorter than a crossover length (which grows with the strength of surface tension), the effective interface roughness exponent $\zeta$ is $\simeq 1.20$, close to the expected value for the universality class of the quenched Edwards-Wilkinson model. We find that the waiting times between avalanches are fully uncorrelated, as the wavelet transform of their autocorrelations scales as white noise. Similarly, detrended size-size correlations give a white-noise wavelet transform. Consideration of finite driving rates, still deep within the intermittent regime, shows the wavelet transform of correlations scaling as $1/f^{1.5}$ for intermediate frequencies. This behavior is ascribed to intra-avalanche correlations.Comment: RevTeX, 10 pages, 9 .eps figures; Physical Review E, to be publishe

Coevolution of agents and networks: Opinion spreading and community disconnection

We study a stochastic model for the coevolution of a process of opinion formation in a population of agents and the network which underlies their interaction. Interaction links can break when agents fail to reach an opinion agreement. The structure of the network and the distribution of opinions over the population evolve towards a state where the population is divided into disconnected communities whose agents share the same opinion. The statistical properties of this final state vary considerably as the model parameters are changed. Community sizes and their internal connectivity are the quantities used to characterize such variations.Comment: To appear in Phys. Lett.

Dynamical Critical Phenomena and Large Scale Structure of the Universe: the Power Spectrum for Density Fluctuations

As is well known, structure formation in the Universe at times after decoupling can be described by hydrodynamic equations. These are shown here to be equivalent to a generalization of the stochastic Kardar--Parisi--Zhang equation with time-- dependent viscosity in epochs of dissipation. As a consequence of the Dynamical Critical Scaling induced by noise and fluctuations, these equations describe the fractal behavior (with a scale dependent fractal dimension) observed at the smaller scales for the galaxy--to--galaxy correlation function and $also$ the Harrison--Zel'dovich spectrum at decoupling. By a Renormalization Group calculation of the two--point correlation function between galaxies in the presence of (i) the expansion of the Universe and (ii) non--equilibrium, we can account, from first principles, for the main features of the observed shape of the power spectrum.Comment: 13 pages with 2 encapsulated PostScript figures included, gzipped tar forma

Kinetic roughening, global quantities, and fluctuation-dissipation relations

Growth processes and interface fluctuations can be studied through the properties of global quantities. We here discuss a global quantity that not only captures better the roughness of an interface than the widely studied surface width, but that is also directly conjugate to an experimentally accessible parameter, thereby allowing us to study in a consistent way the global response of the system to a global change of external conditions. Exploiting the full analyticity of the linear Edwards-Wilkinson and Mullins-Herring equations, we study in detail various two-time functions related to that quantity. This quantity fulfills the fluctuation-dissipation theorem when considering steady-state equilibrium fluctuations.Comment: 13 pages, 5 figure

Symmetry based determination of space-time functions in nonequilibrium growth processes

We study the space-time correlation and response functions in nonequilibrium growth processes described by linear stochastic Langevin equations. Exploiting exclusively the existence of space and time dependent symmetries of the noiseless part of these equations, we derive expressions for the universal scaling functions of two-time quantities which are found to agree with the exact expressions obtained from the stochastic equations of motion. The usefulness of the space-time functions is illustrated through the investigation of two atomistic growth models, the Family model and the restricted Family model, which are shown to belong to a unique universality class in 1+1 and in 2+1 space dimensions. This corrects earlier studies which claimed that in 2+1 dimensions the two models belong to different universality classes.Comment: 18 pages, three figures included, submitted to Phys. Rev.

Non-equilibrium processes: driven lattice gases, interface dynamics, and quenched disorder effects on density profiles and currents

Properties of the one-dimensional totally asymmetric simple exclusion process (TASEP), and their connection with the dynamical scaling of moving interfaces described by a Kardar-Parisi-Zhang (KPZ) equation are investigated. With periodic boundary conditions, scaling of interface widths (the latter defined via a discrete occupation-number-to-height mapping), gives the exponents $\alpha=0.500(5)$, $z=1.52(3)$, $\beta=0.33(1)$. With open boundaries, results are as follows: (i) in the maximal-current phase, the exponents are the same as for the periodic case, and in agreement with recent Bethe ansatz results; (ii) in the low-density phase, curve collapse can be found to a rather good extent, with $\alpha=0.497(3)$, $z=1.20(5)$, $\beta=0.41(2)$, which is apparently at variance with the Bethe ansatz prediction $z=0$; (iii) on the coexistence line between low- and high- density phases, $\alpha=0.99(1)$, $z=2.10(5)$, $\beta=0.47(2)$, in relatively good agreement with the Bethe ansatz prediction $z=2$. From a mean-field continuum formulation, a characteristic relaxation time, related to kinematic-wave propagation and having an effective exponent $z^\prime=1$, is shown to be the limiting slow process for the low density phase, which accounts for the above-mentioned discrepancy with Bethe ansatz results. For TASEP with quenched bond disorder, interface width scaling gives $\alpha=1.05(5)$, $z=1.7(1)$, $\beta=0.62(7)$. From a direct analytic approach to steady-state properties of TASEP with quenched disorder, closed-form expressions for the piecewise shape of averaged density profiles are given, as well as rather restrictive bounds on currents. All these are substantiated in numerical simulations

A systems biology approach to the evolution of plant-virus interactions

[EN] Omic approaches to the analysis of plant-virus interactions are becoming increasingly popular. These types of data, in combination with models of interaction networks, will aid in revealing not only host components that are important for the virus life cycle, but also general patterns about the way in which different viruses manipulate host regulation of gene expression for their own benefit and possible mechanisms by which viruses evade host defenses. Here, we review studies identifying host genes regulated by viruses and discuss how these genes integrate in host regulatory and interaction networks, with a particular focus on the physical properties of these networks. © 2011 Elsevier Ltd.This work was supported by grants from the Spanish MICINN (BFU2009-06993) and Generalitat Valenciana (PROMETEO2010/019). GR is supported by a fellowship from Generalitat Valenciana (BFPI2007-160) and JC by a contract from MICINN (Grant TIN2006-12860). We thank Jose-Antonio Dares and Gustavo G. Gomez for comments.Elena Fito, SF.; Carrera, J.; Rodrigo, J. (2011). A systems biology approach to the evolution of plant-virus interactions. Current Opinion in Plant Biology. 14(4):372-377. https://doi.org/10.1016/j.pbi.2011.03.013S37237714

Towards an integrated molecular model of plant-virus interactions

[EN] The application in recent years of network theory methods to the study of host-virus interactions is providing a new perspective to the way viruses manipulate the host to promote their own replication. An integrated molecular model of such pathosystems require three detailed maps describing, firstly, the interactions between viral elements, secondly, the interactions between host elements, and thirdly, the cross-interactions between viral and host elements. Here, we compile available information for Potyvirus infecting Arabidopsis thaliana. With an integrated model, it is possible to analyze the mode of virus action and how the perturbation of the virus targets propagates along the network. These studies suggest that viral pathogenicity results not only from the alteration of individual elements but it is a systemic property.This work was supported by the grant BFU2009-06993 from the Spanish Ministry of Science and Innovation to S.F.E. G.R. thanks an EMBO long-term fellowship co-funded by Marie Curie actions (ALTF-1177-2011).Elena Fito, SF.; Rodrigo Tarrega, G. (2012). Towards an integrated molecular model of plant-virus interactions. Current Opinion in Virology. 2(6):719-724. https://doi.org/10.1016/j.coviro.2012.09.004S7197242