Social inertia in collaboration networks

This work is a study of the properties of collaboration networks employing the formalism of weighted graphs to represent their one-mode projection. The weight of the edges is directly the number of times that a partnership has been repeated. This representation allows us to define the concept of "social inertia" that measures the tendency of authors to keep on collaborating with previous partners. We use a collection of empirical datasets to analyze several aspects of the social inertia: 1) its probability distribution, 2) its correlation with other properties, and 3) the correlations of the inertia between neighbors in the network. We also contrast these empirical results with the predictions of a recently proposed theoretical model for the growth of collaboration networks.Comment: 7 pages, 5 figure

Is local scale invariance a generic property of ageing phenomena ?

In contrast to recent claims by Enss, Henkel, Picone, and Schollwoeck [J. Phys. A 37, 10479] it is shown that the critical autoresponse function of the 1+1-dimensional contact process is not in agreement with the predictions of local scale invariance.Comment: 7 pages, 3 figures, final form, c++ source code on reques

Ageing and dynamical scaling in the critical Ising spin glass

The non-equilibrium ageing behaviour of the 3D and 4D critical Ising spin glass is studied for both binary and gaussian disorder. The same phenomenology of the time-dependent scaling as in non-disordered magnets is found but the non-equilibrium exponents and the universal limit fluctuation-dissipation ratio depend on the distribution of the coupling constants.Comment: Latex2e, 7 pages with epl macro, 4 figures included, final for

Ageing in disordered magnets and local scale-invariance

The ageing of the bond-disordered two-dimensional Ising model quenched to below its critical point is studied through the two-time autocorrelator and thermoremanent magnetization (TRM). The corresponding ageing exponents are determined. The form of the scaling function of the TRM is well described by the theory of local scale-invariance.Comment: Latex2e, with epl macros, 7 pages, final for

Ageing without detailed balance: local scale invariance applied to two exactly solvable models

I consider ageing behaviour in two exactly solvable reaction-diffusion systems. Ageing exponents and scaling functions are determined. I discuss in particular a case in which the equality of two critical exponents, known from systems with detailed balance, does not hold any more. Secondly it is shown that the form of the scaling functions can be understood by symmetry considerations.Comment: 6 pages, contribution to the summer school "Ageing and the Glass Transition" held in Luxemburg in September 05. Published versio

Interface Depinning in the Absence of External Driving Force

We study the pinning-depinning phase transition of interfaces in the quenched Kardar-Parisi-Zhang model as the external driving force $F$ goes towards zero. For a fixed value of the driving force we induce depinning by increasing the nonlinear term coefficient $\lambda$, which is related to lateral growth, up to a critical threshold. We focus on the case in which there is no external force applied (F=0) and find that, contrary to a simple scaling prediction, there is a finite value of $\lambda$ that makes the interface to become depinned. The critical exponents at the transition are consistent with directed percolation depinning. Our results are relevant for paper wetting experiments, in which an interface gets moving with no external driving force.Comment: 4 pages, 3 figures included, uses epsf. Submitted to PR

Self-organization of collaboration networks

We study collaboration networks in terms of evolving, self-organizing bipartite graph models. We propose a model of a growing network, which combines preferential edge attachment with the bipartite structure, generic for collaboration networks. The model depends exclusively on basic properties of the network, such as the total number of collaborators and acts of collaboration, the mean size of collaborations, etc. The simplest model defined within this framework already allows us to describe many of the main topological characteristics (degree distribution, clustering coefficient, etc.) of one-mode projections of several real collaboration networks, without parameter fitting. We explain the observed dependence of the local clustering on degree and the degree--degree correlations in terms of the ``aging'' of collaborators and their physical impossibility to participate in an unlimited number of collaborations.Comment: 10 pages, 8 figure

Out-of-equilibrium relaxation of the Edwards-Wilkinson elastic line

We study the non-equilibrium relaxation of an elastic line described by the Edwards-Wilkinson equation. Although this model is the simplest representation of interface dynamics, we highlight that many (not though all) important aspects of the non-equilibrium relaxation of elastic manifolds are already present in such quadratic and clean systems. We analyze in detail the aging behaviour of several two-times averaged and fluctuating observables taking into account finite-size effects and the crossover to the stationary and equilibrium regimes. We start by investigating the structure factor and extracting from its decay a growing correlation length. We present the full two-times and size dependence of the interface roughness and we generalize the Family-Vicsek scaling form to non-equilibrium situations. We compute the incoherent cattering function and we compare it to the one measured in other glassy systems. We analyse the response functions, the violation of the fluctuation-dissipation theorem in the aging regime, and its crossover to the equilibrium relation in the stationary regime. Finally, we study the out-of-equilibrium fluctuations of the previously studied two-times functions and we characterize the scaling properties of their probability distribution functions. Our results allow us to obtain new insights into other glassy problems such as the aging behavior in colloidal glasses and vortex glasses.Comment: 33 pages, 16 fig

Exact two-time correlation and response functions in the one-dimensional coagulation-diffusion process by the empty-interval-particle method

The one-dimensional coagulation-diffusion process describes the strongly fluctuating dynamics of particles, freely hopping between the nearest-neighbour sites of a chain such that one of them disappears with probability 1 if two particles meet. The exact two-time correlation and response function in the one-dimensional coagulation-diffusion process are derived from the empty-interval-particle method. The main quantity is the conditional probability of finding an empty interval of n consecutive sites, if at distance d a site is occupied by a particle. Closed equations of motion are derived such that the probabilities needed for the calculation of correlators and responses, respectively, are distinguished by different initial and boundary conditions. In this way, the dynamical scaling of these two-time observables is analysed in the longtime ageing regime. A new generalised fluctuation-dissipation ratio with an universal and finite limit is proposed.Comment: 31 pages, submitted to J.Stat.Mec

Ageing in the contact process: Scaling behavior and universal features

We investigate some aspects of the ageing behavior observed in the contact process after a quench from its active phase to the critical point. In particular we discuss the scaling properties of the two-time response function and we calculate it and its universal ratio to the two-time correlation function up to first order in the field-theoretical epsilon-expansion. The scaling form of the response function does not fit the prediction of the theory of local scale invariance. Our findings are in good qualitative agreement with recent numerical results.Comment: 20 pages, 3 figure