Dynamically Driven Renormalization Group Applied to Sandpile Models

The general framework for the renormalization group analysis of self-organized critical sandpile models is formulated. The usual real space renormalization scheme for lattice models when applied to nonequilibrium dynamical models must be supplemented by feedback relations coming from the stationarity conditions. On the basis of these ideas the Dynamically Driven Renormalization Group is applied to describe the boundary and bulk critical behavior of sandpile models. A detailed description of the branching nature of sandpile avalanches is given in terms of the generating functions of the underlying branching process.Comment: 18 RevTeX pages, 5 figure

Steady-State Dynamics of the Forest Fire Model on Complex Networks

Many sociological networks, as well as biological and technological ones, can be represented in terms of complex networks with a heterogeneous connectivity pattern. Dynamical processes taking place on top of them can be very much influenced by this topological fact. In this paper we consider a paradigmatic model of non-equilibrium dynamics, namely the forest fire model, whose relevance lies in its capacity to represent several epidemic processes in a general parametrization. We study the behavior of this model in complex networks by developing the corresponding heterogeneous mean-field theory and solving it in its steady state. We provide exact and approximate expressions for homogeneous networks and several instances of heterogeneous networks. A comparison of our analytical results with extensive numerical simulations allows to draw the region of the parameter space in which heterogeneous mean-field theory provides an accurate description of the dynamics, and enlights the limits of validity of the mean-field theory in situations where dynamical correlations become important.Comment: 13 pages, 9 figure

Challenges in Complex Systems Science

FuturICT foundations are social science, complex systems science, and ICT. The main concerns and challenges in the science of complex systems in the context of FuturICT are laid out in this paper with special emphasis on the Complex Systems route to Social Sciences. This include complex systems having: many heterogeneous interacting parts; multiple scales; complicated transition laws; unexpected or unpredicted emergence; sensitive dependence on initial conditions; path-dependent dynamics; networked hierarchical connectivities; interaction of autonomous agents; self-organisation; non-equilibrium dynamics; combinatorial explosion; adaptivity to changing environments; co-evolving subsystems; ill-defined boundaries; and multilevel dynamics. In this context, science is seen as the process of abstracting the dynamics of systems from data. This presents many challenges including: data gathering by large-scale experiment, participatory sensing and social computation, managing huge distributed dynamic and heterogeneous databases; moving from data to dynamical models, going beyond correlations to cause-effect relationships, understanding the relationship between simple and comprehensive models with appropriate choices of variables, ensemble modeling and data assimilation, modeling systems of systems of systems with many levels between micro and macro; and formulating new approaches to prediction, forecasting, and risk, especially in systems that can reflect on and change their behaviour in response to predictions, and systems whose apparently predictable behaviour is disrupted by apparently unpredictable rare or extreme events. These challenges are part of the FuturICT agenda

Simulations of the Static Friction Due to Adsorbed Molecules

The static friction between crystalline surfaces separated by a molecularly thin layer of adsorbed molecules is calculated using molecular dynamics simulations. These molecules naturally lead to a finite static friction that is consistent with macroscopic friction laws. Crystalline alignment, sliding direction, and the number of adsorbed molecules are not controlled in most experiments and are shown to have little effect on the friction. Temperature, molecular geometry and interaction potentials can have larger effects on friction. The observed trends in friction can be understood in terms of a simple hard sphere model.Comment: 13 pages, 13 figure

Critical behavior of the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy

We study the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy. We compute and analyze the fixed-dimension perturbative expansion of the renormalization-group functions to four loops. The relations of these models with N-color Ashkin-Teller models, discrete cubic models, planar model with fourth order anisotropy, and structural phase transition in adsorbed monolayers are discussed. Our results for N=2 (XY model with cubic anisotropy) are compatible with the existence of a line of fixed points joining the Ising and the O(2) fixed points. Along this line the exponent $\eta$ has the constant value 1/4, while the exponent $\nu$ runs in a continuous and monotonic way from 1 to $\infty$ (from Ising to O(2)). For N\geq 3 we find a cubic fixed point in the region $u, v \geq 0$, which is marginally stable or unstable according to the sign of the perturbation. For the physical relevant case of N=3 we find the exponents $\eta=0.17(8)$ and $\nu=1.3(3)$ at the cubic transition.Comment: 14 pages, 9 figure

Evidence, and replication thereof, that molecular-genetic and environmental risks for psychosis impact through an affective pathway

Background There is evidence that environmental and genetic risk factors for schizophrenia spectrum disorders are transdiagnostic and mediated in part through a generic pathway of affective dysregulation. Methods We analysed to what degree the impact of schizophrenia polygenic risk (PRS-SZ) and childhood adversity (CA) on psychosis outcomes was contingent on co-presence of affective dysregulation, defined as significant depressive symptoms, in (i) NEMESIS-2 (n = 6646), a representative general population sample, interviewed four times over nine years and (ii) EUGEI (n = 4068) a sample of patients with schizophrenia spectrum disorder, the siblings of these patients and controls. Results The impact of PRS-SZ on psychosis showed significant dependence on co-presence of affective dysregulation in NEMESIS-2 [relative excess risk due to interaction (RERI): 1.01, p = 0.037] and in EUGEI (RERI = 3.39, p = 0.048). This was particularly evident for delusional ideation (NEMESIS-2: RERI = 1.74, p = 0.003; EUGEI: RERI = 4.16, p = 0.019) and not for hallucinatory experiences (NEMESIS-2: RERI = 0.65, p = 0.284; EUGEI: -0.37, p = 0.547). A similar and stronger pattern of results was evident for CA (RERI delusions and hallucinations: NEMESIS-2: 3.02, p < 0.001; EUGEI: 6.44, p < 0.001; RERI delusional ideation: NEMESIS-2: 3.79, p < 0.001; EUGEI: 5.43, p = 0.001; RERI hallucinatory experiences: NEMESIS-2: 2.46, p < 0.001; EUGEI: 0.54, p = 0.465). Conclusions The results, and internal replication, suggest that the effects of known genetic and non-genetic risk factors for psychosis are mediated in part through an affective pathway, from which early states of delusional meaning may arise

Microflares and the Statistics of X-ray Flares

This review surveys the statistics of solar X-ray flares, emphasising the new views that RHESSI has given us of the weaker events (the microflares). The new data reveal that these microflares strongly resemble more energetic events in most respects; they occur solely within active regions and exhibit high-temperature/nonthermal emissions in approximately the same proportion as major events. We discuss the distributions of flare parameters (e.g., peak flux) and how these parameters correlate, for instance via the Neupert effect. We also highlight the systematic biases involved in intercomparing data representing many decades of event magnitude. The intermittency of the flare/microflare occurrence, both in space and in time, argues that these discrete events do not explain general coronal heating, either in active regions or in the quiet Sun.Comment: To be published in Space Science Reviews (2011