Simulation of large deviation functions using population dynamics

In these notes we present a pedagogical account of the population dynamics methods recently introduced to simulate large deviation functions of dynamical observables in and out of equilibrium. After a brief introduction on large deviation functions and their simulations, we review the method of Giardin\`a \emph{et al.} for discrete time processes and that of Lecomte \emph{et al.} for the continuous time counterpart. Last we explain how these methods can be modified to handle static observables and extract information about intermediate times.Comment: Proceedings of the 10th Granada Seminar on Computational and Statistical Physic

Boundary-induced heterogeneous absorbing states

We study two different types of systems with many absorbing states (with and without a conservation law) and scrutinize the effect of walls/boundaries (either absorbing or reflecting) into them. In some cases, non-trivial structured absorbing configurations (characterized by a background field) develop around the wall. We study such structures using a mean-field approach as well as computer simulations. The main results are: i) for systems in the directed percolation class, a very fast (exponential) convergence of the background to its bulk value is observed; ii) for systems with a conservation law, power-law decaying landscapes are induced by both types of walls: while for absorbing walls this effect is already present in the mean-field approximation, for reflecting walls the structured background is a noise-induced effect. The landscapes are shown to converge to their asymptotic bulk values with an exponent equal to the inverse of the bulk correlation length exponent. Finally, the implications of these results in the context of self-organizing systems are discussed.Comment: 8 pages, 2 figure

Pattern formation in systems with competing interactions

There is a growing interest, inspired by advances in technology, in the low temperature physics of thin films. These quasi-2D systems show a wide range of ordering effects including formation of striped states, reorientation transitions, bubble formation in strong magnetic fields, etc. The origins of these phenomena are, in many cases, traced to competition between short ranged exchange ferromagnetic interactions, favoring a homogeneous ordered state, and the long ranged dipole-dipole interaction, which opposes such ordering on the scale of the whole sample. The present theoretical understanding of these phenomena is based on a combination of variational methods and a variety of approximations, e.g., mean-field and spin-wave theory. The comparison between the predictions of these approximate methods and the results of MonteCarlo simulations are often difficult because of the slow relaxation dynamics associated with the long-range nature of the dipole-dipole interactions. In this note we will review recent work where we prove existence of periodic structures in some lattice and continuum model systems with competing interactions. The continuum models have also been used to describe micromagnets, diblock polymers, etc.Comment: 11 pages, 1 figure, to appear in the AIP conference proceedings of the 10th Granada Seminar on Computational Physics, Sept. 15-19, 2008. (v2) Updated reference

Exact computation of current cumulants in small Markovian systems

We describe an algorithm computing the exact value of the mean current, its variance, and higher order cumulants for stochastic driven systems. The method uses a Rayleigh-Schrodinger perturbation expansion of the generating function of the current, and can be extended to compute covariances of multiple currents. As an example of application of the method, we give numerical evidence for a simple relation [Eq.(5)] between the second and the fourth cumulants of the current in a symmetric exclusion process.Comment: 5 pages, 1 figure, submitted to AIP Proceedings of Granada Seminar 200

On the relaxation dynamics of glass-forming systems: Insights from computer simulations

We discuss the relaxation dynamics of a simple lattice gas model for glass-forming systems and show that with increasing density of particles this dynamics slows down very quickly. By monitoring the trajectory of tagged particles we find that their motion is very heterogeneous in space and time, leading to regions in space in which there is a fast dynamics and others in which it is slow. We determine how the geometric properties of these quickly relaxing regions depend on density and time. Motivated by this heterogeneous hopping dynamics, we use a simple model, a variant of a continuous time random walk, to characterize the relaxation dynamics. In particular we find from this model that for large displacements the self part of the van Hove function shows an exponential tail, in agreement with recent findings from experiments and simulations of glass-forming systems.Comment: Paper presented at the 10th Granada Conference on Computational and Statistical physic

Static and dynamic properties of a reversible gel

We study a microscopically realistic model of a physical gel and use computer simulations to investigate its static and dynamic properties at thermal equilibrium. The phase diagram comprises a sol phase, a coexistence region ending at a critical point, a gelation line, and an equilibrium gel phase unrelated to phase separation. The global structure of the gel is homogeneous, but the stress is supported by a fractal network. Gelation results in a dramatic slowing down of the dynamics, which can be used to locate the transition, which otherwise shows no structural signatures. Moreover, the equilibrium gel dynamics is highly heterogeneous as a result of the presence of particle families with different mobilities. An analysis of gel dynamics in terms of mobile and arrested particles allows us to elucidate several differences between the dynamics of equilibrium gels and that of glass-formers.Comment: 9 pages, 7 figures, paper presented at the 10th Granada Seminar on Computational and Statistical Physic

Dynamical behavior of heat conduction in solid Argon

Background: Imunoglobulin A (IgA) deficiency (IgAD) is the most common form of primary immunodeficiency in Western countries. There have been several reports on IgAD complicated by glomerulonephritis in adults, but only very few cases of IgAD with nephropathy have been reported in children. We present two cases of IgAD with relapsing nephrotic syndrome in pediatric age. Case presentation: A 4-year-old boy and a 2-year-old boy presented with bilateral periorbital oedema and weight gain. The results of laboratory tests revealed IgAD (IgA < 7 mg/dL), normal creatinine, hypoprotidaemia, hypoalbuminaemia, and nephrotic proteinuria. A diagnosis of IgAD and idiopathic nephrotic syndrome was made, and steroid treatment (prednisone 60 mg/mq/day) was started. During steroid tapering, the children experienced several relapses and to obtain a positive outcome they required therapy with human monoclonal anti-CD20 antibodies (rituximab in the first child, ofatumumab in the second one). Conclusions: Our cases highlight that IgAD can be observed in nephrotic syndrome and nephropathy in children with IgAD appears to be complicated and difficult to treat with corticosteroids alone. Further research is needed to better describe the clinical manifestations and pathological pictures among subjects with IgAD and nephrotic syndrome to understand whether IgAD has a prognostic value in children with nephrotic syndrome and to let clinical physicians define a more personalized and appropriate approach for the management of these patients