Dynamics of the two-dimensional gonihedric spin model

In this paper, we study dynamical aspects of the two-dimensional (2D) gonihedric spin model using both numerical and analytical methods. This spin model has vanishing microscopic surface tension and it actually describes an ensemble of loops living on a 2D surface. The self-avoidance of loops is parametrized by a parameter ¿. The ¿=0 model can be mapped to one of the six-vertex models discussed by Baxter, and it does not have critical behavior. We have found that allowing for ¿¿0 does not lead to critical behavior either. Finite-size effects are rather severe, and in order to understand these effects, a finite-volume calculation for non-self-avoiding loops is presented. This model, like his 3D counterpart, exhibits very slow dynamics, but a careful analysis of dynamical observables reveals nonglassy evolution (unlike its 3D counterpart). We find, also in this ¿=0 case, the law that governs the long-time, low-temperature evolution of the system, through a dual description in terms of defects. A power, rather than logarithmic, law for the approach to equilibrium has been found.

Mean field model for spatially extended systems in the presence of multiplicative noise

We present a mean field model that describes the effect of multiplicative noise in spatially extended systems. The model can be solved analytically. For the case of the phi4 potential it predicts that the phase transition is shifted. This conclusion is supported by numerical simulations of this model in two dimensions.

Studying Avalanches in the ground-state of the two-dimensional random field Ising model driven by an external field

We study the exact ground state of the two-dimensional random-field Ising model as a function of both the external applied field B and the standard deviation ¿ of the Gaussian random-field distribution. The equilibrium evolution of the magnetization consists in a sequence of discrete jumps. These are very similar to the avalanche behavior found in the out-of-equilibrium version of the same model with local relaxation dynamics. We compare the statistical distributions of magnetization jumps and find that both exhibit power-law behavior for the same value of ¿. The corresponding exponents are compared.

Slow dynamis in the 3D gonihedric model

We provide analytical evidence of stochastic resonance in polarization switching vertical-cavity surface-emitting lasers (VCSELs). We describe the VCSEL by a two-mode stochastic rate equation model and apply a multiple time-scale analysis. We were able to reduce the dynamical description to a single stochastic differential equation, which is the starting point of the analytical study of stochastic resonance. We confront our results with numerical simulations on the original rate equations, validating the use of a multiple time-scale analysis on stochastic equations as an analytical tool.

Phase-field model for Hele-Shaw flows with arabitrary contrast II: numerical approach

We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right Hele-Shaw equations in the sharp-interface limit, and compute the corrections to these equations to first order in the interface thickness. We also compute the effect of such corrections on the linear dispersion relation of the planar interface. We discuss in detail the conditions on the interface thickness to control the accuracy and convergence of the phase-field model to the limiting Hele-Shaw dynamics. In particular, the convergence appears to be slower for high viscosity contrasts.

Reentrant transition induced by multiplictative noise in the Time Dependent Ginzburg-Landau model

An effect of multiplicative noise in the time-dependent Ginzburg-Landau model is reported, namely, that noise at a relatively low intensity induces a phase transition towards an ordered state, whereas strong noise plays a destructive role, driving the system back to its disordered state through a reentrant phase transition. The phase diagram is calculated analytically using a mean-field theory and a more sophisticated approach and is compared with the results from extensive numerical simulations.

Model-Free Reconstruction of Excitatory Neuronal Connectivity from Calcium Imaging Signals

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically infeasible, even in simpler systems like dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct structural connectivity from network activity monitored through calcium imaging. We focus in this study on the inference of excitatory synaptic links. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the functional network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (bursting or non-bursting). Thus by conditioning with respect to the global mean activity, we improve the performance of our method. This allows us to focus the analysis to specific dynamical regimes of the network in which the inferred functional connectivity is shaped by monosynaptic excitatory connections, rather than by collective synchrony. Our method can discriminate between actual causal influences between neurons and spurious non-causal correlations due to light scattering artifacts, which inherently affect the quality of fluorescence imaging. Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good estimation of the excitatory network clustering coefficient, allowing for discrimination between weakly and strongly clustered topologies. Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local.

Fragile-glass behavior of a short-range p-spin model

We propose a short-range generalization of the p-spin interaction spin-glass model. The model is well suited to test the idea that an entropy collapse is at the bottom line of the dynamical singularity encountered in structural glasses. The model is studied in three dimensions through Monte Carlo simulations, which put in evidence fragile glass behavior with stretched exponential relaxation and super-Arrhenius behavior of the relaxation time. Our data are in favor of a Vogel-Fulcher behavior of the relaxation time, related to an entropy collapse at the Kauzmann temperature. We, however, encounter difficulties analogous to those found in experimental systems when extrapolating thermodynamical data at low temperatures. We study the spin-glass susceptibility, investigating the behavior of the correlation length in the system. We find that the increase of the relaxation time is accompanied by a very slow growth of the correlation length. We discuss the scaling properties of off-equilibrium dynamics in the glassy regime, finding qualitative agreement with the mean-field theory.

Chaotic, memory, and cooling rate effects in spin glasses: Evaluation of the Edwards-Anderson model

We investigate chaotic, memory, and cooling rate effects in the three-dimensional Edwards-Anderson model by doing thermoremanent (TRM) and ac susceptibility numerical experiments and making a detailed comparison with laboratory experiments on spin glasses. In contrast to the experiments, the Edwards-Anderson model does not show any trace of reinitialization processes in temperature change experiments (TRM or ac). A detailed comparison with ac relaxation experiments in the presence of dc magnetic field or coupling distribution perturbations reveals that the absence of chaotic effects in the Edwards-Anderson model is a consequence of the presence of strong cooling rate effects. We discuss possible solutions to this discrepancy, in particular the smallness of the time scales reached in numerical experiments, but we also question the validity of the Edwards-Anderson model to reproduce the experimental results.

Stationary states and phase diagram for a model of the Gunn effect under realistic boundary conditions

A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to study the classical unipolar drift-diffusion model for the Gunn effect. The analysis of its stationary solutions reveals the presence of bistability and hysteresis for a certain range of contact parameters. Several types of Gunn effect are predicted to occur in the model, when no stable stationary solution exists, depending on the value of the parameters of the injecting contact appearing in the boundary condition. In this way, the critical role played by contacts in the Gunn effect is clearly established.

Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model.

Interior crises are understood as discontinuous changes of the size of a chaotic attractor that occur when an unstable periodic orbit collides with the chaotic attractor. We present here numerical evidence and theoretical reasoning which prove the existence of a chaos-chaos transition in which the change of the attractor size is sudden but continuous. This occurs in the Hindmarsh¿Rose model of a neuron, at the transition point between the bursting and spiking dynamics, which are two different dynamic behaviors that this system is able to present. Moreover, besides the change in attractor size, other significant properties of the system undergoing the transitions do change in a relevant qualitative way. The mechanism for such transition is understood in terms of a simple one-dimensional map whose dynamics undergoes a crossover between two different universal behaviors

The Besançon Galaxy Model renewed. I. Constraints on the Galactic thin disc evolution from Tycho data

Context. The understanding of Galaxy evolution can be facilitated by the use of population synthesis models, which allow to test hypotheses on the star formation history, star evolution, as well as chemical and dynamical evolution of the Galaxy. Aims. The new version of the Besanc¸on Galaxy Model (hereafter BGM) aims to provide a more flexible and powerful tool to investigate the Initial Mass Function (IMF) and Star Formation Rate (SFR) of the Galactic disc. Methods. We present a new strategy for the generation of thin disc stars which assumes the IMF, SFR and evolutionary tracks as free parameters. We have updated most of the ingredients for the star count production and, for the first time, binary stars are generated in a consistent way. We keep in this new scheme the local dynamical self-consistency as in Bienayme et al (1987). We then compare simulations from the new model with Tycho-2 data and the local luminosity function, as a first test to verify and constrain the new ingredients. The effects of changing thirteen different ingredients of the model are systematically studied. Results. For the first time, a full sky comparison is performed between BGM and data. This strategy allows to constrain the IMF slope at high masses which is found to be close to 3.0, excluding a shallower slope such as Salpeter"s one. The SFR is found decreasing whatever IMF is assumed. The model is compatible with a local dark matter density of 0.011 M pc−3 implying that there is no compelling evidence for significant amount of dark matter in the disc. While the model is fitted to Tycho2 data, a magnitude limited sample with V<11, we check that it is still consistent with fainter stars. Conclusions. The new model constitutes a new basis for further comparisons with large scale surveys and is being prepared to become a powerful tool for the analysis of the Gaia mission data.

From Full stopping to transparency in a holographic model of heavy ion collisions

We numerically simulate planar shock wave collisions in anti-de Sitter space as a model for heavy ion collisions of large nuclei. We uncover a crossover between two different dynamical regimes as a function of the collision energy. At low energies the shocks first stop and then explode in a manner approximately described by hydrodynamics, in close similarity with the Landau model. At high energies the receding fragments move outwards at the speed of light, with a region of negative energy density and negative longitudinal pressure trailing behind them. The rapidity distribution of the energy density at late times around midrapidity is not approximately boost invariant but Gaussian, albeit with a width that increases with the collision energy.

The Besançon Galaxy Model renewed. I. Constraints on the Galactic thin disc evolution from Tycho data

Context. The understanding of Galaxy evolution can be facilitated by the use of population synthesis models, which allow to test hypotheses on the star formation history, star evolution, as well as chemical and dynamical evolution of the Galaxy. Aims. The new version of the Besanc¸on Galaxy Model (hereafter BGM) aims to provide a more flexible and powerful tool to investigate the Initial Mass Function (IMF) and Star Formation Rate (SFR) of the Galactic disc. Methods. We present a new strategy for the generation of thin disc stars which assumes the IMF, SFR and evolutionary tracks as free parameters. We have updated most of the ingredients for the star count production and, for the first time, binary stars are generated in a consistent way. We keep in this new scheme the local dynamical self-consistency as in Bienayme et al (1987). We then compare simulations from the new model with Tycho-2 data and the local luminosity function, as a first test to verify and constrain the new ingredients. The effects of changing thirteen different ingredients of the model are systematically studied. Results. For the first time, a full sky comparison is performed between BGM and data. This strategy allows to constrain the IMF slope at high masses which is found to be close to 3.0, excluding a shallower slope such as Salpeter"s one. The SFR is found decreasing whatever IMF is assumed. The model is compatible with a local dark matter density of 0.011 M pc−3 implying that there is no compelling evidence for significant amount of dark matter in the disc. While the model is fitted to Tycho2 data, a magnitude limited sample with V<11, we check that it is still consistent with fainter stars. Conclusions. The new model constitutes a new basis for further comparisons with large scale surveys and is being prepared to become a powerful tool for the analysis of the Gaia mission data.

Persistent random walk model for transport trough thin slabs

We present a model for transport in multiply scattering media based on a three-dimensional generalization of the persistent random walk. The model assumes that photons move along directions that are parallel to the axes. Although this hypothesis is not realistic, it allows us to solve exactly the problem of multiple scattering propagation in a thin slab. Among other quantities, the transmission probability and the mean transmission time can be calculated exactly. Besides being completely solvable, the model could be used as a benchmark for approximation schemes to multiple light scattering.