Collective behavior of heterogeneous neural networks

We investigate a network of integrate-and-fire neurons characterized by a distribution of spiking frequencies. Upon increasing the coupling strength, the model exhibits a transition from an asynchronous regime to a nontrivial collective behavior. At variance with the Kuramoto model, (i) the macroscopic dynamics is irregular even in the thermodynamic limit, and (ii) the microscopic (single-neuron) evolution is linearly stable.Comment: 4 pages, 5 figure

Entropy potential and Lyapunov exponents

According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function: the entropy potential. The validity and the consequences of this hypothesis are explored in detail. The numerical investigation of a continuous-time model provides a further confirmation to the existence of the entropy potential. Furthermore, it is shown that the knowledge of the entropy potential allows determining also Lyapunov spectra in general reference frames where the time-like and space-like axes point along generic directions in the space-time plane. Finally, the existence of an entropy potential implies that the integrated density of positive exponents (Kolmogorov-Sinai entropy) is independent of the chosen reference frame.Comment: 20 pages, latex, 8 figures, submitted to CHAO

Breakdown of metastable step-flow growth on vicinal surfaces induced by nucleation

We consider the growth of a vicinal crystal surface in the presence of a step-edge barrier. For any value of the barrier strength, measured by the length l_es, nucleation of islands on terraces is always able to destroy asymptotically step-flow growth. The breakdown of the metastable step-flow occurs through the formation of a mound of critical width proportional to L_c=1/sqrt(l_es), the length associated to the linear instability of a high-symmetry surface. The time required for the destabilization grows exponentially with L_c. Thermal detachment from steps or islands, or a steeper slope increase the instability time but do not modify the above picture, nor change L_c significantly. Standard continuum theories cannot be used to evaluate the activation energy of the critical mound and the instability time. The dynamics of a mound can be described as a one dimensional random walk for its height k: attaining the critical height (i.e. the critical size) means that the probability to grow (k->k+1) becomes larger than the probability for the mound to shrink (k->k-1). Thermal detachment induces correlations in the random walk, otherwise absent.Comment: 10 pages. Minor changes. Accepted for publication in Phys. Rev.

From anomalous energy diffusion to Levy walks and heat conductivity in one-dimensional systems

The evolution of infinitesimal, localized perturbations is investigated in a one-dimensional diatomic gas of hard-point particles (HPG) and thereby connected to energy diffusion. As a result, a Levy walk description, which was so far invoked to explain anomalous heat conductivity in the context of non-interacting particles is here shown to extend to the general case of truly many-body systems. Our approach does not only provide a firm evidence that energy diffusion is anomalous in the HPG, but proves definitely superior to direct methods for estimating the divergence rate of heat conductivity which turns out to be $0.333\pm 0.004$, in perfect agreement with the dynamical renormalization--group prediction (1/3).Comment: 4 pages, 3 figure

Coupled transport in rotor models

Acknowledgement One of us (AP) wishes to acknowledge S. Flach for enlightening discussions about the relationship between the DNLS equation and the rotor model.Peer reviewedPublisher PD

Collective chaos in pulse-coupled neural networks

We study the dynamics of two symmetrically coupled populations of identical leaky integrate-and-fire neurons characterized by an excitatory coupling. Upon varying the coupling strength, we find symmetry-breaking transitions that lead to the onset of various chimera states as well as to a new regime, where the two populations are characterized by a different degree of synchronization. Symmetric collective states of increasing dynamical complexity are also observed. The computation of the the finite-amplitude Lyapunov exponent allows us to establish the chaoticity of the (collective) dynamics in a finite region of the phase plane. The further numerical study of the standard Lyapunov spectrum reveals the presence of several positive exponents, indicating that the microscopic dynamics is high-dimensional.Comment: 6 pages, 5 eps figures, to appear on Europhysics Letters in 201

Lonely adatoms in space

There is a close relation between the problems of second layer nucleation in epitaxial crystal growth and chemical surface reactions, such as hydrogen recombination, on interstellar dust grains. In both cases standard rate equation analysis has been found to fail because the process takes place in a confined geometry. Using scaling arguments developed in the context of second layer nucleation, I present a simple derivation of the hydrogen recombination rate for small and large grains. I clarify the reasons for the failure of rate equations for small grains, and point out a logarithmic correction to the reaction rate when the reaction is limited by the desorption of hydrogen atoms (the second order reaction regime)

Energy diffusion in hard-point systems

We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square--well potential. The evolution of initially localized infinitesimal and finite perturbations is numerically investigated for different density values. All cases belong to the same universality class which can be also interpreted as a Levy walk of the energy with scaling exponent 3/5. The zero-pressure limit is nevertheless exceptional in that normal diffusion is found in tangent space and yet anomalous diffusion with a different rate for perturbations of finite amplitude. The different behaviour of the two classes of perturbations is traced back to the "stable chaos" type of dynamics exhibited by this model. Finally, the effect of an additional internal degree of freedom is investigated, finding that it does not modify the overall scenarioComment: 16 pages, 15 figure

Coarsening in surface growth models without slope selection

We study conserved models of crystal growth in one dimension [$\partial_t z(x,t) =-\partial_x j(x,t)$] which are linearly unstable and develop a mound structure whose typical size L increases in time ($L = t^n$). If the local slope ($m =\partial_x z$) increases indefinitely, $n$ depends on the exponent $\gamma$ characterizing the large $m$ behaviour of the surface current $j$ ($j = 1/|m|^\gamma$): $n=1/4$ for $1< \gamma <3$ and $n=(1+\gamma)/(1+5\gamma)$ for $\gamma>3$.Comment: 7 pages, 2 EPS figures. To be published in J. Phys. A (Letter to the Editor