We demonstrate numerically that a brief burst consisting of two to six spikes can propagate in a stable manner through a one-dimensional homogeneous feedforward chain of nonbursting neurons with excitatory synaptic connections. Our results are obtained for two kinds of neuronal models: leaky integrate-and-fire neurons and Hodgkin-Huxley neurons with five conductances. Over a range of parameters such as the maximum synaptic conductance, both kinds of chains are found to have multiple attractors of propagating bursts, with each attractor being distinguished by the number of spikes and total duration of the propagating burst. These results make plausible the hypothesis that sparse, precisely timed sequential bursts observed in projection neurons of nucleus HVC of a singing zebra finch are intrinsic and causally related.

We study two-dimensional (2D) fronts propagating up a comoving reaction rate gradient in finite number reaction-diffusion systems. We show that in a 2D rectangular channel, planar solutions to the deterministic mean-field equation are stable with respect to deviations from planarity. We argue that planar fronts in the corresponding stochastic system, on the other hand, are unstable if the channel width exceeds a critical value. Furthermore, the velocity of the stochastic fronts is shown to depend on the channel width in a simple and interesting way, in contrast to fronts in the deterministic mean-field equation. Thus fluctuations alter the behavior of these fronts in an essential way. These effects are shown to be partially captured by introducing a density cutoff in the reaction rate. Moreover, some of the predictions of the cutoff mean-field approach are shown to be in quantitative accord with the stochastic results.

Extending the parameter space of the three-dimensional $(d=3)$ Ising model, we search for a regime of eliminated corrections to finite-size scaling. For that purpose, we consider a real-space renormalization group (RSRG) with respect to a couple of clusters simulated with the transfer-matrix (TM) method. Imposing a criterion of “scale invariance,” we determine a location of the nontrivial RSRG fixed point. Subsequent large-scale TM simulation around the fixed point reveals eliminated corrections to finite-size scaling. As anticipated, such an elimination of corrections admits systematic finite-size-scaling analysis. We obtained the estimates for the critical indices as $\nu =0.6245\left(28\right)$ and $y_h=2.4709\left(73\right)$. As demonstrated, with the aid of the preliminary RSRG survey, the transfer-matrix simulation provides rather reliable information on criticality even for $d=3$, where the tractable system size is restricted severely.

Using numerical integrations of the Boussinesq equations in rotating cylindrical domains with realistic boundary conditions, we have computed the value of the largest Lyapunov exponent ${\lambda }_1$ for a variety of aspect ratios and driving strengths. We study in particular the domain chaos state, which bifurcates supercritically from the conducting fluid state and involves extended propagating fronts as well as point defects. We compare our results with those from Egolf et al., [Nature 404, 733 (2000)], who suggested that the value of ${\lambda }_1$ for the spiral defect chaos state of a convecting fluid was determined primarily by bursts of instability arising from short-lived, spatially localized dislocation nucleation events. We also show that the quantity ${\lambda }_1$ is not intensive for aspect ratios $\Gamma$ over the range $20<\Gamma <40$ and that the scaling exponent of ${\lambda }_1$ near onset is consistent with the value predicted by the amplitude equation formalism.

We present a useful framework within which we can understand some of the physical phenomena that drive thermal emission in one-dimensional periodic metallic photonic crystals, emphasizing phenomenology and physical intuition. We perform detailed numerical calculations for these systems and find that polarization and periodicity play key roles in determining the types of physical phenomena that can arise. Two promising structures are identified as good candidates for thermal design. We conclude with a discussion of how the emissive properties of these systems can be tailored to our needs.

A tight-binding model together with a statistical method are used to investigate the relation between the sequence-dependent electric transport properties and the sequences of protein-coding regions of complete genomes. A correlation parameter $\Omega$ is defined to analyze the relation. For some particular propagation length $w_{\mathit{max}}$, the transport behaviors of the coding and noncoding sequences are very different and the correlation reaches its maximal value ${\Omega }_{\mathit{max}}$. $w_{\mathit{max}}$ and ${\Omega }_{\mathit{max}}$ are characteristic values for each species. A possible reason for the difference between the features of transport properties in the coding and noncoding regions is the mechanism of DNA damage repair processes together with natural selection.

We have carried out extensive $NPT$ molecular-dynamics simulation studies of binary Lennard-Jones mixtures to calculate directly the bridge function at state points lying in a very narrow single fluid phase region between the vapor-liquid and solid-liquid coexistence lines [Lamm and Hall, Fluid Phase Equilib. 182, 37 (2001); 194–197, 197 (2002)]. By varying the density close to the liquid-vapor coexistence line, significant deviations are observed at intermediate distances between the simulated bridge function and two widely used approximate closures in the integral equation theory of liquids, viz. the hybrid mean spherical approximation and the Duh-Henderson closures. The overall qualitative agreement remains the same with small variation in temperature that brings the system closer to either the liquid-vapor or liquid-solid coexistence curve. We also report a comparison of the direct and indirect correlation functions obtained from our simulation studies as well as from the integral equation theory of liquids. Our results emphasize the need for developing new closures applicable to binary fluid mixtures over a wide range of thermodynamic parameters.

We have measured the flux of grains from a hole in the bottom of a shaken container of grains. We find that the peak velocity of the vibration, $v_{\mathit{max}}$, controls the flux, i.e., the flux is nearly independent of the frequency and acceleration amplitude for a given value of $v_{\mathit{max}}$. The flux decreases with increasing peak velocity and then becomes almost constant for the largest values of $v_{\mathit{max}}$. The data at low peak velocity can be quantitatively described by a simple model, but the crossover to nearly constant flux at larger peak velocity suggests a regime in which the granular density near the container bottom is independent of the energy input to the system.

Using molecular dynamics simulation we examine changeovers among crystal, glass, and liquid at high density in a two dimensional binary mixture. We change the ratio between the diameters of the two components and the temperature. The transitions from crystal to glass or liquid occur with proliferation of defects. We visualize the defects in terms of a disorder variable $D_j\left(t\right)$ representing a deviation from the hexagonal order for particle $j$. The defect structures are heterogeneous and are particularly extended in polycrystal states. They look similar at the crystal-glass crossover and at the melting. Taking the average of $D_j\left(t\right)$ over the particles, we define a disorder parameter $D\left(t\right)$, which measures the degree of overall disorder. The relaxation of $D\left(t\right)$ after quenching becomes slow at low temperature in the presence of size dispersity. Its steady state average is small in crystal and large in glass and liquid. We also find that grain boundaries tend to be pinned with increasing size dispersity in polycrystal states.

Spinodal decomposition of deeply quenched mixtures is studied experimentally, with particular emphasis on the domain growth rate during the late stage of coarsening. We provide some experimental evidence that at high Péclet number, the process is isotropic and the domain growth is linear in time, even at finite quenching rates. In fact, the quenching rate appears to influence the magnitude of the growth rate, but not its scaling law. In the second part of the work we analyze the effect of viscosity on the growth rate. As predicted by the diffuse interface model, we do not find any effect of viscosity on the growth rate of the nucleating drops, although, as expected, the viscosity of the continuous phase does influence the settling speed and thus the total separation time.

We present results on a series of two-dimensional atomistic computer simulations of amorphous systems subjected to simple shear in the athermal, quasistatic limit. The athermal quasistatic trajectories are shown to separate into smooth, reversible elastic branches which are intermittently broken by discrete catastrophic plastic events. The onset of a typical plastic event is studied with precision, and it is shown that the mode of the system which is responsible for the loss of stability has structure in real space which is consistent with a quadrupolar source acting on an elastic matrix. The plastic events themselves are shown to be composed of localized shear transformations which organize into lines of slip which span the length of the simulation cell, and a mechanism for the organization is discussed. Although within a single event there are strong spatial correlations in the deformation, we find little correlation from one event to the next, and these transient lines of slip are not to be confounded with the persistent regions of localized shear—so-called “shear bands”—found in related studies. The slip lines give rise to particular scalings with system length of various measures of event size. Strikingly, data obtained using three differing interaction potentials can be brought into quantitative agreement after a simple rescaling, emphasizing the insensitivity of the emergent plastic behavior in these disordered systems to the precise details of the underlying interactions. The results should be relevant to understanding plastic deformation in systems such as metallic glasses well below their glass temperature, soft glassy systems (such as dense emulsions), or compressed granular materials.

The self-consistent signal-to-noise analysis (SCSNA) is an alternative to the replica method for deriving the set of order parameter equations for associative memory neural network models and is closely related with the Thouless-Anderson-Palmer equation (TAP) approach. In the recent paper by Shiino and Yamana the Onsager reaction term of the TAP equation has been found to be obtained from the SCSNA for Hopfield neural networks with two-body interaction. We study the TAP equation for an associative memory stochastic analog neural network with three-body interaction to investigate the structure of the Onsager reaction term, in connection with the term proportional to the output characteristic to the SCSNA. We report on the SCSNA framework for analog networks with three-body interactions as well as provide a recipe based on the cavity concept that involves two cavities and the hybrid use of the SCSNA to obtain the TAP equation.

In this Comment, we show that the expression for $R_0$ as proposed by R. Breban, R. Vardavas, and S. Blower, Phys. Rev. E 72, 046110 (2005) is incorrect and we reveal the underlying conceptual mistake.

We disagree with Bootsma and Diekmann that our formula for the basic reproduction ratio $\left(R_0\right)$ has an underlying conceptual mistake. In Phys. Rev. E 72, 046110 (2005), we propose a large class of growing networks (which we call Kinetic Monte Carlo (KMC) growing networks) as individual-level models for the transmission of infectious diseases. KMC growing networks are conceptually different from the well-established Crump-Mode-Jagers continuous-time branching processes. Thus, the branching process definition of $R_0$ is not valid for KMC growing networks, and a different implementation of the biological definition of $R_0$ is necessary.

We have investigated the effect of air on the density segregation of fine, equal-sized bronze and glass particles under vertical sinusoidal vibrations by numerical simulation, using a hybrid granular dynamics-computational fluid dynamics model. We find both the bronze-on-top and the sandwich configurations as observed in previous experiments. The simulations allow us to give a detailed explanation of the phenomena. The key observation is the precise timing of the decompaction of the bed with the oscillating gas flow, which will cause the bronze to move to the top, due to the difference in acceleration from the air drag. For higher frequencies, the different inertia in collisions will cause the bronze clusters on top to sink through the bed, leading to a sandwich formation.

Chaotic noisy transport of electron pairs in a superconducting junction device (thermal-inertia ratchets) is investigated. The study shows that when the temperature is low enough, the transport of the electron pairs can be mainly chaotic; when the temperature is high enough, it can be mainly stochastic. By controlling the temperature and the amplitude of the input ac signal, the current of electron pairs can be reversed.

A special family of solvable five-vertex model is introduced on a square lattice. In addition to the usual nearest-neighbor interactions, the vertices defining the model also interact along one of the diagonals of the lattice. This family of models includes in a special limit the standard six-vertex model. The exact solution of these models is an application of the matrix product ansatz introduced recently and applied successfully in the solution of quantum chains. The phase diagram and the free energy of the models are calculated in the thermodynamic limit. The models exhibit massless phases, and our analytical and numerical analyses indicate that such phases are governed by a conformal field theory with central charge $c=1$ and continuously varying critical exponents.

In this paper, we study the boundary-induced phase transitions in a particle nonconserving asymmetric simple exclusion process with open boundaries. Using a boundary layer analysis on the mean field version of the model, we show that the key signatures of various bulk phase transitions are present in the boundary layers of the density profiles. In addition, we also find surface transitions in the low- and high-density phases. The surface transition in the low-density phase provides a complete description of the nonequilibrium critical point found in this system.

We simulate a disordered assembly of particles interacting through a repulsive Yukawa potential with a small fraction of the particles coupled to an external drive. Distortions in the arrangement of the nondriven particles produce a dynamically induced effective attraction between the driven particles, giving rise to intermittent one-dimensional stringlike structures. The velocity of a moving string increases with the number of driven particles in the string. We identify the average stable string length as a function of driving force, background particle density, and particle charge. This model represents a type of collective transport system composed of interacting particles moving through deformable disorder.

We study the behavior of a fluid quenched from the disordered into the lamellar phase under the action of a shear flow. The dynamics of the system is described by Navier-Stokes and convection-diffusion equations with the pressure tensor and the chemical potential derived by the Brazovskii free energy. Our simulations are based on a mixed numerical method with the lattice Boltzmann equation and a finite difference scheme for Navier-Stokes and order parameter equations, respectively. We focus on cases where banded flows are observed with two different slopes for the component of velocity in the direction of the applied flow. Close to the walls the system reaches a lamellar order with very few defects, and the slope of the horizontal velocity is higher than the imposed shear rate. In the middle of the system the local shear rate is lower than the imposed one, and the system looks like a mixture of tilted lamellae, droplets, and small elongated domains. We refer to this as a region with a shear-induced structures (SIS) configuration. The local behavior of the stress shows that the system with the coexisting lamellar and SIS regions is in mechanical equilibrium. This phenomenon occurs, at fixed viscosity, for shear rates under a certain threshold; when the imposed shear rate is sufficiently large, lamellar order develops in the whole system. Effects of different viscosities have been also considered. The SIS region is observed only at low enough viscosity. We compare the above scenario with the usual one of shear banding. In particular, we do not find evidence for a plateau of the stress at varying imposed shear rates in the region with banded flow. We interpret our results as due to a tendency of the lamellar system to oppose the presence of the applied flow.