Subthreshold oscillations provide neurons with a filtering mechanism that allows their membrane potential to respond selectively to oscillatory currents depending on their frequency. On the other hand, the phase of such oscillations is known to affect the precise timing at which action potentials can be elicited by input spikes. Here we study the combined effect of these two properties by examining the response of a model neuron to periodic spike trains of defined frequency, in the presence of subthreshold oscillatory activity. Numerical results show a marked resonance with the input firing rate, irrespective of the initial relative phase between the input spike train and the intrinsic subthreshold oscillation. This behavior can be understood in terms of a delayed phase transition curve, from which an iterative map can be built that describes the evolution of the phase response to the periodic succession of input spike perturbations. Depending on the input period, the map exhibits stationary, periodic, or chaotic dynamics that predict in a quantitative way the response of the neuron to the spike train. Propagation of the spike train through a chain of neurons is also examined, and the resonant behavior is seen to be enhanced upon propagation.

The anisotropic stress-dependent velocity of elastic waves in glass beads—as observed by Khidas and Jia [Phys. Rev. E 81, 021303 (2010)]—is shown to be well accounted for by “granular solid hydrodynamics,” a broad-range macroscopic theory of granular behavior. As the theory makes no reference to fabric anisotropy, the influence of which on sound is in doubt.

The characterization of the “most connected” nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness against failures, vulnerability to deliberate attacks, and diffusion properties. However, recent empirical research of large dynamic networks (characterized by irregular connections that evolve rapidly) has demonstrated that there is little continuity in degree centrality of nodes over time, even when their degree distributions follow a power law. This unexpected dynamic centrality suggests that the connections in these systems are not driven by preferential attachment or other known mechanisms. We present an approach to explain real-world dynamic networks and qualitatively reproduce these dynamic centrality phenomena. This approach is based on a dynamic preferential attachment mechanism, which exhibits a sharp transition from a base pure random walk scheme.

We present a hydrodynamic lattice gas model for two-dimensional flows on curved surfaces with dynamical geometry. This model is an extension to two dimensions of the dynamical geometry lattice gas model previously studied in one dimension. We expand upon a variation of the two-dimensional flat space Frisch-Hasslacher-Pomeau (FHP) model created by Frisch et al. [Phys. Rev. Lett. 56, 1505 (1986)] and independently by Wolfram, and modified by Boghosian et al. [Philos. Trans. R. Soc. London, Ser. A 360, 333 (2002)]. We define a hydrodynamic lattice gas model on an arbitrary triangulation whose flat space limit is the FHP model. Rules that change the geometry are constructed using the Pachner moves, which alter the triangulation but not the topology. We present results on the growth of the number of triangles as a function of time. Simulations show that the number of triangles grows with time as $t^{1/3}$, in agreement with a mean-field prediction. We also present preliminary results on the distribution of curvature for a typical triangulation in these simulations.

Using the positive P-representation of the density matrix, we develop an algorithm for calculating the quantum many-body nonlinear response functions of a system of bosons driven impulsively by external fields. The formalism maps the quantum time evolution of $N$ boson degrees of freedom into a stochastic dynamics of $4N$ classical degrees of freedom. The first- and the third-order response functions are calculated by propagating the parameters of the P-representation using a set of coupled Langevin equations with multiplicative noise. These parameters serve as classical variables. Two classical ways for computing the response functions are presented. In the nonequilibrium method, an observable is calculated for weak impulsive pulses, and the response functions are obtained by taking its derivatives with respect to the pulse amplitudes. In the alternative, equilibrium simulation, the response functions are expressed in terms of time-correlation functions involving the P-representation parameters and stability matrices representing the perturbation of the trajectories. The stability matrices can be propagated simultaneously with the Langevin equations for the parameters. The formalism is generalized for a many-body boson system coupled to a harmonic bath.

We use molecular dynamics simulations to explore the force oscillation mechanism of a simple fluid confined between two surfaces. Force profiles obtained through simulations are qualitatively similar to those in surface force measurements. Our results demonstrate that the layering transition is an abrupt, liquid-to-solid phase transition. The nucleation of solid phase starts at the central region of the confined film that can sustain a finite shear stress. The packing structure of the solid film is a hexagonal close-packed (hcp) crystalline structure, whose mechanical property is highly asymmetric. The elastic modulus and repulsive peaks of oscillatory forces during normal approach are always larger than those during retraction.

The microcanonical transfer matrix is used to evaluate the exact integer values for the number of states $\Omega \left(E,M\right)$, as a function of energy $E$ and magnetization $M$, of the Ising model in an external magnetic field $H$ on $L\times 2L$ honeycomb lattices $\left(L=6,8,\dots ,14\right)$ and (due to memory limitations) the exact real values for $\overline{\Omega }\left(a,M\right)={\sum }_E\Omega \left(E,M\right)a^E$ $\left(L=16,\dots ,22\right)$, where $a=e^{2\beta J}$. Given $\Omega \left(E,M\right)$ or $\overline{\Omega }\left(a,M\right)$, the exact partition functions $Z\left(a,x\right)={\sum }_{E,M}\Omega \left(E,M\right)a^E{x}^M={\sum }_M\overline{\Omega }\left(a,M\right)x^M$, where $x=e^{-2\beta H}$, are obtained. From the exact partition functions, the precise distributions of the partition function zeros in the complex $x$ plane of the honeycomb-lattice Ising antiferromagnet in a uniform external magnetic field, where the famous circle theorem for the partition function zeros of the Ising ferromagnet is not applicable, are determined. In addition, the critical points $x_{cp}\left(a\right)$ and the magnetic scaling exponents $y_h\left(a\right)$ of the honeycomb-lattice Ising antiferromagnet in a uniform magnetic field are estimated using its partition function zeros in the complex $x$ plane. Our results for the critical points are also compared to those of the two different closed-form approximations.

We study the percolation properties of the growing clusters model on a 2D square lattice. In this model, a number of seeds placed on random locations on the lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually touch each other they immediately stop their growth. The model exhibits a discontinuous transition for very low values of the seed concentration $p$ and a second, nontrivial continuous phase transition for intermediate $p$ values. Here we study in detail this continuous transition that separates a phase of finite clusters from a phase characterized by the presence of a giant component. Using finite size scaling and large scale Monte Carlo simulations we determine the value of the percolation threshold where the giant component first appears, and the critical exponents that characterize the transition. We find that the transition belongs to a different universality class from the standard percolation transition.

We present a generalization of the modified smooth particle hydrodynamics simulation technique capable of simulating static and dynamic liquid crystalline behavior. This generalization is then implemented in the context of the Qian-Sheng description of nematodynamics. To test the method, we first use it to simulate switching in both a Fréedericksz setup and a chiral hybrid aligned nematic cell. In both cases, the results obtained give excellent agreement with previously published results. We then apply the technique in a three-dimensional simulation of the switching dynamics of the post aligned bistable nematic device.

Unstable attractors whose nearby points will almost leave the neighborhood have been observed in pulse-coupled oscillators. In this model, an oscillator fires and sends out a pulse when reaching the threshold. In terms of these firing events, we find that the unstable attractors have a simple property hidden in the event sequences. They coexist with active simultaneous firing events. That is, at least two oscillators reach the threshold simultaneously, which is not directly caused by the receiving pulses. We show that the split of the active simultaneous firing events by general perturbations can make the nearby points leave the unstable attractors. Furthermore, this structure can be applied to study the bifurcation of unstable attractors. Unstable attractors can bifurcate due to the failure of establishing active simultaneous firing events.

We investigate the probability density of rescaled sum of iterates of sine-circle map within quasiperiodic route to chaos. When the dynamical system is strongly mixing (i.e., ergodic), standard central limit theorem (CLT) is expected to be valid, but at the edge of chaos where iterates have strong correlations, the standard CLT is not necessarily valid anymore. We discuss here the main characteristics of the probability densities for the sums of iterates of deterministic dynamical systems which exhibit quasiperiodic route to chaos. At the golden-mean onset of chaos for the sine-circle map, we numerically verify that the probability density appears to converge to a $q$-Gaussian with $q<1$ as the golden mean value is approached.

We present an off-lattice kinetic Monte Carlo method, which is useful to simulate reactions in solutions. We derive the method from first-principles. We assume that diffusion leads to a Gaussian distribution for the position of the particles. This allows us to deal with the diffusion analytically, and we only need to simulate the reactive processes. The rate constants of these reactions can be computed before a simulation is started, and need not be computed on-the-fly as in other off-lattice kinetic Monte Carlo methods. We show how solvent molecules can be removed from the simulations, which minimizes the number of particles that have to be simulated explicitly. We present the relation with the customary macroscopic rate equations, and compare the results of these equations and our method on a variation of the Lotka model.

In the present paper, the discharge avalanche model, initially proposed by Dissado and co-workers, is modified to explore (by correlating its results with experimental information) the role of the space-charge characteristics in the fractal nature of electric trees. Stochastic fluctuations of the local electrical field in each site of the polymer sample $\left(E_{loc}\right)$ around the Laplacian field $\left(E_{lap}\right)$ are allowed and limited to intermediate values of $E_{lap}$. The major achievements of the modified model are the prediction of a nonmonotonic behavior in both the average time to failure and the average fractal dimension of the electrical trees, and the prediction of a transition from branched to runaway trees as the applied voltage is increased.

We simulate binary soft-disk systems in two dimensions and investigate how the dynamics slow as the area fraction is increased toward the glass transition. The “fragility” quantifies how sensitively the relaxation time scale depends on the area fraction, and the fragility strongly depends on the composition of the mixture. We confirm prior results for mixtures of particles with similar sizes, where the ability to form small crystalline regions correlates with fragility. However, for mixtures with particle size ratios above 1.4, we find that the fragility is not correlated with structural ordering, but rather with the spatial distribution of large particles. The large particles have slower motion than the small particles and act as confining “walls” which slow the motion of nearby small particles. The rearrangement of these confining structures governs the lifetime of dynamical heterogeneity, that is, how long local regions exhibit anomalously fast or slow behavior. The strength of the confinement effect is correlated with the fragility and also influences the aging behavior of glassy systems.

An exact method is developed for computing the height of an elastic medium subjected to centrifugal compression, for arbitrary constitutive relation between stress and strain. Example solutions are obtained for power-law media and for cases where the stress diverges at a critical strain—for example as required by packings composed of deformable but incompressible particles. Experimental data are presented for the centrifugal compression of thermo-responsive N-isopropylacrylamide (NIPA) microgel beads in water. For small radial acceleration, the results are consistent with Hertzian elasticity, and are analyzed in terms of the Young elastic modulus of the bead material. For large radial acceleration, the sample compression asymptotes to a value corresponding to a space-filling particle volume fraction of unity. Therefore we conclude that the gel beads are incompressible, and deform without deswelling. In addition, we find that the Young elastic modulus of the particulate gel material scales with cross-link density raised to the power $3.3\pm 0.8$, somewhat larger than the Flory expectation.

We study the mechanics of nematically ordered semiflexible networks showing that they, like isotropic networks, undergo an affine to nonaffine crossover controlled by the ratio of the filament length to the nonaffinity length. Deep in the nonaffine regime, however, these anisotropic networks exhibit a much more complex mechanical response characterized by a vanishing linear-response regime for highly ordered networks and a dependence of the shear modulus on shear direction at both small (linear) and finite (nonlinear) strains that is different from the affine prediction of orthotropic continuum linear elasticity. We show that these features can be understood in terms of a generalized floppy modes analysis of the nonaffine mechanics and a type of cooperative Euler buckling.

We introduce a simple model describing a mechanism for transient pattern formation driven by subdominant attractive forces. The patterns can be stabilized if they are confined by means of a particular multiplicative noise into the region where such mechanism is active. The scope of the results appears to transcend the original application context.

The finite-size scaling (FSS) theory for continuous phase transitions has been useful in determining the critical behavior from the size-dependent behaviors of thermodynamic quantities. When the phase transition is discontinuous, however, FSS approach has not been well established yet. Here, we develop a FSS theory for the explosive percolation transition arising in the Erdős and Rényi model under the Achlioptas process. A scaling function is derived based on the observed fact that the derivative of the curve of the order parameter at the critical point $t_c$ diverges with system size in a power-law manner, which is different from the conventional one based on the divergence of the correlation length at $t_c$. We show that the susceptibility is also described in the same scaling form. Numerical simulation data for different system sizes are well collapsed on the respective scaling functions.

In developed economies, the sign of the price increment influences the volatility in an asymmetric fashion—negative increments tend to result in larger volatility (increments with larger magnitudes), while positive increments result in smaller volatility. We explore whether this asymmetry extends from developed economies to European transition economies and, if so, how such asymmetry changes over time as these transition economies develop and mature. We analyze eleven European transition economies and compare the results with those obtained by analyzing U.S. market indices. Specifically, we calculate parameters that quantify both the volatility asymmetry and the strength of its dependence on prior increments. We find that, like their developed economy counterparts, almost all transition economy indices exhibit a significant volatility asymmetry, and the parameter $\gamma$ characterizing asymmetry fluctuates more over time for transition economies. We also investigate how the association between volatility and volatility asymmetry varies by type of market. We test the hypothesis of a negative correlation between volatility and volatility asymmetry. We find that, for developed economies, $\gamma$ experiences local minima during (i) “Black Monday” on October 19, 1987, (ii) the dot-com bubble crash in 2002, and (iii) the 2007–2009 global crisis while for transition economies, $\gamma$ experiences local maxima during times of economic crisis.

Gradients in magnetic field applied to electrically insulating fluids result in an effective body force—the Kelvin force, which can potentially be used to control flow and thermal processes, particularly in microgravity environments. We study the influence of the Kelvin force on the mass, momentum, and energy transport of fluid arising from the melting of a semi-infinite solid substrate subjected to temperature and magnetic-field gradients. The governing equations of the magnetothermal free convection of the melt under the boundary layer approximation with a suitable transformation lead to a similarity solution. Closed-form analytical solutions for the limiting case of smaller Prandtl numbers are presented. The nonlinear similarity equations are solved numerically using an iterative boundary-value technique based on a finite-difference approach. Based on the numerical results, the effect of various characteristic nondimensional parameters on the structure of the melt boundary layer and transport rates of heat and mass across the substrate are elucidated and discussed.