The population activity of random networks of excitatory and inhibitory leaky integrate-and-fire neurons has been studied extensively. In particular, a state of asynchronous activity with low firing rates and low pairwise correlations emerges in sparsely connected networks. We apply linear response theory to evaluate the influence of detailed network structure on neuron dynamics. It turns out that pairwise correlations induced by direct and indirect network connections can be related to the matrix of direct linear interactions. Furthermore, we study the influence of the characteristics of the neuron model. Interpreting the reset as self-inhibition, we examine its influence, via the spectrum of single-neuron activity, on network autocorrelation functions and the overall correlation level. The neuron model also affects the form of interaction kernels and consequently the time-dependent correlation functions. We find that a linear instability of networks with Erdös-Rényi topology coincides with a global transition to a highly correlated network state. Our work shows that recurrent interactions have a profound impact on spike train statistics and provides tools to study the effects of specific network topologies.

We present a model to describe the response of chip-based nanocavity sensors during extracellular recording of action potentials. These sensors feature microelectrodes which are embedded in liquid-filled cavities. They can be used for the highly localized detection of electrical signals on a chip. We calculate the sensor's impedance and simulate the propagation of action potentials. Subsequently we apply our findings to analyze cell-chip coupling properties. The results are compared to experimental data obtained from cardiomyocyte-like cells. We show that both the impedance and the modeled action potentials fit the experimental data well. Furthermore, we find evidence for a large seal resistance of cardiomyocytes on nanocavity sensors compared to conventional planar recording systems.

We study how much water can be retained without leaking through boundaries when each unit square of a two-dimensional lattice is randomly assigned a block of unit bottom area but with different heights from zero to $n-1$. As more blocks are put into the system, there exists a phase transition beyond which the system retains a macroscopic volume of water. We locate the critical points and verify that the criticality belongs to the two-dimensional percolation universality class. If the height distribution can be approximated as continuous for large $n$, the system is always close to a critical point and the fraction of the area below the resulting water level is given by the percolation threshold. This provides a universal upper bound of areas that can be covered by water in a random landscape.

The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of nonequilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in arbitrary interaction networks. Our aim is to extract topological features of the connectivity pattern from purely dynamical measures based on the fact that in a heterogeneous network the global dynamics is not only affected by the distribution of the natural frequencies but also by the location of the different values. In order to perform a quantitative study we focused on a very simple frequency distribution considering that all the frequencies are equal but one, that of the pacemaker node. We then analyze the dynamical behavior of the system at the transition point and slightly above it as well as very far from the critical point, when it is in a highly incoherent state. The gathered topological information ranges from local features, such as the single-node connectivity, to the hierarchical structure of functional clusters and even to the entire adjacency matrix.

We propose a Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions, including systems that are out of equilibrium. We combine the proposed path sampling algorithm with thermodynamic integration to calculate transition rates. We demonstrate our method on the well-studied two-dimensional Ising model with periodic boundary conditions, and show agreement with other results for both large and small system sizes. The method scales well with the system size, allowing one to simulate systems with many degrees of freedom, and providing complementary information with respect to other algorithms.

We study the vibrational spectra of one-dimensional statically compressed granular crystals (arrays of elastic particles in contact) containing light-mass defects. We focus on the prototypical settings of one or two spherical defects (particles of smaller radii) interspersed in a chain of larger uniform spherical particles. We present a systematic measurement, using continuous noise, of the near-linear frequency spectrum within the spatial vicinity of the defect(s). Using this technique, we identify the frequencies of the localized defect modes as a function of the defect size and the position of the defects relative to each other. We also compare the experimentally determined frequencies with those obtained by numerical eigenanalysis and by analytical expressions based on few-site considerations. These approximate analytical expressions, based on normal-mode analysis, are found to be in excellent agreement with numerics for a wide range of mass ratios. We also observe that the experimentally measured frequencies of the localized defect modes are uniformly upshifted, compared to the numerically and theoretically predicted values.

We map the Markov-switching multifractal model (MSM) onto the random energy model (REM). The MSM is, like the REM, an exactly solvable model in one-dimensional space with nontrivial correlation functions. According to our results, four different statistical physics phases are possible in random walks with multifractal behavior. We also introduce the continuous branching version of the model, calculate the moments, and prove multiscaling behavior. Different phases have different multiscaling properties.

We study by kinetic Monte Carlo simulations the catalytic oxidation of carbon monoxide on a surface in the presence of contaminants in the gas phase. The process is simulated by a Ziff-Gulari-Barshad (ZGB) model that has been modified to include the effect of the contaminants and to eliminate an unphysical oxygen poisoned phase at very low CO partial pressures. The impurities can adsorb and desorb on the surface but otherwise remain inert. We find that if the impurities cannot desorb, no matter how small their proportion in the gas mixture, the reactive window and discontinuous transition to a CO poisoned phase at high CO pressures that characterize the original ZGB model disappear. The coverages become continuous, and once the surface has reached a steady state there is no production of CO${}_2$. This is quite different from the behavior of systems in which the surface presents a fixed percentage of impurities. When the contaminants are allowed to desorb, the reactive phase appears again for CO pressures below a value that depends on the proportion of contaminants in the gas and on their desorption rate.

We have studied the motion of an underdamped Brownian particle in (i) a bistable periodic potential and (ii) washboard potentials subjected to a sinusoidal external field. The particles are shown to be effectively in two dynamical states of their trajectories with distinct amplitudes and phase relationship with the external drive. These dynamical states are stable with fixed energies at low temperatures, but transitions between them take place as the temperature is increased. The average input energy loss to the environment per period of the drive shows a stochastic resonance (SR) peak as a function of temperature for the underdamped system potentials studied. The occurrence of SR in these systems is explained using the statistics of transitions between the two dynamical states.

We report a striking effect observed experimentally in several granular materials when shaken horizontally: The material displays a recurrent alternation between a slow inflation phase, characterized by an increase in its volume, and a fast collapse phase, when the volume abruptly returns to its original value. The frequency of such phase alternations is totally decoupled from the frequency of the external drive. We argue that the inflation and collapse alternation arises from an interplay between the mechanical stability of the material and Reynolds dilatancy due to convective motion.

Spiral waves in excitable biological media are associated with pathological situations. In the heart an action potential vortex pinned by an obstacle has to be removed through defibrillation protocols fine-tuned theoretically by using electrophysiological nonlinear mathematical models. Cardiac tissue, however, is an electroelastic medium whose electrical properties are strongly affected by large deformations. In this paper we specifically investigate the electroelastic pinning-unpinning mechanism in order to include cardiac contraction in the preexisting theoretically modeled defibrillation scenarios. Based on a two-dimensional minimal electromechanical model, we show numerically the existence of an unpinning band characterized by the size of the obstacle, the pacing site, and the frequency. Similar numerical simulations, performed in the absence of elastic coupling, show small differences in comparison with the electroelastic studies, suggesting for this specific scenario of pinning-unpinning dynamics a nonprominent role of elasticity.

We present experimental results obtained for a one-dimensional pedestrian flow using high precision motion capture. The full pedestrians’ trajectories are obtained. In this paper, we focus on the fundamental diagram, and on the relation between the instantaneous velocity and spatial headway (distance to the predecessor). While the latter was found to be linear in previous experiments, we show that it is rather a piecewise linear behavior which is found if larger density ranges are covered. Indeed, our data clearly exhibits three distinct regimes in the behavior of pedestrians that follow each other. The transitions between these regimes occur at spatial headways of about $1.1$ and 3 m, respectively. This finding could be useful for future modeling.

In two-dimensional forced Navier-Stokes turbulence, energy cascades to the largest scales in the system to form a pair of coherent vortices known as the Bose condensate. We show, both numerically and analytically, that the energy condensation saturates and the system reaches a statistically stationary state. The time scale of saturation is inversely proportional to the viscosity and the saturation energy level is determined by both the viscosity and the force. We further show that, without sufficient resolution to resolve the small-scale enstrophy spectrum, numerical simulations can give a spurious result for the saturation energy level. We also find that the movement of the condensate is similar to the motion of an inertial particle with an effective drag force. Furthermore, we show that the profile of the saturated coherent vortices can be described by a Gaussian core with exponential wings.

We develop a systematic methodology for classifying the periodic orbits of homogeneous ordered granular chains with no dissipation, under the assumption that all granules oscillate with the same frequency. The analysis is based on the idea of balancing linear momentum for sets of auxiliary models consisting of “effective particles.” The auxiliary models may be defined for any given finite, ordered granular chain composed of $n$ identical granules (beads) that interact with each other through strongly nonlinear Hertzian interaction law. In turn, the auxiliary models may be effectively used for theoretically predicting the total number of periodic orbits and the corresponding amplitude ratios of the granules. Good correspondence between the theoretical models and results of direct numerical simulations is reported. The results presented herein can be used to understand the complex intrinsic dynamics of ordered granular media, and to systematically study the generation of mode localization in these strongly nonlinear systems. The derived analytical models can be utilized to predict the response of the effective particles, and based on that, to predict primary pulse transmission in periodic layered media with granular interfaces. Moreover, our analysis can be extended to the general class of nonlinear chains of particles with smooth interacting potentials and possible separation between particles during the motion.

The model of Cairns et al. [Geophys. Res. Lett. 22, 2709 (1995)] is generalized. A physically meaningful nonextensive nonthermal velocity distribution is outlined. As the nonextensive character of the nonthermal electrons increases, the distribution shoulders may become less or more prominent and high-energy states are less or more probable than in the extensive nonthermal case. It is found that our plasma model supports the coexistence of smooth rarefactive and spiky compressive ion-acoustic solitary waves. The rarefactive solitons are more affected by nonextensivity than their compressive counterpart and a slight increase in the nonextensive parameter may destroy this dual nature.

We study aging during surface growth processes described by the one-dimensional Kardar-Parisi-Zhang equation. Starting from a flat initial state, the systems undergo simple aging in both correlators and linear responses, and its dynamical scaling is characterized by the aging exponents $a=-1/3$, $b=-2/3$, ${\lambda }_C={\lambda }_R=1$, and $z=3/2$. The form of the autoresponse scaling function is well described by the recently constructed logarithmic extension of local scale invariance.

In uniform and isotropic systems the three-dimensional pair distribution function and the structure factor can be restored from two-dimensional observations of the sliced volume with finite thickness without scanning along the third dimension. By numerically simulating such observations of a known system, it is explicitly shown that proposed formulas for such restorations are applicable, at least when the thickness of the sliced volume is smaller than or comparable to the mean distance between particles. It is also pointed out that one cannot simply guess the behavior of the long-wavelength limit of the three-dimensional structure factor from the two-dimensional observation: Even when the (true) three-dimensional structure factor vanishes, the observed two-dimensional structure factor goes to a finite value which depends on the thickness. The correct behavior of the three-dimensional structure factor is given by the restoration formula.

Pattern and dynamics during phase separation in a symmetrical binary ($A+B$) Lennard-Jones fluid are studied via molecular dynamics simulations after quenching homogeneously mixed critical (50:50) systems to temperatures below the critical one. The morphology of the domains, rich in $A$ or $B$ particles, is observed to be bicontinuous. The early-time growth of the average domain size is found to be consistent with the Lifshitz-Slyozov law for diffusive domain coarsening. After a characteristic time, dependent on the temperature, we find a clear crossover to an extended viscous hydrodynamic regime where the domains grow linearly with time. Pattern formation in the present system is compared with that in solid binary mixtures, as a function of temperature. Important results for the finite-size and temperature effects on the small-wave-vector behavior of the scattering function are also presented.

We study the vortex lines that are a feature of many random or disordered three-dimensional systems. These show universal statistical properties on long length scales, and geometrical phase transitions analogous to percolation transitions but in distinct universality classes. The field theories for these problems have not previously been identified, so that while many numerical studies have been performed, a framework for interpreting the results has been lacking. We provide such a framework with mappings to simple supersymmetric models. Our main focus is on vortices in short-range-correlated complex fields, which show a geometrical phase transition that we argue is described by the ${\mathrm{CP}}^{k|k}$ model (essentially the ${\mathrm{CP}}^{n-1}$ model in the replica limit $n\to 1$). This can be seen by mapping a lattice version of the problem to a lattice gauge theory. A related field theory with a noncompact gauge field, the ‘${\mathrm{NCCP}}^{k|k}$ model’, is a supersymmetric extension of the standard dual theory for the $XY$ transition, and we show that $XY$ duality gives another way to understand the appearance of field theories of this type. The supersymmetric descriptions yield results relevant, for example, to vortices in the $XY$ model and in superfluids, to optical vortices, and to certain models of cosmic strings. A distinct but related field theory, the ${\mathrm{RP}}^{2l|2l}$ model (or the ${\mathrm{RP}}^{n-1}$ model in the limit $n\to 1$) describes the unoriented vortices that occur, for instance, in nematic liquid crystals. Finally, we show that in two dimensions, a lattice gauge theory analogous to that discussed in three dimensions gives a simple way to see the known relation between two-dimensional percolation and the ${\mathrm{CP}}^{k|k}$ $\sigma$ model with a $\theta$ term.

We use molecular dynamics (MD) to simulate diffusion in molten aluminum-copper (AlCu) alloys. The self-diffusivities and Maxwell-Stefan diffusivities are calculated for AlCu mixtures using the Green-Kubo formulas at temperatures from 1000 to 4000 K and pressures from 0 to 25 GPa, along with additional points at higher temperatures and pressures. The diffusivities are corrected for finite-size effects. The Maxwell-Stefan diffusivity is compared to the diffusivity calculated from the self-diffusivities using a generalization of the Darken equation. We find that the effects of cross-correlation are small. Using the calculated self-diffusivities, we have assessed whether dilute hard-sphere and dilute Lennard-Jones models apply to the molten mixture. Neither of the two dilute gas diffusivities describes the diffusivity in molten Al and Cu. We report generalized analytic models for the self-diffusivities and interdiffusivity (mutual diffusivity) that fit the MD results well. The MD-derived transport coefficients are in good agreement with the available experimental data. We also report MD calculations of the viscosity and an analytic fit to those results. The ionic thermal conductivity is discussed briefly.