We investigate the collective dynamics of excitatory-inhibitory excitable networks in response to external stimuli. How to enhance the dynamic range, which represents the ability of networks to encode external stimuli, is crucial to many applications. We regard the system as a two-layer network (E layer and I layer) and explore the criticality and dynamic range on diverse networks. Interestingly, we find that phase transition occurs when the dominant eigenvalue of the E layer's weighted adjacency matrix is exactly 1, which is only determined by the topology of the E layer. Meanwhile, it is shown that the dynamic range is maximized at a critical state. Based on theoretical analysis, we propose an inhibitory factor for each excitatory node. We suggest that if nodes with high inhibitory factors are cut out from the I layer, the dynamic range could be further enhanced. However, because of the sparseness of networks and passive function of inhibitory nodes, the improvement is relatively small compared to the original dynamic range. Even so, this provides a strategy to enhance the dynamic range.

We show that polarons can sustain looplike configurations in flexible biopolymers and that the size of the loops depend on both the flexural rigidity of the polymer and the electron-phonon coupling constant. In particular we show that for single stranded DNA (ssDNA) and polyacetylene such loops can have as few as seven monomers. We also show that these configurations are very stable under thermal fluctuations and so could facilitate the formation of hairpin loops of ssDNA.

We introduce a population model for species under cyclic competition. This model allows individuals to coexist and interact on single cells while migration takes place between adjacent cells. In contrast to the model introduced by Reichenbach, Mobilia, and Frey [Reichenbach, Mobilia, and Frey, Nature (London) 448, 1046 (2007)], we find that the emergence of spirals results in an ambiguous behavior regarding the stability of coexistence. The typical time until extinction exhibits, however, a qualitatively opposite dependence on the newly introduced nonunit carrying capacity in the spiraling and the nonspiraling regimes. This allows us to determine a critical mobility that marks the onset of this spiraling state sharply. In contrast, we demonstrate that the conventional finite size stability analysis with respect to spatial size is of limited use for identifying the onset of the spiraling regime.

The emergence and promotion of cooperation are two of the main issues in evolutionary game theory, as cooperation is amenable to exploitation by defectors, which take advantage of cooperative individuals at no cost, dooming them to extinction. It has been recently shown that the existence of purely destructive agents (termed jokers) acting on the common enterprises (public goods games) can induce stable limit cycles among cooperation, defection, and destruction when infinite populations are considered. These cycles allow for time lapses in which cooperators represent a relevant fraction of the population, providing a mechanism for the emergence of cooperative states in nature and human societies. Here we study analytically and through agent-based simulations the dynamics generated by jokers in finite populations for several selection rules. Cycles appear in all cases studied, thus showing that the joker dynamics generically yields a robust cyclic behavior not restricted to infinite populations. We also compute the average time in which the population consists mostly of just one strategy and compare the results with numerical simulations.

We present a general variational framework designed to consider constrained optimization and sensitivity analysis of spatially and temporally evolving flows defined as solutions of partial differential equations. We particularly focus on seminorm constraints which naturally arise for instance when the quantity which we wish to optimize can have contributions from several terms in the PDE through different physical mechanisms in a specific physical system. We show that this case implicitly requires that constraints be placed on the magnitude of complementary (with respect to the first constraining seminorm) seminorms of initial perturbations such that the sum of these complementary seminorms defines a total “true” norm of the state vector. A simple (true) norm constraint naturally satisfies this property. Therefore, the use of this framework requires the introduction of new parameters which describe the relative magnitude of the initial perturbation state vector calculated using the various constrained complementary seminorms to the magnitude calculated using the true norm, even for linear problems. We demonstrate that any required optimization has to be carried out by prescribing these new parameters as initial conditions on the admissible perturbations; the influence and significance of each seminorm component, partitioning the initial total norm of the perturbation, can then be considered quantitatively. To demonstrate the utility of this framework, we consider an idealized problem, the (linear) nonmodal stability analysis of a mean flow given by a “Reynolds averaging” of the one-dimensional stochastically forced Burgers equation. We close the mean flow equation by introducing a turbulent viscosity to model the turbulent mixing, which we allow to evolve subject to a new transport equation. Since we are interested in optimizing the relative amplification of the perturbation kinetic energy (i.e., the perturbation's “gain”) this problem naturally requires the use of our new framework, as the kinetic energy is a seminorm of the full state velocity-viscosity vector, with a new adjustable parameter, describing the ratio of an appropriate viscosity seminorm to the sum of this viscosity seminorm and the kinetic energy seminorm. Using this framework, we demonstrate that the dynamics of the full system, allowing the turbulent viscosity to evolve subject to its transport equation, is qualitatively different from the behavior when the turbulent viscosity is “frozen” at a fixed, mean value, since a new mechanism of perturbation energy production appears, through the coupling of the evolving turbulent viscosity perturbation and the mean velocity field.

A technique of hyperbolic scaling is applied to calculate a reaction front velocity in an irreversible autocatalytic conversion reaction $A+B\to 2A$ under subdiffusion. The method, based on the geometric optics approach is a technically elegant observation of the propagation front failure obtained in Phys. Rev. E 78, 011128 (2008).

We analyze an idealized model for the transmission or flow of particles, or discrete packets of information, in a weight bearing branching hierarchical two dimensional network and its variants. The capacities add hierarchically down the clusters. Each node can accommodate a limited number of packets, depending on its capacity, and the packets hop from node to node, following the links between the nodes. The statistical properties of this system are given by the Maxwell-Boltzmann distribution. We obtain analytical expressions for the mean occupation numbers as functions of capacity, for different network topologies. The analytical results are shown to be in agreement with the numerical simulations. The traffic flow in these models can be represented by the site percolation problem. It is seen that the percolation transitions in the 2D model and in its variant lattices are continuous transitions, whereas the transition is found to be explosive (discontinuous) for the V lattice, the critical case of the 2D lattice. The scaling behavior of the second-order percolation case is studied in detail. We discuss the implications of our analysis.

We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems.

We present a robust and computationally efficient numerical scheme for simulating steady electrohydrodynamic atomization processes (electrospray). The main simplification assumed in this scheme is that all the free electrical charges are distributed over the interface. A comparison of the results with those calculated with a volume-of-fluid method showed that the numerical scheme presented here accurately describes the flow pattern within the entire liquid domain. Experiments were performed to partially validate the numerical predictions. The simulations reproduced accurately the experimental shape of the liquid cone jet, providing correct values of the emitted electric current even for configurations very close to the cone-jet stability limit.

Directed motion and depinning of topological solitons in a strongly discrete damped and biharmonically ac-driven array of Josephson junctions is studied. The mechanism of the depinning transition is investigated in detail. We show that the depinning process takes place through chaotization of an initially standing fluxon periodic orbit. Detailed investigation of the Floquet multipliers of these orbits shows that, depending on the depinning parameters (either the driving amplitude or the phase shift between harmonics), the chaotization process can take place either along the period-doubling scenario or due to the type I intermittency.

In the present paper, we develop an accurate error estimate of the nonbonded short-range interactions for the inhomogeneous molecular systems. The root-mean-square force error is proved to be decomposed into three additive parts: the homogeneity error, the inhomogeneity error, and the correlation error. The magnitude of the inhomogeneity error, which is dominant in the interfacial regions, can be more than one order of magnitude larger than the homogeneity error. This is the reason why a standard simulation with fixed cutoff radius is either less accurate if the cutoff is too small, or wastes considerable computational effort if the cutoff is too large. Therefore, based on the error estimate, the adaptive cutoff and long-range force correction methods are proposed to boost the efficiency and accuracy of the simulation, respectively. The way of correcting the long-range contribution of pressure is also developed for the inhomogeneous system. The effectiveness of the proposed methods is demonstrated by molecular dynamics simulations of the liquid-vapor equilibrium and the nanoscale particle collision. Different roles of the homogeneity error and inhomogeneity error are also discussed.

The Lagrange-mesh method is a powerful method to solve eigenequations written in configuration space. It is very easy to implement and very accurate. Using a Gauss quadrature rule, the method requires only the evaluation of the potential at some mesh points. The eigenfunctions are expanded in terms of regularized Lagrange functions which vanish at all mesh points except one. It is shown that this method can be adapted to solve eigenequations written in momentum space, keeping the convenience and the accuracy of the original technique. In particular, the kinetic operator is a diagonal matrix. Observables and wave functions in both configuration space and momentum space can also be easily computed with good accuracy using only eigenfunctions computed in the momentum space. The method is tested with Gaussian and Yukawa potentials, requiring, respectively, a small and a large mesh to reach convergence. Corresponding wave functions in both spaces are compared with each other using the Fourier transform.

Certain types of plasma waves are known to become parametrically unstable under specific plasma conditions, in which the pump wave will decay into several daughter waves with different wavenumbers and frequencies. In the past, the related plasma instabilities have been treated analytically for various parameter regimes and by use of various numerical methods, yet the oblique propagation with respect to the background magnetic field has rarely been dealt with in two dimensions, mainly because of the high computational demand. Here we present a hybrid-simulation study of the parametric decay of a moderately oblique Alfvén wave having elliptical polarization. It is found that such a compressive wave can decay into waves with higher and lower wavenumbers than the pump.

We present experimental results for the penetration of a solid sphere when released onto wet sand. We show, by measuring the final penetration depth, that the cohesion induced by the water can result in either a deeper or shallower penetration for a given release height compared to dry granular material. Thus the presence of water can either lubricate or stiffen the granular material. By assuming the shear rate is proportional to the impact velocity and using the depth-averaged stopping force in calculating the shear stress, we derive effective viscosities for the wet granular materials.

Many driven threshold systems display a spectrum of avalanche event sizes, often characterized by power-law scaling. An important problem is to compute probabilities of the largest events (“Black Swans”). We develop a data-driven approach to the problem by transforming to the event index frame, and relating this to Shannon information. For earthquakes, we find the 12-month probability for magnitude $m>6$ earthquakes in California increases from about 30$\%$ after the last event, to 40$\%$–50$\%$ prior to the next one.

Glass transition in thin (1–200 nm thick) spin-cast polystyrene films on silicon surfaces is probed by ellipsometry in a controlled vacuum environment. A temperature-modulated modification of the method is used alongside a traditional linear temperature scan. A clear glass transition is detected in films with thicknesses as low as 1–2 nm. The glass transition temperature ($T_g$) shows no substantial dependence on thickness for coatings greater than 20 nm. Thinner films demonstrate moderate $T_g$ depression achieving 18 K for thicknesses 4–7 nm. Less than 4 nm thick samples are excluded from the $T_g$ comparison due to significant thickness nonuniformity (surface roughness). The transition in 10–20 nm thick films demonstrates excessive broadening. For some samples, the broadened transition is clearly resolved into two separate transitions. The thickness dependence of the glass transition can be well described by a simple 2-layer model. It is also shown that $T_g$ depression in 5 nm thick films is not sensitive to a wide range of experimental factors including molecular weight characteristics of the polymer, specifications of solvent used for spin casting, substrate composition, and pretreatment of the substrate surface.

Many biological, geophysical, and technological systems involve the transport of a resource over a network. In this paper, we present an efficient method for calculating the exact quantity of the resource in each part of an arbitrary network, where the resource is lost or delivered out of the network at a given rate, while being subject to advection and diffusion. The key conceptual step is to partition the resource into material that does or does not reach a node over a given time step. As an example application, we consider resource allocation within fungal networks, and analyze the spatial distribution of the resource that emerges as such networks grow over time. Fungal growth involves the expansion of fluid filled vessels, and such growth necessarily involves the movement of fluid. We develop a model of delivery in growing fungal networks, and find good empirical agreement between our model and experimental data gathered using radio-labeled tracers. Our results lead us to suggest that in foraging fungi, growth-induced mass flow is sufficient to account for long-distance transport, if the system is well insulated. We conclude that active transport mechanisms may only be required at the very end of the transport pathway, near the growing tips.

Nuclear magnetic resonance (NMR) diffusion experiments offer a unique opportunity to study boundaries restricting the diffusion process. In a recent Letter [Phys. Rev. Lett. 107, 048102 (2011)], we introduced the idea and concept that such diffusion experiments can be interpreted as NMR imaging experiments. Consequently, images of closed pores, in which the spins diffuse, can be acquired. In the work presented here, an in-depth description of the diffusion pore imaging technique is provided. Image artifacts due to gradient profiles of finite duration, field inhomogeneities, and surface relaxation are considered. Gradients of finite duration lead to image blurring and edge enhancement artifacts. Field inhomogeneities have benign effects on diffusion pore images, and surface relaxation can lead to a shrinkage and shift of the pore image. The relation between boundary structure and the imaginary part of the diffusion weighted signal is analyzed, and it is shown that information on pore coherence can be obtained without the need to measure the phase of the diffusion weighted signal. Moreover, it is shown that quite arbitrary gradient profiles can be used for diffusion pore imaging. The matrices required for numerical calculations are stated and provided as supplemental material.

Sixty years ago, it was observed that any independent and identically distributed (i.i.d.) random variable would produce a pattern of peak-to-peak sequences with, on average, three events per sequence. This outcome was employed to show that randomness could yield, as a null hypothesis for animal populations, an explanation for their apparent 3-year cycles. We show how we can explicitly obtain a universal distribution of the lengths of peak-to-peak sequences in time series and that this can be employed for long data sets as a test of their i.i.d. character. We illustrate the validity of our analysis utilizing the peak-to-peak statistics of a Gaussian white noise. We also consider the nearest-neighbor cluster statistics of point processes in time. If the time intervals are random, we show that cluster size statistics are identical to the peak-to-peak sequence statistics of time series. In order to study the influence of correlations in a time series, we determine the peak-to-peak sequence statistics for the Langevin equation of kinetic theory leading to Brownian motion. To test our methodology, we consider a variety of applications. Using a global catalog of earthquakes, we obtain the peak-to-peak statistics of earthquake magnitudes and the nearest neighbor interoccurrence time statistics. In both cases, we find good agreement with the i.i.d. theory. We also consider the interval statistics of the Old Faithful geyser in Yellowstone National Park. In this case, we find a significant deviation from the i.i.d. theory which we attribute to antipersistence. We consider the interval statistics using the AL index of geomagnetic substorms. We again find a significant deviation from i.i.d. behavior that we attribute to mild persistence. Finally, we examine the behavior of Standard and Poor's 500 stock index's daily returns from 1928–2011 and show that, while it is close to being i.i.d., there is, again, significant persistence. We expect that there will be many other applications of our methodology both to interoccurrence statistics and to time series.

A kinetic theory of the expansion into a vacuum of a plasma thin foil with initially a hot and a cold Maxwellian electron population is examined with a one-dimensional kinetic code. Whereas hot electrons always lose energy to expanding ions, cold electrons can either gain or lose energy depending on the initial temperature and density ratios and on time. When the cold electrons’ density is not too large, they experience initially an adiabatic compression by the electric field associated with the rarefaction wave. The corresponding temperature increase can be as large as a factor of a few tens. Later on, as expected, the cold electrons eventually lose energy to the expansion. When cold electrons are numerically dominant, a rarefaction shock appears during the first phase of the expansion. Hot electrons cool down faster than cold electrons, thus reducing the effective temperature ratio. Furthermore, the amplitude of the rarefaction shock and the dip that it causes on the ion velocity spectrum tend to be smoothed out by the expansion.