Using the quasistatic approximation, we show that in a subdiffusion-reaction system with arbitrary nonzero values of subdiffusion coefficients, the reaction front $x_f\left(t\right)$ evolves in time as $x_f\left(t\right)=K{t}^{\alpha ∕2}$, with $\alpha$ being the subdiffusion parameter and $K$ being controlled by the subdiffusion coefficients. To check the correctness of our analysis, we compare approximate analytical solutions of the subdiffusion-reaction equations with the numerical ones.

An analysis to describe statistical properties of weighted complex networks is proposed. Effective structures of weighted networks depend on how strongly weights $w$ are paid attention or which weights are relevant to the network problem. Defining the metaweight $w^q$ with a real parameter $q$, we characterize systematically weighted complex networks depending on the level of importance of weights. It is found that power-law distribution functions $R_q\left[s\left(q\right)\right]$ of metastrengths $s\left(q\right)$ defined by $s_i\left(q\right)={\sum }_j{w}_{ij}^q$, where $i$ and $j$ denote node indices for any $q$ are characterized by only three exponents if the weight distribution is independent of network topology. We also examine the validity of our analytical arguments and the meaning of power-law forms of $R_q\left[s\left(q\right)\right]$ for different $q$ values by illustrating some examples.

We study the effect of time-delayed feedback control and Gaussian white noise on the spatiotemporal charge dynamics in a semiconductor superlattice. The system is prepared in a regime where the deterministic dynamics is close to a global bifurcation, namely, a saddle-node bifurcation on a limit cycle. In the absence of control, noise can induce electron charge front motion through the entire device, and coherence resonance is observed. We show that with appropriate selection of the time-delayed feedback parameters the effect of coherence resonance can be either enhanced or destroyed, and the coherence of stochastic domain motion at low noise intensity is dramatically increased. Additionally, the purely delay-induced dynamics in the system is investigated, and a homoclinic bifurcation of a limit cycle is found.

We find equilibrium configurations of open and closed lines of charge on a sphere, and track them with respect to varying sphere radius. Closed lines transition from a circle to a spiral-like shape through two low-wave-number bifurcations—“baseball seam” and “twist”—which minimize Coulomb energy. The spiral shape is the unique stable equilibrium of the closed line. Other unstable equilibria arise through tip-splitting events. An open line transitions smoothly from an arc of a great circle to a spiral as the sphere radius decreases. Under repulsive potentials with faster-than-Coulomb power-law decay, the spiral is tighter in initial stages of sphere shrinkage, but at later stages of shrinkage the equilibria for all repulsive potentials converge on a spiral with uniform spacing between turns. Multiple stable equilibria of the open line are observed.

A consistent explanation for the abrupt appearance of the mist zone in high velocity brittle fractures is given. The dependence of the boundary on flaw sizes is calculated. For low velocity fractures a gradual mirror-mist transition is demonstrated.

In this Brief Report, the convergence of the $1∕t$ and Wang-Landau algorithms in the calculation of multidimensional numerical integrals is analyzed. Both simulation methods are applied to a wide variety of integrals without restrictions in one, two, and higher dimensions. The efficiency and accuracy of both algorithms are determined by the dynamical behavior of the errors between the exact and the calculated values of the integral. It is observed that the time dependence of the error calculated with the $1∕t$ algorithm varies as $N^{-1∕2}$ [with $N$ the number of Monte Carlo (MC) trials], in quantitative agreement with the simple sampling Monte Carlo method. In contrast, the error calculated with the Wang-Landau algorithm saturates in time, evidencing the nonconvergence of this method. The sources of error for both methods are also determined.

We show, both heuristically and numerically, that three-dimensional periodic Lorentz gases—clouds of particles scattering off crystalline arrays of hard spheres—often exhibit normal diffusion, even when there are gaps through which particles can travel without ever colliding—i.e., when the system has an infinite horizon. This is the case provided that these gaps are not “too large,” as measured by their dimension. The results are illustrated with simulations of a simple three-dimensional model having different types of diffusive regime and are then extended to higher-dimensional billiard models, which include hard-sphere fluids.

The solvation force for two-dimensional Ising strips is calculated via exact diagonalization of the transfer matrix in two cases: the symmetric case corresponds to identical surface fields and the antisymmetric case to exactly opposite surface fields. In the symmetric case the solvation force is always negative (attractive), while in the antisymmetric case the solvation force is positive (repulsive) at high temperatures and negative at low temperatures. It changes sign close to the critical wetting temperature characterizing the semi-infinite system. The properties of the solvation force are discussed, and the scaling function describing its dependence on temperature, surface field, and strip’s width is proposed.

We use Hamilton’s equations of classical mechanics to investigate the behavior of a cortical neuron on the approach to an action potential. We use a two-component dynamic model of a single neuron, due to Wilson, with added noise inputs. We derive a Lagrangian for the system, from which we construct Hamilton’s equations. The conjugate momenta are found to be linear combinations of the noise input to the system. We use this approach to consider theoretically and computationally the most likely manner in which such a modeled neuron approaches a firing event. We find that the firing of a neuron is a result of a drop in inhibition, due to a temporary increase in negative bias of the mean noise input to the inhibitory control equation. Moreover, we demonstrate through theory and simulation that, on average, the bias in the noise increases in an exponential manner on the approach to an action potential. In the Hamiltonian description, an action potential can therefore be considered a result of the exponential growth of the conjugate momenta variables pulling the system away from its equilibrium state, into a nonlinear regime.

A time-convolutionless master equation is established for describing the amide-I vibrational energy flow in a lattice of H-bonded peptide units. The dynamics is addressed within the small polaron formalism to account for the strong coupling between the amide-I vibron and the phonons describing the H-bond vibrations. Therefore, special attention is paid to characterize the influence of the amide-I relaxation on the polaron transport properties. This relaxation is modeled by assuming that each amide-I mode interacts with a bath of intramolecular normal modes whose displacements are strongly localized on the $\mathrm{C}=\mathrm{O}$ groups. It has been shown that the energy relaxation occurs over a very short time scale which prevents any significant delocalization of the polaron. At biological temperature, the polaron explores a finite region around the excited site whose size is about one or two lattice parameters. However, two regimes occur depending on whether the vibron-phonon coupling is weak or strong. For a weak coupling, the energy propagates coherently along the lattice until the polaron disappears. By contrast, for a strong coupling, a diffusive regime occurs so that the polaron explores a finite size region incoherently. In both cases, the finite polaron lifetime favors the localization of the vibron density whose amplitude decreases exponentially.

We present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each other’s basin volume. This counterintuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed interactions. We analytically show that upon continuously removing a local noninvertibility of the system, the two unstable attractors become a set of two nonattracting saddle states that are heteroclinically connected. This transition equally occurs from larger networks of unstable attractors to heteroclinic structures and constitutes a new type of singular bifurcation in dynamical systems.

A stochastic lattice gas automata model for formation of river networks is proposed. The model is based on two-dimensional lattice gas automata with three fundamental principles at each node. The water source is regarded as a fixed point where a drop of water drips every time step. This system can be treated as a memory network: the probability of water moving along a direction relies on the history of the channel segment along which water drops have moved. Last, we find that the width of the river channel and the number of channels with this width meet a scaling law when the system reaches a critical status.

We investigate the spatiotemporal coding of low amplitude inputs to a simple system of globally coupled phase oscillators with coupling function $g\left(\varphi \right)=-\sin (\varphi +\alpha )+r\sin (2\varphi +\beta )$ that has robust heteroclinic cycles (slow switching between cluster states). The inputs correspond to detuning of the oscillators. It was recently noted that globally coupled phase oscillators can encode their frequencies in the form of spatiotemporal codes of a sequence of cluster states [P. Ashwin, G. Orosz, J. Wordsworth, and S. Townley, SIAM J. Appl. Dyn. Syst. 6, 728 (2007)]. Concentrating on the case of $N=5$ oscillators we show in detail how the spatiotemporal coding can be used to resolve all of the information that relates the individual inputs to each other, providing that a long enough time series is considered. We investigate robustness to the addition of noise and find a remarkable stability, especially of the temporal coding, to the addition of noise even for noise of a comparable magnitude to the inputs.

By using finite Lyapunov exponent distributions, we get insight into both the local and global properties of a dynamical flow, including its nonhyperbolic behavior. Several distributions of finite Lyapunov exponents have been computed in two prototypical four-dimensional phase-space Hamiltonian systems. They have been computed calculating the growth rates of a set of orthogonal axes arbitrarily pointed at given intervals. We analyze how such distributions serve or not for tracing the orbit nature and local flow properties such as the unstable dimension variability, as the axes are allowed or not to tend to the largest stretching direction. The relationship between the largest and closest to zero exponent distribution is analyzed. It shows a linear dependency at short intervals, related to the number of degrees of freedom of the system. Finally, the hyperbolicity indexes, associated to the shadowing times, are calculated. They provide interesting information at very local scales, even when there are no Gaussian distributions and the values cannot be regarded as random variables.

We investigate and clarify the notion of locality as it pertains to the cascades of two-dimensional turbulence. The mathematical framework underlying our analysis is the infinite system of balance equations that govern the generalized unfused structure functions, first introduced by L’vov and Procaccia. As a point of departure we use a revised version of the system of hypotheses that was proposed by Frisch for three-dimensional turbulence. We show that both the enstrophy cascade and the inverse energy cascade are local in the sense of nonperturbative statistical locality. We also investigate the stability conditions for both cascades. We have shown that statistical stability with respect to forcing applies unconditionally for the inverse energy cascade. For the enstrophy cascade, statistical stability requires large-scale dissipation and a vanishing downscale energy dissipation. A careful discussion of the subtle notion of locality is given at the end of the paper.

This paper describes the formation of a temporary wall between two fluid streams in a microfluidic channel. Diffusion of ions from one fluid stream into a costreaming thermally responsive polymer solution is used to lower the local gelation temperature of the polymer, leading to formation of a gel wall in the center of the flow channel. The mechanisms driving either the generation or removal of the wall on its both sides are described and discussed. This wall allows well-controlled transport of particles from one stream into the other.

An energy-minimal simulation is proposed to study the patterns and mechanical properties of elastically crumpled wires in two dimensions. Our aim is to describe the behavior at the intermediate occupancy of the cavity so that its radius of gyration is varied up to one twentieth of the wire length. We tuned the bending rigidity and stretching modulus to measure the energy allocation, size-mass exponent, and the stiffness exponent. The mass exponent is shown to be constant at value $D_M=1.33$, so is the stiffness exponent $\alpha =-0.25$. But the latter varies with the plasticity parameters $s$ and ${\theta }_p$. These numerical findings agree excellently with the experimental results.

We investigate the effect of loading rate on drainage in molecularly thin films of a simple fluid made of quasispherical molecules [octamethylcyclotetrasiloxane (OMCTS)]. We find that (i) rapidly confined OMCTS retains its tendency to organize into layers parallel to the confining surfaces, and (ii) flow resistance in such layered films can be described by bulklike viscous forces if one accounts for the existence of one monolayer immobilized on each surface. The latter result is fully consistent with the recent work of Becker and Mugele, who reached a similar conclusion by analyzing the dynamics of squeeze-out fronts in OMCTS [T. Becker and F. Mugele, Phys. Rev. Lett. 91, 166104 (2003)]. Furthermore, we show that the confinement rate controls the nature of the thinning transitions: layer-by-layer expulsion of molecules in metastable, slowly confined films proceeds by a nucleation-growth mechanism, whereas deeply and rapidly quenched films are unstable and undergo thinning transitions akin to spinodal decomposition.