We investigate a directed polymer in random media with an attractive defect at the center of the one-dimensional substrate. Without the defect, the end to end distance $\Delta x$ of the polymer follows $\Delta x\sim t^{1/z}$, with $z=3/2$ and $t$ is the polymer length. When the defect strength $ϵ$ is weak, its contribution to $\Delta x$ is negligible. If $ϵ\ge {ϵ}_c$, then $\Delta x$ approaches a finite value $\Delta x_{\text{sat}}\left(ϵ\right)$ in large $t$ limit, and we find $\Delta x_{\text{sat}}\sim {\left(ϵ-{ϵ}_c\right)}^{-\delta }$, with $\delta \approx 3.0$. Such transition is related to the queuing phenomena of the asymmetric simple exclusion process. The polymer energy fluctuation is also discussed.

The influences of noise flatness and friction coefficient on the long-time behavior of the first two moments and the correlation function for the output signal of a harmonic oscillator with fluctuating frequency subjected to an external periodic force are considered. The colored fluctuations of the oscillator frequency are modeled as a trichotomous noise. The study is a follow up of the previous investigation of a stochastic oscillator [Phys. Rev. E 78, 031120 (2008)], where the connection between the occurrence of energetic instability and stochastic multiresonance is established. Here we report some unexpected results not considered in the previous work. Notably, we have found a nonmonotonic dependence of several stochastic resonance characteristics such as spectral amplification, variance of the output signal, and signal-to-noise ratio on the friction coefficient and on the noise flatness. In particular, in certain parameter regions spectral amplification exhibits a resonancelike enhancement at intermediate values of the friction coefficient.

We simulate directed site percolation on two lattices with four spatial and one timelike dimensions (simple and body-centered hypercubic in space) with the standard single cluster spreading scheme. For efficiency, the code uses the same ingredients (hashing, histogram reweighing, and improved estimators) as described by Grassberger [Phys. Rev. E 67, 036101 (2003)]. Apart from providing the most precise estimates for $p_c$ on these lattices, we provide a detailed comparison with the logarithmic corrections calculated by [Janssen and Stenull [Phys. Rev. E 69, 016125 (2004)]. Fits with the leading logarithmic terms alone would give estimates of the powers of these logarithms which are too big by typically 50%. When the next-to-leading terms are included, each of the measured quantities (the average number of sites wetted at time $t$, their average distance from the seed, and the probability of cluster survival) can be fitted nearly perfectly. But these fits would not be mutually consistent. With a consistent set of fit parameters, one obtains still much improvement over the leading log approximation. In particular we show that there is one combination of these three observables which seems completely free of logarithmic terms.

In analogy to gas-dynamical detonation waves, which consist of a shock with an attached exothermic reaction zone, we consider herein nonlinear traveling wave solutions to the hyperbolic (“inviscid”) continuum traffic equations. Generic existence criteria are examined in the context of the Lax entropy conditions. Our analysis naturally precludes traveling wave solutions for which the shocks travel downstream more rapidly than individual vehicles. Consistent with recent experimental observations from a periodic roadway [Y. Sugiyama et al., N. J. Phys. 10, 033001 (2008)], our numerical calculations show that nonlinear traveling waves are attracting solutions, with the time evolution of the system converging toward a wave-dominated configuration. Theoretical principles are elucidated by considering examples of traffic flow on open and closed roadways.

We show that the transition from regular to chaotic spectral statistics in interacting many-body quantum systems has an unambiguous signature in the distribution of Schmidt coefficients dynamically generated from a generic initial state, and thus limits the efficiency of the time-dependent density-matrix renormalization-group algorithm. We investigate this mechanism on the tilted Bose-Hubbard model; however the emergence of universal spectral properties allows translation of our conclusions to generic many-body quantum systems.

We discuss the emergence of a spontaneous temperature and critical current spatial modulation in current-carrying high-temperature superconducting wire. The modulation of the critical current along the wire on a scale of 3–10 mm forces a fraction of the transport current to crisscross the resistive interface between the superconducting film and normal metal stabilizer attached to it. This generates additional heat that allows such a structure to be self-sustainable. Stability and the conditions for experimental observation of this phenomenon are also discussed.

The Nikolaevskiy model for pattern formation with continuous symmetry exhibits spatiotemporal chaos with strong scale separation. Extensive numerical investigations of the chaotic attractor reveal unexpected scaling behavior of the long-wave modes. Surprisingly, the computed amplitude and correlation time scalings are found to differ from the values obtained by asymptotically consistent multiple-scale analysis. However, when higher-order corrections are added to the leading-order theory of Matthews and Cox, the anomalous scaling is recovered.

The projection operator formalism yields a time evolution equation for the time correlation function $U_n\left(t\right)$ of the chaotic modes of interest in terms of the memory function ${\Gamma }_n\left(t\right)$. On the assumption of similarity between $U_n\left(t\right)$ and ${\Gamma }_n\left(t\right)$, this equation leads to a closed equation for $U_n\left(t\right)$, which yields the asymptotic behavior of the time correlation function $U_n\left(t\right)$ and the corresponding power spectrum $I_n\left(\omega \right)$ analytically. Thus it turns out that the time correlation function takes the algebraic form $1/\left(1+t^2\right)$ for $t\to 0$ as predicted previously, and can be classified into three decay forms for $t\to \infty$ according to the wave number $k_n$: the exponential decay $e^{-t}$, the oscillatory exponential decay $e^{-t}\text{cos}t$, and the oscillatory power-law decay $t^{-3/2}\text{cos}t$. All the corresponding power spectra form a dual structure which is Lorentzian as $\omega \to 0$ and decays exponentially as $\omega \to \infty$. In the entire domain $0\le t<\infty$, solutions to the closed equation are quite consistent with the numerical results for small $k_n$, while they are consistent with those for large $k_n$, except for the phase. In the case that the integral time scale of $U_n\left(t\right)$ is equal to that of ${\Gamma }_n\left(t\right)$, the closed equation is identical to the direct interaction approximation equation for fluid turbulence in the limit $k_n\to \infty$.

The nonlinear convective regimes in multilayer system air-ethylene glycol-fluorinert FC75 heated from below under the joint action of buoyant and thermocapillary mechanisms of instability are investigated. The periodic boundary conditions on the lateral boundaries are considered. It is found that the competition of both mechanisms of instability may lead to the development of specific types of flow: buoyant-thermocapillary traveling wave and pulsating traveling wave.

We use optical interferometry to study the propagation of femtosecond laser pulses in gases. We show the measurements of propagation in a nitrogen gas jet and we compare the results with propagation in He under the same irradiation conditions. We find that in the case of nitrogen, the detailed temporal structure of the laser pulse can be tracked and visualized by measuring the phase and the resulting electron-density map. A dramatically different behavior occurs in He gas jets, where no details of the temporal structure of the laser pulse are visible. These observations are explained in terms of the ionization dynamics of nitrogen compared to helium. These circumstances make ${\text{N}}_2$ gas sensitive to variations in the electric field and, therefore, allow the laser-pulse temporal and spatial structures to be visualized in detail.

Exact radiation boundary conditions on the surface of a sphere are presented for the single-particle time-dependent Schrödinger equation with a localized interaction. With these boundary conditions, numerical computations of spatially unbounded outgoing wave solutions can be restricted to the finite volume of a sphere. The boundary conditions are expressed in terms of the free-particle Green’s function for the outside region. The Green’s function is analytically calculated by an expansion in spherical harmonics and by the method of Laplace transformation. For each harmonic number a discrete boundary condition between the function values at adjacent radial grid points is obtained. The numerical method is applied to quantum tunneling through a spherically symmetric potential barrier with different angular-momentum quantum numbers $l$. Calculations for $l=0$ are compared to exact theoretical results.

Phase-separation fronts leave in their wakes morphologies that are substantially different from the morphologies formed in homogeneous phase separation. In this paper we focus on fronts in binary mixtures that are enslaved phase-separation fronts, i.e., fronts that follow in the wake of a control-parameter front. In the one-dimensional case, which is the focus of this paper, the formed morphology is deceptively simple: alternating domains of a regular size. However, determining the size of these domains as a function of the front speed and other system parameters is a nontrivial problem. We present an analytical solution for the case where no material is deposited ahead of the front and numerical solutions and scaling arguments for more general cases. Through these enslaved phase-separation fronts large domains can be formed that are practically unattainable in homogeneous one-dimensional phase separation.

We present an efficient variance-reduced particle simulation technique for solving the linearized Boltzmann transport equation in the relaxation-time approximation used for phonon, electron, and radiative transport, as well as for kinetic gas flows. The variance reduction is achieved by simulating only the deviation from equilibrium. We show that in the limit of small deviation from equilibrium of interest here, the proposed formulation achieves low relative statistical uncertainty that is also independent of the magnitude of the deviation from equilibrium, in stark contrast to standard particle simulation methods. Our results demonstrate that a space-dependent equilibrium distribution improves the variance reduction achieved, especially in the collision-dominated regime where local equilibrium conditions prevail. We also show that by exploiting the physics of relaxation to equilibrium inherent in the relaxation-time approximation, a very simple collision algorithm with a clear physical interpretation can be formulated.

We study the spreading of a quantum-mechanical wave packet in a tight-binding model with a noisy potential and analyze the emergence of classical diffusion from the quantum dynamics due to decoherence. We consider a finite correlation time of the noisy environment and treat the system by utilizing the separation of fast (dephasing) and slow (diffusion) processes. We show that classical diffusive behavior emerges at long times and we calculate analytically the dependence of the classical diffusion coefficient on the noise magnitude and correlation time. This method provides a general solution to this problem for arbitrary conditions of the noisy environment. The calculation can be done in any dimension, but we demonstrate it in one dimension for clarity of representation. The results are relevant to a large variety of physical systems, from electronic transport in solid-state physics to light transmission in optical devices, diffusion of excitons, and quantum computation.

The Boltzmann’s entropy of a continuous Markov process, in local thermal equilibrium, in contact with a reservoir at temperature $T$, is analyzed. Assuming that the corresponding Fokker-Planck equation has constant coefficients and satisfies detailed balance, an equation for the entropy density is derived, from which it is possible to obtain expressions for the transport coefficients as functions of the diffusion matrix. Expressions for the entropy production terms of the system and of the combination of system plus reservoir are obtained. Known relations among transport coefficients are derived. The multicomponent case is also analyzed and the Prigogine theorem of minimum entropy production is derived in the context of reaction diffusion systems. The derivations presented in this paper are proposed as a framework for a deeper understanding of concepts used in nonequilibrium diffusion systems.

It is known that when the steady state of a one-dimensional multispecies system, which evolves via a random-sequential updating mechanism, is written in terms of a linear combination of Bernoulli shock measures with random-walk dynamics, it can be equivalently expressed as a matrix-product state. In this case the quadratic algebra of the system always has a two-dimensional matrix representation. Our investigations show that this equivalence exists at least for the systems with deterministic sublattice-parallel update. In this paper we consider the totally asymmetric simple exclusion process on a finite lattice with open boundaries and sublattice-parallel update as an example.

With Monte Carlo methods, we simulate the critical domain-wall dynamics of model B, taking the two-dimensional Ising model as an example. In the macroscopic short-time regime, a dynamic scaling form is revealed. Due to the existence of the quasirandom walkers, the magnetization shows intrinsic dependence on the lattice size $L$. An exponent which governs the $L$ dependence of the magnetization is measured to be $\sigma =0.243\left(8\right)$.

We present a detailed analysis of a free surface-saturated liquid-granular mixture flowing over a static loose bed of grains, where the coexistence of layers dominated by collisional and frictional interactions among particles was observed. Kinetic theory was applied to the flow described above and it proved suitable for describing a realistic behavior of the collisional layers, although it failed to interpret the regions of the flow domain dominated by the frictional contacts. The paper provides a conceptual scheme with which to overcome this problem by focusing on the mechanisms governing the transition from the frictional to the collisional regime. In particular we observed that in highly concentrated flows the transition layer exhibits a typical intermittency of the dominating rheological regime, switching alternately from the frictional to the collisional one. By filtering the velocity signal, we introduced an intermittency function that made it possible to extend the validity of the equations derived from dense gas analogy, typical of the collisional regimes, also in the intermittent phase of the flow. Owing to the small values of the Stokes number, in the application of the kinetic theory we accounted for the possible variation of the elastic restitution coefficient along the flow depth.

Our quasielastic neutron-scattering experiments and molecular-dynamics simulations probing surface water on rutile $\left({\text{TiO}}_2\right)$ have demonstrated that a sufficiently high hydration level is a prerequisite for the temperature-dependent crossover in the nanosecond dynamics of hydration water. Below the monolayer coverage of mobile surface water, a weak temperature dependence of the relaxation times with no apparent crossover is observed. We associate the dynamic crossover with interlayer jumps of the mobile water molecules, which become possible only at a sufficiently high hydration level.

Motivated by its relevance to various types of dynamical behavior of network systems, the maximum eigenvalue ${\lambda }_A$ of the adjacency matrix $A$ of a network has been considered and mean-field-type approximations to ${\lambda }_A$ have been developed for different kinds of networks. Here $A$ is defined by $A_{ij}=1$ $\left(A_{ij}=0\right)$ if there is (is not) a directed network link to $i$ from $j$. However, in at least two recent problems involving networks with heterogeneous node properties (percolation on a directed network and the stability of Boolean models of gene networks), an analogous but different eigenvalue problem arises, namely, that of finding the largest eigenvalue ${\lambda }_Q$ of the matrix $Q$, where $Q_{ij}=q_i{A}_{ij}$ and the “bias” $q_i$ may be different at each node $i$. (In the previously mentioned percolation and gene network contexts, $q_i$ is a probability and so lies in the range $0\le q_i\le 1$.) The purposes of this paper are to extend the previous considerations of the maximum eigenvalue ${\lambda }_A$ of $A$ to ${\lambda }_Q$, to develop suitable analytic approximations to ${\lambda }_Q$, and to test these approximations with numerical experiments. In particular, three issues considered are (i) the effect of the correlation (or anticorrelation) between the value of $q_i$ and the number of links to and from node $i$, (ii) the effect of correlation between the properties of two nodes at either end of a network link (“assortativity”), and (iii) the effect of community structure allowing for a situation in which different $q$ values are associated with different communities.