We study the continuous absorbing-state phase transition in the one-dimensional pair contact process with diffusion (PCPD). In previous studies [Dickman and de Menezes, Phys. Rev. E 66, 045101(R) (2002)], the critical point moment ratios of the order parameter showed anomalous behavior, growing with system size rather than taking universal values, as expected. Using the quasistationary simulation method we determine the moments of the order parameter up to fourth order at the critical point, in systems of up to 40 960 sites. Due to strong finite-size effects, the ratios converge only for large system sizes. Moment ratios and associated order-parameter histograms are compared with those of directed percolation. We also report an improved estimate $[p_c=0.077092\left(1\right)]$ for the location of the critical point in the nondiffusive pair contact process.

We study an active random walker model in which a particle’s motion is determined by a self-generated field. The field encodes information about the particle’s path history. This leads to either self-attractive or self-repelling behavior. For self-repelling behavior, we find a phase transition in the dynamics: when the coupling between the field and the walker exceeds a critical value, the particle’s behavior changes from renormalized diffusion to one characterized by a diverging diffusion coefficient. The dynamical behavior for all cases is surprisingly independent of dimension and of the noise amplitude.

This paper discusses concepts of stochastic resonance and noise-induced synchronization in a bistable oscillator subject to both periodic signal and noise. We demonstrate that stochastic resonance is not directly correlated with the matching of the signal frequency and the switching rate. The phenomena of stochastic resonance and noise-induced synchronization are the limiting cases of noise-induced transitions, and the spectral response heavily depends on the input signal-to-noise ratio. The lower and upper bounds of noise intensity allowing synchronization are found as functions of the system’s parameters.

We report on Monte Carlo simulations of continuum percolation thresholds, by implementing highly efficient algorithms for very large samples. Our work, which includes percolation of hyperspheres, hypercubes, and boxes, in various dimensions, sizes, and shapes, has confirmed the expected dependence of the threshold on $V_{\mathrm{ex}}$, the total excluded volume, and on $B_c$, the average number of bonds per site. We have further confirmed that $V_{\mathrm{ex}}=B_c$, and that $B_c$ is dependent on the objects shape, for which we offer a possible explanation. In particular we find that, counterintuitively, one can have $B_c<1$, as we have found for hyperspheres of dimension $⩾12$. From our many results for differently sized hyperspheres, we were also able to derive the correlation length exponent $\nu$ solely from the behavior of the thresholds using finite-size scaling.

Numerous theoretical and numerical works have been devoted to the study of the algebraic decrease at large times of the velocity autocorrelation function of particles in a fluid. The derivation of this behavior, the so-called long-time tail, generally based on linearized hydrodynamics, makes no reference to any specific characteristic of the particle interactions. However, in the literature doubts have been expressed about the possibility that by numerical simulations the long-time tail can be observed in the whole fluid phase domain of systems in which the particles interact by soft-core and attractive pair potentials. In this work, extensive and accurate molecular-dynamics simulations establish that the predicted long-time tail of the velocity autocorrelation function exists in a low-density fluid of particles interacting by a soft-repulsive potential and near the liquid-gas critical point of a Lennard-Jones system. These results contribute to the confirmation that the algebraic decay of the velocity autocorrelation function is universal in these fluid systems.

We study a restricted solid-on-solid model involving deposition and evaporation with probabilities $p$ and $1-p$, respectively, in one-dimensional substrates. It presents a crossover from Edwards-Wilkinson (EW) to Kardar-Parisi-Zhang (KPZ) scaling for $p\approx 0.5$. The associated KPZ equation is analytically derived, exhibiting a coefficient $\lambda$ of the nonlinear term proportional to $q\equiv p-1∕2$, which is confirmed numerically by calculation of tilt-dependent growth velocities for several values of $p$. This linear $\lambda -q$ relation contrasts to the apparently universal parabolic law obtained in competitive models mixing EW and KPZ components. The regions where the interface roughness shows pure EW and KPZ scaling are identified for $0.55⩽p⩽0.8$, which provides numerical estimates of the crossover times $t_c$. They scale as $t_c\sim {\lambda }^{-\varphi }$ with $\varphi =4.1\pm 0.1$, which is in excellent agreement with the theoretically predicted universal value $\varphi =4$ and improves previous numerical estimates, which suggested $\varphi \approx 3$.

We study the undulations instability, also known as the Helfrich-Hurault or layers buckling effect, in a cholesteric liquid crystal confined between two parallel plates and caused by an electric field applied along the normal to layers. The cholesteric pitch is much smaller than the cell thickness but sufficiently large for optical study. The three-dimensional patterns of the undulating layers in the bulk and at the surfaces of the cells are determined by fluorescence confocal polarizing microscopy. We demonstrate that the finite surface anchoring at the bounding plates plays a crucial role in the system behavior both near and well above the undulations threshold. The displacement of the layers immediately above the undulation threshold is much larger than the value expected from the theories that assume an infinitely strong surface anchoring. We describe the experimentally observed features by taking into account the finite surface anchoring at the bounding plates and using Lubensky-de Gennes coarse-grained elastic theory of cholesteric liquid crystals. Fitting the data allows us to determine the polar anchoring coefficient $W_p$ and shows that $W_p$ varies strongly with the type of substrates. As the applied field increases well above the threshold value $E_c$, the layers profile changes from sinusoidal to the sawtooth one. The periodicity of distortions increases through propagation of edge dislocations in the square lattice of the undulations pattern. At $E\approx 1.9E_c$ a phenomenon is observed: the two-dimensional square lattice of undulations transforms into the one-dimensional periodic stripes. The stripes are formed by two sublattices of defect walls of parabolic shape. The main reason for the structure is again the finite surface anchoring, as the superposition of parabolic walls allows the layers to combine a significant tilt in the bulk of the cell with practically unperturbed orientation of layers near the bounding plates.

We investigate the adaptation of the time headways in car-following models as a function of the local velocity variance, which is a measure of the inhomogeneity of traffic flow. We apply this mechanism to several car-following models and simulate traffic breakdowns in open systems with an on-ramp as bottleneck and in a closed ring road. Single-vehicle data and one-minute aggregated data generated by several virtual detectors show a semiquantitative agreement with microscopic and flow-density data from the Dutch freeway A9. This includes the observed distributions of the net time headways for free and congested traffic, the velocity variance as a function of density, and the fundamental diagram. The modal value of the time headway distribution is shifted by a factor of about 2 under congested conditions. Macroscopically, this corresponds to the capacity drop at the transition from free to congested traffic. The simulated fundamental diagram shows free, synchronized, and jammed traffic, and a wide scattering in the congested traffic regime. We explain this by a self-organized variance-driven process that leads to the spontaneous formation and decay of long-lived platoons even for a deterministic dynamics on a single lane.

The internet structure is extremely complex. The positive-feedback preference (PFP) model is a recently introduced internet topology generator. The model uses two generic algorithms to replicate the evolution dynamics observed on the internet historic data. The phenomenological model was originally designed to match only two topology properties of the internet, i.e., the rich-club connectivity and the exact form of degree distribution, whereas numerical evaluation has shown that the PFP model accurately reproduces a large set of other nontrivial characteristics as well. This paper aims to investigate why and how this generative model captures so many diverse properties of the internet. Based on comprehensive simulation results, the paper presents a detailed analysis on the exact origin of each of the topology properties produced by the model. This work reveals how network evolution mechanisms control the obtained topology properties and it also provides insights on correlations between various structural characteristics of complex networks.

We investigate the robustness against both random and targeted node removal of networks in which $P\left(k\right)$, the distribution of nodes with degree $k$, is a multimodal distribution, $P\left(k\right)\propto {\sum }_{i=1}^m{a}^{-(i-1)}\delta (k-k_i)$ with $k_i\propto b^{-(i-1)}$ and Dirac’s delta function $\delta \left(x\right)$. We refer to this type of network as a scale-free multimodal network. For $m=2$, the network is a bimodal network; in the limit $m$ approaches infinity, the network models a scale-free network. We calculate and optimize the robustness for given values of the number of modes $m$, the total number of nodes $N$, and the average degree $⟨k⟩$, using analytical formulas for the random and targeted node removal thresholds for network collapse. We find, when $N\gg 1$, that (i) the robustness against random and targeted node removal for this multimodal network is controlled by a single combination of variables, $N^{1∕(m-1)}$, (ii) the robustness of the multimodal network against targeted node removal decreases rapidly when the number of modes becomes larger than a critical value that is of the order of $\ln N$, and (iii) the values of exponent ${\lambda }^{\mathrm{opt}}$ that characterizes the scale-free degree distribution of the multimodal network that maximize the robustness against both random and targeted node removal fall between 2.5 and 3.

We study the dynamics of the Olami-Feder-Christensen (OFC) model of earthquakes, focusing on the behavior of sequences of epicenters regarded as a growing complex network. Besides making a detailed and quantitative study of the effects of the borders (the occurrence of epicenters is dominated by a strong border effect which does not scale with system size), we examine the degree distribution and the degree correlation of the graph. We detect sharp differences between the conservative and nonconservative regimes of the model. Removing border effects, the conservative regime exhibits a Poisson-like degree statistics and is uncorrelated, while the nonconservative has a broad power-law-like distribution of degrees (if the smallest events are ignored), which reproduces the observed behavior of real earthquakes. In this regime the graph has also an unusually strong degree correlation among the vertices with higher degree, which is the result of the existence of temporary attractors for the dynamics: as the system evolves, the epicenters concentrate increasingly on fewer sites, exhibiting strong synchronization, but eventually spread again over the lattice after a series of sufficiently large earthquakes. We propose an analytical description of the dynamics of this growing network, considering a Markov process network with hidden variables, which is able to account for the mentioned properties.

Signals obtained in land seismic surveys are usually contaminated with coherent noise, among which the ground roll (Rayleigh surface waves) is of major concern for it can severely degrade the quality of the information obtained from the seismic record. This paper presents an optimized filter based on the Karhunen-Loève transform for processing seismic images contaminated with ground roll. In this method, the contaminated region of the seismic record, to be processed by the filter, is selected in such way as to correspond to the maximum of a properly defined coherence index. The main advantages of the method are that the ground roll is suppressed with negligible distortion of the remnant reflection signals and that the filtering procedure can be automated. The image processing technique described in this study should also be relevant for other applications where coherent structures embedded in a complex spatiotemporal pattern need to be identified in a more refined way. In particular, it is argued that the method is appropriate for processing optical coherence tomography images whose quality is often degraded by coherent noise (speckle).

We show that characteristic features of noise-induced spatiotemporal patterns in excitable media can be effectively controlled by applying delayed feedback. Actually, by variation of the time delay and of the strength of the feedback one can deliberately change both spatial and temporal coherence, as well as adjust the characteristic time scales.

Classically, large-scale forced turbulence is characterized by a transfer of energy from large to small scales via nonlinear interactions. We have investigated the changes in this energy transfer process in broadband forced turbulence where an additional perturbation of flow at smaller scales is introduced. The modulation of the energy dynamics via the introduction of forcing at smaller scales occurs not only in the forced region but also in a broad range of length scales outside the forced bands due to nonlocal triad interactions. Broadband forcing changes the energy distribution and energy transfer function in a characteristic manner leading to a significant modulation of the turbulence. We studied the changes in this transfer of energy when changing the strength and location of the small-scale forcing support. The energy content in the larger scales was observed to decrease, while the energy transport power for scales in between the large and small scale forcing regions was enhanced. This was investigated further in terms of the detailed transfer function between the triad contributions and observing the long-time statistics of the flow. The energy is transferred toward smaller scales not only by wave numbers of similar size as in the case of large-scale forced turbulence, but by a much wider extent of scales that can be externally controlled.

We investigate a class of reactive advection-diffusion problems motivated by an ecological mixing process. We use analytical and numerical methods to determine reaction rates between two initially distinct scalar point masses that are separated from one another by a third (nonreactive) scalar. The scalars are stirred by a single two-dimensional vortex in a variety of geometrical configurations. We show that the aggregate second-order reaction rate in the low-concentration limit is enhanced by the instantaneous stirring processes, relative to the rate predicted by an equivalent eddy diffusivity. The peak reaction rate grows as $P^{1∕3}$, and the time to reach the peak decreases as $P^{-2∕3}$, where $P$ is the Péclet number. The results of this study have important implications not only for ecological modeling, but for the general understanding of turbulent reactive flows.

We investigate the nature of the ordered phase for a model of colloidal particles confined within a quasi-one-dimensional (Q1D) strip between two parallel boundaries, or walls, separated a distance $D$ in two dimensions (2D). Using Monte Carlo simulations we find that at densities typical of the bulk 2D triangular solid the order in the D1D strip is determined by the nature of the boundaries. While the order is enhanced for a suitably corrugated boundary potential, for a uniformly repulsive smooth boundary potential ordering normal to the walls is enhanced (“layering”), but destroyed parallel to the wall.

Characterization of the electrical properties of the DNA bases (adenine, cytosine, guanine, and thymine), in addition to building the basic knowledge on these fundamental constituents of a DNA, is a crucial step in developing a DNA sequencing technology. We present a first-principles study of the current-voltage characteristics of nucleotidelike molecules of the DNA bases, placed in a $1.5\mathrm{nm}$ gap formed between gold nanoelectrodes. The quantum transport calculations in the tunneling regime are shown to vary strongly with the electrode-molecule geometry and the choice of the density-functional theory exchange-correlation functionals. Analysis of the results in the zero-bias limit indicates that distinguishable current-voltage characteristics of different DNA bases are dominated by the geometrical conformations of the bases and nanoelectrodes.

The dynamics of a kicked quantum mechanical wave packet at a quantum resonance is studied in the framework of Floquet analysis. It is seen how a directed current can be created out of a homogeneous initial state at certain resonances in an asymmetric potential. The almost periodic parameter dependence of the current is found to be connected with level crossings in the Floquet spectrum.

For many years quasilinear renormalization has been applied to numerous problems in turbulent transport. This scheme relies on the localization hypothesis to derive a linear transport equation from a simplified stochastic description of the underlying microscopic dynamics. However, use of the localization hypothesis narrows the range of transport behaviors that can be captured by the renormalized equations. In this paper, we construct a renormalization procedure that manages to avoid the localization hypothesis completely and produces renormalized transport equations, expressed in terms of fractional differential operators, that exhibit much more of the transport phenomenology observed in nature. This technique provides a first step toward establishing a rigorous link between the microscopic physics of turbulence and the fractional transport models proposed phenomenologically for a wide variety of turbulent systems such as neutral fluids or plasmas.

Propagation and absorption of electromagnetic waves with electron cyclotron resonance (ECR) frequency are investigated for the case of inhomogeneously magnetized plasmas, when the left-hand polarized wave (LHPW) is selectively launched. The LHPW with axisymmetric-azimuthal and second-order radial modes is absorbed near the ECR point at any radial position, which is caused by the polarization reversal to the right-hand polarized wave. On the other hand, it is clarified that the LHPW with fundamental radial mode penetrates the ECR point without polarization reversal. In addition, it is theoretically suggested that polarization reversal can partially occur in the plasma column for the case of nonaxisymmetric modes.