We observe standing waves of chemical concentration in thin layers [quasi-two-dimensional (2D)] and capillaries [three-dimensional (3D)] containing the aqueous Belousov-Zhabotinsky reaction in a reverse microemulsion stabilized by the ionic surfactant sodium bis-2-ethylhexyl sulfosuccinate (AOT) and with cyclo-octane as the continuous phase. The 3D structures are oscillatory lamellae or square-packed cylinders at high and low volume fractions, respectively, of aqueous droplets. These patterns correspond to oscillatory labyrinthine stripes and square-packed spots in the 2D configuration. Computer simulations, as well as observations in E. coli, give qualitative agreement with the observed patterns and suggest that, in contrast to Turing patterns, the structures are sensitive to the size and shape of the system.

Earthquakes are a complex spatiotemporal phenomenon, the underlying mechanism for which is still not fully understood despite decades of research and analysis. We propose and develop a network approach to earthquake events. In this network, a node represents a spatial location while a link between two nodes represents similar activity patterns in the two different locations. The strength of a link is proportional to the strength of the cross correlation in activities of two nodes joined by the link. We apply our network approach to a Japanese earthquake catalog spanning the 14-year period 1985–1998. We find strong links representing large correlations between patterns in locations separated by more than 1000 kilometers, corroborating prior observations that earthquake interactions have no characteristic length scale. We find network characteristics not attributable to chance alone, including a large number of network links, high node assortativity, and strong stability over time.

Is there a way to describe pedestrian movement with simple rules, as in a cellular automaton, but without being restricted to a cellular grid? Inspired by the natural stepwise movement of humans, we develop a model that uses local discretization on a circle around virtual pedestrians. This allows for movement in arbitrary directions, only limited by the chosen optimization algorithm and numerical resolution. The radii of the circles correspond to the step lengths of pedestrians and thus are model parameters, which must be derived from empirical observation. Therefore, we conducted a controlled experiment, collected empirical data for step lengths in relation with different speeds, and used the findings in our model. We complement the model with a simple calibration algorithm that allows reproducing known density-velocity relations, which constitutes a proof of concept. Further validation of the model is achieved by reenacting an evacuation scenario from experimental research. The simulated egress times match the values reported for the experiment very well. A new normalized measure for space occupancy serves to visualize the results.

The fact that the elements in some realistic systems are influenced by each other indirectly through a common environment has stimulated a new surge of studies on the collective behavior of coupled oscillators. Most of the previous studies, however, consider only the case of coupled periodic oscillators, and it remains unknown whether and to what extent the findings can be applied to the case of coupled chaotic oscillators. Here, using the population density and coupling strength as the tuning parameters, we explore the synchronization and quorum sensing behaviors in an ensemble of chaotic oscillators coupled through a common medium, in which some interesting phenomena are observed, including the appearance of the phase synchronization in the process of progressive synchronization, the various periodic oscillations close to the quorum sensing transition, and the crossover of the critical population density at the transition. These phenomena, which have not been reported for indirectly coupled periodic oscillators, reveal a corner of the rich dynamics inherent in indirectly coupled chaotic oscillators, and are believed to have important implications to the performance and functionality of some realistic systems.

We consider a voltage-biased nanoelectromechanical Josephson junction, where a suspended nanowire forms a superconducting weak link, in an inhomogeneous magnetic field. We show that a nonlinear coupling between the Josephson current and the magnetic field generates a Laplace force that induces a whirling motion of the nanowire. By performing an analytical and a numerical analysis, we demonstrate that at resonance, the amplitude-phase dynamics of the whirling movement presents different regimes depending on the degree of inhomogeneity of the magnetic field: time independent, periodic, and chaotic. Transitions between these regimes and attractor merging crisis are also discussed.

The structure formation of convection rolls in Maxwellian fluids that are heated from below in a Rayleigh-Bénard setup is investigated close to onset with a simple few-modes ansatz and by solving the hydrodynamic field equations with a finite-difference method. Depending on the magnitude of the viscoelastic relaxation time one can have besides stationary convection also oscillatory patterns in the form of standing or traveling waves. The existence and stability regions of these convection structures are determined. The convection behavior of the model is compared with the results of full numerical simulations. Furthermore, the effect of modulating the heating periodically in time on the stability of the quiescent conductive state of the fluid and on its convection behavior is investigated as a function of the fluid's viscoelasticity.

We present a fully nonlinear theory for dust acoustic (DA) shocks and DA solitary pulses in a strongly coupled dusty plasma, which have been recently observed experimentally by Heinrich et al. [Phys. Rev. Lett. 103, 115002 (2009)], Teng et al. [Phys. Rev. Lett. 103, 245005 (2009)], and Bandyopadhyay et al. [Phys. Rev. Lett. 101, 065006 (2008)]. For this purpose, we use a generalized hydrodynamic model for the strongly coupled dust grains, accounting for arbitrary large-amplitude dust number density compressions and potential distributions associated with fully nonlinear nonstationary DA waves. Time-dependent numerical solutions of our nonlinear model compare favorably well with the recent experimental works (mentioned above) that have reported the formation of large-amplitude nonstationary DA shocks and DA solitary pulses in low-temperature dusty plasma discharges.

A practical physically motivated interpolation formula is presented for the self-diffusion coefficient in Yukawa one-component plasmas that is valid for a wide range of inverse screening lengths and over the entire fluid region.

We introduce a between-ness-based distance metric to extract local and global information for each pair of nodes (or “vertices” used interchangeably) located in a binary network. Since this distance then superimposes a weighted graph upon such a binary network, a multiscale clustering mechanism, called data cloud geometry, is applicable to discover hierarchical communities within a binary network. This approach resolves many shortcomings of community finding approaches, which are primarily based on modularity optimization. Using several contrived and real binary networks, our community hierarchies compare favorably with results derived from a recently proposed approach based on time-scale differences of random walks and has already demonstrated significant improvements over module-based approaches, especially on the multiscale and the determination of the number of communities.

The Fortuin-Kasteleyn and heat-bath damage-spreading temperatures $T_{\text{FK}}\left(p\right)$ and $T_{\text{DS}}\left(p\right)$ are studied on random-bond Ising models of dimensions 2–5 and as functions of the ferromagnetic interaction probability $p$; the conjecture that $T_{\text{DS}}\left(p\right)\sim T_{\text{FK}}\left(p\right)$ is tested. It follows from a statement by Nishimori that in any such system, exact coordinates can be given for the intersection point between the Fortuin-Kasteleyn $T_{\text{FK}}\left(p\right)$ transition line and the Nishimori line $[p_{\text{NL,FK}},T_{\text{NL,FK}}]$. There are no finite-size corrections for this intersection point. In dimension 3, at the intersection concentration $\left[p_{\text{NL,FK}}\right]$, the damage spreading $T_{\text{DS}}\left(p\right)$ is found to be equal to $T_{\text{FK}}\left(p\right)$ to within $0.1\%$. For the other dimensions, however, $T_{\text{DS}}\left(p\right)$ is observed to be systematically a few percent lower than $T_{\text{FK}}\left(p\right)$.

We report an interesting phenomenon of noise-induced vortex reversal in a two-dimensional system of self-propelled particles (SPPs) with soft-core interactions. With the aid of forward flux sampling, we analyze the configurations along the reversal pathway and thus identify the mechanism of vortex reversal. We find that the reversal exhibits a hierarchical process: those particles at the periphery first change their motion directions, and then more inner layers of particles reverse later on. Furthermore, we calculate the dependence of the average reversal rate on noise intensity $D$ and the number $N$ of SPPs. We find that the rate decreases exponentially with the reciprocal of $D$. Interestingly, the rate varies nonmonotonically with $N$ and a local minimal rate exists for an intermediate value of $N$.

Nonlinear acoustic processes of second harmonic generation and nonlinear resonances in a diatomic granular chain (a granular phononic crystal) with static precompression are reported. The observed nonlinear self-action process which manifests itself as shifts in resonance frequencies of the chain leads to amplitude-dependent band edges: the properties of the phononic crystal change as a function of wave amplitude. Observed nonlinear effects at the band edges are exceptionally strong (self-induced attenuation and self-induced transparency) due to the peculiar frequency dependence of the attenuation in these frequency regions. The reported effects open the way for applications in wave tailoring by nonlinear phononic crystals, using amplitude-dependent processes, such as passive amplitude-dependent attenuators or amplifiers and various logical elements.

We used top-down fabrication techniques to create both an ordered hexagonal array and a disordered array of 1 $\mu$m diameter cylindrical posts in a silicon dioxide microchannel with the same number of posts per unit area. The electrophoretic mobility and dispersion coefficient of $\lambda$ DNA in each of the arrays were obtained as a function of the electric field using ensembles of DNA molecules in a double channel device that minimizes experimental artifacts. To deepen our understanding of the transport, we also used fluorescence microscopy to examine the dynamics of single DNA molecules as they interact with the arrays at a fixed value of the electric field. Based on the results of these two types of experiments, we conclude that the electrophoretic mobility is not dependent on the array order but that band broadening in the device is greater in the disordered array.

Intrinsically disordered proteins (IDPs) do not possess well-defined three-dimensional structures in solution under physiological conditions. We develop all-atom, united-atom, and coarse-grained Langevin dynamics simulations for the IDP $\alpha$-synuclein that include geometric, attractive hydrophobic, and screened electrostatic interactions and are calibrated to the inter-residue separations measured in recent single-molecule fluorescence energy transfer (smFRET) experiments. We find that $\alpha$-synuclein is disordered, with conformational statistics that are intermediate between random walk and collapsed globule behavior. An advantage of calibrated molecular simulations over constraint methods is that physical forces act on all residues, not only on residue pairs that are monitored experimentally, and these simulations can be used to study oligomerization and aggregation of multiple $\alpha$-synuclein proteins that may precede amyloid formation.

The process of stochastic Turing instability on a scale-free network is discussed for a specific case study: the stochastic Brusselator model. The system is shown to spontaneously differentiate into activator-rich and activator-poor nodes outside the region of parameters classically deputed to the deterministic Turing instability. This phenomenon, as revealed by direct stochastic simulations, is explained analytically and eventually traced back to the finite-size corrections stemming from the inherent graininess of the scrutinized medium.

Network topology plays a crucial role in determining a network's intrinsic dynamics and function, thus understanding and modeling the topology of a complex network will lead to greater knowledge of its evolutionary mechanisms and to a better understanding of its behaviors. In the past few years, topology identification of complex networks has received increasing interest and wide attention. Many approaches have been developed for this purpose, including synchronization-based identification, information-theoretic methods, and intelligent optimization algorithms. However, inferring interaction patterns from observed dynamical time series is still challenging, especially in the absence of knowledge of nodal dynamics and in the presence of system noise. The purpose of this work is to present a simple and efficient approach to inferring the topologies of such complex networks. The proposed approach is called “piecewise partial Granger causality.” It measures the cause-effect connections of nonlinear time series influenced by hidden variables. One commonly used testing network, two regular networks with a few additional links, and small-world networks are used to evaluate the performance and illustrate the influence of network parameters on the proposed approach. Application to experimental data further demonstrates the validity and robustness of our method.

To derive tests for randomness, nonlinear-independence, and stationarity, we combine surrogates with a nonlinear prediction error, a nonlinear interdependence measure, and linear variability measures, respectively. We apply these tests to intracranial electroencephalographic recordings (EEG) from patients suffering from pharmacoresistant focal-onset epilepsy. These recordings had been performed prior to and independent from our study as part of the epilepsy diagnostics. The clinical purpose of these recordings was to delineate the brain areas to be surgically removed in each individual patient in order to achieve seizure control. This allowed us to define two distinct sets of signals: One set of signals recorded from brain areas where the first ictal EEG signal changes were detected as judged by expert visual inspection (“focal signals”) and one set of signals recorded from brain areas that were not involved at seizure onset (“nonfocal signals”). We find more rejections for both the randomness and the nonlinear-independence test for focal versus nonfocal signals. In contrast more rejections of the stationarity test are found for nonfocal signals. Furthermore, while for nonfocal signals the rejection of the stationarity test increases the rejection probability of the randomness and nonlinear-independence test substantially, we find a much weaker influence for the focal signals. In consequence, the contrast between the focal and nonfocal signals obtained from the randomness and nonlinear-independence test is further enhanced when we exclude signals for which the stationarity test is rejected. To study the dependence between the randomness and nonlinear-independence test we include only focal signals for which the stationarity test is not rejected. We show that the rejection of these two tests correlates across signals. The rejection of either test is, however, neither necessary nor sufficient for the rejection of the other test. Thus, our results suggest that EEG signals from epileptogenic brain areas are less random, more nonlinear-dependent, and more stationary compared to signals recorded from nonepileptogenic brain areas. We provide the data, source code, and detailed results in the public domain.

Recent studies of the evolution of weakly nonlinear long waves in shear flows have revealed that when the wave field contains a critical layer, a new nonlinear wave equation is needed to describe the wave evolution. This equation is of the same type as the well-known Korteweg-de Vries equation but has a more complicated nonlinear structure. Our main interest is in the steady solitary wave solutions when a nonlinear transformation converts the equation to a form equivalent to a steady Korteweg-de Vries equation. This enables the explicit construction of the steady solitary wave solutions.

Motivated by the search for best lattice sphere packings in Euclidean spaces of large dimensions we study randomly generated perfect lattices in moderately large dimensions (up to $d=19$ included). Perfect lattices are relevant in the solution of the problem of lattice sphere packing, because the best lattice packing is a perfect lattice and because they can be generated easily. Their number, however, grows superexponentially with the dimension, so to get an idea of their properties we propose to study a randomized version of the generating algorithm and to define a random ensemble with an effective temperature in a way reminiscent of a Monte Carlo simulation. We therefore study the distribution of packing fractions and kissing numbers of these ensembles and show how as the temperature is decreased the best known packers are easily recovered. We find that, even at infinite temperature, the typical perfect lattices are considerably denser than known families (like $A_d$ and $D_d$), and we propose two hypotheses between which we cannot distinguish in this paper: one in which they improve the Minkowsky bound $\phi \sim 2^{-(0.84\pm 0.06)d}$, and a competitor in which their packing fraction decreases superexponentially, namely, $\phi \sim d^{-ad}$ but with a very small coefficient $a=0.06\pm 0.04$. We also find properties of the random walk which are suggestive of a glassy system already for moderately small dimensions. We also analyze local structure of network of perfect lattices conjecturing that this is a scale-free network in all dimensions with constant scaling exponent $2.6\pm 0.1$.

We present a truncation scheme of the effective-average-action approach of the nonperturbative renormalization group that allows for an accurate description of the critical regime as well as of correlation functions at finite momenta. The truncation is a natural modification of the standard derivative expansion that includes both all local correlations and two-point and four-point irreducible correlations to all orders in the derivatives. We discuss schemes for both the symmetric and the symmetry broken phase of the $\text{O}\left(N\right)$ model and present results for $D=3$. All approximations are done directly in the effective average action rather than in the flow equations of irreducible vertices. The approach is numerically relatively easy to implement and yields good results for all $N$ both for the critical exponents and for the momentum dependence of the two-point function.