We study reaction-diffusion processes on graphs through an extension of the standard reaction-diffusion equation starting from first principles. We focus on reaction spreading, i.e., on the time evolution of the reaction product $M\left(t\right)$. At variance with pure diffusive processes, characterized by the spectral dimension $d_s$, the important quantity for reaction spreading is found to be the connectivity dimension $d_l$. Numerical data, in agreement with analytical estimates based on the features of $n$ independent random walkers on the graph, show that $M\left(t\right)\sim t^{d_l}$. In the case of Erdös-Renyi random graphs, the reaction product is characterized by an exponential growth $M\left(t\right)\sim e^{\alpha t}$ with $\alpha$ proportional to $\ln \langle k\rangle$, where $\langle k\rangle$ is the average degree of the graph.

A time-correlated single-photon counting technique was used to verify the formation of a cathode-directed streamer inside the narrow cathode region following the interpulse phase of regular negative corona Trichel pulses in ambient air. A purely experimental approach was used to determine the spatiotemporal development of the electric field during the Trichel pulse rise with an extremely high resolution of 10 $\mu$m and tens of picoseconds. The results confirm the positive-streamer mechanism for Trichel pulse formation and provide supportive evidence for the hypothesis that the formation of a primary cathode-directed streamer occurs always in any streamer-initiated breakdown and prebreakdown phenomena associated with cathode spot formation.

Complex networks possess a rich, multiscale structure reflecting the dynamical and functional organization of the systems they model. Often there is a need to analyze multiple networks simultaneously, to model a system by more than one type of interaction, or to go beyond simple pairwise interactions, but currently there is a lack of theoretical and computational methods to address these problems. Here we introduce a framework for clustering and community detection in such systems using hypergraph representations. Our main result is a generalization of the Perron-Frobenius theorem from which we derive spectral clustering algorithms for directed and undirected hypergraphs. We illustrate our approach with applications for local and global alignment of protein-protein interaction networks between multiple species, for tripartite community detection in folksonomies, and for detecting clusters of overlapping regulatory pathways in directed networks.

We propose two alternate information theoretical approaches to assess non-Gaussian fluctuations in the return dynamics of financial markets. Specifically, we use superinformation, which is a measure of the disorder of the entropy of time series. We argue on theoretical grounds on its usefulness and show that it can be applied effectively for analyzing returns. A study of stock market data for over five years has been carried out using this approach. We show how superinformation helps to identify and classify important signals in the time series. The financial crisis of 2008 comes out very clearly in the superinformation plots. In addition, we introduce the super mutual information. Distinct super mutual information signatures are observed that might be used to mitigate idiosyncratic risk. The universality of our approach has been tested by carrying out the analysis for the 100 stocks listed in S&P100 index. The average superinformation values for the S&P100 stocks correlates very well with the VIX.

Although several mechanisms can promote cooperative behavior, there is no general consensus about why cooperation survives when the most profitable action for an individual is to defect, especially when the population is well mixed. Here we show that when a replicator such as evolutionary game dynamics takes place on interdependent networks, cooperative behavior is fixed on the system. Remarkably, we analytically and numerically show that this is even the case for well-mixed populations. Our results open the path to mechanisms able to sustain cooperation and can provide hints for controlling its rise and fall in a variety of biological and social systems.

We study synchronization in an ensemble of oscillators residing in a finite two-dimensional space. The interaction between the oscillators is governed by their spatial movement. The coupling is unidirectional and is of the intermediate kind, with the spatial vision of each oscillator deciding the number of oscillators to which it is coupled. We also analyze how the extent of synchronization, characterized by the order parameter, depends upon the system parameters, such as spatial vision, spatial motion, and strength of the coupling. The model systems employed here are the Van der Pol oscillator and the Brusselator. Furthermore, for the same spatial configuration, both linear and nonlinear coupling schemes are studied and their results compared.

In nonlinear disordered Hamiltonian lattices, where there are no propagating phonons, the spreading of energy is of subdiffusive nature. Recently, the universality class of the subdiffusive spreading according to the nonlinear diffusion equation (NDE) has been suggested and checked for one-dimensional lattices. Here, we apply this approach to two-dimensional strongly nonlinear lattices and find a nice agreement of the scaling predicted from the NDE with the spreading results from extensive numerical studies. Moreover, we show that the scaling works also for regular lattices with strongly nonlinear coupling, for which the scaling exponent is estimated analytically. This shows that the process of chaotic diffusion in such lattices does not require disorder.

We study a version of the mathematical Ruijsenaars-Schneider model and reinterpret it physically in order to describe the spreading with time of quantum wave packets in a system where multifractality can be tuned by varying a parameter. We compare different methods to measure the multifractality of wave packets and identify the best one. We find the multifractality to decrease with time until it reaches an asymptotic limit, which is different from the multifractality of eigenvectors but related to it, as is the rate of the decrease. Our results could guide the study of experimental situations where multifractality is present in quantum systems.

We present direct numerical simulations of turbulent channel flow with passive Lagrangian polymers. To understand the polymer behavior we investigate the behavior of infinitesimal line elements and calculate the probability distribution function (PDF) of finite-time Lyapunov exponents and from them the corresponding Cramer's function for the channel flow. We study the statistics of polymer elongation for both the Oldroyd-B model (for Weissenberg number $\mathrm{Wi}<1$) and the FENE model. We use the location of the minima of the Cramer's function to define the Weissenberg number precisely such that we observe coil-stretch transition at Wi $\approx 1$. We find agreement with earlier analytical predictions for PDF of polymer extensions made by Balkovsky, Fouxon, and Lebedev [Phys. Rev. Lett. 84, 4765 (2000)] for linear polymers (Oldroyd-B model) with Wi $<1$ and by Chertkov [Phys. Rev. Lett. 84, 4761 (2000)] for nonlinear FENE-P model of polymers. For Wi $>1$ (FENE model) the polymer are significantly more stretched near the wall than at the center of the channel where the flow is closer to homogenous isotropic turbulence. Furthermore near the wall the polymers show a strong tendency to orient along the streamwise direction of the flow, but near the center line the statistics of orientation of the polymers is consistent with analogous results obtained recently in homogeneous and isotropic flows.

We numerically investigate the radial dependence of the velocity and temperature fluctuations and of the time-averaged heat flux $\overline{j}\left(r\right)$ in a cylindrical Rayleigh-Bénard cell with aspect ratio $\Gamma =1$ for Rayleigh numbers Ra between $2\times {10}^6$ and $2\times {10}^9$ at a fixed Prandtl number $\text{Pr}=5.2$. The numerical results reveal that the heat flux close to the sidewall is larger than in the center and that, just as the global heat transport, it has an effective power law dependence on the Rayleigh number, $\overline{j}\left(r\right)\propto {\text{Ra}}^{{\gamma }_j\left(r\right)}$. The scaling exponent ${\gamma }_j\left(r\right)$ decreases monotonically from $0.43$ near the axis ($r\approx 0$) to $0.29$ close to the sidewalls ($r\approx D/2$). The effective exponents near the axis and the sidewall agree well with the measurements of Shang et al. [Phys. Rev. Lett. 100, 244503 (2008)] and the predictions of Grossmann and Lohse [Phys. Fluids 16, 1070 (2004)]. Extrapolating our results to large Rayleigh number would imply a crossover at $\text{Ra}\approx {10}^{15}$, where the heat flux near the axis would begin to dominate. In addition, we find that the local heat flux is more than twice as high at the location where warm or cold plumes go up or down than in plume depleted regions.

In a recent paper [Das et al., Phys. Rev. E 85, 046311 (2012)], we delineated the role of electrokinetic transport in modifying the classical “coffee stain” effect. In this study, we extend this calculation to incorporate the consequences of a generalized electromagnetohydrodynamic transport in the coffee stain phenomenon. The magnetohydrodynamic (MHD) effect enhances the velocities at the beginning of the drop life, whereas the electrokinetic effect increases the “disordering” effect in particle deposition at the end of the drop, triggered by a velocity divergence. For a suitable combination of the strength of the MHD and electrokinetic transport, however, this disordering effect is substantially enhanced, and, most nonintuitively, such velocity divergence and the disordering effect may occur at a time that is much earlier than the end of the drop life, or may occur even instantaneously after the start of the drop evaporation. This work will provide useful insight in the understanding of the dynamics of mesoscopic patterns formed as the magnetic nanocrystals deposit in the presence of a combined transport driven by evaporation and magnetic field effects.

We study the effects of ion-dust collisions and ion kinematic viscosities on the linear ion-acoustic instability as well as the nonlinear propagation of small-amplitude solitary waves and shocks (SWS) in a negative-ion plasma with immobile charged dusts. The existence of two linear ion modes, namely the “fast” and “slow” waves, is shown, and their properties are analyzed in the collisional negative-ion plasma. Using the standard reductive perturbation technique, we derive a modified Korteweg-de Vries-Burger (KdVB) equation which describes the evolution of small-amplitude SWS. The profiles of the latter are numerically examined with parameters relevant for laboratory and space plasmas where charged dusts may be positively or negatively charged. It is found that negative-ion plasmas containing positively charged dusts support the propagation of SWS with negative potential. However, the perturbations with both positive and negative potentials may exist when dusts are negatively charged. The results may be useful for the excitation of SWS in laboratory negative-ion plasmas as well as for observation in space plasmas where charged dusts may be positively or negatively charged.

We present a method for approximating the solution of the three-dimensional, time-dependent Gross-Pitaevskii equation (GPE) for Bose-Einstein-condensate systems where the confinement in one dimension is much tighter than in the other two. This method employs a hybrid Lagrangian variational technique whose trial wave function is the product of a completely unspecified function of the coordinates in the plane of weak confinement and a Gaussian in the strongly confined direction having a time-dependent width and quadratic phase. The hybrid Lagrangian variational method produces equations of motion that consist of (1) a two-dimensional (2D) effective GPE whose nonlinear coefficient contains the width of the Gaussian and (2) an equation of motion for the width that depends on the integral of the fourth power of the solution of the 2D effective GPE. We apply this method to the dynamics of Bose-Einstein condensates confined in ring-shaped potentials and compare the approximate solution to the numerical solution of the full 3D GPE.

We report Monte Carlo simulation studies of tilted smectic liquid crystal phases exhibited by systems of rodlike molecules having permanent dipole moments. For a theoretical understanding of the microscopic origin of the tilted smectic phases, different systems consisting of prolate ellipsoidal molecules of three different lengths, embedded with two symmetrically placed terminal antiparallel dipoles, are investigated. We find that the presence of a stable tilted phase depends crucially on the molecular elongation, which effectively makes the dipolar separation longer. We observe that in the case of molecules with transverse dipoles the tilt angle in the smectic phase gradually increases from zero to a large magnitude as we increase the molecular length, whereas systems with longitudinal dipoles show small tilts over different elongations. In this work we determine the combined contribution of dipolar separation and transverse orientations in generating biaxial liquid crystal phases with large tilt angles.

By considering three different spin models belonging to the generalized voter class for ordering dynamics in two dimensions [Dornic et al., Phys. Rev. Lett. 87, 045701 (2001)], we show that they behave differently from the linear voter model when the initial configuration is an unbalanced mixture of up and down spins. In particular, we show that for nonlinear voter models the exit probability (probability to end with all spins up when starting with an initial fraction $x$ of them) assumes a nontrivial shape. This is the first time a nontrivial exit probability is observed in two-dimensional systems. The change is traced back to the strong nonconservation of the average magnetization during the early stages of dynamics. Also the time needed to reach the final consensus state $T_N\left(x\right)$ has an anomalous nonuniversal dependence on $x$.

We investigate the strong-coupling regime of the stationary Kardar-Parisi-Zhang equation for interfaces growing on a substrate of dimension $d=1$, 2, and 3 using a nonperturbative renormalization group (NPRG) approach. We compute critical exponents, correlation and response functions, extract the related scaling functions, and calculate universal amplitude ratios. We work with a simplified implementation of the second-order (in the response field) approximation proposed in a previous work [Phys. Rev. E 84, 061150 (2011) and Phys. Rev. E 86, 019904(E) (2012)], which greatly simplifies the frequency sector of the NPRG flow equations, while keeping a nontrivial frequency dependence for the two-point functions. The one-dimensional scaling function obtained within this approach compares very accurately with the scaling function obtained from the full second-order NPRG equations and with the exact scaling function. Furthermore, the approach is easily applicable to higher dimensions and we provide scaling functions and amplitude ratios in $d=2$ and $d=3$. We argue that our ansatz is reliable up to $d\simeq 3.5$.

The alignment, ordering, and rotation of elongated granular particles was studied in shear flow. The time evolution of the orientation of a large number of particles was monitored in laboratory experiments by particle tracking using optical imaging and x-ray computed tomography. The experiments were complemented by discrete element simulations. The particles develop an orientational order. In the steady state the time- and ensemble-averaged direction of the main axis of the particles encloses a small angle with the streamlines. This shear alignment angle is independent of the applied shear rate, and it decreases with increasing grain aspect ratio. At the grain level the steady state is characterized by a net rotation of the particles, as dictated by the shear flow. The distribution of particle rotational velocities was measured both in the steady state and also during the initial transients. The average rotation speed of particles with their long axis perpendicular to the shear alignment angle is larger, while shear aligned particles rotate slower. The ratio of this fast/slow rotation increases with particle aspect ratio. During the initial transient starting from an unaligned initial condition, particles having an orientation just beyond the shear alignment angle rotate opposite to the direction dictated by the shear flow.

In single-particle coherent x-ray diffraction imaging experiments, performed at x-ray free-electron lasers (XFELs), samples are exposed to intense x-ray pulses to obtain single-shot diffraction patterns. The high intensity induces electronic dynamics on the femtosecond time scale in the system, which can reduce the contrast of the obtained diffraction patterns and adds an isotropic background. We quantify the degradation of the diffraction pattern from ultrafast electronic damage by performing simulations on a biological sample exposed to x-ray pulses with different parameters. We find that the contrast is substantially reduced and the background is considerably strong only if almost all electrons are removed from their parent atoms. This happens at fluences of at least one order of magnitude larger than provided at currently available XFEL sources.

We discuss generalizations of a previously published coarse-grained description [Mergell et al., Phys. Rev. E 68, 021911 (2003)] of double stranded DNA (dsDNA). The model is defined at the base-pair level and includes the electrostatic repulsion between neighbor helices. We show that the model reproduces mechanical and elastic properties of several DNA nanostructures (DNA origamis). We also show that electrostatic interactions are necessary to reproduce atomic force microscopy measurements on planar DNA origamis.

Recent numerical experiments of Pecora et al. [Phys. Rev. E 83, 065201 (2011)] have investigated tunneling between two-dimensional symmetric double wells separated by a tunneling barrier. The wells were bounded by hard walls and by the potential barrier which was created by a step increase from the zero potential within a well to a uniform barrier potential within the barrier region, which is a situation potentially realizable in the context of quantum dots. Numerical results for the splitting of energy levels between symmetric and antisymmetric eigenstates were calculated. It was found that the splittings vary erratically from state to state, and the statistics of these variations were studied for different well shapes with the fluctuation levels being much less in chaotic wells than in comparable nonchaotic wells. Here we develop a quantitative theory for the statistics of the energy level splittings for chaotic wells. Our theory is based on the random plane wave hypothesis of Berry. While the fluctuation statistics are very different for chaotic and nonchaotic well dynamics, we show that the mean splittings of differently shaped wells, including integrable and chaotic wells, are the same if their well areas and barrier parameters are the same. We also consider the case of tunneling from a single well into a region with outgoing quantum waves.