By numerically solving the three-dimensional Gross-Pitaevskii equation we analyze the cascade process associated with the evolution and decay of a pair of linked vortex rings. The system decays through a series of reconnections to produce finally three unlinked, unfolded, almost planar vortex loops. Total helicity, initially zero, remains unchanged throughout the process. The gradual transfer from writhe (due to initial linking) to twist helicity, followed by a continuous relaxation of twist across scales during the evolution is shown to be a generic mechanism that consistently takes place on each individual component.

The freak oscillation in one-dimensional dusty plasma is studied numerically by particle-in-cell method. Using a perturbation method, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation (NLSE). The rational solution of the NLSE is presented, which is proposed as an effective tool for studying the rogue waves in dusty plasma. Additionally, the application scope of the analytical solution of the rogue wave described by the NLSE is given.

Understanding the three-dimensional (3D) stochastic structure of a porous medium is helpful for studying its physical properties. A 3D stochastic structure can be reconstructed from a two-dimensional (2D) training image (TI) using mathematical modeling. In order to predict what specific morphology belonging to a TI can be reconstructed at the 3D orthogonal slices by the method of 3D reconstruction, this paper begins by introducing the concept of orthogonal chords. After analyzing the relationship among TI morphology, orthogonal chords, and the 3D morphology of orthogonal slices, a theory for evaluating the morphological completeness of a TI is proposed for the cases of three orthogonal slices and of two orthogonal slices. The proposed theory is evaluated using four TIs of porous media that represent typical but distinct morphological types. The significance of this theoretical evaluation lies in two aspects: It allows special morphologies, for which the attributes of a TI can be reconstructed at a special orthogonal slice of a 3D structure, to be located and quantified, and it can guide the selection of an appropriate reconstruction method for a special TI.

The condition for stationary engines to attain the Carnot efficiency in and beyond the linear response regime is investigated. We find that this condition for finite-size engines is significantly different from that for macroscopic engines in the thermodynamic limit. For the case of finite-size engines, the tight-coupling condition in the linear response regime directly implies the attainability of the Carnot efficiency beyond the linear response regime. As opposed to this, for the case of macroscopic engines in the thermodynamic limit, there are three types of mechanisms to attain the Carnot efficiency. One mechanism allows engines to attain the Carnot efficiency only in the linear response limit, while the other two mechanisms enable engines to attain the Carnot efficiency beyond the linear response regime. These three mechanisms are classified by introducing a tight-coupling window.

We analytically derive, in the context of the replica formalism, the first finite-size corrections to the average optimal cost in the random assignment problem for a quite generic distribution law for the costs. We show that, when moving from a power-law distribution to a $\mathrm{\Gamma }$ distribution, the leading correction changes both in sign and in its scaling properties. We also examine the behavior of the corrections when approaching a $\delta$-function distribution. By using a numerical solution of the saddle-point equations, we provide predictions that are confirmed by numerical simulations.

Origami-inspired structures and materials have shown extraordinary properties and performances originating from the intricate geometries of folding. However, current state of the art studies have mostly focused on static and quasistatic characteristics. This research performs a comprehensive experimental and analytical study on the dynamics of origami folding through investigating a stacked Miura-Ori (SMO) structure with intrinsic bistability. We fabricate and experimentally investigated a bistable SMO prototype with rigid facets and flexible crease lines. Under harmonic base excitation, the SMO exhibits both intrawell and interwell oscillations. Spectrum analyses reveal that the dominant nonlinearities of SMO are quadratic and cubic, which generate rich dynamics including subharmonic and chaotic oscillations. The identified nonlinearities indicate that a third-order polynomial can be employed to approximate the measured force-displacement relationship. Such an approximation is validated via numerical study by qualitatively reproducing the phenomena observed in the experiments. The dynamic characteristics of the bistable SMO resemble those of a Helmholtz-Duffing oscillator (HDO); this suggests the possibility of applying the established tools and insights of HDO to predict origami dynamics. We also show that the bistability of SMO can be programmed within a large design space via tailoring the crease stiffness and initial stress-free configurations. The results of this research offer a wealth of fundamental insights into the dynamics of origami folding, and provide a solid foundation for developing foldable and deployable structures and materials with embedded dynamic functionalities.

We investigate the instantaneous behavior of synchronized temporal wave forms in two mutually coupled semiconductor lasers numerically and experimentally. The temporal wave forms of two lasers are synchronized with a propagation delay time, with one laser oscillating in advance of the other, known as the leader-laggard relationship. The leader-laggard relationship can be determined by measuring the cross-correlation between the two temporal wave forms with the propagation delay time. The leader can be identified when the optical carrier frequency of the leader laser is higher than that of the other laser. However, spontaneous exchange between the leader and laggard lasers can be observed in low-frequency fluctuations by short-term cross-correlation measurements, even for a fixed initial optical frequency detuning. The spontaneous exchange of the leader-laggard relationship originates from alternation of partial optical frequency locking between the two lasers. This observation is analyzed using a phase space trajectory on steady-state solutions for mutually coupled lasers with optical frequency detuning.

Diffusion in a multiplex depends on the specific link distribution between the nodes in each layer, but also on the set of the intralayer and interlayer diffusion coefficients. In this work we investigate, in a quantitative way, the efficiency of multiplex diffusion as a function of the topological similarity among multiplex layers. This similarity is measured by the distance between layers, taken among the pairs of layers. Results are presented for a simple two-layer multiplex, where one of the layers is held fixed, while the other one can be rewired in a controlled way in order to increase or decrease the interlayer distance. The results indicate that, for fixed values of all intra- and interlayer diffusion coefficients, a large interlayer distance generally enhances the global multiplex diffusion, providing a topological mechanism to control the global diffusive process. For some sets of networks, we develop an algorithm to identify the most sensitive nodes in the rewirable layer, so that changes in a small set of connections produce a drastic enhancement of the global diffusion of the whole multiplex system.

Based on a recently proposed $q$-dependent detrended cross-correlation coefficient, ${\rho }_q$ [J. Kwapień, P. Oświęcimka, and S. Drożdż, Phys. Rev. E 92, 052815 (2015)], we generalize the concept of the minimum spanning tree (MST) by introducing a family of $q$-dependent minimum spanning trees ($q\mathrm{MST}\mathrm{s}$) that are selective to cross-correlations between different fluctuation amplitudes and different time scales of multivariate data. They inherit this ability directly from the coefficients ${\rho }_q$, which are processed here to construct a distance matrix being the input to the MST-constructing Kruskal's algorithm. The conventional MST with detrending corresponds in this context to $q=2$. In order to illustrate their performance, we apply the $q\mathrm{MSTs}$ to sample empirical data from the American stock market and discuss the results. We show that the $q\mathrm{MST}$ graphs can complement ${\rho }_q$ in disentangling “hidden” correlations that cannot be observed in the MST graphs based on ${\rho }_{\mathrm{DCCA}}$, and therefore, they can be useful in many areas where the multivariate cross-correlations are of interest. As an example, we apply this method to empirical data from the stock market and show that by constructing the $q\mathrm{MSTs}$ for a spectrum of $q$ values we obtain more information about the correlation structure of the data than by using $q=2$ only. More specifically, we show that two sets of signals that differ from each other statistically can give comparable trees for $q=2$, while only by using the trees for $q\ne 2$ do we become able to distinguish between these sets. We also show that a family of $q\mathrm{MSTs}$ for a range of $q$ expresses the diversity of correlations in a manner resembling the multifractal analysis, where one computes a spectrum of the generalized fractal dimensions, the generalized Hurst exponents, or the multifractal singularity spectra: the more diverse the correlations are, the more variable the tree topology is for different $q$'s. As regards the correlation structure of the stock market, our analysis exhibits that the stocks belonging to the same or similar industrial sectors are correlated via the fluctuations of moderate amplitudes, while the largest fluctuations often happen to synchronize in those stocks that do not necessarily belong to the same industry.

We compare forces resisting DNA packaging and forces driving DNA ejection in bacteriophage phi29 with theoretical predictions. Ejection of DNA from prohead-motor complexes is triggered by heating complexes after in vitro packaging and force is inferred from the suppression of ejection by applied osmotic pressure. Ejection force from $0\%$ to $80\%$ filling is found to be in quantitative agreement with predictions of a continuum mechanics model that assumes a repulsive DNA-DNA interaction potential based on DNA condensation studies and predicts an inverse-spool conformation. Force resisting DNA packaging from $\sim 80\%$ to $100\%$ filling inferred from optical tweezers studies is also consistent with the predictions of this model. The striking agreement with these two different measurements suggests that the overall energetics of DNA packaging is well described by the model. However, since electron microscopy studies of phi29 do not reveal a spool conformation, our findings suggest that the spool model overestimates the role of bending rigidity and underestimates the role of intrastrand repulsion. Below $\sim 80\%$ filling the inferred forces resisting packaging are unexpectedly lower than the inferred ejection forces, suggesting that in this filling range the forces are less accurately determined or strongly temperature dependent.

An analytical steady-state solution of the stochastic model describing the integrated dynamics of the membrane voltage and the gating of a single channel is presented. The voltage density function experiences bifurcation in the parameter space, and the threshold is determined by the comparison between the rates of the voltage evolution and that of the channel gating. It is singular at the reversal potential if the voltage evolves faster than the channel gating. As an application, the entropy production rate associated with the gating currents is calculated; its variation tendency in parameter space is consistent to that of the number of transitions counted from the sample paths. The analysis in this paper identifies the values of parameters that justify the formation of the voltage pulse and the efficient energy cost, which is associated with the singularity of the voltage density functions.

Inhalant flows draw fluid into an orifice from a reservoir and are ubiquitous in engineering and biology. Surprisingly, there is a lack of quantitative information on viscous inhalant flows. We consider here laminar flows (Reynolds number $\text{Re}\le 100$) developing after impulsive inhalation begins. We implement finite element simulations of flows with varying Re and extraction height $h$ (orifice height above a bottom bed). Numerical results are experimentally validated using particle image velocimetry measurements in a physical model for a representative flow case in the middle of the Re-$h$ parameter space. We use two metrics to characterize the flow in space and time: regions of influence (ROIs), which describe the spatial extent of the flow field, and inhalation volumes, which describe the initial distribution of inhaled fluid. The transient response for all Re features an inviscid sinklike component at early times followed by a viscous diffusive component. At lower Re, diffusion entrains an increasing volume of fluid over time, enlarging the ROI indefinitely. In some geometries, these flows spatially bifurcate, with some fluid being inhaled through the orifice and some bypassing into recirculation. At higher Re, inward advection dominates outward viscous diffusion and the flow remains trapped in a sinklike state. Both ROIs and inhalation volumes are strongly dependent on Re and extraction height, suggesting that organisms or engineers could tune these parameters to achieve specific inhalation criteria.

A physical model has been developed for the linear Rayleigh-Taylor instability of a finite-thickness elastic slab laying on top of a semi-infinite ideal fluid. The model includes the nonideal effects of elasticity as boundary conditions at the top and bottom interfaces of the slab and also takes into account the finite transit time of the elastic waves across the slab thickness. For Atwood number $A_T=1$, the asymptotic growth rate is found to be in excellent agreement with the exact solution [Plohr and Sharp, Z. Angew. Math. Mech. 49, 786 (1998)], and a physical explanation is given for the reduction of the stabilizing effectiveness of the elasticity for the thinner slabs. The feedthrough factor is also calculated.

We perform two-dimensional implosion simulations using a Monte Carlo kinetic particle code. The application of a kinetic transport code is motivated, in part, by the occurrence of nonequilibrium effects in inertial confinement fusion capsule implosions, which cannot be fully captured by hydrodynamic simulations. Kinetic methods, on the other hand, are able to describe both continuum and rarefied flows. We perform simple two-dimensional disk implosion simulations using one-particle species and compare the results to simulations with the hydrodynamics code rage. The impact of the particle mean free path on the implosion is also explored. In a second study, we focus on the formation of fluid instabilities from induced perturbations. We find good agreement with hydrodynamic studies regarding the location of the shock and the implosion dynamics. Differences are found in the evolution of fluid instabilities, originating from the higher resolution of rage and statistical noise in the kinetic studies.

We numerically analyze the density field of three-dimensional randomly jammed packings of monodisperse soft frictionless spherical particles, paying special attention to fluctuations occurring at large length scales. We study in detail the two-point static structure factor at low wave vectors in Fourier space. We also analyze the nature of the density field in real space by studying the large-distance behavior of the two-point pair correlation function, of density fluctuations in subsystems of increasing sizes, and of the direct correlation function. We show that such real space analysis can be greatly improved by introducing a coarse-grained density field to disentangle genuine large-scale correlations from purely local effects. Our results confirm that both Fourier and real space signatures of vanishing density fluctuations at large scale are absent, indicating that randomly jammed packings are not hyperuniform. In addition, we establish that the pair correlation function displays a surprisingly complex structure at large distances, which is however not compatible with the long-range negative correlation of hyperuniform systems but fully compatible with an analytic form for the structure factor. This implies that the direct correlation function is short ranged, as we also demonstrate directly. Our results reveal that density fluctuations in jammed packings do not follow the behavior expected for random hyperuniform materials, but display instead a more complex behavior.

Permutation entropy (PE) is a widely used measure for complexity, often used to distinguish between complex systems (or complex systems in different states). Here, the PE variance for a stationary time series is derived, and the influence of ordinal pattern selection, specifically whether the ordinal patterns are permitted to overlap or not, is examined. It was found that permitting ordinal patterns to overlap reduces the PE variance, improving the ability of this statistic to distinguish between complex system states for both numeric (fractional Gaussian noise) and experimental (semiconductor laser with optical feedback) systems. However, with overlapping ordinal patterns, the precision to which the PE variance can be estimated becomes diminished, which can manifest as increased incidences of false positive and false negative errors when applying PE to statistical inference problems.

The theoretical description of nonrenewal stochastic systems is a challenge. Analytical results are often not available or can be obtained only under strong conditions, limiting their applicability. Also, numerical results have mostly been obtained by ad hoc Monte Carlo simulations, which are usually computationally expensive when a high degree of accuracy is needed. To gain quantitative insight into these systems under general conditions, we here introduce a numerical iterated first-passage time approach based on solving the time-dependent Fokker-Planck equation (FPE) to describe the statistics of nonrenewal stochastic systems. We illustrate the approach using spike-triggered neuronal adaptation in the leaky and perfect integrate-and-fire model, respectively. The transition to stationarity of first-passage time moments and their sequential correlations occur on a nontrivial time scale that depends on all system parameters. Surprisingly this is so for both single exponential and scale-free power-law adaptation. The method works beyond the small noise and time-scale separation approximations. It shows excellent agreement with direct Monte Carlo simulations, which allow for the computation of transient and stationary distributions. We compare different methods to compute the evolution of the moments and serial correlation coefficients (SCCs) and discuss the challenge of reliably computing the SCCs, which we find to be very sensitive to numerical inaccuracies for both the leaky and perfect integrate-and-fire models. In conclusion, our methods provide a general picture of nonrenewal dynamics in a wide range of stochastic systems exhibiting short- and long-range correlations.

We study the synchronization of chaotic units connected through time-delayed fluctuating interactions. Focusing on small-world networks of Bernoulli and Logistic units with a fixed chiral backbone, we compare the synchronization properties of static and fluctuating networks in the regime of large delays. We find that random network switching may enhance the stability of synchronized states. Synchronization appears to be maximally stable when fluctuations are much faster than the time-delay, whereas it disappears for very slow fluctuations. For fluctuation time scales of the order of the time-delay, we report a resynchronizing effect in finite-size networks. Moreover, we observe characteristic oscillations in all regimes, with a periodicity related to the time-delay, as the system approaches or drifts away from the synchronized state.

Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterization of empirical data. Here we investigate the effects of the (multi)fractal properties of a signal, common in time series arising from chaotic dynamics or strange attractors, on the topology of a suitably projected network. Relying on the box-counting formalism, we map boxes into the nodes of a network and establish analytic expressions connecting the natural measure of a box with its degree in the graph representation. We single out the conditions yielding to the emergence of a scale-free topology and validate our findings with extensive numerical simulations. We finally present a numerical analysis on the properties of weighted and directed network projections.

Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.