We report the transitions among different oscillation quenching states induced by the interplay of diffusive (direct) coupling and environmental (indirect) coupling in coupled identical oscillators. This coupling scheme was introduced by Resmi et al. [Phys. Rev. E 84, 046212 (2011)] as a general scheme to induce amplitude death (AD) in nonlinear oscillators. Using a detailed bifurcation analysis we show that, in addition to AD, which actually occurs only in a small region of parameter space, this coupling scheme can induce other oscillation quenching states, namely oscillation death (OD) and a novel nontrvial AD (NAD) state, which is a nonzero bistable homogeneous steady state; more importantly, this coupling scheme mediates a transition from the AD state to the OD state and a new transition from the AD state to the NAD state. We identify diverse routes to the NAD state and map all the transition scenarios in the parameter space for periodic oscillators. Finally, we present the first experimental evidence of oscillation quenching states and their transitions induced by the interplay of direct and indirect coupling.

Based on the Peregrine solution (PS) of the nonlinear Schrödinger (NLS) equation, the evolution of rational fraction pulses surrounded by zero background is investigated. These pulses display the behavior of a breatherlike solitons. We study the generation and evolution of such solitons extracted, by means of the spectral-filtering method, from the PS in the model of the optical fiber with realistic values of coefficients accounting for the anomalous dispersion, Kerr nonlinearity, and higher-order effects. The results demonstrate that the breathing solitons stably propagate in the fibers. Their robustness against small random perturbations applied to the initial background is demonstrated too.

Parity-violating fluids in two spatial dimensions can appear in a variety of contexts such as liquid crystal films, anyon fluids, and quantum Hall fluids. Nonetheless, the consequences of parity violation on the solutions to the equations of motion are largely unexplored. In this paper, we explore phenomenological consequences of parity violation through simple, illustrative examples. Although incompressible velocity fields are essentially unchanged by parity violation, we discuss examples where parity violation plays a role at boundaries, or in the dynamics of temperature. We then discuss types of compressible flows which only exist in a parity-violating fluid, including sound waves, and solitons in the dissipationless limit. We conclude with a discussion of some curious features in Rayleigh-Bénard convection of a parity-violating fluid.

Magnetically actuated microswimmers have recently attracted attention due to many possible biomedical applications. In this study we investigate the dynamics of rigid magnetically rotated microswimmers with permanent magnetic dipoles. Our approach uses a boundary element method to calculate a mobility matrix, accurate for arbitrary geometries, which is then used to identify the steady periodically rotating orbits in a co-rotating body-fixed frame. We evaluate the stability of each of these orbits. We map the magnetoviscous behavior as a function of dimensionless Mason number and as a function of the angle that the magnetic field makes with its rotation axis. We describe the wobbling motion of these swimmers by investigating how the rotation axis changes as a function of experimental parameters. We show that for a given magnetic field strength and rotation frequency, swimmers can have more than one stable periodic orbit with different rotation axes. Finally, we demonstrate that one can improve the controllability of these types of microswimmers by adjusting the relative angle between the magnetic field and its axis of rotation.

We present a theoretical expression for the acoustic interaction force between small spherical particles suspended in an ideal fluid exposed to an external acoustic wave. The acoustic interaction force is the part of the acoustic radiation force on one given particle involving the scattered waves from the other particles. The particles, either compressible liquid droplets or elastic microspheres, are considered to be much smaller than the acoustic wavelength. In this so-called Rayleigh limit, the acoustic interaction forces between the particles are well approximated by gradients of pair-interaction potentials with no restriction on the interparticle distance. The theory is applied to studies of the acoustic interaction force on a particle suspension in either standing or traveling plane waves. The results show aggregation regions along the wave propagation direction, while particles may attract or repel each other in the transverse direction. In addition, a mean-field approximation is developed to describe the acoustic interaction force in an emulsion of oil droplets in water.

The time- and space-dependent optical emissions of nanosecond high-power microwave discharges near a dielectric-air interface have been observed by nanosecond-response four-framing intensified-charged-coupled device cameras. The experimental observations indicate that plasma developed more intensely at the dielectric-air interface than at the free-space region with a higher electric-field amplitude. A thin layer of intense light emission above the dielectric was observed after the microwave pulse. The mechanisms of the breakdown phenomena are analyzed by a three-dimensional electromagnetic-field modeling and a two-dimensional electromagnetic particle-in-cell simulation, revealing the formation of a space-charge microwave sheath near the dielectric surface, accelerated by the normal components of the microwave field, significantly enhancing the local-field amplitude and hence ionization near the dielectric surface. The nonlinear positive feedback of ionization, higher electron mobility, and ultraviolet-driven photoemission due to the elevated electron temperature are crucial for achieving the ultrafast discharge. Following the high-power microwave pulse, the sheath sustains a glow discharge until the sheath collapses.

Controlling the divergence of laser-driven fast electrons is compulsory to meet the ignition requirements in the fast ignition inertial fusion scheme. It was shown recently that using two consecutive laser pulses one can improve the electron-beam collimation. In this paper we propose an extension of this method by using a sequence of several laser pulses with a gradually increasing intensity. Profiling the laser-pulse intensity opens a possibility to transfer to the electron beam a larger energy while keeping its divergence under control. We present numerical simulations performed with a radiation hydrodynamic code coupled to a reduced kinetic module. Simulation with a sequence of three laser pulses shows that the proposed method allows one to improve the efficiency of the double pulse scheme at least by a factor of 2. This promises to provide an efficient energy transport in a dense matter by a collimated beam of fast electrons, which is relevant for many applications such as ion-beam sources and could present also an interest for fast ignition inertial fusion.

We analyze the mean squared displacement of a Brownian particle in a medium with a spatially varying local diffusivity, which is assumed to be periodic. When the system is asymptotically diffusive, the mean-squared displacement, characterizing the dispersion in the system, is, at late times, a linear function of time. A Kubo-type formula is given for the mean-squared displacement, which allows the recovery of some known results for the effective diffusion constant $D_e$ in a direct way, but also allows an understanding of the asymptotic approach to the diffusive limit. In particular, as well as as computing the slope of a linear fit to the late-time mean-squared displacement, we find a formula for the constant where the fit intersects the $y$ axis.

The waiting time distribution (WTD) is a common tool for analyzing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete, or where it is favourable to discuss the dynamics on a discretized and a continuous level in parallel. An example is the hindered motion of particles through potential landscapes with barriers. In the present paper we propose a consistent generalization of the WTD from the discrete case to situations where the particles perform continuous barrier crossing characterized by a finite duration. To this end, we introduce a recipe to calculate the WTD from the Fokker-Planck (Smoluchowski) equation. In contrast to the closely related first passage time distribution (FPTD), which is frequently used to describe continuous processes, the WTD contains information about the direction of motion. As an application, we consider the paradigmatic example of an overdamped particle diffusing through a washboard potential. To verify the approach and to elucidate its numerical implications, we compare the WTD defined via the Smoluchowski equation with data from direct simulation of the underlying Langevin equation and find full consistency provided that the jumps in the Langevin approach are defined properly. Moreover, for sufficiently large energy barriers, the WTD defined via the Smoluchowski equation becomes consistent with that resulting from the analytical solution of a (two-state) master equation model for the short-time dynamics developed previously by us [Phys. Rev. E 86, 061135 (2012)]. Thus, our approach “interpolates” between these two types of stochastic motion. We illustrate our approach for both symmetric systems and systems under constant force.

We use the $(1+1)$-dimensional Kardar-Parisi-Zhang equation driven by a Gaussian white noise and employ the dynamic renormalization-group of Yakhot and Orszag without rescaling [J. Sci. Comput. 1, 3 (1986)]. Hence we calculate the second- and third-order moments of height distribution using the diagrammatic method in the large-scale and long-time limits. The moments so calculated lead to the value $S=0.3237$ for the skewness. This value is comparable with numerical and experimental estimates.

We propose a straightforward extension of symbolic transfer entropy to enable the investigation of delayed directional relationships between coupled dynamical systems from time series. Analyzing time series from chaotic model systems, we demonstrate the applicability and limitations of our approach. Our findings obtained from applying our method to infer delayed directed interactions in the human epileptic brain underline the importance of our approach for improving the construction of functional network structures from data.

We propose a simple model to interpret the optical absorption spectra of porphyrin in different solvents. Our model successfully explains the decrease in the intensity of optical absorption at maxima of increased wavelengths. We also prove the dependence of the intensity and peak positions in the absorption spectra on the environment. The nature of the Soret band is supposed to derive from $\pi$ plasmon. Our theoretical calculations are consistent with previous experimental studies.

Interacting epidemics on diverse multilayer networks are increasingly important in modeling and analyzing the diffusion processes of real complex systems. A viral agent spreading on one layer of a multilayer network can interact with its counterparts by promoting (cooperative interaction), suppressing (competitive interaction), or inducing (collaborating interaction) its diffusion on other layers. Collaborating interaction displays different patterns: (i) random collaboration, where intralayer or interlayer induction has the same probability; (ii) concentrating collaboration, where consecutive intralayer induction is guaranteed with a probability of 1; and (iii) cascading collaboration, where consecutive intralayer induction is banned with a probability of 0. In this paper, we develop a top-bottom framework that uses only two distributions, the overlaid degree distribution and edge-type distribution, to model collaborating epidemics on multilayer networks. We then state the response of three collaborating patterns to structural diversity (evenness and difference of network layers). For viral agents with small transmissibility, we find that random collaboration is more effective in networks with higher diversity (high evenness and difference), while the concentrating pattern is more suitable in uneven networks. Interestingly, the cascading pattern requires a network with moderate difference and high evenness, and the moderately uneven coupling of multiple network layers can effectively increase robustness to resist cascading failure. With large transmissibility, however, we find that all collaborating patterns are more effective in high-diversity networks. Our work provides a systemic analysis of collaborating epidemics on multilayer networks. The results enhance our understanding of biotic and informative diffusion through multiple vectors.

In economic and financial networks, the strength of each node has always an important economic meaning, such as the size of supply and demand, import and export, or financial exposure. Constructing null models of networks matching the observed strengths of all nodes is crucial in order to either detect interesting deviations of an empirical network from economically meaningful benchmarks or reconstruct the most likely structure of an economic network when the latter is unknown. However, several studies have proved that real economic networks and multiplexes topologically differ from configurations inferred only from node strengths. Here we provide a detailed analysis of the world trade multiplex by comparing it to an enhanced null model that simultaneously reproduces the strength and the degree of each node. We study several temporal snapshots and almost 100 layers (commodity classes) of the multiplex and find that the observed properties are systematically well reproduced by our model. Our formalism allows us to introduce the (static) concept of extensive and intensive bias, defined as a measurable tendency of the network to prefer either the formation of extra links or the reinforcement of link weights, with respect to a reference case where only strengths are enforced. Our findings complement the existing economic literature on (dynamic) intensive and extensive trade margins. More generally, they show that real-world multiplexes can be strongly shaped by layer-specific local constraints.

Numerical studies of three-dimensional (3D) time-periodic flow inside a lid-driven cylinder revealed that a weak perturbation of the noninertial state (Reynolds number $\text{Re}=0$) has a strong impact on the Lagrangian flow structure by inducing transition of a global family of nested spheroidal invariant surfaces into intricate coherent structures consisting of adiabatic invariant surfaces connected by tubes. These tubes provide paths for passive tracers to escape from one invariant surface to another. Perturbation is introduced in two ways: (i) weak fluid inertia by nonzero $\text{Re}\sim O\left({10}^{-3}\right)$; (ii) small disturbance of the external flow forcing. Both induce essentially the same dynamics, implying a universal response in the limit of a weak perturbation. Moreover, we show that the motion inside tubes possesses an adiabatic invariant. Long-term experiments were conducted using 3D particle-tracking velocimetry and relied on experimental imperfections as natural weak perturbations. This provided first experimental evidence of the tube formation and revealed close agreement with numerical simulations. We experimentally validated the universality of the perturbation response and, given the inevitability of imperfections, exposed the weakly perturbed state as the true “unperturbed state” in realistic systems.

We perform large-eddy simulations of turbulent convection in a cubic cell for Rayleigh numbers, Ra, between ${10}^6$ and ${10}^{10}$ and the molecular Prandtl number, $\text{Pr}=0.7$. The simulations were carried out using a second-order-accurate finite-difference method in which subgrid-scale fluxes of momentum and heat were both parametrized using a Lagrangian and dynamic Smagorinsky model. The scaling of the root-mean-square fluctuations of density (temperature) and velocity measured in the cell center are in excellent agreement with the scaling measured in the laboratory experiments of Daya and Ecke [Phys. Rev. Lett. 87, 184501 (2001)] and differ substantially from that observed in cylindrical cells. We also observe the time-averaged spatial distributions of the local heat flux and density fluctuations, and find that they are strongly inhomogeneous in the horizontal midplane, with the largest density gradients occurring at the corners at the midheight, where hot and cold plumes mix in the form of strong counter-rotating eddies.

A single-wave-number representation of a nonlinear energy spectrum, i.e., a stretching-energy spectrum, is found in elastic-wave turbulence governed by the Föppl–von Kármán (FvK) equation. The representation enables energy decomposition analysis in the wave-number space and analytical expressions of detailed energy budgets in the nonlinear interactions. We numerically solved the FvK equation and observed the following facts. Kinetic energy and bending energy are comparable with each other at large wave numbers as the weak turbulence theory suggests. On the other hand, stretching energy is larger than the bending energy at small wave numbers, i.e., the nonlinearity is relatively strong. The strong correlation between a mode $a_{\mathit{k}}$ and its companion mode $a_{-\mathit{k}}$ is observed at the small wave numbers. The energy is input into the wave field through stretching-energy transfer at the small wave numbers, and dissipated through the quartic part of kinetic-energy transfer at the large wave numbers. Total-energy flux consistent with energy conservation is calculated directly by using the analytical expression of the total-energy transfer, and the forward energy cascade is observed clearly.

Pedestrian dynamic models are typically designed for comfortable walking or slightly congested conditions and typically use a single disk or combination of three disks for the shape of a pedestrian. Under crowd conditions, a more accurate pedestrian shape has advantages over the traditional single or three-disks model. We developed a method for simulating pedestrian dynamics in a large dense crowd of spheropolygons adapted to the cross section of the chest and arms of a pedestrian. Our numerical model calculates pedestrian motion from Newton's second law, taking into account viscoelastic contact forces, contact friction, and ground-reaction forces. Ground-reaction torque was taken to arise solely from the pedestrians' orientation toward their preferred destination. Simulations of counterflow pedestrians dynamics in corridors were used to gain insight into a tragic incident at the Madrid Arena pavilion in Spain, where five girls were crushed to death. The incident took place at a Halloween Celebration in 2012, in a long, densely crowded hallway used as entrance and exit at the same time. Our simulations reconstruct the mechanism of clogging in the hallway. The hypothetical case of a total evacuation order was also investigated. The results highlights the importance of the pedestrians' density and the effect of counterflow in the onset of avalanches and clogging and provides an estimation of the number of injuries based on a calculation of the contact-force network between the pedestrians.

We present a methodology for fast band-structure calculations that is generally applicable to problems of elastic wave propagation in periodic media. The methodology, called Bloch mode synthesis, represents an extension of component mode synthesis, a set of substructuring techniques originally developed for structural dynamics analysis. In Bloch mode synthesis, the unit cell is divided into interior and boundary degrees-of-freedom, which are described, respectively, by a set of normal modes and a set of constraint modes. A combination of these mode sets then forms a reduced basis for the band structure eigenvalue problem. The reduction is demonstrated on a phononic-crystal model and a locally resonant elastic-metamaterial model and is shown to accurately predict the frequencies and Bloch mode shapes with a dramatic decrease in computation time in excess of two orders of magnitude.