Microswimmers show a variety of collective motions. Despite extensive study, questions remain regarding the role of near-field fluid mechanics in collective motion. In this paper, we describe precisely the Stokes flow around hydrodynamically interacting ellipsoidal squirmers in a monolayer suspension. The results showed that various collective motions, such as ordering, aggregation, and whirls, are dominated by the swimming mode and the aspect ratio. The collective motions are mainly induced by near-field fluid mechanics, despite Stokes flow propagation over a long range. These results emphasize the importance of particle shape in collective motion.

By using large scale numerical simulations, we obtain fractal structure, which develops at originally planar flame fronts due to the hydrodynamic Darrieus-Landau (DL) instability bending the fronts. We clarify some important issues regarding the DL fractal flames, which have been debated for a long time. We demonstrate an increase of the flame propagation speed with the hypothetic channel width, which controls the length scale of the instability development. We show that this increase may be fitted by a power law indicating the mean fractal properties of the flame front structure. The power exponent in this law is found to be not a universal constant, rather it depends on the flame properties—on the density drop at the front. Using box counting on the simulated flame front shapes we show the fractal flame dimension at the intermediate scale is smaller than the one given by the power law, but it has a similar dependency on the density drop. We also obtain a formation of pockets at the DL fractal flame fronts, which previously has been associated only with turbulent burning.

The nonlinear theory of amplitude modulation of electrostatic wave envelopes in a collisionless electron-positron (EP) pair plasma is studied by using a set of Vlasov-Poisson equations in the context of Tsallis' $q\text{-nonextensive}$ statistics. In particular, the previous linear theory of Langmuir oscillations in EP plasmas [Saberian and Esfandyari-Kalejahi, Phys. Rev. E 87, 053112 (2013)] is rectified and modified. Applying the multiple scale technique (MST), it is shown that the evolution of electrostatic wave envelopes is governed by a nonlinear Schrödinger (NLS) equation with a nonlocal nonlinear term $\propto \mathcal{P}\int |\varphi ({\xi }^{\prime },\tau ){|}^{2}d{\xi }^{\prime }\varphi /(\xi -{\xi }^{\prime })$ [where $\mathcal{P}$ denotes the Cauchy principal value, $\varphi$ is the small-amplitude electrostatic (complex) potential, and $\xi$ and $\tau$ are the stretched coordinates in MST], which appears due to the wave-particle resonance. It is found that a subregion $1/3<q\lesssim 3/5$ of superextensivity $(q<1)$ exists where the carrier-wave frequency can turn over with the group velocity going to zero and then to negative values. The effects of the nonlocal nonlinear term and the nonextensive parameter $q$ are examined on the modulational instability of wave envelopes, as well as on the solitary wave solution of the NLS equation. It is found that the modulated wave packet is always unstable (nonlinear Landau damping) due to the nonlocal nonlinearity in the NLS equation. Furthermore, the effect of the nonlinear Landau damping is to slow down the amplitude of the wave envelope, and the corresponding decay rate can be faster the larger is the number of superthermal particles in pair plasmas.

The development of transverse instability in the radiation-pressure-acceleration dominant laser-foil interaction is numerically examined by two-dimensional particle-in-cell simulations. When a plane laser impinges on a foil with modulated surface, the transverse instability is incited, and periodic perturbations of the proton density develop. The growth rate of the transverse instability is numerically diagnosed. It is found that the linear growth of the transverse instability lasts only a few laser periods, then the instability gets saturated. In order to optimize the modulation wavelength of the target, a method of information entropy is put forward to describe the chaos degree of the transverse instability. With appropriate modulation, the transverse instability shows a low chaos degree, and a quasi-monoenergetic proton beam is produced.

The equations of motion of a single particle subject to an arbitrary electric and a static magnetic field form a Poisson system. We present a second-order time integration method which preserves well the Poisson structure and compare it to commonly used algorithms, such as the Boris scheme. All the methods are represented in a general framework of splitting methods. We use the so-called $\varphi$ functions, which give efficient ways for both analyzing and implementing the algorithms. Numerical experiments show an excellent long term stability for the method considered.

We propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize “perturbation modularity,” defined as the autocovariance of coarse-grained perturbed trajectories. The measure effectively separates the fast intramodular from the slow intermodular dynamics of perturbation spreading (in this respect, it is a generalization of the “Markov stability” method of network community detection). Our approach captures variation of modular organization across different system states, time scales, and in response to different kinds of perturbations: aspects of modularity which are all relevant to real-world dynamical systems. It offers a principled alternative to detecting communities in networks of statistical dependencies between system variables (e.g., “relevance networks” or “functional networks”). Using coupled logistic maps, we demonstrate that the method uncovers hierarchical modular organization planted in a system's coupling matrix. Additionally, in homogeneously coupled map lattices, it identifies the presence of self-organized modularity that depends on the initial state, dynamical parameters, and type of perturbations. Our approach offers a powerful tool for exploring the modular organization of complex dynamical systems.

Disordered jammed packings under confinement have received considerably less attention than their bulk counterparts and yet arise in a variety of practical situations. In this work, we study binary sphere packings that are confined between two parallel hard planes and generalize the Torquato-Jiao (TJ) sequential linear programming algorithm [Phys. Rev. E 82, 061302 (2010)] to obtain putative maximally random jammed (MRJ) packings that are exactly isostatic with high fidelity over a large range of plane separation distances $H$, small to large sphere radius ratio $\alpha$, and small sphere relative concentration $x$. We find that packing characteristics can be substantially different from their bulk analogs, which is due to what we term “confinement frustration.” Rattlers in confined packings are generally more prevalent than those in their bulk counterparts. We observe that packing fraction, rattler fraction, and degree of disorder of MRJ packings generally increase with $H$, though exceptions exist. Discontinuities in the packing characteristics as $H$ varies in the vicinity of certain values of $H$ are due to associated discontinuous transitions between different jammed states. When the plane separation distance is on the order of two large-sphere diameters or less, the packings exhibit salient two-dimensional features; when the plane separation distance exceeds about 30 large-sphere diameters, the packings approach three-dimensional bulk packings. As the size contrast increases (as $\alpha$ decreases), the rattler fraction dramatically increases due to what we call “size-disparity” frustration. We find that at intermediate $\alpha$ and when $x$ is about 0.5 (50-50 mixture), the disorder of packings is maximized, as measured by an order metric $\psi$ that is based on the number density fluctuations in the direction perpendicular to the hard walls. We also apply the local volume-fraction variance ${\sigma }_{\tau }^2\left(R\right)$ to characterize confined packings and find that these packings possess essentially the same level of hyperuniformity as their bulk counterparts. Our findings are generally relevant to confined packings that arise in biology (e.g., structural color in birds and insects) and may have implications for the creation of high-density powders and improved battery designs.

Some issues that arise when modeling elastic energy for binary alloys are discussed within the context of a Keating model and density-functional calculations. The Keating model is a simplified atomistic formulation based on modeling elastic interactions of a binary alloy with harmonic springs whose equilibrium length is species dependent. It is demonstrated that the continuum limit for the strain field are the usual equations of linear elasticity for alloys and that they correctly capture the coarse-grained behavior of the displacement field. In addition, it is established that Euler-Lagrange equation of the continuum limit of the elastic energy will yield the same strain field equation. This is the same energy functional that is often used to model elastic effects in binary alloys. However, a direct calculation of the elastic energy atomistic model reveals that the continuum expression for the elastic energy is both qualitatively and quantitatively incorrect. This is because it does not take atomistic scale compositional nonuniformity into account. Importantly, this result also shows that finely mixed alloys tend to have more elastic energy than segregated systems, which is the exact opposite of predictions made by some continuum theories. It is also shown that for strained thin films the traditionally used effective misfit for alloys systematically underestimate the strain energy. In some models, this drawback is handled by including an elastic contribution to the enthalpy of mixing, which is characterized in terms of the continuum concentration. The direct calculation of the atomistic model reveals that this approach suffers serious difficulties. It is demonstrated that elastic contribution to the enthalpy of mixing is nonisotropic and scale dependent. It is also shown that such effects are present in density-functional theory calculations for the Si-Ge system. This work demonstrates that it is critical to include the microscopic arrangements in any elastic model to achieve even qualitatively correct behavior.

We investigated the effect of charge on the membrane morphology of giant unilamellar vesicles (GUVs) composed of various mixtures containing charged lipids. We observed the membrane morphologies by fluorescent and confocal laser microscopy in lipid mixtures consisting of a neutral unsaturated lipid [dioleoylphosphatidylcholine (DOPC)], a neutral saturated lipid [dipalmitoylphosphatidylcholine (DPPC)], a charged unsaturated lipid [dioleoylphosphatidylglycerol $\left(\mathrm{DOP}{\mathrm{G}}^{(-)}\right)$], a charged saturated lipid [dipalmitoylphosphatidylglycerol $\left(\mathrm{DPP}{\mathrm{G}}^{(-)}\right)$], and cholesterol (Chol). In binary mixtures of neutral DOPC-DPPC and charged $\mathrm{DOPC}\text{−}\mathrm{DPP}{\mathrm{G}}^{(-)}$, spherical vesicles were formed. On the other hand, pore formation was often observed with GUVs consisting of $\mathrm{DOP}{\mathrm{G}}^{(-)}$ and DPPC. In a $\text{DPPC-DPP}{\mathrm{G}}^{(-)}$-Chol ternary mixture, pore-formed vesicles were also frequently observed. The percentage of pore-formed vesicles increased with the $\mathrm{DPP}{\mathrm{G}}^{(-)}$ concentration. Moreover, when the head group charges of charged lipids were screened by the addition of salt, pore-formed vesicles were suppressed in both the binary and ternary charged lipid mixtures. We discuss the mechanisms of pore formation in charged lipid mixtures and the relationship between phase separation and the membrane morphology. Finally, we reproduce the results seen in experimental systems by using coarse-grained molecular dynamics simulations.

We revisit the deduction of the exit probability of the one-dimensional Sznajd model through the Kirkwood approximation [F. Slanina et al., Europhys. Lett. 82, 18006 (2008)]. This approximation is peculiar in that, in spite of the agreement with simulation results [F. Slanina et al., Europhys. Lett. 82, 18006 (2008); R. Lambiotte and S. Redner, Europhys. Lett. 82, 18007 (2008); A. M. Timpanaro and C. P. C. Prado, Phys. Rev. E 89, 052808 (2014)], the hypothesis about the correlation lengths behind it are inconsistent and fixing these inconsistencies leads to the same results as a simple mean field. We use an extended version of the Sznajd model to test the Kirkwood approximation in a wider context. This model includes the voter, Sznajd, and “United we stand, divided we fall” models [R. A. Holley and T. M. Liggett, Ann. Prob. 3, 643 (1975); K. Sznajd-Weron and J. Sznajd, Int. J. Mod. Phys. C 11, 1157 (2000)] as different parameter combinations, meaning that some analytical results from these models can be used to evaluate the performance of the Kirkwood approximation. We also compare the predicted exit probability with simulation results for networks with ${10}^3$ sites. The results show clearly the regions in parameter space where the approximation gives accurate predictions, as well as where it starts failing, leading to a better understanding of its reliability.

We have revealed a growing local speed wave of increase in speed that can randomly occur in synchronized flow (S) at a highway bottleneck. The development of such a traffic flow instability leads to free flow (F) at the bottleneck; therefore, we call this instability an $\mathrm{S}\to \mathrm{F}$ instability. Whereas the $\mathrm{S}\to \mathrm{F}$ instability leads to a local increase in speed (growing acceleration wave), in contrast, the classical traffic flow instability introduced in the 1950s–1960s and incorporated later in a huge number of traffic flow models leads to a growing wave of a local decrease in speed (growing deceleration wave). We have found that the $\mathrm{S}\to \mathrm{F}$ instability can occur only if there is a finite time delay in driver overacceleration. The initial speed disturbance of increase in speed (called “speed peak”) that initiates the $\mathrm{S}\to \mathrm{F}$ instability occurs usually at the downstream front of synchronized flow at the bottleneck. There can be many speed peaks with random amplitudes that occur randomly over time. It has been found that the $\mathrm{S}\to \mathrm{F}$ instability exhibits a nucleation nature: Only when a speed peak amplitude is large enough can the $\mathrm{S}\to \mathrm{F}$ instability occur; in contrast, speed peaks of smaller amplitudes cause dissolving speed waves of a local increase in speed (dissolving acceleration waves) in synchronized flow. We have found that the $\mathrm{S}\to \mathrm{F}$ instability governs traffic breakdown—a phase transition from free flow to synchronized flow ($\mathrm{F}\to \mathrm{S}$ transition) at the bottleneck: The nucleation nature of the $\mathrm{S}\to \mathrm{F}$ instability explains the metastability of free flow with respect to an $\mathrm{F}\to \mathrm{S}$ transition at the bottleneck.

The dissipative chaotic dynamics of a particle subjected to a horizontally vibrating periodic potential is characterized theoretically and confirmed numerically in the case of an external chaos-controlling periodic excitation also acting on the particle. Theoretical predictions concerning the chaotic threshold in parameter space are deduced from the application of Melnikov's method that fully determine the chaos-control scenario. Also, the structure of diverse regularization regions in parameter space is explained theoretically with the aid of an energy analysis. It was found that the phase difference between the two periodic excitations involved plays a crucial role in the chaos-control scenario, with the particular feature that its optimal value depends upon the ratio between the damping coefficient and the excitation frequency. This constitutes a genuine feature of the chaos-control scenario associated with nonsteady potentials which is in contrast to the case of steady potentials. Additionally, we demonstrate the robustness of the chaos-control scenario against the presence of low-intensity Gaussian noise and reshaping of chaos-suppressing excitations.

The finest state-space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation, the stochastic neighborhoods of deterministic periodic orbits can be computed from distributions stationary under the action of a local Fokker-Planck operator and its adjoint. We derive explicit formulas for widths of these distributions in the case of chaotic dynamics, when the periodic orbits are hyperbolic. The resulting neighborhoods form a basis for functions on the attractor. The global stationary distribution, needed for calculation of long-time expectation values of observables, can be expressed in this basis.

Capillary desaturation experiments produce disconnected (trapped) ganglia of mesoscopic sizes intermediate between pore size and system size. Experimental evidence for interactions between these mesoscale clusters during desaturation is analyzed and discussed within the established microscopic and macroscopic laws of Newton, Young-Laplace, and Darcy. A theoretical expression for capillary number correlations is introduced that seems to have remained unnoticed. It expresses capillary desaturation curves in terms of stationary capillary pressures and relative permeabilities. The theoretical expression shows that the plateau saturation in capillary desaturation curves may in general differ from the residual nonwetting saturation defined through the saturation limit of the main hysteresis loop. Hysteresis effects as well as the difference between wetting and nonwetting fluids are introduced into the analysis of capillary desaturation experiments. The article examines experiments with different desaturation protocols and discusses the existence of a mesoscopic length scale intermediate between pore scale and sample scale. The theoretical expression is derived entirely within the existing traditional theory of two-phase flow in porous media and compared to a recent experiment.

We consider a harmonically driven acoustic medium in the form of a (finite length) highly nonlinear granular crystal with an amplitude- and frequency-dependent boundary drive. Despite the absence of a linear spectrum in the system, we identify resonant periodic propagation whereby the crystal responds at integer multiples of the drive period and observe that this can lead to local maxima of transmitted force at its fixed boundary. In addition, we identify and discuss minima of the transmitted force (“antiresonances”) between these resonances. Representative one-parameter complex bifurcation diagrams involve period doublings and Neimark-Sacker bifurcations as well as multiple isolas (e.g., of period-3, -4, or -5 solutions entrained by the forcing). We combine them in a more detailed, two-parameter bifurcation diagram describing the stability of such responses to both frequency and amplitude variations of the drive. This picture supports a notion of a (purely) “nonlinear spectrum” in a system which allows no sound wave propagation (due to zero sound speed: the so-called sonic vacuum). We rationalize this behavior in terms of purely nonlinear building blocks: apparent traveling and standing nonlinear waves.

In this work, a numerical scheme based on multipoles and Stokeslet is proposed for calculating the radiation force acting on a single rigid sphere in a viscous fluid. First-order velocity and pressure are obtained from the multipole series solution, and the volumetric force in the acoustic streaming is subsequently calculated from the first-order velocity and pressure. The acoustic streaming equations are solved using the Stokeslet method within a finite domain descretized by tetrahedral elements. The boundary conditions for streaming are imposed using the weighted residue method to obtain the unknown coefficients in the multipole series expansion for the second-order velocity potentials. The radiation forces obtained from this multipole-Stokeslet method match well with Doinikov's series solution, for a wide range of the sphere size. Compared to the complicated series solution, the multipole-Stokeslet method can be easily implemented without the evaluation of the semi-infinite integrals.

The article by M. Wacławczyk et al. [Phys. Rev. E 90, 013022 (2014)] proposes two new statistical symmetries in the classical theory for turbulent hydrodynamic flows. In this Comment, however, we show that both symmetries are unphysical due to violating the principle of causality. In addition, they must get broken in order to be consistent with all physical constraints naturally arising in the statistical Lundgren-Monin-Novikov (LMN) description of turbulence. As a result, we state that besides the well-known classical symmetries of the LMN equations no new statistical symmetries exist. Finally, we criticize the relation between intermittency and global symmetries as it is presented throughout that study.

In this Reply we respond to the criticism of Frewer et al. presented in the Comment on “Statistical symmetries of the Lundgren-Monin-Novikov hierarchy” by Wacławczyk et al. [Phys. Rev. E 90, 013022 (2014)]. We discuss physical interpretation of the statistical symmetries, and respond to criticism on the violation of the causality principle. We derive the Lundgren-Monin-Novikov equations for a flow with boundaries. Last, we stress that our work addressed the phenomenon of “external intermittency” (separation between laminar and turbulent flow), and not “internal intermittency” (strong fluctuations at small scales).

We derive a local-time path-integral representation for a generic one-dimensional time-independent system. In particular, we show how to rephrase the matrix elements of the Bloch density matrix as a path integral over $x$-dependent local-time profiles. The latter quantify the time that the sample paths $x\left(t\right)$ in the Feynman path integral spend in the vicinity of an arbitrary point $x$. Generalization of the local-time representation that includes arbitrary functionals of the local time is also provided. We argue that the results obtained represent a powerful alternative to the traditional Feynman-Kac formula, particularly in the high- and low-temperature regimes. To illustrate this point, we apply our local-time representation to analyze the asymptotic behavior of the Bloch density matrix at low temperatures. Further salient issues, such as connections with the Sturm-Liouville theory and the Rayleigh-Ritz variational principle, are also discussed.