We introduce a way of characterizing an ensemble of interacting oscillators in terms of their mean-field variability index $\kappa$, a dimensionless parameter defined as the variance of the oscillators’ mean field $r$ divided by the mean square of $r$. Based on the assumption that the overall mean field is the sum of a very large number of oscillators, each giving a small contribution to the total signal, we show that $\kappa$ depends on the mutual interactions between the oscillators, independently of their number or spectral properties. For purely random phasors, or a noninteracting ensemble of oscillators, $\kappa$ converges on $0.215$. Interactions push $\kappa$ in different directions: lower where there is interoscillator phase coherence, tending to zero for complete phase synchronization, or higher for amplitude synchronization or intermittent synchronization. We calculate $\kappa$ for several different cases to illustrate its utility, using both numerically simulated data and electroencephalograph signals from the brains of human subjects while awake, while anesthetized, and while undergoing an epileptic fit.

Spontaneous rotation of a droplet induced by the Marangoni flow is analyzed in a two-dimensional system. The droplet with the small particle which supplies a surfactant at the interface is considered. We calculated flow field around the droplet using the Stokes equation and found that advective nonlinearity breaks symmetry for rotation. Theoretical calculation indicates that the droplet spontaneously rotates when the radius of the droplet is an appropriate size. The theoretical results were validated through comparison with the experiments.

Understanding the influence of topographic heterogeneities on liquid flows has become an important issue with the development of microfluidic systems, and more generally for the manipulation of liquids at the small scale. Most studies of the boundary flow past such surfaces have concerned poorly wetting liquids for which the topography acts to generate superhydrophobic slip. Here we focus on topographically patterned but chemically homogeneous surfaces, and measure a drag force on a sphere approaching a plane decorated with lyophilic microscopic grooves. A significant decrease in the force compared with predicted even for a superhydrophobic surface is observed. To quantify the force we use the effective no-slip boundary condition, which is applied at the imaginary smooth homogeneous isotropic surface located at an intermediate position between the top and bottom of grooves. We relate its location to a surface topology by a simple, but accurate analytical formula. Since grooves represent the most anisotropic surface, our conclusions are valid for any texture, and suggest rules for the rational design of topographically patterned surfaces to generate desired drag.

This paper studies a periodic one-dimensional exclusion process composed of a driven part and a biased diffusive part in a mesoscopic limit. It is shown that, depending on the biased diffusion parameter $\delta$, rich phase diagram structures appear in which diverse phases have been exhibited and the density profile in the diffusive part is qualitatively different. This is because the domain wall is behaving differently. Our analytical results are in good agreement with Monte Carlo simulations.

The apparent shear viscosity of $p$-methoxybenzylidene-$p$${}^{\prime }$-$n$-butylaniline in the presence of electrohydrodynamic convection (EHC) is investigated experimentally. In the absence of an electric field, directors are almost aligned along the flow direction such that the viscosity is close to the minimum of the Miesowicz viscosities. Since EHC disturbs the flow-aligned director configuration, the viscosity increases as the applied voltage is increased in the low-voltage regime. In the high-voltage regime, however, further increasing the voltage leads to a decrease in viscosity. Microscope observations using a rheometer reveal that the decrease in viscosity occurs in the dynamic scattering mode 2 (DSM2) state, whose spatial director distribution is anisotropic due to the shear flow. By adopting the Ericksen-Leslie theory for the shear flow under the electric field, we find that the viscosity decrease can be attributed to the negative contribution of the electric stress caused by the anisotropic director distribution of the DSM2 state.

Lognormality was found experimentally for coarse-grained squared turbulence velocity and velocity increment when the coarsening scale is comparable to the correlation scale of the velocity [Mouri et al., Phys. Fluids 21, 065107 (2009)]. We investigate this large-scale lognormality by using a simple stochastic process with correlation, the Ornstein-Uhlenbeck (OU) process. It is shown that the OU process has a similar large-scale lognormality, which is studied numerically and analytically.

The coupling between deformation and motion in a self-propelled system has attracted broader interest. In the present study, we consider an elliptic camphor particle for investigating the effect of particle shape on spontaneous motion. It is concluded that the symmetric spatial distribution of camphor molecules at the water surface becomes unstable first in the direction of a short axis, which induces the camphor disk motion in this direction. Experimental results also support the theoretical analysis. From the present results, we suggest that when an elliptic particle supplies surface-active molecules to the water surface, the particle can exhibit translational motion only in the short-axis direction.

A finite quantum system evolving unitarily equilibrates in a probabilistic fashion. In the general many-body setting the time fluctuations of an observable $\mathcal{A}$ are typically exponentially small in the system size. We consider here quasifree Fermi systems where the Hamiltonian and observables are quadratic in the Fermi operators. We first prove a bound on the temporal fluctuations $\Delta {\mathcal{A}}^2$ and then map the equilibration dynamics to a generalized classical $XY$ model in the infinite temperature limit. Using this insight, we conjecture that, in most cases, a central limit theorem can be formulated, leading to what we call Gaussian equilibration: observables display a Gaussian distribution with relative error $\Delta \mathcal{A}/\overline{\mathcal{A}}=O\left(L^{-1/2}\right)$, where $L$ is the dimension of the single-particle space. The conjecture, corroborated by numerical evidence, is proven analytically under mild assumptions for the magnetization in the quantum $XY$ model and for a class of observables in a tight-binding model. We also show that the variance is discontinuous at the transition between a quasifree model and a nonintegrable one.

A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass $m$, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter ($\chi$) controlling the nonlinearity of the moving wall. For large $\chi$, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization.

A refined two-term helical subgrid-scale (SGS) stress model with respect to that suggested by Li et al. [Phys. Rev. E 74, 026310 (2006)] is designed for large-eddy simulation (LES) of helical turbulence. The model coefficients in the new model are verified a priori to be scale invariant in inertial range, which proves that our model is local in scale. A dynamic method based on minimizing the residual resolved energy and helicity dissipations is suggested to simultaneously evaluate the coefficients of the mixed SGS model as the simulation progresses. In addition, an SGS helicity dissipation (or helicity flux) constraint condition is proposed to optimize the mixed two-term model. Both techniques are first tested and validated in the LES of forced isotropic helical turbulence. The statistical results are analyzed and compared with those obtained from the dynamic Smagorinsky model, the traditional dynamic mixed model, and the direct numerical simulation. It is found that the introduction of this dynamic procedure can help overcome the drawback of the traditional dynamic method which can not capture the negative helicity fluxes and SGS dissipations. The probability density functions of the energy flux and the conditioned helicity flux and SGS stress demonstrate that the helicity flux constrained dynamic SGS model can effectively predict the real SGS helical effects on the resolved scales, such as backscatters of energy and helicity, accurate helicity dissipation rate, and so on. The present models are also applied to the simulation of freely decaying isotropic turbulence with no apparent improvement observed in comparison with the traditional SGS models. The underlying reasons for these issues are addressed in detail.

The formalisms of Wyld [Ann. Phys. 14, 143 (1961)] and Martin, Siggia, and Rose (MSR) [Phys. Rev. A 8, 423 (1973)] address the closure problem of a statistical treatment of homogeneous isotropic turbulence (HIT) based on techniques primarily developed for quantum field theory. In the Wyld formalism, there is a well-known double-counting problem, for which an ad hoc solution was suggested by Lee [Ann. Phys. 32, 292 (1965)]. We show how to implement this correction in a more natural way from the basic equations of the formalism. This leads to what we call the Improved Wyld-Lee Renormalized Perturbation Theory. MSR had noted that their formalism had more vertex functions than Wyld's formalism and based on this felt Wyld's formalism was incorrect. However a careful comparison of both formalisms here shows that the Wyld formalism follows a different procedure to that of the MSR formalism and so the treatment of vertex corrections appears in different ways in the two formalisms. Taking that into account, along with clarifications made to both formalisms, we find that they are equivalent and we demonstrate this up to fourth order.

A two-dimensional (2D) linear theory of the instability of Sweet-Parker (SP) current sheets is developed in the framework of reduced magnetohydrodynamics. A local analysis is performed taking into account the dependence of a generic equilibrium profile on the outflow coordinate. The plasmoid instability [Loureiro et al., Phys. Plasmas 14, 100703 (2007)] is recovered, i.e., current sheets are unstable to the formation of a large-wave-number chain of plasmoids ($k_{\max }{L}_{\mathrm{CS}}\sim S^{3/8}$, where $k_{\max }$ is the wave number of fastest growing mode, $S=L_{\mathrm{CS}}{V}_A/\eta$ is the Lundquist number, $L_{\mathrm{CS}}$ is the length of the sheet, $V_A$ is the Alfvén speed, and $\eta$ is the plasma resistivity), which grows super Alfvénically fast (${\gamma }_{\max }{\tau }_A\sim S^{1/4}$, where ${\gamma }_{\max }$ is the maximum growth rate, and ${\tau }_A=L_{\mathrm{CS}}/V_A$). For typical background profiles, the growth rate and the wave number are found to increase in the outflow direction. This is due to the presence of another mode, the Kelvin-Helmholtz (KH) instability, which is triggered at the periphery of the layer, where the outflow velocity exceeds the Alfvén speed associated with the upstream magnetic field. The KH instability grows even faster than the plasmoid instability ${\gamma }_{\max }{\tau }_A\sim k_{\max }{L}_{\mathrm{CS}}\sim S^{1/2}$. The effect of viscosity ($\nu$) on the plasmoid instability is also addressed. In the limit of large magnetic Prandtl numbers $\mathrm{Pm}=\nu /\eta$, it is found that ${\gamma }_{\max }\sim S^{1/4}{\mathrm{Pm}}^{-5/8}$ and $k_{\max }{L}_{\mathrm{CS}}\sim S^{3/8}{\mathrm{Pm}}^{-3/16}$, leading to the prediction that the critical Lundquist number for plasmoid instability in the $\mathrm{Pm}\gg 1$ regime is $S_{\mathrm{crit}}\sim {10}^4{\mathrm{Pm}}^{1/2}$. These results are verified via direct numerical simulation of the linearized equations, using an analytical 2D SP equilibrium solution.

An effect of a nonlocal plasma response caused by local laser radiation exciting atoms in resonant and metastable states is observed in a dc neon glow discharge. Starting at the perturbed position, spatially damped oscillations in the direction of the anode effecting all plasma quantities are created. Depending on the excitation of resonant or metastable atoms, the oscillations are phase-shifted by $\pi$. If the laser excites in particular a cycling transition, no nonlocal plasma response is observed. The relaxation of the plasma is investigated by means of visible light measurements using a line camera in the vicinity of the axial perturbation position. The effect is modeled in terms of nonlocal electron kinetics by solving the spatially inhomogeneous electron Boltzmann equation.

We experimentally study the role of forcing on gravity-capillary wave turbulence. Previous laboratory experiments using spatially localized forcing (vibrating blades) have shown that the frequency power-law exponent of the gravity wave spectrum depends on the forcing parameters. By horizontally vibrating the whole container, we observe a spectrum exponent that does not depend on the forcing parameters for both gravity and capillary regimes. This spatially extended forcing leads to a gravity spectrum exponent in better agreement with the theory than by using a spatially localized forcing. The role of the vessel shape has been also studied. Finally, the wave spectrum is found to scale linearly with the injected power for both regimes whatever the forcing type used.

We propose a toy model of a heteropolymer chain capable of forming planar secondary structures typical for RNA molecules. In this model, the sequential intervals between neighboring monomers along a chain are considered as quenched random variables, and energies of nonlocal bonds are assumed to be concave functions of those intervals. A few factors are neglected: the contribution of loop factors to the partition function, the variation in energies of different types of complementary nucleotides, the stacking interactions, and constraints on the minimal size of loops. However, the model captures well the formation of folded structures without pseudoknots in an arbitrary sequence of nucleotides. Using the optimization procedure for a special class of concave-type potentials, borrowed from optimal transport analysis, we derive the local difference equation for the ground state free energy of the chain with the planar (RNA-like) architecture of paired links. We consider various distribution functions of intervals between neighboring monomers (truncated Gaussian and scale free) and demonstrate the existence of a topological crossover from sequential to essentially nested configurations of paired links.

We study the effect of spatial structure, genetic drift, mutation, and selective pressure on the evolutionary dynamics in a simplified model of asexual organisms colonizing a new territory. Under an appropriate coarse-graining, the evolutionary dynamics is related to the directed percolation processes that arise in voter models, the Domany-Kinzel (DK) model, contact process, and so on. We explore the differences between linear (flat front) expansions and the much less familiar radial (curved front) range expansions. For the radial expansion, we develop a generalized, off-lattice DK model that minimizes otherwise persistent lattice artifacts. With both simulations and analytical techniques, we study the survival probability of advantageous mutants, the spatial correlations between domains of neutral strains, and the dynamics of populations with deleterious mutations. “Inflation” at the frontier leads to striking differences between radial and linear expansions. For a colony with initial radius $R_0$ expanding at velocity $v$, significant genetic demixing, caused by local genetic drift, occurs only up to a finite time $t^{*}=R_0/v$, after which portions of the colony become causally disconnected due to the inflating perimeter of the expanding front. As a result, the effect of a selective advantage is amplified relative to genetic drift, increasing the survival probability of advantageous mutants. Inflation also modifies the underlying directed percolation transition, introducing novel scaling functions and modifications similar to a finite-size effect. Finally, we consider radial range expansions with deflating perimeters, as might arise from colonization initiated along the shores of an island.

We present the results of a large-scale numerical study of the equilibrium three-dimensional Edwards-Anderson Ising spin glass with Gaussian disorder. Using parallel tempering (replica exchange) Monte Carlo we measure various static, as well as dynamical quantities, such as the autocorrelation times and round-trip times for the parallel tempering Monte Carlo method. The correlation between static and dynamic observables for 5000 disorder realizations and up to 1000 spins down to temperatures at 20$\%$ of the critical temperature is examined. Our results show that autocorrelation times are directly correlated with the roughness of the free-energy landscape.

We apply a unified and trade-off based optimization for low-dissipation models of cyclic heat devices which accounts for both useful energy and losses. The resulting performance regime lies between those of maximum first-law efficiency and maximum $\chi$ (a unified figure of merit corresponding to power output of heat engines). The bounds available for both symmetric and extremely asymmetric heat devices are explicitly obtained. The similarities for heat engines and refrigerators and the energetic advantages of the trade-off optimization are especially stressed.

Nonequilibrium mode-coupling theory (MCT) for uniformly sheared underdamped systems is developed, starting from the microscopic thermostated Sllod equation and the corresponding Liouville equation. Special attention is paid to the translational invariance in the sheared frame, which requires an appropriate definition of the transient time correlators. The derived MCT equation satisfies the alignment of the wave vectors and is manifestly translationally invariant. Isothermal condition is implemented by the introduction of current fluctuation in the dissipative coupling to the thermostat. This current fluctuation grows in the $\alpha$ relaxation regime, which generates a pronounced relaxation of the yield stress compared to the overdamped case. This result fills the gap between the molecular dynamics simulation and the overdamped MCT reported previously. The response to a perturbation of the shear rate demonstrates an inertia effect which is not observed in the overdamped case. Our theory turns out to be a nontrivial extension of the theory by Fuchs and Cates [J. Rheol. 53, 957 (2009)] to underdamped systems. Since our starting point is identical to that of Chong and Kim [Phys. Rev. E 79, 021203 (2009)], the contradictions between Fuchs-Cates and Chong-Kim are resolved.