Anticipation is a strategy used by neural fields to compensate for transmission and processing delays during the tracking of dynamical information and can be achieved by slow, localized, inhibitory feedback mechanisms such as short-term synaptic depression, spike-frequency adaptation, or inhibitory feedback from other layers. Based on the translational symmetry of the mobile network states, we derive generic fluctuation-response relations, providing unified predictions that link their tracking behaviors in the presence of external stimuli to the intrinsic dynamics of the neural fields in their absence.

Despite disassortativity being commonly observed in many biological networks, our current understanding of its evolutionary origin is inadequate. Motivated by the occurrence of mutations during an evolutionary time span that results in changes in the behavior of interactions, we demonstrate that if we maximize the stability of the underlying system, the genetic algorithm leads to the evolution of a disassortative structure. The mutation probability governs the degree of saturation of the disassortativity coefficient, and this reveals the origin of the wide range of disassortativity values found in real systems. We analytically verify these results for star networks, and by considering various values for the antisymmetric couplings, we find a regime in which scale-free networks are more stable than the corresponding random networks.

We investigate the evolution of hydromagnetic perturbations in a small section of accretion disks. It is known that molecular viscosity is negligible in accretion disks. Hence, it has been argued that a mechanism, known as magnetorotational instability (MRI), is responsible for transporting matter in the presence of a weak magnetic field. However, there are some shortcomings, which question the effectiveness of MRI. Now the question arises, whether other hydromagnetic effects, e.g., transient growth (TG), can play an important role in bringing nonlinearity into the system, even at weak magnetic fields. In addition, it should be determined whether MRI or TG is primarily responsible for revealing nonlinearity in order to make the flow turbulent. Our results prove explicitly that the flows with a high Reynolds number (Re), which is the case for realistic astrophysical accretion disks, exhibit nonlinearity via TG of perturbation modes faster than that by modes producing MRI. For a fixed wave vector, MRI dominates over transient effects only at low Re, lower than the value expected to be in astrophysical accretion disks, and low magnetic fields. This calls into serious question the (overall) persuasiveness of MRI in astrophysical accretion disks.

The convective-to-absolute instability transition in an Oldroyd-B capillary jet subject to unrelaxed axial stress is examined theoretically. There is a critical Weber number below which the jet is absolutely unstable under axisymmetric perturbations. We analyze the dependence of this critical parameter with respect to the Reynolds and Deborah numbers, as well as the unrelaxed axial stress. For small Deborah numbers, the unrelaxed stress destabilizes the viscoelastic jet, increasing the critical Weber number for which the convective-to-absolute instability transition takes place. If the Deborah number takes higher values, then the transitional Weber number decreases as the unrelaxed stress increases until two solution branches cross each other. The dominant branch for large axial stress leads to a threshold of this quantity above which the viscoelastic jet becomes absolutely unstable independently of the Weber number. The threshold depends on neither the Reynolds nor the Deborah number for sufficiently large values of these parameters.

The drop, exposed to an air flow parallel to the substrate, starts to dislodge when the air velocity reaches some threshold value, which depends on the substrate wetting properties and drop volume. In this study the critical air velocity is measured for different drop volumes, on substrates of various wettabilities. The substrate initial temperatures varied between the normal room temperature ($24.5^{\circ }\mathrm{C}$) and subfreezing temperatures ($-5^{\circ }\mathrm{C}$ and $-1^{\circ }\mathrm{C}$). The physics of the drop did not change at the subfreezing temperatures of the substrates, which clearly indicates that the drop does not freeze and remains liquid for a relatively long time. During this time solidification is not initiated, neither by the air flow nor by mechanical disturbances. An approximate theoretical model is proposed that allows estimation of the aerodynamic forces acting on the sessile drop. The model is valid for the case when the drop height is of the same order as the thickness of the viscous boundary in the airflow, but the inertial effects are still dominant. Such a situation, relevant to many practical applications, was never modeled before. The theoretical predictions for the critical velocity of drop dislodging agree well with the experimental data for both room temperature and lower temperatures of the substrates.

We present a general approach to compute the absolute free energy of a system of particles with constrained center of mass based on the Monte Carlo thermodynamic coupling integral method. The version of the Frenkel-Ladd approach [J. Chem. Phys. 81, 3188 (1984)], which uses a harmonic coupling potential, is recovered. Also, we propose a different choice, based on one-particle square-well coupling potentials, which is much simpler, more accurate, and free from some of the difficulties of the Frenkel-Ladd method. We apply our approach to hard spheres and compare with the standard harmonic method.

Controlling segregation is both a practical and a theoretical challenge. Using a novel drum design comprising concave and convex geometry, we explore, through the application of both discrete particle simulations and positron emission particle tracking, a means by which radial size segregation may be used to drive axial segregation, resulting in an order of magnitude increase in the rate of separation. The inhomogeneous drum geometry explored also allows the direction of axial segregation within a binary granular bed to be controlled, with a stable, two-band segregation pattern being reliably and reproducibly imposed on the bed for a variety of differing system parameters. This strong banding is observed to persist even in systems that are highly constrained in the axial direction, where such segregation would not normally occur. These findings, and the explanations provided of their underlying mechanisms, could lead to radical new designs for a broad range of particle processing applications but also may potentially prove useful for medical and microflow applications.

The effect of methanol mixing on a nanoscale water flow was examined by using nonequilibrium molecular dynamics simulations of a Couette-type flow between nonpolarized smooth solid surfaces. Water and methanol molecules were uniformly mixed in the bulk, whereas at the solid-liquid interface methanol molecules showed a tendency to be adsorbed on the solid surface. Similar to a macroscale Couette flow, the shear stress exerted on the solid surface was equal to the shear stress in the liquid, showing that the mechanical balance holds in nanoscale. In addition, the shear stress in the liquid bulk was equal to the viscous stress which is a product of viscosity and velocity gradient. When more methanol molecules were adsorbed on the solid surface, the friction coefficient (FC) between solid and liquid was largely reduced with a small amount of methanol and that led to a remarkable decrease of the shear stress. The cause of the FC reduction was investigated in terms of the local rotational diffusion coefficient (RDC) near the solid surface, and it was shown that different from an existing model, the FC and local RDC were not simply inversely proportional to each other in the mixture system because the solid-liquid interfacial state was more complex.

Stimulated Brillouin scattering (SBS) is a noise-driven nonlinear interaction between acoustical and optical waves. In optical fibers, SBS can be observed at relatively low optical powers and can severely limit signal transmission. Although SBS is initiated by high dimensional noise, it also exhibits many of the hallmarks of a complex nonlinear dynamical system. We report here a comprehensive experimental and numerical study of the fluctuations in the reflected Stokes wave produced by SBS in optical fibers. Using time series analysis, we demonstrate a reduction of dimensionality and dynamical filtering of the Stokes wave. We begin with a careful comparison of the measured average transmitted and reflected intensities from below the SBS threshold to saturation of the transmitted power. Initially the power spectra and correlation functions of the time series of the reflected wave fluctuations at the SBS threshold and above are measured and simulated. Much greater dynamical insight is provided when we study the scaling behavior of the intensity fluctuations using Hurst exponents and detrended fluctuation analysis for time scales extending over six orders of magnitude. At the highest input powers, we notice the emergence of three distinct dynamical scaling regimes: persistent, Brownian, and antipersistent. Next, we explore the Hilbert phase fluctuations of the intensity time series and amplitude-phase coupling. Finally, time-delay embedding techniques reveal a gradual reduction in dimensionality of the spatiotemporal dynamics as the laser input is increased toward saturation of the transmitted power. Through all of these techniques, we find a transition from noisier to smoother dynamics with increasing input power. We find excellent agreement between our experimental measurements and simulations.

The fluctuations exhibited by the cross sections generated in a compound-nucleus reaction or, more generally, in a quantum-chaotic scattering process, when varying the excitation energy or another external parameter, are characterized by the width ${\mathrm{\Gamma }}_{\mathrm{corr}}$ of the cross-section correlation function. Brink and Stephen [Phys. Lett. 5, 77 (1963)] proposed a method for its determination by simply counting the number of maxima featured by the cross sections as a function of the parameter under consideration. They stated that the product of the average number of maxima per unit energy range and ${\mathrm{\Gamma }}_{\mathrm{corr}}$ is constant in the Ercison region of strongly overlapping resonances. We use the analogy between the scattering formalism for compound-nucleus reactions and for microwave resonators to test this method experimentally with unprecedented accuracy using large data sets and propose an analytical description for the regions of isolated and overlapping resonances.

We report unexpected results of a drastic difference in the transition to fully developed turbulent and turbulent drag reduction (TDR) regimes and in their properties in a von Karman swirling flow with counter-rotating disks of water-based polymer solutions for viscous (by smooth disks) as well as inertial (by bladed disks) forcing and by tracking just torque $\mathrm{\Gamma }\left(t\right)$ and pressure $p\left(t\right)$. For the viscous forcing, just a single TDR regime is found with the transition values of the Reynolds number (Re) ${\mathrm{Re}}_c^{\mathrm{turb}}={\mathrm{Re}}_c^{\mathrm{TDR}}\simeq (4.8\pm 0.2)\times {10}^5$ independent of $\varphi$, whereas for the inertial forcing two turbulent regimes are revealed. The first transition is to fully developed turbulence, and the second one is to the TDR regime with both ${\mathrm{Re}}_c^{\mathrm{turb}}$ and ${\mathrm{Re}}_c^{\mathrm{TDR}}$ depending on polymer concentration $\varphi$. Both regimes differ by the values of $C_f$ and $C_p$, by the scaling exponents of the fundamental turbulent characteristics, by the nonmonotonic dependencies of skewness and flatness of the pressure PDFs on Re, and by the different frequency power spectra of $p$ with the different dependencies of the main vortex peak frequency in the $p$ power spectra on $\varphi$ and Re. Thus our experimental results show the transition to the TDR regime in a von Karman swirling flow for the viscous and inertial forcings in a sharp contrast to the recent experiments [Phys. Fluids 10, 426 (1998); Phys. Rev. E 47, R28(R) (1993); and J. Phys.: Condens. Matter 17, S1195 (2005)] where the transition to TDR is observed in the same swirling flow with counter-rotating disks only for the viscous forcing. The latter result has led its authors to the wrong conclusion that TDR is a solely boundary effect contrary to the inertial forcing associated with the bulk effect, and this conception is currently rather widely accepted in literature.

We analyze the motion and deformation of a buoyant drop suspended in an unbounded fluid which is undergoing a quadratic shearing flow at small Reynolds number in the presence of slip at the interface of the drop. The boundary condition at the interface is accounted for by means of a simple Navier slip condition. Expressions for the velocity and the shape deformation of the drop are derived considering small but finite interface deformation, and results are presented for the specific cases of sedimentation, shear flow, and Poiseuille flow with previously reported results as the limiting cases of our general expressions. The presence of interfacial slip is found to markedly affect axial as well as cross-stream migration velocity of the drop in Poiseuille flow. The effect of slip is more prominent for drops with larger viscosity wherein the drop velocity increases. The presence of significant interface slippage always leads to migration of a deformed drop towards the centerline of the channel for any drop-to-medium viscosity ratio, which is in contrast to the case of no slip at the interface, which allows drop migration towards or away from the centerline depending on the viscosity ratio. We obtain the effect of slip on the cross-stream migration time scale, which quantifies the time required to reach a final steady radial position in the channel. The presence of slip at the drop interface leads to a decrease in the cross-stream migration time scale, which further results in faster motion of the drop in the cross-stream direction. Gravity in the presence of Poiseuille flow is shown to affect not only the axial motion, but also the cross-stream migration velocity of the drop; interfacial slip always increases the drop velocities.

Despite their practical and academic relevance, studies of interfacial pattern formation in confined magnetorheological (MR) fluids have been largely overlooked in the literature. In this work, we present a contribution to this soft matter research topic and investigate the emergence of interfacial instabilities when an inviscid, initially circular bubble of a Newtonian fluid is surrounded by a MR fluid in a Hele-Shaw cell apparatus. An externally applied, in-plane azimuthal magnetic field produced by a current-carrying wire induces interfacial disturbances at the two-fluid interface, and pattern-forming structures arise. Linear stability analysis, weakly nonlinear theory, and a vortex sheet approach are used to access early linear and intermediate nonlinear time regimes, as well as to determine stationary interfacial shapes at fully nonlinear stages.

Swimming cells often have to self-propel through fluids displaying non-Newtonian rheology. While past theoretical work seems to indicate that stresses arising from complex fluids should systematically hinder low-Reynolds number locomotion, experimental observations suggest that locomotion enhancement is possible. In this paper we propose a physical mechanism for locomotion enhancement of microscopic swimmers in a complex fluid. It is based on the fact that microstructured fluids will generically phase-separate near surfaces, leading to the presence of low-viscosity layers, which promote slip and decrease viscous friction near the surface of the swimmer. We use two models to address the consequence of this phase separation: a nonzero apparent slip length for the fluid and then an explicit modeling of the change of viscosity in a thin layer near the swimmer. Considering two canonical setups for low-Reynolds number locomotion, namely the waving locomotion of a two-dimensional sheet and that of a three-dimensional filament, we show that phase-separation systematically increases the locomotion speeds, possibly by orders of magnitude. We close by confronting our predictions with recent experimental results.

We present simulations of a four-component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5–200 eV with densities ranging between 0.184 and 36.8 ${\mathrm{g}/\mathrm{cm}}^3$. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. Additionally, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models based on the Coulomb coupling parameter and one-component plasmas.

Temperature inversions occur in nature, e.g., in the solar corona and in interstellar molecular clouds: Somewhat counterintuitively, denser parts of the system are colder than dilute ones. We propose a simple and appealing way to spontaneously generate temperature inversions in systems with long-range interactions, by preparing them in inhomogeneous thermal equilibrium states and then applying an impulsive perturbation. In similar situations, short-range systems would typically relax to another thermal equilibrium, with a uniform temperature profile. By contrast, in long-range systems, the interplay between wave-particle interaction and spatial inhomogeneity drives the system to nonequilibrium stationary states that generically exhibit temperature inversion. We demonstrate this mechanism in a simple mean-field model and in a two-dimensional self-gravitating system. Our work underlines the crucial role the range of interparticle interaction plays in determining the nature of steady states out of thermal equilibrium.

We report on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field, which microscopically is equivalent to a hypernetwork organization of interactions. Using a self-consistent approach and direct numerical simulations, we argue that a transition to synchrony occurs only for finite-size ensembles and disappears in the thermodynamic limit. For all considered setups, which include purely deterministic oscillators with or without heterogeneity in natural oscillatory frequencies, and an ensemble of noise-driven identical oscillators, we establish scaling relations describing the order parameter as a function of the coupling constant and the system size.

We propose an exactly solvable multisite interaction spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice for the rigorous studies of chaotic entanglement. By making use of the generalized star-triangle transformation, we map the initial model onto an effective Ising one on a Husimi lattice, which we solve then exactly by applying the recursive method. Expressing the entanglement of the Heisenberg spins, that we quantify by means of the concurrence, in terms of the magnetic quantities of the system, we demonstrate its bifurcation and chaotic behavior. Furthermore, we show that the underlying chaos may slightly enhance the amount of the entanglement and present on the phase diagram the transition lines from the uniform to periodic and from the periodic to chaotic regimes.

An Ising spin-glass model with nearest-neighbor interactions, following a symmetric probability distribution, is investigated on a hierarchical lattice of the Wheatstone-bridge family characterized by a fractal dimension $D\approx 3.58$. The interaction distribution considered is a stretched exponential, which has been shown recently to be very close to the fixed-point coupling distribution, and such a model has been considered lately as a good approach for Ising spin glasses on a cubic lattice. An exact recursion procedure is implemented for calculating site magnetizations, $m_i={\langle S_i\rangle }_T$, as well as correlations between pairs of nearest-neighbor spins, ${\langle S_i{S}_j\rangle }_T$ (${\langle \rangle }_T$ denote thermal averages), for a given set of interaction couplings on this lattice. From these local magnetizations and correlations, one can compute important physical quantities, such as the Edwards-Anderson order parameter, the internal energy, and the specific heat. Considering extrapolations to the thermodynamic limit for the order parameter, such as a finite-size scaling approach, it is possible to obtain directly the critical temperature and critical exponents. The transition between the spin-glass and paramagnetic phases is analyzed, and the associated critical exponents $\beta$ and $\nu$ are estimated as $\beta =0.82\left(5\right)$ and $\nu =2.50\left(4\right)$, which are in good agreement with the most recent results from extensive numerical simulations on a cubic lattice. Since these critical exponents were obtained from a fixed-point distribution, they are universal, i.e., valid for any coupling distribution considered.

We simulate dense assemblies of frictional spherical grains in steady shear flow under controlled normal stress $P$ in the presence of a small amount of an interstitial liquid, which gives rise to capillary menisci, assumed isolated (pendular regime), and attractive forces, which are hysteretic: Menisci form at contact, but do not break until grains are separated by a finite rupture distance. The system behavior depends on two dimensionless control parameters, inertial number $I$ and reduced pressure $P^{*}=aP/\left(\pi \mathrm{\Gamma }\right)$, comparing confining forces $\sim a^{2}P$ to meniscus tensile strength $F_0=\pi \mathrm{\Gamma }a$, for grains of diameter $a$ joined by menisci with surface tension $\mathrm{\Gamma }\mathrm{.}$ We pay special attention to the quasistatic limit of slow flow and observe systematic, enduring strain localization in some of the cohesion-dominated $(P^{*}\sim 0.1)$ systems. Homogeneous steady flows are characterized by the dependence of internal friction coefficient ${\mu }^{*}$ and solid fraction $\mathrm{\Phi }$ on $I$ and $P^{*}\mathrm{.}$ We also record normal stress differences, fairly small but not negligible and increasing for decreasing $P^{*}\mathrm{.}$ The system rheology is moderately sensitive to saturation within the pendular regime, but would be different in the absence of capillary hysteresis. Capillary forces have a significant effect on the macroscopic behavior of the system, up to $P^{*}$ values of several units, especially for longer force ranges associated with larger menisci. The concept of effective pressure may be used to predict an order of magnitude for the strong increase of ${\mu }^{*}$ as $P^{*}$ decreases but such a crude approach is unable to account for the complex structural changes induced by capillary cohesion, with a significant decrease of $\mathrm{\Phi }$ and different agglomeration states and anisotropic fabric. Likewise, the Mohr-Coulomb criterion for pressure-dependent critical states is, at best, an approximation valid within a restricted range of pressures, with $P^{*}\ge 1\mathrm{.}$ At small enough $P^{*}$, large clusters of interacting grains form in slow flows, in which liquid bonds survive shear strains of several units. This affects the anisotropies associated with different interactions and the shape of function ${\mu }^{*}\left(I\right)$, which departs more slowly from its quasistatic limit than in cohesionless systems (possibly explaining the shear banding tendency).