We investigate hydrodynamic fluctuations in a two-dimensional granular fluid excited by a vibrating base and in the presence of gravity, focusing on the transverse velocity modes. Since the system is inhomogeneous, we measure fluctuations in horizontal layers whose width is smaller than the characteristic hydrodynamic lengths: they can be considered as almost-homogeneous subsystems. The large time decay of the autocorrelations of modes is exponential and compatible with vorticity diffusion due to shear viscosity, as in equilibrium fluids. The velocity structure factor, which strongly deviates from the equilibrium constant behavior, is well reproduced by an effective fluctuating hydrodynamics described by two noise terms: the first associated with vorticity diffusion and the second with the local energy exchange, which have internal and external character, respectively.

Monodisperse microscale drops formed with microfluidic devices are useful for encapsulating cells, microgel particles, or even additional drops. These techniques are thus useful for applications ranging from high-throughput biology to monodisperse particle and capsule synthesis, which require encapsulation of such objects. However, it is challenging to efficiently encapsulate the objects in all drops; often, the objects are encapsulated inefficiently, resulting in many improperly filled, unusable drops. Here, we describe a phenomenon that allows very efficient encapsulation. We use the inflow of the object to plug the drop maker nozzle; the continued injection of the outer phase pinches off a drop, thereby encapsulating the object; this yields precisely one object encapsulated per drop.

Apart from other classes of materials, supramolecular structures may exist in H-bonded liquids due to the existence of hydrogen bonding. The dynamics of these structures remains one of the most exciting topics of interest of modern science because of its crucial meaning for the behavior of water and its participation in biological processes. A special group of these liquids form monohydroxy alcohols due to their similarity to water, their ability to vitrification, and the existence of the Debye relaxation process in dielectric loss spectra reflecting the dynamics of H-bond structures. Dynamics of these structures can be studied by changes of thermodynamic conditions, by immersion of the liquid into the constraint geometry, and by dilution in a nonassociated solvent. Herein we studied the behavior of relaxation dynamics of mixtures of 2-ethyl-1-hexanol with bromobutane using broadband dielectric spectroscopy. Analysis of the results exhibits the existence of crossover in temperature dependence of static permittivity of the Debye process at some particular temperature $T_c$. This temperature shifts to lower values with increasing concentration of bromobutane. Moreover, below some “critical” concentration of alcohol in the mixture the shape of the Debye process loses exponentiality and the temperature dependence of relaxation times starts to change. This change was illuminated based on the analysis of the steepness index. For the lowest concentration, the value of this parameter becomes the same as the value of the steepness index of faster relaxation, called process II, of pure alcohol at ambient pressure. The observed change in relaxation dynamics with lowering concentration of alcohol is astonishingly similar to the behavior observed in the same material at elevated pressure. A possible origin of these similarities is also discussed.

Lattice growth models where uncorrelated random deposition competes with some aggregation dynamics that generates correlations are studied with rates of the correlated component decreasing as a power law. These models have anomalous roughening, with anomalous exponents related to the normal exponents of the correlated dynamics, to an exponent characterizing the aggregation mechanism and to that power-law exponent. This is shown by a scaling approach extending the Family-Vicsek relation previously derived for the models with time-independent rates, thus providing a connection of normal and anomalous growth models. Simulation results for several models support those conclusions. Remarkable anomalous effects are observed even for slowly decreasing rates of the correlated component, which may correspond to feasible temperature changes in systems with activated dynamics. The scaling exponents of the correlated component can be obtained only from the estimates of three anomalous exponents, without knowledge of the aggregation mechanism, and a possible application is discussed. For some models, the corresponding Edwards-Wilkinson and Kardar-Parisi-Zhang equations are also discussed.

The functional network of the brain is known to demonstrate modular structure over different hierarchical scales. In this paper, we systematically investigated the hierarchical modular organizations of the brain functional networks that are derived from the extent of phase synchronization among high-resolution EEG time series during a visual task. In particular, we compare the modular structure of the functional network from EEG channels with that of the anatomical parcellation of the brain cortex. Our results show that the modular architectures of brain functional networks correspond well to those from the anatomical structures over different levels of hierarchy. Most importantly, we find that the consistency between the modular structures of the functional network and the anatomical network becomes more pronounced in terms of vision, sensory, vision-temporal, motor cortices during the visual task, which implies that the strong modularity in these areas forms the functional basis for the visual task. The structure-function relationship further reveals that the phase synchronization of EEG time series in the same anatomical group is much stronger than that of EEG time series from different anatomical groups during the task and that the hierarchical organization of functional brain network may be a consequence of functional segmentation of the brain cortex.

A flexible membrane deforming its shape in time can self-propel in a viscous fluid. Alternatively, if the membrane is anchored, its deformation will lead to fluid transport. Past work in this area focused on situations where the deformation kinematics of the membrane were prescribed. Here we consider models where the deformation of the membrane is not prescribed, but instead the membrane is internally forced. Both the time-varying membrane shape and the resulting fluid motion result then from a balance between prescribed internal active stresses, internal passive resistance, and external viscous stresses. We introduce two specific models for such active internal forcing: one where a distribution of active bending moments is prescribed, and one where active inclusions exert normal stresses on the membrane by pumping fluid through it. In each case, we asymptotically calculate the membrane shape and the fluid transport velocities for small forcing amplitudes, and recover our results using scaling analysis.

Ignition of exothermic chemical reactions in small volumes is considered as difficult or impossible due to the large surface-to-volume ratio. Here observation of the spontaneous reaction is reported between hydrogen and oxygen in bubbles whose diameter is smaller than a threshold value around 150 nm. The effect is attributed to high Laplace pressure and to fast dynamics in nanobubbles and is the first indication on combustion in the nanoscale. In this study the bubbles were produced by water electrolysis using successive generation of H${}_2$ and O${}_2$ above the same electrode with short voltage pulses in the microsecond range. The process was observed in a microsystem at current densities $>1000$ A/cm${}^2$ and relative supersaturations $>1000$.

A prototype population dynamics model with cyclic domination of four species and empty sites is proposed for studying transition to synchronization. At the mean-field level the dynamics shows quasiperiodicity and chaos depending on the parameter values. The realization of the model on a square lattice shows that spatial restrictions and intrinsic stochasticity change the whole picture. The mean-field dynamics qualitatively remains only under global reactions, while local reactions drive the lattice to poisoning, where only some of the species survive. Nontrivial oscillatory steady states are developed if long-distance exchange is introduced due to gradual mixing with a certain probability. The mixing probability is shown to control the transition to synchronization which emerges abruptly following a phase slip scenario. Near the transition a typical intermittency crisis takes place, with phase slips becoming more infrequent as the transition is approached.

Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes, we obtain expressions similar to those of the critical banded random matrix ensemble extensively discussed in the literature. For certain ensembles, the leading-order term for weak multifractality can be calculated within standard perturbation theory. For other models, such a direct approach requires modifications, which are briefly discussed. Our analytical formulas are in good agreement with numerical calculations.

This Brief Report is devoted to the study of the solitary surface wave rotating in the azimuthal direction, arising during water drainage from a cylindrical reservoir, when shallow flow conditions are reached. The linear dependence between the wave speed and its amplitude is shown to be similar to that expected from the classical Korteweg–de Vries equation.

We study the probability distribution of the time-averaged mean-square displacement of a discrete Gaussian process. An empirical approximation for the probability density is suggested and numerically validated for fractional Brownian motion. The optimality of quadratic forms for inferring dynamical and microrheological quantities from individual random trajectories is discussed, with emphasis on a reliable interpretation of single-particle tracking experiments.

We use event driven simulations to analyze glassy dynamics as a function of density and energy dissipation in a two-dimensional bidisperse granular fluid under stationary conditions. Clear signatures of a glass transition are identified, such as an increase of relaxation times over several orders of magnitude. As the inelasticity is increased, the glass transition is shifted to higher densities, and the precursors of the transition become less and less pronounced, in agreement with a recent mode-coupling theory. We analyze the long-time tails of the velocity autocorrelation and discuss its consequences for the nonexistence of the diffusion constant in two dimensions.

Ferroelectric behavior in the recently reported orthogonal ferroelectric Sm-$A_d{P}_F$ phase in an unsymmetric bent-core molecule with a carbosilane terminal group was studied. The ferroelectricity of the Sm-$A_d{P}_F$ phase was unambiguously confirmed by optical second-harmonic generation activity in the absence of an electric field, ferroelectric response, and high dielectric strength. The long-range polar order is a consequence of weakened interlayer coupling due to the formation of carbosilane sublayers, which allows for the parallel order of dipole moments of bent-core molecules in the neighboring layers. It develops in the system gradually through the second-order phase transition from the orthogonal Sm-$A_d$ phase. In the Sm-$A_d{P}_F$ phase the strong surface anchoring results in the splay of polarization across the sample thickness. The polar surface anchoring also brings about strongly thickness-dependent polar fluctuations, as proved by the dielectric measurements (Goldstone-like mode). The relaxation frequency and dielectric strength vary more than one order of magnitude with cell thickness; in particular the dielectric strength attains more than 2000 in a 25 $\mu$m-thick cell and continues to increase for thicker cells. Simple theory developed qualitatively explains the experimental results, supporting the polarization splay model proposed.

We analyze the structural behavior of a single polymer chain grafted to an attractive, flexible surface. Our model is composed of a coarse-grained bead-and-spring polymer and a tethered membrane. By means of extensive parallel tempering Monte Carlo simulations it is shown that the system exhibits a rich phase behavior ranging from highly ordered, compact to extended random coil structures, and from desorbed to completely adsorbed or even partially embedded conformations. These findings are summarized in a pseudophase diagram indicating the predominant class of conformations as a function of the external parameters temperature and polymer-membrane interaction strength. By comparison with adsorption to a stiff membrane surface it is shown that the flexibility of the membrane gives rise to qualitatively new behavior such as stretching of adsorbed conformations.

The Tumbleweed (TW) is a concept for an artificial, tri-pedal, protein-based motor designed to move unidirectionally along a linear track by a diffusive tumbling motion. Artificial motors offer the unique opportunity to explore how motor performance depends on design details in a way that is open to experimental investigation. Prior studies have shown that TW's ability to complete many successive steps can be critically dependent on the motor's diffusional step time. Here, we present a simulation study targeted at determining how to minimize the diffusional step time of the TW motor as a function of two particular design choices: nonspecific motor-track interactions and molecular flexibility. We determine an optimal nonspecific interaction strength and establish a set of criteria for optimal molecular flexibility as a function of the nonspecific interaction. We discuss our results in the context of similarities to biological, linear stepping diffusive molecular motors with the aim of identifying general engineering principles for protein motors.

We study the distribution function $P\left(\omega \right)$ of the random variable $\omega ={\tau }_1/({\tau }_1+\cdots +{\tau }_N)$, where ${\tau }_k$’s are the partial Wigner delay times for chaotic scattering in a disordered system with $N$ independent, statistically equivalent channels. In this case, ${\tau }_k$’s are independent and identically distributed random variables with a distribution $\Psi \left(\tau \right)$ characterized by a “fat” power-law intermediate tail $\sim$$1/{\tau }^{1+\mu }$, truncated by an exponential (or a log-normal) function of $\tau$. For $N=2$ and $N=3$, we observe a surprisingly rich behavior of $P\left(\omega \right)$, revealing a breakdown of the symmetry between identical independent channels. For $N=2$, numerical simulations of the quasi-one-dimensional Anderson model confirm our findings.

We use Heisenberg’s approximation to derive analytic expressions for eddy viscosity and eddy diffusivity from the transfer integrals of energy and mean-square scalar arising from the Navier-Stokes and passive scalar dynamics. In the same scheme, we evaluate the flux integrals for the transports of energy and mean-square scalar. These procedures allow for the evaluation of relevant amplitude ratios, from which we calculate the universal numbers, namely, Batchelor constant $\mathcal{B}$, Kolmogorov constant $C$, and turbulent Prandtl number $\sigma$, under two different schemes (with and without $\epsilon$ expansion). Our results are comparable with existing theoretical, numerical, and experimental values. As a byproduct, we obtain a relation between $C$, $\mathcal{B}$, and $\sigma$, namely, $\mathcal{B}=\sigma C$. To compare our results with the experimental values, we calculate Batchelor constant in one dimension (${\mathcal{B}}^{\prime }$). Within the same framework, we also see that with increasing values of space dimension $d$, the Prandtl number $\sigma$ increases and approaches unity, while the Kolmogorov constant $C$ and Batchelor constant $\mathcal{B}$ approach very close to each other. For large space dimensions, we find the asymptotic $\mathcal{B}={\mathcal{B}}_0{d}^{1/3}$, and evaluate ${\mathcal{B}}_0$.

We elucidate the universal scaling and multiscaling properties of the nonequilibrium steady states in a driven symmetric binary fluid (SBF) mixture in its homogeneous miscible phase in three dimensions. We show, via direct numerical simulations (DNSs) that structure functions of the velocity and the concentration gradient exhibit multiscaling in three dimensions (3D) and extended self-similarity. We also find that, in contrast to the well-known passive scalar turbulence problem, structure functions of the concentration show simple scaling. We propose a shell model for SBF turbulence that preserves all the invariances in the ideal limit of the SBF equations and reduces to a well-known shell model for fluid turbulence in the zero concentration field limit. We show that the shell model has the same scaling properties as the three-dimensional SBF equations. Our combined results from our DNSs of the SBF equations and shell-model studies consistently bring out the multiscaling of the velocity and concentration gradient fields and simple scaling of the concentration field.

This paper demonstrates the use of magnetically controlled microfluidic devices to produce monodispersed ferrofluid emulsions. By applying a uniform magnetic field on flow-focusing and T-junction configurations, the size of the ferrofluid emulsions can be actively controlled. The influences of the flow rates, the orientation, and the polarity of the magnetic field on the size of ferrofluid emulsions produced in both flow-focusing and T-junction configurations are compared and discussed.

A comprehensive study of the properties of light propagation through one-dimensional photonic disordered quasiperiodic superlattices, composed of alternating layers with random thicknesses of air and a dispersive metamaterial, is theoretically performed. The superlattices consist of the successive stacking of $N$ quasiperiodic Fibonacci or Thue-Morse heterostructures. The width of the slabs in the photonic superlattice may randomly fluctuate around its mean value, which introduces a structural disorder into the system. It is assumed that the left-handed layers have a Drude-type dispersive response for both the dielectric permittivity and magnetic permeability, and Maxwell's equations are solved for oblique incidence by using the transfer-matrix formalism. The influence of both quasiperiodicity and structural disorder on the localization length and Brewster anomalies are thoroughly discussed.