The symmetry in a network of oscillators determines the spatiotemporal patterns of activity that can emerge. We study how a delay in the coupling affects symmetry-breaking and -restoring bifurcations. We are able to draw general conclusions in the limit of long delays. For one class of networks we derive a criterion that predicts that delays have a symmetrizing effect. Moreover, we demonstrate that for any network admitting a steady-state solution, a long delay can solely advance the first bifurcation point as compared to the instantaneous-coupling regime.

In this study, the transverse permeability of fibrous porous media is studied both experimentally and theoretically. A scale analysis technique is employed for determining the transverse permeability of various fibrous matrices including square, staggered, and hexagonal arrangements of unidirectionally aligned fibers, as well as simple two-directional mats and simple cubic structures. In the present approach, the permeability is related to the porosity, fiber diameter, and tortuosity of the medium. In addition, the pressure drop in several samples of tube banks of different arrangements and metal foams are measured in the creeping flow regime. The pressure-drop results are then used to calculate the permeability of the samples. The developed compact relationships are successfully verified through comparison with these experimental results and the data reported by others. Our results suggest that fiber orientation has an important effect on the permeability; however, these effects are more pronounced in low porosities, i.e., $\varepsilon <0.7$.

Thermal convection in nanofluids is investigated by means of a continuum model for binary-fluid mixtures, with a thermal conductivity depending on the local concentration of colloidal particles. The applied temperature difference between the upper and the lower boundary leads via the Soret effect to a variation of the colloid concentration and, therefore, to a spatially varying heat conductivity. An increasing difference between the heat conductivity of the mixture near the colder and the warmer boundary results in a shift of the onset of convection to higher values of the Rayleigh number for positive values of the separation ratio $\psi >0$ and to smaller values in the range $\psi <0$. Beyond some critical difference of the thermal conductivity between the two boundaries, we find an oscillatory onset of convection not only for $\psi <0$, but also within a finite range of $\psi >0$. This range can be extended by increasing the difference in the thermal conductivity, and it is bounded by two codimension-2 bifurcations.

The displacement of liquids from confined geometries by using a gas phase is a problem that is relevant to many technologies. Efficient removal of the liquid phase is achieved when an extremely thin residual fluid film is produced as it is displaced. Here the dynamics of air, at constant pressure, displacing a glycerol-water drop in a radial Hele-Shaw cell is studied in this context at low Reynolds numbers. Empirically derived expressions relating the input parameters (fluid viscosity, pressure, and drop volume) to characteristic gas flow and liquid displacement rates, and the steady-state film thickness, are proposed and compared with experiments. The experiments consist of measuring cross-sectional areas of the penetrating gas (air) and displaced liquid using glycerol-water mixtures with viscosities ranging from 4 to 280 cSt and with inlet pressures ranging from 3.5 to 10.5 kPa at gap spacings of 50–100 $\mu$m. We estimate that the system produces residual film thicknesses in the range of 5–95 $\mu$m.

Colloidal particles provide an efficient means of building multiple scale structured materials from colloidal dispersions. In this Brief Report we account for experimental evidence on the formation of a colloidal cluster array at a three-phase contact line. We study the influence of low frequency external alternating electric fields on a diluted colloidal dispersion opened to the air. We focus on the cluster formation and their evolution in the meniscus by measuring characteristic times and lengths. We observe that the clusters are separated by a well-defined length and that, in our experimental conditions, they survive between 5 and 15 min. These new results could be of technological relevance in building tailored colloidal structures in nonpatterned substrates.

The effect of rigid surfaces on the dynamics of thin liquid films that are amenable to the lubrication approximation is considered. It is shown that the Helfrich energy of the layer gives rise to additional terms in the time-evolution equations of the liquid film. The dynamics is found to depend on the absolute value of the spontaneous curvature, irrespective of its sign. Due to the additional terms, the effective surface-tension can be negative and an instability at intermediate wavelengths is observed. Furthermore, the dependence of the shape of a droplet on the bending rigidity as well as on the spontaneous curvature is discussed.

This paper studies the quantum dynamics of a charged particle in a two-dimensional square lattice, under the influence of electric and magnetic fields, the former being aligned with one of the lattice axes and the latter perpendicular to the lattice plane. While in free space these dynamics consist of uniform motions in the direction orthogonal to the electric field vector, we find that, in a lattice, this directed drift takes place only for specific initial conditions and for electric field magnitudes smaller than a critical value. Otherwise, the quantum wave packet spreads ballistically in both directions orthogonal to the electric field. We quantify this ballistic spreading and identify the subspace of initial conditions ensuring directed transport with the drift velocity. We also describe the effect of disorder in the system.

Reaction rate theory in solids is modified taking into account intrinsic localized modes or discrete breathers (DBs) that can appear in crystals with sufficient anharmonicity, resulting in violation of Arrhenius’ law. Large-amplitude oscillations of atoms about their equilibrium positions in the lattice cause local potentials of alternating sign, which are described in terms of time-periodic modulations of the potential barriers for chemical reactions taking place in the vicinity of DBs. The reaction rate averaged over large macroscopic volumes and times including many DBs is increased by a factor that depends on the DB statistics. The breather statistics in thermal equilibrium and in thermal spikes in solids under irradiation with swift particles is considered, and the corresponding reaction rate amplification factors are derived.

We use the recently introduced theory for the kinetics of systems of classical particles to investigate systems driven by Smoluchowski dynamics. We investigate the existence of ergodic-nonergodic (ENE) transitions near the liquid-glass transition. We develop a self-consistent perturbation theory in terms of an effective two-body potential and work to second order in this potential. At second order, we have an explicit relationship between the static structure factor and the effective potential and choose the static structure factor in the case of hard spheres to be given by the solution of the Percus-Yevick approximation for hard spheres. Then, using the analytically determined ENE equation for the ergodicity function, we find an ENE transition for packing fraction $\eta$ greater than a critical value ${\eta }^{*}=0.76$, which is physically unaccessible. The existence of a linear fluctuation-dissipation theorem in the problem is shown and used to great advantage.

It is shown that the fluctuation-dissipation theorem is satisfied by the solutions of a general set of nonlinear Langevin equations with a quadratic free-energy functional (constant susceptibility) and field-dependent kinetic coefficients, provided the kinetic coefficients satisfy the Onsager reciprocal relations for the irreversible terms and the antisymmetry relations for the reversible terms. The analysis employs a perturbation expansion of the nonlinear terms, and a functional integral calculation of the correlation and response functions, and it is shown that the fluctuation-dissipation relation is satisfied at each order in the expansion.

The main precondition of simulating systems of hard particles by means of event-driven modeling is the assumption of instantaneous collisions. The aim of this paper is to quantify the deviation of event-driven modeling from the solution of Newton’s equation of motion using a paradigmatic example: If a tennis ball is held above a basketball with their centers vertically aligned, and the balls are released to collide with the floor, the tennis ball may rebound at a surprisingly high speed. We show in this article that the simple textbook explanation of this effect is an oversimplification, even for the limit of perfectly elastic particles. Instead, there may occur a rather complex scenario including multiple collisions which may lead to a very different final velocity as compared with the velocity resulting from the oversimplified model.

We analyze the glassy dynamics of binary mixtures of hard disks in two dimensions. Predictions of the mode-coupling theory (MCT) are tested with extensive Brownian dynamics simulations. Measuring the collective particle density correlation functions in the vicinity of the glass transition, we verify four predicted mixing effects. For instance, for large size disparities, adding a small amount of small particles at a fixed packing fraction leads to a speedup in the long-time dynamics, while for small size disparities it leads to a slowing-down. Qualitative features of the nonergodicity parameters and the $\beta$ relaxation, which both depend in a nontrivial way on the mixing ratio, are found in the simulated correlators. Studying one system in detail, we are able to determine its ideal MCT glass transition point as $\phi {}^c=0.7948$ and test MCT predictions quantitatively.

We present a phase-field model of solid-liquid transitions with inhomogeneous temperature in one-component systems, including hydrodynamics and elasticity. Our model can describe plastic deformations at large elastic strains. We use it to investigate the melting of a solid domain, accounting for the latent heat effect, where there appears a velocity field in liquid and an elastic field in solid. We present simulation results in two dimensions for three cases of melting. First, a solid domain is placed on a heated wall, which melts mostly near the solid-liquid-wall contact region. Second, a solid domain is suspended in a warmer liquid under shear flow, which rotates as a whole because of elasticity and melts gradually. Cooling of the surrounding liquid is accelerated by convection. Third, a solid rod is under high compression in liquid, where slips appear from the solid-liquid interface, leading to a plastic deformation. Subsequently, melting starts in the plastically deformed areas, eventually resulting in the fracture of the rod into pieces. In these phase-transition processes, the interface temperature is kept nearly equal to the coexisting temperature $T_{\mathrm{cx}}(p)$ away from the heated wall, but this local equilibrium is not attained near the the contact region. We also examine a first-order liquid-liquid phase transition under heating from a boundary in one-component liquids.

The effects of cluster diffusion on the submonolayer island density and island-size distribution are studied for the case of irreversible growth of compact islands on a 2D substrate. In our model we assume instantaneous coalescence of circular islands, while the cluster mobility is assumed to exhibit power-law decay as a function of island size with exponent $\mu$. Results are presented for $\mu =1/2,1,$ and $3/2$ corresponding to cluster diffusion via Brownian motion, correlated evaporation condensation, and edge diffusion respectively, as well as for higher values including $\mu =2,3,$ and $6$. We also compare our results with those obtained in the limit of no cluster mobility ($\mu =\infty$). In agreement with theoretical predictions of power-law behavior of the island-size distribution (ISD) for $\mu <1$, for $\mu =1/2$ we find $N_s(\theta )~s^{-\tau }$ [where $N_s(\theta )$ is the number of islands of size $s$ at coverage $\theta$] up to a crossover island-size $S_c$. However, the value of the exponent $\tau$ obtained in our simulations is higher than the mean-field (MF) prediction $\tau =(3-\mu )/2$. Similarly, the measured value of the exponent $\zeta$ corresponding to the dependence of $S_c$ on the average island-size $S$ (e.g., $S_c~S^{\zeta }$) is also significantly higher than the MF prediction $\zeta =2/(\mu +1)$. A generalized scaling form for the ISD [$N_s(\theta )=\theta /S^{1+\tau \zeta }f(s/S^{\zeta })$] is also proposed for $\mu <1$, and using this form excellent scaling is found for $\mu =1/2$. However, for finite $\mu ⩾1$ neither the generalized scaling form nor the standard scaling form $N_s(\theta )=\theta /S^{2}f(s/S)$ lead to scaling of the entire ISD for finite values of the ratio $R$ of the monomer diffusion rate to deposition flux. Instead, the scaled ISD becomes more sharply peaked with increasing $R$ and coverage. This is in contrast to models of epitaxial growth with limited cluster mobility for which good scaling occurs over a wide range of coverages.

Spherical colloidal particles with normal and tangential surface director alignment in a nematic liquid crystal induce elastic quadrupoles of opposite signs that attract one another along and perpendicular to the director. We utilize this unique angular profile of the mixed quadrupolar interaction to build 2D crystals with square lattices by laser tweezers.

Birdsong is a complex behavior, which results from the interaction between a nervous system and a biomechanical peripheral device. While much has been learned about how complex sounds are generated in the vocal organ, little has been learned about the signature on the vocalizations of the nonlinear effects introduced by the acoustic interactions between a sound source and the vocal tract. The variety of morphologies among bird species makes birdsong a most suitable model to study phenomena associated to the production of complex vocalizations. Inspired by the sound production mechanisms of songbirds, in this work we study a mathematical model of a vocal organ, in which a simple sound source interacts with a tract, leading to a delay differential equation. We explore the system numerically, and by taking it to the weakly nonlinear limit, we are able to examine its periodic solutions analytically. By these means we are able to explore the dynamics of oscillatory solutions of a sound source-tract coupled system, which are qualitatively different from those of a sound source-filter model of a vocal organ. Nonlinear features of the solutions are proposed as the underlying mechanisms of observed phenomena in birdsong, such as unilaterally produced “frequency jumps,” enhancement of resonances, and the shift of the fundamental frequency observed in heliox experiments.

Canonical-correlation analysis as a multivariate statistical technique has been applied to multivariate Granger causality analysis to infer information flow in complex systems. It shows unique appeal and great superiority over the traditional vector autoregressive method, due to the simplified procedure that detects causal interaction between multiple time series, and the avoidance of potential model estimation problems. However, it is limited to the linear case. Here, we extend the framework of canonical correlation to include the estimation of multivariate nonlinear Granger causality for drawing inference about directed interaction. Its feasibility and effectiveness are verified on simulated data.

The bacterial cell wall is a network of sugar strands crosslinked by peptides that serve as the primary structure for bearing osmotic stress. Despite its importance in cellular survival, the robustness of the cell wall to network defects has been relatively unexplored. Treatment of the Gram-negative bacterium Escherichia coli with the antibiotic vancomycin, which disrupts the crosslinking of new material during growth, leads to the development of pronounced bulges and eventually of cell lysis. Here, we model the mechanics of the bulging of the cytoplasmic membrane through pores in the cell wall. We find that the membrane undergoes a transition between a nearly flat state and a spherical bulge at a critical pore radius of $~$20 nm. This critical pore size is large compared to the typical distance between neighboring peptides and glycan strands, and hence pore size acts as a constraint on network integrity. We also discuss the general implications of our model to membrane deformations in eukaryotic blebbing and vesiculation in red blood cells.

Compartmentalization into biochemically distinct organelles constantly exchanging material is one of the hallmarks of eukaryotic cells. In the most naive picture of interorganelle transport driven by concentration gradients, concentration differences between organelles should relax. We determine the conditions under which cooperative transport, i.e., based on molecular recognition, allows for the existence and maintenance of distinct organelle identities. Cooperative transport is also shown to control the flux of material transiting through a compartmentalized system, dramatically increasing the transit time under high incoming flux. By including chemical processing of the transported species, we show that this property provides a strong functional advantage to a system responsible for protein maturation and sorting.

We propose a method called the residual edge-betweenness gradient (REBG) to enhance the synchronizability of networks by assigning the link direction while keeping the topology and link weights unchanged. Direction assignment has been shown to improve the synchronizability of undirected networks in general, but we find that in some cases incommunicable components emerge and networks fail to synchronize. We show that the REBG method improves the residual degree gradient (RDG) method by effectively avoiding the synchronization failure. Further experiments show that the REBG method enhances the synchronizability in networks with a community structure compared with the RDG method.