Our experiments disentangle the low and high frequency dispersions in perfluorosulfonate ionomer solutions and membranes, providing a reasonable model for understanding these relaxations. Dielectric spectroscopy (DS) and small angle x-ray scattering (SAXS) measurements revealed that the dielectric relaxations observed at low (α relaxation) and high (β relaxation) frequencies show typical features of the longitudinal and radial polarization, respectively, of rodlike polymeric aggregates. Such relaxations were attributed to counterion fluctuations in the vicinity of sulfonic acid groups, in resemblance with polyelectrolytes. Characteristic correlation lengths calculated from both DS and SAXS data are in good agreement adding further evidence to the proposed model. Such description provides insights for the understanding of the crossover from polyelectrolytes, dominated by charge repulsion, to ionomers, dominated by dipolar attraction.

Link weight evolution is studied in a network of coupled chemical oscillators. Oscillators are perturbed by adjustments in imposed light intensity based on excitatory or inhibitory links to other oscillators undergoing excitation. Experimental and modeling studies demonstrate that the network is capable of producing sustained coordinated activity. The individual nodes of the network exhibit incoherent firing events; however, a dominant frequency can be discerned within the collective signal by Fourier analysis. The introduction of spike-timing-dependent plasticity yields a network that evolves to a stable unimodal link weight distribution.

We employ an efficient list-based kinetic Monte Carlo (KMC) method to study traffic flow models on one-dimensional (1D) and two-dimensional (2D) lattices based on the exclusion principle and Arrhenius microscopic dynamics. This model implements stochastic rules for cars' movements based on the configuration of the traffic ahead of each car. In particular, we compare two different look-ahead rules: one is based on the distance from the car under consideration to the car in front of it, and the other one is based on the density of cars ahead. The 1D numerical results of these two rules suggest different coarse-grained macroscopic limits in the form of integro-differential Burgers equations. The 2D results of both rules exhibit a sharp phase transition from freely flowing to fully jammed, as a function of the initial density of cars. However, the look-ahead rule based on the density of the traffic produces more realistic results. The KMC simulations reported in this paper are compared with those from other well-known traffic flow models and the corresponding empirical results from real traffic.

A fundamental Poisson-Nernst-Planck-Stokes model is presented for the impedance response of a long nanochannel under zero bias, capturing the effects of surface conduction and the coupling between transverse momentum and axial ion distribution in a manner reminiscent of Taylor dispersion. This is shown to result in a shift of the impedance frequency spectrum with bulk concentration similar to previous experimental observation [Schiffbauer, Liel, and Yossifon, Phys. Rev. E 89, 033017 (2014)]. It further predicts an additional downward shift in frequency with increasing viscosity. Finally, the introduction of a phenomenological model for the impedance response of a dynamic Stern layer in parallel with the diffuse layer transport model is shown to yield good agreement between theory and experiment. As a result, we are able to obtain an equivalent circuit model based on the fundamental model and proposed corrections.

Passing a fluid through a grid is a well-known mechanism used to study the properties of turbulence. Oscillating a horizontal grid vertically in a tank has also been used extensively and is considered to be a source of almost homogenous isotropic turbulence. When the oscillating grid is turned on a turbulent flow is induced. A front translates into the experimental tank, behind which the flow is highly turbulent. Long predicted that the growth of such a front would grow diffusively as the square root of time (i.e., $d\sim \sqrt{t}$) and Dickinson and Long presented experimental evidence for the diffusive result at a low mesh Reynolds number of 555. This paper revisits these experiments and attempts a set of two models for the advancing front in both square and round tanks. We do not observe significant differences between runs in square and round tanks. The experiments in water reach mesh Reynolds numbers of order $30000$. Using some data from superfluid helium experiments we are able to explore mesh Reynolds numbers to about $43000$. We find the power law for the advancing front decreases weakly with the mesh Reynolds number. Using a very long tank we find that the turbulent front stops completely at a certain depth and attempt a simple explanation for that behavior. We study the propagation of the turbulent front into tubes of different diameters inserted into the main tank. We show that these tubes exclude wavelengths much larger than the tube diameter. We explore the variation of the position of the steady-state boundary $H$ on tube diameter $D$ and find that $H=cD$ with $c\sim 2$. We suggest this may be explained by saturation of the energy-containing length scale ${\ell }_e$. We also report on the effect of plugging up just one hole of the grid. Finally, we recall some earlier oscillating grid experiments in superfluid ${}^4$He in the light of the present results.

The interactions between supersonic streamwise vortices and oblique shock waves are theoretically and numerically investigated by three-dimensional (3D) Navier-Stokes equations. Based on the two inequalities, a criterion for shock-induced breakdown of the streamwise vortex is proposed. The simple breakdown condition depends on the Mach number, the swirl number, the velocity deficit, and the shock angle. According to the proposed criterion, the breakdown region expands as the Mach number increases. In numerical simulations, vortex breakdown appeared under conditions of multiple pressure increases and the helicity disappeared behind the oblique shock wave along the line of the vortex center. The numerical results are consistent with the predicted breakdown condition at Mach numbers 2.0 and 3.0. This study also found that the axial velocity deficit is important for classifying the breakdown configuration.

This paper presents an extended multicomponent lattice Boltzmann model for the simulation of electrolytes. It is derived by means of a finite discrete velocity model and its discretization. The model recovers momentum and mass transport according to the incompressible Navier-Stokes equation and Maxwell-Stefan formulation, respectively. It includes external driving forces (e.g., electric field) on diffusive and viscous scales, concentration-dependent Maxwell-Stefan diffusivities, and thermodynamic factors. The latter take into account nonideal diffusion behavior, which is essential as electrolytes involve charged species and therefore nonideal long and short-range interactions among the molecules of the species. Furthermore, we couple our scheme to a finite element method to include electrostatic interactions on the macroscopic level. Numerical experiments show the validity of the presented model.

We generalize the model of transition-metal nanocluster growth in aqueous solution, proposed recently [J. Jȩdrak, Phys. Rev. E 87, 022132 (2013)], by introducing a more complete description of chemical reactions. In order to model time evolution of the system, equations describing chemical reaction kinetics are combined with the Smoluchowski coagulation equation. In the absence of coagulation and fragmentation processes, the model equations are solved in two steps. First, we obtain the explicit analytical form of the $i$-mer concentration, ${\xi }_i$, as a function of ${\xi }_1$. This result allows us to reduce considerably the number of time-evolution equations. In the simplest situation, the remaining single kinetic equation for ${\xi }_1\left(t\right)$ is solved in quadratures. In a general case, we obtain a small system of time-evolution equations, which, although rarely analytically tractable, can be relatively easily solved numerically.

Conway's cellular automaton Game of Life has been conjectured to be a critical (or quasicritical) dynamical system. This criticality is generally seen as a continuous order-disorder transition in cellular automata (CA) rule space. Life's mean-field return map predicts an absorbing vacuum phase ($\rho =0$) and an active phase density, with $\rho =0.37$, which contrasts with Life's absorbing states in a square lattice, which have a stationary density of ${\rho }_{2\mathrm{D}}\approx 0.03$. Here, we study and classify mean-field maps for 6144 outer-totalistic CA and compare them with the corresponding behavior found in the square lattice. We show that the single-site mean-field approach gives qualitative (and even quantitative) predictions for most of them. The transition region in rule space seems to correspond to a nonequilibrium discontinuous absorbing phase transition instead of a continuous order-disorder one. We claim that Life is a quasicritical nucleation process where vacuum phase domains invade the alive phase. Therefore, Life is not at the “border of chaos,” but thrives on the “border of extinction.”

The phase diagram of a system of monodispersed hard rectangles of size $m\times mk$ on a square lattice is numerically determined for $m=2,3$ and aspect ratio $k=1,2,...,7$. We show the existence of a disordered phase, a nematic phase with orientational order, a columnar phase with orientational and partial translational order, and a solidlike phase with sublattice order, but no orientational order. The asymptotic behavior of the phase boundaries for large $k$ is determined using a combination of entropic arguments and a Bethe approximation. This allows us to generalize the phase diagram to larger $m$ and $k$, showing that for $k\ge 7$, the system undergoes three entropy-driven phase transitions with increasing density. The nature of the different phase transitions is established and the critical exponents for the continuous transitions are determined using finite size scaling.

We study, by computer simulations, the roles of different dissipation forces in the rheological properties of highly dense particle-laden flows. In particular, we are interested in the close-packing limit (jamming) and the question of whether “universal” observables can be identified that do not depend on the details of the dissipation model. To this end, we define a simplified lubrication force and systematically vary the range $h_c$ of this interaction. For fixed $h_c$ a crossover is seen from a Newtonian flow regime at small strain rates to inertia-dominated flow at larger strain rates. The same crossover is observed as a function of the lubrication range $h_c$. At the same time, but only at high densities close to jamming, single-particle velocities as well as local density distributions are unaffected by changes in the lubrication range—they are candidates for universal behavior. At densities away from jamming, this invariance is lost: short-range lubrication forces lead to pronounced particle clustering, while longer-ranged lubrication does not. These findings highlight the importance of “geometric” packing constraints for particle motion—independent of the specific dissipation model. With the free volume vanishing at random close packing, particle motion is more and more constrained by the ever smaller amount of free space. On the other hand, macroscopic rheological observables as well as higher-order correlation functions retain the variability of the underlying dissipation model.

We demonstrate that flows in confined systems are controlled by slip heterogeneities below a certain size. To show this we image the motion of soft glassy suspensions in microchannels whose inner walls impose different slip velocities. As the channel height decreases, the flow ceases to have the symmetric shape expected for yield-stress fluids. A theoretical model accounts for the role of slip heterogeneities and captures the velocity profiles. We generalize these results by introducing a length scale, valid for all fluids, below which slip heterogeneities dominate the flow in confined systems. General implications of this notion, concerning the interplay between slip and confinement, are presented.

Viral fibers play a central role in many virus infection mechanisms since they recognize the corresponding host and establish a mechanical link to its surface. Specifically, bacteriophages have to anchor to bacteria through the fibers surrounding the tail before starting the viral DNA translocation into the host. The protein gene product (gp) 37 from bacteriophage T4 long tail fibers forms a fibrous parallel homotrimer located at the distal end of the long tail fibers. Biochemical data indicate that, at least, three of these fibers are required for initial host cell interaction but do not reveal why three and no other numbers are required. By using atomic force microscopy, we obtained high-resolution images of gp37 fibers adsorbed on a mica substrate in buffer conditions and probed their local mechanical properties. Our experiments of radial indentation at the nanometer scale provided a radial stiffness of $\sim$0.08 N/m and a breaking force of $\sim$120 pN. In addition, we performed finite element analysis and determined a Young's modulus of $\sim$20 MPa. From these mechanical parameters, we hypothesize that three viral fibers provide enough mechanical strength to prevent a T4 virus from being detached from the bacteria by the viral particle Brownian motion, delivering a biophysical justification for the previous biochemical data.

Using a continuum model for inhomogeneous flocks, we show that a finite but arbitrarily large moving “packet” of active particles (e.g., moving creatures) can form in a background of a lower density disordered phase of these particles, like a liquid drop surrounded by vapor. The “vapor density” of the disordered background can be made arbitrarily low. We find three basic types of quasi-one-dimensional states: “longitudinal”, “transverse”, and “oblique” states, with their internal velocity fields, respectively, parallel, perpendicular, and oblique to the interface. The transitions between these states are also studied.

We examine the dynamics of a layer of viscous liquid on an inclined plate. If the layer's upstream depth $h_{-}$ exceeds the downstream depth $h_{+}$, a smooth hydraulic jump (bore) forms and starts propagating down the slope. If the ratio $\eta =h_{+}/h_{-}$ is sufficiently small and/or the plate's inclination angle is sufficiently large, the bore overturns and no smooth steadily propagating solution exists in this case. In this work, the dynamics of bores is examined using a heuristic depth-averaged model where the vertical structure of the flow is approximated by a polynomial. It turns out that even the simplest version of the model (based on the parabolic approximation) is remarkably accurate, producing results which agree, both qualitatively and quantitatively, with those obtained through the Stokes equations. Furthermore, the depth-averaged model allows one to derive a sufficient criterion of bore overturning, which happens to be valid for the exact model as well. Physically, this criterion reflects the fact that, for small $\eta$, a stagnation point appears in the flow, causing wave overturning.

We investigate free-surface instabilities occurring in various industrial processes involving liquid metal. Of particular interest is the behavior of the free surface of a pool of liquid metal when it is submitted to an alternating magnetic field. Experimentally, we study the effect of a vertical alternating medium-frequency magnetic field on an initially circular pool. We observe various types of behavior according to magnetic field amplitude, e.g., axisymmetric deformations, azimuthal mode structures, slow radial oscillation of the pool perimeter, and random rotation of the pool around its center. Drop rotation could be attributed to nonsymmetric shape deformations. The effect of oxidation leads to drastic changes in pool behavior. The experimental results are then compared to a linear stability analysis of the free surface of a circular liquid drop.

The paper presents an approach that extends the flexibility of the standard lattice Boltzmann single relaxation time scheme in terms of spatial variation of dissipative terms (e.g., diffusion coefficient) and stability for high Péclet mass transfer problems. Spatial variability of diffusion coefficient in SRT is typically accommodated through the variation of relaxation time during the collision step. This method is effective but cannot deal with large diffusion coefficient variations, which can span over several orders of magnitude in some natural systems. The approach explores an alternative way of dealing with large diffusion coefficient variations in advection-diffusion transport systems by introducing so-called diffusion velocity. The diffusion velocity is essentially an additional convective term that replaces variations in diffusion coefficients vis-à-vis a chosen reference diffusion coefficient which defines the simulation time step. Special attention is paid to the main idea behind the diffusion velocity formulation and its implementation into the lattice Boltzmann framework. Finally, the performance, stability, and accuracy of the diffusion velocity formulation are discussed via several advection-diffusion transport benchmark examples. These examples demonstrate improved stability and flexibility of the proposed scheme with marginal consequences on the numerical performance.

Observability of state variables and parameters of a dynamical system from an observed time series is analyzed and quantified by means of the Jacobian matrix of the delay coordinates map. For each state variable and each parameter to be estimated, a measure of uncertainty is introduced depending on the current state and parameter values, which allows us to identify regions in state and parameter space where the specific unknown quantity can(not) be estimated from a given time series. The method is demonstrated using the Ikeda map and the Hindmarsh-Rose model.

Two nematic shells brought in contact coalesce in order to reduce their combined interfacial tension, and, following this topological transition, relax to an equilibrium state. In this work, we study the defect textures as the combined shell shape evolves. By varying the sizes of the shells, we perform a quasistatic investigation of the director field and the defect valence on the doublet. Regimes are found where positive and negative defects exist due to the large negative Gaussian curvature at the neck. Using large-scale computer simulations, we determine how annihilating defect pairs on coalescing shells are selected and the stage of coalescence at which annihilation occurs.