We measure the dispersion coefficient through homogeneous bead or sand packings at different flow rates from direct magnetic resonance imaging (MRI) visualizations of the transport characteristics of a pulse of paramagnetic nanoparticles. Through two-dimensional imaging we observe homogeneous dispersion inside the sample, but we show that entrance effects may induce significant radial heterogeneities, which would affect the interpretation of the breakthrough curve. Another MRI approach then provides quantitative measurements of the evolution in time of the longitudinal particle distribution in the sample. These data can be analyzed to deduce the coefficient of dispersion independently of entrance effects. The values obtained for this “effective” dispersion coefficient are almost ten times lower than the commonly accepted values.

We point out, and show the implications of resolving, an apparent conceptual difficulty in a recent article by De Corato et al. [Phys. Rev. E 92, 053008 (2015)] on the locomotion of certain microorganisms in a second-grade fluid. The difficulty arises due to the assumption that ${\alpha }_1<0$, where ${\alpha }_1$ is the first normal stress modulus of the (non-Newtonian) liquid, was chosen for this study. In particular, this choice of sign for ${\alpha }_1$ is inconsistent with thermodynamics, and as such casts considerable doubt on De Corato et al.'s assumption regarding the existence of a steady-state solution of the equations of motion of the fluid.

In the present reply we show that the comments casting doubts on the results of our recent paper [M. De Corato et al., Phys. Rev. E 92, 053008 (2015)] are based on a misinterpretation of the second-order fluid constitutive equation. Nevertheless, we show that, by considering alternative constitutive equations for the viscoelastic stress, we recover, to first-order in the Deborah number, the same results already obtained by De Corato et al. [Phys. Rev. E 92, 053008 (2015)], thus dissipating any possible doubt about their validity.

We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or microscale particles where rolling is an approximation for strong static friction. We consider the simplest possible nontrivial system: a linear polymer of three disks constrained to remain in contact and immersed in an equilibrium heat bath so the internal angle of the polymer changes due to stochastic fluctuations. We compare two cases: one where the disks can slide relative to each other and the other where they are constrained to roll, like gears. Starting from the Langevin equations with arbitrary linear velocity constraints, we use formal homogenization theory to derive the overdamped equations that describe the process in configuration space only. The resulting dynamics have the formal structure of a Brownian motion on a Riemannian or sub-Riemannian manifold, depending on if the velocity constraints are holonomic or nonholonomic. We use this to compute the trimer's equilibrium distribution with and without the rolling constraints. Surprisingly, the two distributions are different. We suggest two possible interpretations of this result: either (i) dry friction (or other dissipative, nonequilibrium forces) changes basic thermodynamic quantities like the free energy of a system, a statement that could be tested experimentally, or (ii) as a lesson in modeling rolling or friction more generally as a velocity constraint when stochastic fluctuations are present. In the latter case, we speculate there could be a “roughness” entropy whose inclusion as an effective force could compensate the constraint and preserve classical Boltzmann statistics. Regardless of the interpretation, our calculation shows the word “rolling” must be used with care when stochastic fluctuations are present.

We propose a method for the recovery of coupling architecture and the parameters of elements in networks consisting of coupled oscillators described by delay-differential equations. For each oscillator in the network, we introduce an objective function characterizing the distance between the points of the reconstructed nonlinear function. The proposed method is based on the minimization of this objective function and the separation of the recovered coupling coefficients into significant and insignificant coefficients. The efficiency of the method is shown for chaotic time series generated by model equations of diffusively coupled time-delay systems and for experimental chaotic time series gained from coupled electronic oscillators with time-delayed feedback.

Complex networks are a recent type of framework used to study complex systems with many interacting elements, such as self-organized criticality (SOC). The network nodes' tendency to link to other nodes of similar type is characterized by assortative mixing. Real networks exhibit assortative mixing by vertex degree, however, typical random network models, such as the Erdős-Rényi or the Barabási-Albert model, show no assortative arrangements. In this paper we introduce the notion of neighborhood assortativity as the tendency of a node to belong to a community (its neighborhood) showing an average property similar to its own. Imposing neighborhood assortative mixing by degree in a network toy model, SOC dynamics can be found. These dynamics are driven only by the network topology. The long-range correlations resulting from criticality have been characterized by means of fluctuation analysis and show an anticorrelation in the node's activity. The model contains only one parameter and its statistics plots for different values of the parameter can be collapsed into a single curve. The simplicity of the model allows us to perform numerical simulations and also to study analytically the statistics for a specific value of the parameter, making use of the Markov chains.

We investigate nonequilibrium lane formation in a generic model of a fluid with attractive interactions, that is, a two-dimensional Lennard-Jones fluid composed of two particle species driven in opposite directions. Performing Brownian dynamics simulations for a wide range of parameters, supplemented by a stability analysis based on dynamical density functional theory, we identify generic features of lane formation in the presence of attraction, including structural properties. In fact, we find a variety of states (as compared to purely repulsive systems), as well as a close relation between laning and long-wavelength instabilities of the homogeneous phase such as demixing and condensation.

We study the macroscopic representation of noise-driven interfaces in stochastic interface growth models in $(1+1)$ dimensions. The interface is characterized macroscopically by saturation, which represents the fluctuating sharp interface by a smoothly varying phase field with values between 0 and 1. We determine the one-point interface height statistics for the Edwards-Wilkinson (EW) and Kadar-Paris-Zhang (KPZ) models in order to determine explicit deterministic equations for the phase saturation for each of them. While we obtain exact results for the EW model, we develop a Gaussian closure approximation for the KPZ model. We identify an interface compression term, which is related to mass transfer perpendicular to the growth direction, and a diffusion term that tends to increase the interface width. The interface compression rate depends on the mesoscopic mass transfer process along the interface and in this sense provides a relation between meso- and macroscopic interface dynamics. These results shed light on the relation between mesoscale and macroscale interface models, and provide a systematic framework for the upscaling of stochastic interface dynamics.

We investigate the impact penetration of spheres into granular media which are compositions of two discrete size ranges, thus creating a polydisperse bimodal material. We examine the penetration depth as a function of the composition (volume fractions of the respective sizes) and impact speed. Penetration depths were found to vary between $\delta =0.5D_0$ and $\delta =7D_0$, which, for mono-modal media only, could be correlated in terms of the total drop height, $H=h+\delta$, as in previous studies, by incorporating correction factors for the packing fraction. Bimodal data can only be collapsed by deriving a critical packing fraction for each mass fraction. The data for the mixed grains exhibit a surprising lubricating effect, which was most significant when the finest grains $[d_s\sim O\left(30\right) \mu \mathrm{m}]$ were added to the larger particles $[d_l\sim O(200-500) \mu \mathrm{m}]$, with a size ratio, $\epsilon =d_l/d_s$, larger than 3 and mass fractions over 25%, despite the increased packing fraction. We postulate that the small grains get between the large grains and reduce their intergrain friction, only when their mass fraction is sufficiently large to prevent them from simply rattling in the voids between the large particles. This is supported by our experimental observations of the largest lubrication effect produced by adding small glass beads to a bed of large sand particles with rough surfaces.

The generation of localized, spatially periodic patterns on a sandy bottom is experimentally and theoretically studied. Tests are performed in a hydrodynamic flume where patterns are produced downstream from a vertical cylinder under a steady current. It is found that patterns appear as a result of a subcritical instability of the water-sand bottom interface. A dependence of the area shape occupied by the patterns on the flow velocity and the cylinder diameter is investigated. It is shown that the patterns' characteristics can be explained using the Swift-Hohenberg equation. Numerical simulations point out that for a correct description of the patterns, an additional term which takes into account the impact of vortices on the sandy bottom in the wake of a cylinder must be added in the Swift-Hohenberg equation.

In this paper we estimate the relative strengths of various terms of the Rayleigh-Bénard equations. Based on these estimates and scaling analysis, we derive a general formula for the large-scale velocity $U$ or the Péclet number that is applicable for arbitrary Rayleigh number Ra and Prandtl number Pr. Our formula fits reasonably well with the earlier simulation and experimental results. Our analysis also shows that the wall-bounded convection has enhanced viscous force compared to free turbulence. We also demonstrate how correlations deviate the Nusselt number scaling from the theoretical prediction of ${\mathrm{Ra}}^{1/2}$ to the experimentally observed scaling of nearly ${\mathrm{Ra}}^{0.3}$.

The self-similar expansion of multispecies ion plasma is investigated by a two-ion fluid model with adiabatic equation of state for each ionic species. Our aim is to elucidate the effect of secondary ions on a plasma expansion front, in combination with energetic (suprathermal) electrons in the background, modeled by a kappa-type distribution function. The plasma density, velocity, and electric-field profile is investigated. It is shown that energetic electrons have a significant effect on the expansion front dynamics, essentially energizing the front, thus enhancing the ion acceleration mechanism. Different special cases are considered as regards the relative magnitude of the ion mass and/or charge state.

Many aspects of physical phenomena occurring when an intense laser pulse with subpicosecond duration and an intensity of ${10}^{18}–{10}^{19}\mathrm{W}/{\mathrm{cm}}^2$ heats an underdense plasma in a supersonic clustered gas jet are studied to determine the relative contribution of thermal and nonthermal processes to soft- and hard-x-ray emission from debris-free plasmas. Experiments were performed at the University of Nevada, Reno (UNR) Leopard laser operated with a 15-J, 350-fs pulse and different pulse contrasts (${10}^7$ or ${10}^5$). The supersonic linear (elongated) nozzle generated Xe cluster-monomer gas jets as well as jets with Kr-Ar or Xe-Kr-Ar mixtures with densities of ${10}^{18}–{10}^{19}{\mathrm{cm}}^{-3}$. Prior to laser heating experiments, all jets were probed with optical interferometry and Rayleigh scattering to measure jet density and cluster distribution parameters. The supersonic linear jet provides the capability to study the anisotropy of x-ray yield from laser plasma and also laser beam self-focusing in plasma, which leads to efficient x-ray generation. Plasma diagnostics included x-ray diodes, pinhole cameras, and spectrometers. Jet signatures of x-ray emission from pure Xe gas, as well as from a mixture with Ar and Kr, was found to be very different. The most intense x-ray emission in the 1–9 KeV spectral region was observed from gas mixtures rather than pure Xe. Also, this x-ray emission was strongly anisotropic with respect to the direction of laser beam polarization. Non-local thermodynamic equilibrium (Non-LTE) models have been implemented to analyze the x-ray spectra to determine the plasma temperature and election density. Evidence of electron beam generation in the supersonic jet plasma was found. The influence of the subpicosecond laser pulse contrast (a ratio between the laser peak intensity and pedestal pulse intensity) on the jets’ x-ray emission characteristics is discussed. Surprisingly, it was found that the x-ray yield was not sensitive to the prepulse contrast ratio.

Direct numerical solution of the coordinate-space integral-equation version of the two-particle Lippmann-Schwinger (LS) equation is considered without invoking the traditional partial-wave decomposition. The singular kernel of the three-dimensional LS equation in coordinate space is regularized by a subtraction technique. The resulting nonsingular integral equation is then solved via the Nystrom method employing a direct-product quadrature rule for three variables. To reduce the computational burden of discretizing three variables, advantage is taken of the fact that, for central potentials, the azimuthal angle can be integrated out, leaving a two-variable reduced integral equation. A regularization method for the kernel of the two-variable integral equation is derived from the treatment of the singularity in the three-dimensional equation. A quadrature rule constructed as the direct product of single-variable quadrature rules for radial distance and polar angle is used to discretize the two-variable integral equation. These two- and three-variable methods are tested on the Hartree potential. The results show that the Nystrom method for the coordinate-space LS equation compares favorably in terms of its ease of implementation and effectiveness with the Nystrom method for the momentum-space version of the LS equation.

This paper deals with the properties of the stochastic generators of the effective (driven) processes associated with atypical values of transition-dependent time-integrated currents with Gallavotti-Cohen symmetry in Markov jump processes. Exploiting the concept of biased ensemble of trajectories by introducing a biasing field $s$, we show that the stochastic generators of the effective processes associated with the biasing fields $s$ and $E-s$ are enantiodromic with respect to each other where $E$ is the conjugated field to the current. We illustrate our findings by considering an exactly solvable creation-annihilation process of classical particles with nearest-neighbor interactions defined on a one-dimensional lattice.

Kinetically constrained spin systems play an important role in understanding key properties of the dynamics of slowly relaxing materials, such as glasses. Recent experimental studies have revealed that manifest kinetic constraints govern the evolution of strongly interacting gases of highly excited atoms in a noisy environment. Motivated by this development we explore which types of kinetically constrained dynamics can generally emerge in quantum spin systems subject to strong noise and show how, in this framework, constraints are accompanied by conservation laws. We discuss an experimentally realizable case of a lattice gas, where the interplay between those and the geometry of the lattice leads to collective behavior and time-scale separation even at infinite temperature. This is in contrast to models of glass-forming substances which typically rely on low temperatures and the consequent suppression of thermal activation.

In this paper, stochastic thermodynamics of delayed bistable Langevin systems near coherence resonance is discussed. We calculate the heat dissipation rate and the information flow of a delayed bistable Langevin system under various noise intensities. Both the heat dissipation rate and the information flow are found to be bell-shaped functions of the noise intensity, which implies that coherence resonance manifests itself in the thermodynamic properties.

We study the integrability of the two-spin elliptic Gaudin model for arbitrary values of the Hamiltonian parameters. The limit of a very large spin coupled to a small one is well described by a semiclassical approximation with just one degree of freedom. Its spectrum is divided into bands that do not overlap if certain conditions are fulfilled. In spite of the fact that there are no quantum phase transitions in each of the band heads, the bands show excited-state quantum phase transitions separating a region in which the parity symmetry is broken from another region in which time-reversal symmetry is broken. We derive analytical expressions for the critical energies in the semiclassical approximation, and confirm the results by means of exact diagonalizations for large systems.