Velocity relaxation of an elastic sphere immersed in a viscous incompressible fluid is studied on the basis of the equations of linear elasticity and the linearized Navier-Stokes equations. It is found that both translational motion after a sudden impulse and rotational motion after a sudden twist show jittery behavior in the long-time regime, with many reversals of velocity if the sphere is sufficiently flexible. In the extreme long-time regime the translational and rotational velocity relaxation functions each decay with a universal algebraic long-time tail. The added mass and the added moment of inertia of the sphere are found to vanish.

Transition from a Taylor-Couette turbulent flow to a completely two-dimensional axisymmetric turbulent state is realized numerically by increasing gradually the strength of the azimuthal magnetic field produced by electric current flowing through the axial rod. With the increase of the Hartmann number, the Taylor-vortex-like structures shrink, move closer to the inner cylinder, and turn into unsteady but perfect tori at sufficiently high Hartmann numbers.

A recently introduced inference method based on system replication and an online message passing algorithm is employed to complete a previously suggested compression scheme based on a nonlinear perceptron. The algorithm is shown to approach the information theoretical bounds for compression as the number of replicated systems increases, offering superior performance compared to basic message passing algorithms. In addition, the suggested method does not require fine-tuning of parameters or other complementing heuristic techniques, such as the introduction of inertia terms, to improve convergence rates to nontrivial results.

We study analytically the tracer particle mobility in single-file systems with distributed friction constants. Our system serves as a prototype for nonequilibrium, heterogeneous, strongly interacting Brownian systems. The long time dynamics for such a single-file setup belongs to the same universality class as the Rouse model with dissimilar beads. The friction constants are drawn from a density $\varrho \left(\xi \right)$, and we derive an asymptotically exact solution for the mobility distribution $P\left[{\mu }_0\left(s\right)\right]$, where ${\mu }_0\left(s\right)$ is the Laplace-space mobility. If $\varrho$ is light tailed (first moment exists), we find a self-averaging behavior: $P\left[{\mu }_0\left(s\right)\right]=\delta [{\mu }_0\left(s\right)-\mu \left(s\right)]$, with $\mu \left(s\right)\propto s^{1/2}$. When $\varrho \left(\xi \right)$ is heavy tailed, $\varrho \left(\xi \right)\simeq {\xi }^{-1-\alpha }(0<\alpha <1)$ for large $\xi$, we obtain moments $\langle {\left[{\mu }_s\left(0\right)\right]}^n\rangle \propto s^{\beta n}$, where $\beta =1/(1+\alpha )$ and there is no self-averaging. The results are corroborated by simulations.

An experimental investigation into the interaction that occurs between an impacting water droplet and a granular bed of loose graded sand has been carried out. High-speed imaging, three-dimensional time-resolved particle tracking, and photogrammetric surface profiling have been used to examine individual impact events. The focus of the study is the quantification and trajectory analysis of the particles ejected from the sand bed, along with measurement of the change in bed morphology. The results from the experiments have detailed two distinct mechanisms of particle ejection: the ejection of water-encapsulated particles from the edge of the wetted region and the ejection of dry sand from the periphery of the impact crater. That the process occurs by these two distinct mechanisms has hitherto been unobserved. Presented in the paper are distributions of the particle ejection velocities, angles, and transport distances for both mechanisms. The ejected water-encapsulated particles, which are few in number, are characterized by low ejection angles and high ejection velocities, leading to large transport distances; the ejected dry particles, which are much greater in number, are characterized by high ejection angles and low velocities, leading to lower transport distances. From the particle ejection data, the momentum of the individual ballistic sand particles has been calculated; it was found that only 2% of the water-droplet momentum at impact is transferred to the ballistic sand particles. In addition to the particle tracking, surface profiling of the granular bed postimpact has provided detailed information on its morphology; these data have demonstrated the consistent nature of the craters produced by the impact and suggest that particle agglomerations released from their edges make up about twice the number of particles involved in ballistic ejection. It is estimated that, overall, about 4% of the water-droplet momentum is taken up in particle movement.

Two problems have intrigued experts for a long time: The one is within the context of the legend of flowing cathedral glass windows and the second is the inaccuracy appearing in very old thermometers of famous scientists. We relate this with the role of the surface on the apparent viscosity of glasses. The apparent viscosity could deviate from the bulk viscosity if the fraction $w$ of the surface molecules, of small samples, is sufficiently large. The effect is more prominent at low temperatures, correspondingly at high viscosities. The interpretation is within the Avramov and Milchev viscosity model, combined with the predictions of the change of heat capacity for extremely small samples. We find that the apparent glass transition temperature could depend on the sample size, in agreement with experimental observations existing in the literature. In addition to glasses, the present results could be of importance for thin films and foams.

The abundance of models of complex networks and the current insufficient validation standards make it difficult to judge which models are strongly supported by data and which are not. We focus here on likelihood maximization methods for models of growing networks with many parameters and compare their performance on artificial and real datasets. While high dimensionality of the parameter space harms the performance of direct likelihood maximization on artificial data, this can be improved by introducing a suitable penalization term. Likelihood maximization on real data shows that the presented approach is able to discriminate among available network models. To make large-scale datasets accessible to this kind of analysis, we propose a subset sampling technique and show that it yields substantial model evidence in a fraction of time necessary for the analysis of the complete data.

This paper deals with the computation of laser beam intensity in large-scale radiative hydrocodes applied to the modeling of nonlinear laser-plasma interactions (LPIs) in inertial confinement fusion (ICF). The paraxial complex geometrical optics (PCGO) is adapted for light waves in an inhomogeneous medium and modified to include the inverse bremsstrahlung absorption and the ponderomotive force. This thick-ray model is compared to the standard ray-tracing (RT) approach, both in the chic code. The PCGO model leads to different power deposition patterns and better diffraction modeling compared to standard RT codes. The intensity-reconstruction technique used in RT codes to model nonlinear LPI leads to artificial filamentation and fails to reproduce realistic ponderomotive self-focusing distances, intensity amplifications, and density channel depletions, whereas PCGO succeeds. Bundles of Gaussian thick rays can be used to model realistic non-Gaussian ICF beams. The PCGO approach is expected to improve the accuracy of ICF simulations and serve as a basis to implement diverse LPI effects in large-scale hydrocodes.

We examine the $\mathcal{PT}$-symmetry-breaking transition for a magnetic metamaterial of a finite extent, modeled as an array of coupled split-ring resonators in the equivalent circuit model approximation. Small-size arrays are solved completely in closed form, while for arrays larger than $N=5$ results were computed numerically for several gain and loss spatial distributions. In all cases, it is found that the parameter stability window decreases rapidly with the size of the array, until at $N=20$ approximately it is not possible to support a stable $\mathcal{PT}$-symmetric phase.

The problem of stochastic advection of passive particles by circulating conserved flows on networks is formulated and investigated. The particles undergo transitions between the nodes, with the transition rates determined by the flows passing through the links. Such stochastic advection processes lead to mixing of particles in the network and, in the final equilibrium state, concentration of particles in all nodes becomes equal. As we find, equilibration begins in the subset of nodes, representing flow hubs, and extends to the periphery nodes with weak flows. This behavior is related to the effect of localization of the eigenvectors of the advection matrix for considered networks. Applications of the results to problems involving spreading of infections or pollutants by traffic networks are discussed.

The frustrated spin-1/2 Ising-Heisenberg ladder with Heisenberg intra-rung and Ising inter-rung interactions is exactly solved in a longitudinal magnetic field by taking advantage of the local conservation of the total spin on each rung and the transfer-matrix method. We have rigorously calculated the ground-state phase diagram, magnetization process, magnetocaloric effect, and basic thermodynamic quantities for the model, which can be alternatively viewed as an Ising-Heisenberg tetrahedral chain. It is demonstrated that a stepwise magnetization curve with an intermediate plateau at half of the saturation magnetization is also reflected in respective stepwise changes of the concurrence serving as a measure of bipartite entanglement. The ground-state phase diagram and zero-temperature magnetization curves of the Ising-Heisenberg tetrahedral chain are contrasted with the analogous results of the purely quantum Heisenberg tetrahedral chain, which have been obtained through density-matrix renormalization group (DMRG) calculations. While both ground-state phase diagrams fully coincide in the regime of weak inter-rung interaction, the purely quantum Heisenberg tetrahedral chain develops Luttinger spin-liquid and Haldane phases for strongly coupled rungs, which are absent in the Ising-Heisenberg counterpart model.

We consider the dynamics of systems driven by compound Poisson colored noise in the presence of inertia. We study the limit when the frictional relaxation time and the noise autocorrelation time both tend to zero. We show that the It$\widehat{\text{o}}$ and Marcus stochastic calculuses naturally arise depending on these two time scales, and an extra intermediate type occurs when the two time scales are comparable. This leads to three different limiting regimes which are supported by numerical simulations. Furthermore, we establish that when the resulting compound Poisson process tends to the Wiener process in the frequent jump limit the It$\widehat{\text{o}}$ and Marcus calculuses, respectively, tend to the classical It$\widehat{\text{o}}$ and Stratonovich calculuses for Gaussian white noise, and the crossover type calculus tends to a crossover between the It$\widehat{\text{o}}$ and Stratonovich calculuses. Our results would be very helpful for understanding relevant experiments when jump type noise is involved.

Correlations in fluids in nonequilibrium steady states are long range. Hence, finite-size effects have important consequences in the nonequilibrium thermodynamics of fluids. One consequence is that nonequilibrium temperature fluctuations induce nonequilibrium Casimir-like pressures proportional to the square of the temperature gradient. Hence, fluctuations cause a breakdown of the concept of local thermal equilibrium. Furthermore, transport coefficients become dependent on boundary conditions and on gravity. Thus nonequilibrium fluctuations affect some traditional concepts in nonequilibrium thermodynamics.

We consider the collision of a rough sphere with a plane by detailed analysis of the collision geometry. Using stochastic methods, the effective coefficient of restitution may be described as a fluctuating quantity whose probability density follows an asymmetric Laplace distribution. This result agrees with recent experiments by Montaine et al. [Phys. Rev. E 84, 041306 (2011)].

We show in numerical simulations that a system of two coupled replicas of a binary mixture of hard spheres undergoes a phase transition in equilibrium at a density slightly smaller than the glass transition density for an unreplicated system. This result is in agreement with the theories that predict that such a transition is a precursor of the standard ideal glass transition. The critical properties are compatible with those of an Ising system. The relations of this approach to the conventional approach based on configurational entropy are briefly discussed.

We investigate the effect of multiwalled carbon nanotubes (MWCNTs) on the magnetorheological properties of an oil based magnetic nanofluid (ferrofluid). The shear resistant plateau observed in a pure ferrofluid disappears when 0.5 wt % of MWCNT is incorporated. The yield stress values of the composite system are slightly smaller than that of the pure system. This shows that the presence of carbon nanotubes (CNTs) weakens the magnetic field induced microstructure of the ferrofluid due to their interaction that affects the hydrodynamic and magnetic interactions between the dispersed nanoparticles. Interestingly, the Mason number plots for both the pure and composite system show scaling of the viscosity curves onto a single master curve for magnetic fields of 80 mT and above while deviations are observed for lower magnetic fields. The weakening of the ferrofluid microstructure in the presence of CNTs is further evident in the amplitude sweep measurements where the linear viscoelastic region develops only at a higher magnetic field strength compared to lower magnetic fields in pure ferrofluids. These results are useful for tailoring ferrofluids with a faster response for various applications.

In cholesteric liquid-crystalline gels, the mechanical role of the polymer network over the structure of the whole gel has been ignored. We show that it is the stress gradient exerted by the network over the helical structure that drives the broadening of the optical band gap, as evidenced by the absence of a gradient in chiral species. Model calculations and finite-difference time-domain simulations show that the network acts as a spring with a stiffness gradient. The present results indicate a revision to the common understanding of the physical properties of liquid-crystalline gels is necessary when a concentration gradient in a polymer network is present.

We consider the approximations behind the typical mean-field model derived for a class of systems made up of type II excitable units influenced by noise and coupling delays. The formulation of the two approximations, referred to as the Gaussian and the quasi-independence approximation, as well as the fashion in which their validity is verified, are adapted to reflect the essential properties of the underlying system. It is demonstrated that the failure of the mean-field model associated with the breakdown of the quasi-independence approximation can be predicted by the noise-induced bistability in the dynamics of the mean-field system. As for the Gaussian approximation, its violation is related to the increase of noise intensity, but the actual condition for failure can be cast in qualitative, rather than quantitative terms. We also discuss how the fulfillment of the mean-field approximations affects the statistics of the first return times for the local and global variables, further exploring the link between the fulfillment of the quasi-independence approximation and certain forms of synchronization between the individual units.