Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random-walk model with long-range memory for which not only the mean-square displacement (MSD) but also the propagator can be obtained exactly in the asymptotic limit. The model consists of a random walker on a lattice, which, at a constant rate, stochastically relocates at a site occupied at some earlier time. This time in the past is chosen randomly according to a memory kernel, whose temporal decay can be varied via an exponent parameter. In the weakly non-Markovian regime, memory reduces the diffusion coefficient from the bare value. When the mean backward jump in time diverges, the diffusion coefficient vanishes and a transition to an anomalous subdiffusive regime occurs. Paradoxically, at the transition, the process is an anticorrelated Lévy flight. Although in the subdiffusive regime the model exhibits some features of the continuous time random walk with infinite mean waiting time, it belongs to another universality class. If memory is very long-ranged, a second transition takes place to a regime characterized by a logarithmic growth of the MSD with time. In this case the process is asymptotically Gaussian and effectively described as a scaled Brownian motion with a diffusion coefficient decaying as $1/t$.

Inspired by the experimental results of Cuevas et al. [Phys. Rev. Lett. 102, 224101 (2009)], we consider theoretically the behavior of a chain of planar rigid pendulums suspended in a uniform gravitational field and subjected to a horizontal periodic driving force applied to the pendulum pivots. We characterize the motion of a single pendulum, finding bistability near the fundamental resonance and near the period-3 subharmonic resonance. We examine the development of modulational instability in a driven pendulum chain and find both a critical chain length and a critical frequency for the appearance of the instability. We study the breather solutions and show their connection to the single-pendulum dynamics and extend our analysis to consider multifrequency breathers connected to the period-3 periodic solution, showing also the possibility of stability in these breather states. Finally we examine the problem of breather generation and demonstrate a robust scheme for generation of on-site and off-site breathers.

Superhydrophobic Cassie textures with trapped gas bubbles reduce drag, by generating large effective slip, which is important for a variety of applications that involve a manipulation of liquids at the small scale. Here we discuss how the dissipation in the gas phase of textures modifies their friction properties. We propose an operator method, which allows us to map the flow in the gas subphase to a local slip boundary condition at the liquid-gas interface. The determined uniquely local slip length depends on the viscosity contrast and underlying topography, and can be immediately used to evaluate an effective slip of the texture. Besides superlubricating Cassie surfaces, our approach is valid for rough surfaces impregnated by a low-viscosity “lubricant,” and even for Wenzel textures, where a liquid follows the surface relief. These results provide a framework for the rational design of textured surfaces for numerous applications.

The wave equation for pressure that governs generation of the photoacoustic effect possesses a forcing term proportional to the time derivative of the energy delivered to the gas per unit volume and time. A positive pressure fluctuation, with its accompanying density increase, thus increases the optical absorption and provides a positive feedback mechanism for sound generation. A theory for self-oscillation in a one-dimensional resonator is given. Expressions for the photoacoustic pressure are derived for the cases of highly and weakly absorbing gases that indicate mode-locked sound generation. Experiments with ${\mathrm{CO}}_2$ lasers are reported where evidence of the self-generation effect was sought.

We study analytically and by numerical simulations the statistics of the aftershocks generated after large avalanches in models of interface depinning that include viscoelastic relaxation effects. We find in all the analyzed cases that the decay law of aftershocks with time can be understood by considering the typical roughness of the interface and its evolution due to relaxation. In models where there is a single viscoelastic relaxation time there is an exponential decay of the number of aftershocks with time. In models in which viscoelastic relaxation is wave-vector dependent we typically find a power-law dependence of the decay rate that is compatible with the Omori law. The factors that determine the value of the decay exponent are analyzed.

We introduce an approximation for the pair distribution function of the inhomogeneous hard sphere fluid. Our approximation makes use of our recently published averaged pair distribution function at contact, which has been shown to accurately reproduce the averaged pair distribution function at contact for inhomogeneous density distributions. This approach achieves greater computational efficiency than previous approaches by enabling the use of exclusively fixed-kernel convolutions and thus allowing an implementation using fast Fourier transforms. We compare results for our pair distribution approximation with two previously published works and Monte Carlo simulation, showing favorable results.

Fundamental measure theory (FMT) for hard particles has great potential for predicting the phase behavior of colloidal and nanometric shapes. The modern versions of FMT are usually derived from the zero-dimensional limit, a system of at most one particle confined in a collection of cavities in the limit that all cavities shrink to the size of the particle. In Phys. Rev. E 85, 041150 (2012), a derivation from an approximated and resummed virial expansion was presented, whose result was not fully consistent with the FMT from the zero-dimensional limit. Here we improve on this derivation and obtain exactly the same FMT functional as was obtained earlier from the zero-dimensional limit. As a result, further improvements of FMT based on the virial expansion can now be formulated, some of which we suggest in the outlook.

We investigate the nonequilibrium phase transition in the disordered contact process in the presence of long-range spatial disorder correlations. These correlations greatly increase the probability for finding rare regions that are locally in the active phase while the bulk system is still in the inactive phase. Specifically, if the correlations decay as a power of the distance, the rare-region probability is a stretched exponential of the rare-region size rather than a simple exponential as is the case for uncorrelated disorder. As a result, the Griffiths singularities are enhanced and take a non-power-law form. The critical point itself is of infinite-randomness type but with critical exponent values that differ from the uncorrelated case. We report large-scale Monte Carlo simulations that verify and illustrate our theory. We also discuss generalizations to higher dimensions and applications to other systems such as the random transverse-field Ising model, itinerant magnets, and the superconductor-metal transition.

We investigate the formation of fingered flow in dry granular media under simulated rainfall using a quasi-two-dimensional experimental setup composed of a random close packing of monodisperse glass beads. Using controlled experiments, we analyze the finger instabilities that develop from the wetting front as a function of fundamental granular (particle size) and fluid properties (rainfall, viscosity). These finger instabilities act as precursors for water channels, which serve as outlets for water drainage. We look into the characteristics of the homogeneous wetting front and channel size as well as estimate relevant time scales involved in the instability formation and the velocity of the channel fingertip. We compare our experimental results with that of the well-known prediction developed by Parlange and Hill [D. E. Hill and J. Y. Parlange, Soil Sci. Soc. Am. Proc. 36, 697 (1972)]. This model is based on linear stability analysis of the growth of perturbations arising at the interface between two immiscible fluids. Results show that, in terms of morphology, experiments agree with the proposed model. However, in terms of kinetics we nevertheless account for another term that describes the homogenization of the wetting front. This result shows that the manner we introduce the fluid to a porous medium can also influence the formation of finger instabilities. The results also help us to calculate the ideal flow rate needed for homogeneous distribution of water in the soil and minimization of runoff, given the grain size, fluid density, and fluid viscosity. This could have applications in optimizing use of irrigation water.

Ferrogels and magnetic elastomers feature mechanical properties that can be reversibly tuned from outside through magnetic fields. Here we concentrate on the question of how their dynamic response can be adjusted. The influence of three factors on the dynamic behavior is demonstrated using appropriate minimal models: first, the orientational memory imprinted into one class of the materials during their synthesis; second, the structural arrangement of the magnetic particles in the materials; and third, the strength of an external magnetic field. To illustrate the latter point, structural data are extracted from a real experimental sample and analyzed. Understanding how internal structural properties and external influences impact the dominant dynamical properties helps to design materials that optimize the requested behavior.

Literature data for picosecond mean square displacements show that the anharmonicity explains only about half of the fragility (with different fractions for different glass formers). The other half must be ascribed to the Adam-Gibbs mechanism of a growing cooperatively rearranging region. One can measure both influences separately by a simultaneous measurement of liquid and crystal in the coexistence region.

Radical-ion-pair reactions, central in photosynthesis and the avian magnetic compass mechanism, have been recently shown to be a paradigm system for applying quantum information science in a biochemical setting. The fundamental quantum master equation describing radical-ion-pair reactions is still under debate. Here we use quantum retrodiction to formally refine the theory put forward in the paper by Kominis [I. K. Kominis, Phys. Rev. E 83, 056118 (2011)]. We also provide a rigorous analysis of the measure of singlet-triplet coherence required for deriving the radical-pair master equation. A Monte Carlo simulation with single-molecule quantum trajectories supports the self-consistency of our approach.

Optimal velocity (OV) car-following models give with few parameters stable stop-and -go waves propagating like in empirical data. Unfortunately, classical OV models locally oscillate with vehicles colliding and moving backward. In order to solve this problem, the models have to be completed with additional parameters. This leads to an increase of the complexity. In this paper, a new OV model with no additional parameters is defined. For any value of the inputs, the model is intrinsically asymmetric and collision-free. This is achieved by using a first-order ordinary model with two predecessors in interaction, instead of the usual inertial delayed first-order or second-order models coupled with the predecessor. The model has stable uniform solutions as well as various stable stop-and -go patterns with bimodal distribution of the speed. As observable in real data, the modal speed values in congested states are not restricted to the free flow speed and zero. They depend on the form of the OV function. Properties of linear, concave, convex, or sigmoid speed functions are explored with no limitation due to collisions.

We study disease spreading in a system of agents moving in a space where the force of infection is not homogeneous. Agents are random walkers that additionally execute long-distance jumps, and the plane in which they move is divided into two regions where the force of infection takes different values. We show the onset of a local epidemic threshold and a global one and explain them in terms of mean-field approximations. We also elucidate the critical role of the agent velocity, jump probability, and density parameters in achieving the conditions for local and global outbreaks. Finally, we show that the results are independent of the specific microscopic rules adopted for agent motion, since a similar behavior is also observed for the distribution of agent velocity based on a truncated power law, which is a model often used to fit real data on motion patterns of animals and humans.

The Shannon entropy of a time series is a standard measure to assess the complexity of a dynamical process and can be used to quantify transitions between different dynamical regimes. An alternative way of quantifying complexity is based on state recurrences, such as those available in recurrence quantification analysis. Although varying definitions for recurrence-based entropies have been suggested so far, for some cases they reveal inconsistent results. Here we suggest a method based on weighted recurrence plots and show that the associated Shannon entropy is positively correlated with the largest Lyapunov exponent. We demonstrate the potential on a prototypical example as well as on experimental data of a chemical experiment.

We study a spatial evolutionary rock-paper-scissors game with synchronized strategy updating. Players gain their payoff from games with their four neighbors on a square lattice and can update their strategies simultaneously according to the logit rule, which is the noisy version of the best-response dynamics. For the synchronized strategy update two types of global oscillations (with an ordered strategy arrangement and periods of three and six generations) can occur in this system in the zero noise limit. At low noise values, all nine oscillating phases are present in the system by forming a self-organizing spatial pattern due to the comprising invasion and speciation processes along the interfaces separating the different domains.

We examine the distribution of the local dissipation scale $\eta$, $Q\left(\eta \right)$, and its temporal evolution in two-dimensional (2D) Rayleigh-Taylor (RT) turbulence using direct numerical simulations at small Atwood number and unit Prandtl number. Within the self-similarity regime of the mixing zone evolution, distributions of $\eta$ at small scales are found to be insensitive to the large-scale anisotropy of the system and independent of position and of the temporal evolution of the mixing zone. Our results further reveal that the present measured $Q\left(\eta \right)$ agrees with those previously observed in homogeneous isotropic turbulence and in turbulent pipe flows, at least for the smallest scales around the classical Kolmogorov dissipation scale. However, the RT case seems to show a different trend from the other two cases for large scales, which may attributed to the absence of the inertial-range intermittency for the velocity field in 2D RT turbulence.

The dispersion of a cylindrical particle ring by a blast or shock wave induces the formation of coherent structures which take the form of particle jets. A blast wave, issuing from the discharge of a planar shock wave at the exit of a conventional shock tube, is generated in the center of a granular medium ring initially confined inside a Hele-Shaw cell. With the present experimental setup, under impulsive acceleration, a solid particle-jet formation is observed in a quasi-two-dimensional configuration. The aim of the present investigation is to observe in detail the formation of very thin perturbations created around the external surface of the dispersed particle layer. By means of fast flow visualization with an appropriate recording window, we focus solely on the first instants during which the external particle ring becomes unstable. We find that the critical area of the destabilization of the external ring surface is constant regardless of the acceleration of the initial layer. Moreover, we observe in detail the external front perturbation wavelength, rendered dimensionless by the initial ring perimeter, and follow its evolution with the initial particle layer acceleration. We report this quantity to be constant regardless of the evolution of the initial particle layer acceleration. Finally, we can reasonably assert that external front perturbations depend solely on the material of the particles.

This paper explains the gain window phenomenon seen in early experimental and computational studies on active, closed-loop control of vortex shedding, whereby shedding is completely suppressed only if the feedback gain lies within some narrow window of stabilizing gains. Using two-dimensional direct numerical simulations and reduced-order modeling techniques, a low-order, linear model of the cylinder wake is formed at a Reynolds number of 60. This model is used to reproduce and to explain the gain window seen in previous studies. It is shown that the gain window is not caused by the destabilization of a higher mode but rather is determined entirely by the behavior of the open-loop unstable mode under the action of the closed-loop controller. It is demonstrated that the time taken for actuated fluid to convect to the sensor location plays an important part in explaining this gain window. A similar analysis at a higher Reynolds number of 80 reveals that the wake remains unstable for all choices of the feedback gain. The study illustrates the limitations of closed-loop suppression of vortex shedding when a very simple control strategy is used.