Granular ratchets are well-known devices that when driven vertically produce a counterintuitive horizontal transport of particles. Here we report the experimental observation of a complementary effect: the striking ability of circular ratchets to convert their vertical vibration into their own rotation. The average revolution speed shows a maximum value for an optimal tooth height. With no special effort the rotation speed could be maintained steady during several hours. Unexpected random arrests and reversals of the velocity were also observed abundantly.

An algorithm is developed for numerical simulation of coupled stochastic dynamics of magnetic moment and magnetic anisotropy axis of a nanoparticle. Time-correlation functions of the magnetic moment and its components longitudinal and transverse to the magnetic anisotropy axis are calculated by averaging along the stochastic trajectory. The longitudinal and transverse relaxation times are found by fitting the time correlation functions. Existing theoretical relations derived by the effective field approach in the limit of small fields are confirmed. The time-correlation functions of magnetic moments of nanoparticles in dependence on their properties are calculated numerically for arbitrary large magnetic fields and it is shown that they may be approximated by a sum of several exponentials. These results are applied for the calculation of relaxivity parameters of nuclear magnetic resonance (NMR) imaging in dependence on the field strength.

We extend the quiescent and stressed versions of naïve mode coupling theory to treat the dynamical arrest, shear modulus, and absolute yielding of particle mixtures where one or more species is a nonrotating nonspherical object. The theory is applied in detail to dense isotropic “chemically matched” mixtures of variable aspect ratio rods and spheres that interact via repulsive and short range attractive site-site pair potentials. A remarkably rich ideal kinetic arrest behavior is predicted with up to eight “dynamical phases” emerging: an ergodic fluid, partially localized states where the spheres remain fluid but the rods can be a gel, repulsive glass or attractive glass, doubly localized glasses and gels, a porous rod gel plus sphere glass, and a narrow window where a type of rod glass and gel localization coexist. Dynamical complexity increases with rod length and the introduction of attractive forces between all species which both enhance gel network formation. Multiple dynamic reentrant features and triple points are predicted, and each dynamic phase has unique particle localization characteristics and mechanical properties. Orders of magnitude variation of the linear shear modulus and absolute yield stress are found as rod length, mixture composition and the detailed nature of interparticle attractions are varied. The interplay of total (high) mixture packing fraction and composition at fixed temperature is also briefly studied. The present work provides a foundation to study more complex rod-sphere mixtures of both biological and synthetic interest that include physical features such as interaction site size asymmetry, rod-sphere specific attractions, and/or Coulomb repulsion.

Using a Monte Carlo method on a lattice model of a vicinal surface with a point-contact-type step-step attraction, we show that, at low temperature and near equilibrium, there is an inhibition of the motion of macrosteps. This inhibition leads to a pinning of steps without defects, adsorbates, or impurities (self-pinning of steps). We show that this inhibition of the macrostep motion is caused by faceted steps, which are macrosteps that have a smooth side surface. The faceted steps result from discontinuities in the anisotropic surface tension (the surface free energy per area). The discontinuities are brought into the surface tension by the point-contact-type step-step attraction. The point-contact-type step-step attraction also originates “step droplets,” which are locally merged steps, at higher temperatures. We derive an analytic equation of the surface stiffness tensor for the vicinal surface around the (001) surface. Using the surface stiffness tensor, we show that step droplets roughen the vicinal surface. Contrary to what we expected, the step droplets slow down the step velocity due to the diminishment of kinks in the merged steps (smoothing of the merged steps).

The director-density coupling theory has been proposed to describe the acousto-optic effect in nematic liquid crystals. On the basis of this theory, we make predictions for an experimental test using two superimposed ultrasonic waves. As a result of the analysis, low-frequency oscillations of the director and optical transparency are predicted to occur around their mean values. The possibility of either verifying or invalidating this prediction is important in order to distinguish the theory from other competitive ones.

We investigated the dynamics of single soft nanotubes of phospholipids to extract nanoscale information such as the size of the tube, which were several tens to hundreds of nanometers thick. The dynamic properties of the tubes obtained from direct observation by fluorescent microscopy, such as their persistence length, enable us to access the nanoscale characteristics through a simple elastic model of the membrane. The present methodology should be applicable to the nanosized membrane structure in living cells.

Recently, we developed a computational model that allowed us to study the influence a semiconductor membrane has on a DNA molecule translocating through a nanopore in this membrane. Our model incorporated both the self-consistent Poisson-Nernst-Planck simulations for the electric potential of a solid state membrane immersed in an electrolyte solution together with the Brownian dynamics of the biomolecule. In this paper, we study how the applied electrolyte bias, the semiconductor membrane bias, and the semiconductor material type ($n$-Si or $p$-Si) affect the translocation dynamics of a single-stranded DNA moving through a nanopore in a single-layered semiconductor membrane. We show that the type of semiconductor material used for the membrane has a prominent effect on the biomolecule's translocation time, with DNA exhibiting much longer translocation times through the $p$-type membrane than through the $n$ type at the same electrolyte and membrane potentials, while the extension of the biomolecule remains practically unchanged. In addition, we find the optimal combination for the membrane-electrolyte system's parameters to achieve the longest translocation time and largest DNA extension. With our single-layered electrically tunable membranes, the DNA translocation time can be manipulated to have an order of magnitude increase.

The opacity of typical objects in the world results in occlusion, an important property of natural scenes that makes inference of the full three-dimensional structure of the world challenging. The relationship between occlusion and low-level image statistics has been hotly debated in the literature, and extensive simulations have been used to determine whether occlusion is responsible for the ubiquitously observed power-law power spectra of natural images. To deepen our understanding of this problem, we have analytically computed the two- and four-point functions of a generalized “dead leaves” model of natural images with parameterized object transparency. Surprisingly, transparency alters these functions only by a multiplicative constant, so long as object diameters follow a power-law distribution. For other object size distributions, transparency more substantially affects the low-level image statistics. We propose that the universality of power-law power spectra for both natural scenes and radiological medical images, formed by the transmission of x-rays through partially transparent tissue, stems from power-law object size distributions, independent of object opacity.

We investigate the mechanism of generation of phase-locked cluster patterns in a globally coupled FitzhHugh-Nagumo model where the fast variable (activator) receives global feedback from the slow variable (inhibitor). We identify three qualitatively different mechanisms (swing-and-release, hold-and-release, and escape-and-release) that contribute to the generation of these patterns. We describe these mechanisms and use this framework to explain under what circumstances two initially out-of-phase oscillatory clusters reach steady phase-locked and in-phase synchronized solutions, and how the phase difference between these steady state cluster patterns depends on the clusters relative size, the global coupling intensity, and other model parameters.

Recent studies have used scaling analysis to obtain simple power-law relations that accurately predict the Prandtl ($\mathrm{Pr}$) number dependency of natural-convection boundary layers subjected to both isothermal and ramped heating conditions, when $\mathrm{Pr}>1$. The analysis used in those studies cannot be extended to $\mathrm{Pr}<1$ fluids, and it is not clear at present whether such simple scaling relations can be developed for $\mathrm{Pr}<1$ fluids. In the present study, the $\mathrm{Pr}>1$ scalings are shown to perform well for the start-up stage of the $\mathrm{Pr}<1$ flow, but not for the fully developed flow. The $\mathrm{Pr}>1$ scalings are modified to provide unified Prandtl number scalings for fully developed natural-convection boundary layers for both $\mathrm{Pr}\gtrsim 1$ and $\mathrm{Pr}\lesssim 1$, with the unknown powers obtained empirically via direct numerical simulation. The modified scalings are shown to perform well for the fully developed flow, with the exception being the prediction of the inner viscous boundary-layer thickness.

A nearly two-dimensional foam is generated inside a Hele-shaw cell and left at rest on its liquid bath. The system is then vertically shaken and, above a well-defined acceleration threshold, surface waves appear at the foam-liquid interface. Those waves are shown to be subharmonic. The acceleration threshold is studied and compared to the common liquid-gas case, emphasizing the energy dissipation inside the foam. An empirical model is proposed for this energy loss, accounting for the foam characteristics such as the bubble size but also the excitation parameter, namely the linear velocity.

We present analytical and numerical studies of the initial stage of the branching process based on an interface dynamics streamer model in the fully three-dimensional case. This model follows from fundamental considerations on charge production by impact ionization and balance laws, and leads to an equation for the evolution of the interface between ionized and nonionized regions. We compare some experimental patterns with the numerically simulated ones, and give an explicit expression for the growth rate of harmonic modes associated with the perturbation of a symmetrically expanding discharge. By means of full numerical simulation, the splitting and formation of characteristic treelike patterns of electric discharges is observed and described.

The existence of two-kink soliton solutions in polynomial potentials was first reported by Bazeia et al. in a special type of scalar field systems [Phys. Rev. Lett. 91, 241601 (2003)]. A general feature of these potentials is that they possess two minima and a local metastable minimum between them. In the present work we investigate the appearance of this special kind of soliton in the sine-Gordon model under the perturbation of a space-dependent force. We show that a pair of solitons is emitted during the process of kink breakup by internal mode instabilities. A possible explanation of these phenomena is an interplay between the solitons repelling interaction and the external force, resulting in a separation or a packing of several kinks.

In this paper we analyze the inviscid regime (for which viscosity is unimportant and the flow occurs due to the balance between the capillary and the inertial effects) that invariably precedes the classical century-old Washburn regime during capillary filling. We demonstrate that a new nondimensional number, namely, the product of the Ohnesorge number and the ratio between the filling length ($\ell$) and the radius of the capillary ($R$), dictates the occurrence of this regime and the other well-known regimes in a capillary filling problem. We also identify that this inviscid regime occurs for the time that is of the order of the capillary time scale and, as has been quantified before [Quere, Eur. Phys. Lett. 39, 533 (1997); Joly, J. Chem. Phys. 135, 214705 (2011)], is characterized by the filling length being linearly proportional to the filling time. We establish the universality of this regime by pinpointing the existence of this regime (showing appropriate dependencies of the capillary radii and density) from existing experimental and Molecular Dynamics Simulation results that signify disparate ranges of length and time scales.

The problem of determining the joint probability distributions for correlated random variables with prespecified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the “most unbiased” choice corresponds to the distribution of maximum entropy. The calculation of the maximum-entropy distribution requires the solution of rather complicated nonlinear coupled integral equations, exact solutions to which are obtained for the case of Gaussian marginals; otherwise, the solution can be expressed as a perturbation around the product of the marginals if the marginal moments exist.

We analyze the steady-state energy transfer in a chain of coupled two-level systems connecting two thermal reservoirs. Through an analytic treatment we find that the energy current is independent of the system size, hence violating Fourier's law of heat conduction. The classical diffusive behavior in Fourier's law of heat conduction can be recovered by introducing decoherence to the quantum systems constituting the chain. We relate these results to recent discussions of energy transport in biological light-harvesting systems, and discuss the role of quantum coherence and entanglement.

The decay of a small homogeneous perturbation in the temperature of a dilute granular gas in the steady uniform shear flow state is investigated. Using kinetic theory based on the inelastic Boltzmann equation, a closed equation for the decay of the perturbation is derived. The equation involves the generalized shear viscosity of the gas in the time-dependent shear flow state, and therefore, it predicts relevant rheological effects beyond the quasielastic limit. Good agreement is found when comparing the theory with molecular dynamics simulation results. Moreover, the Onsager postulate on the regression of fluctuations is fulfilled.

Studies on the macroscopic and microscopic packing properties of nonconvex particles are scarce. As a common concave form, the curved spherocylinder is used in the simulations, and its bending and elongation effects on the random packings are investigated numerically with sphere assembly models and a relaxation algorithm. The aspect ratio is demonstrated to be the main factor regarding the packing density. However, at certain aspect ratios of low densities around 0.3–0.4, the density of curved spherocylinders may increase by 15$\%$ more than that of the straight ones, indicating that bending is also a contributor to the packing density. The excluded volume of the curved spherocylinder decreases with the increase of the bending angle, indicating that the excluded volume is applicable in explaining the bending effect on the packing density variation of nonconvex particles. The packings are verified to be randomly distributed in orientation with no significant layering or in-plane order. The local arrangements are further analyzed from the radial distribution function and contact results. The results show that the random packings of nonconvex particles have significant differences and richer characteristics on both the macroscopic and microscopic properties compared with convex objects.

Scaling structure of the growth rate distribution on the interface of a dendritic pattern is investigated. The distribution is evaluated for an ${\mathit{NH}}_4\mathrm{Cl}$ quasi-two-dimensional crystal by numerically solving the Laplace equation with the boundary condition taking account of the surface tension effect. It is found that the distribution has multifractality and the surface tension effect is almost ineffective in the unscreened large growth region. The values of the minimum singular exponent and the fractal dimension are smaller than those for the diffusion-limited aggregation pattern. The Makarov's theorem, the information dimension equals one, and the Turkevich-Scher conjecture between the fractal dimension and the minimum singularity exponent hold.

Recently, De Martino et al. [J. Stat. Mech. (2009) P08023; Phys. Rev. E 79, 015101 (2009)] have presented a general framework for the study of transportation phenomena on random networks with annealed disorder. One of their most significant achievements was a deeper understanding of the phase transition from the uncongested to the congested phase at a critical traffic load on uncorrelated networks. In this paper, we also study phase transition in transportation networks using a discrete time random walk model. Our aim is to establish a direct connection between the structure of an uncorrelated random graph with quenched disorder and the value of the critical traffic load. We show that if the network is dense, the quenched and annealed formulas for the critical loading probability coincide. For sparse graphs, higher-order corrections, related to the local structure of the network, appear.