With the help of experiments, computer simulations, and a theoretical investigation, a general model is developed of the flow dynamics of dense granular media immersed in air in an intermediate regime where both collisional and frictional interactions may affect the flow behavior. The model is tested using the example of a system in which bubbles and solid structures are produced in granular films shaken vertically. Both experiments and large-scale, three-dimensional simulations of this system are performed. The experimental results are compared with the results of the simulation to verify the validity of the model. The data indicate evidence of formation of bubbles when peak acceleration relative to gravity exceeds a critical value ${\Gamma }_b$. The air-grain interfaces of bubblelike structures are found to exhibit fractal structure with dimension $D=1.7\pm 0.05$.

During directional solidification of the solvent in a colloidal suspension, the colloidal particles segregate from the growing solid, forming high-particle-density regions with structure on a hierarchy of length scales ranging from that of the particle-scale packing to the large-scale spacing between these regions. Previous work has concentrated mostly on the medium- to large-length scale structure, as it is the most accessible and thought to be more technologically relevant. However, the packing of the colloids at the particle scale is an important component not only in theoretical descriptions of the segregation process, but also to the utility of freeze-cast materials for new applications. Here we present the results of experiments in which we investigated this structure across a wide range of length scales using a combination of small-angle x-ray scattering and direct optical imaging. As expected, during freezing the particles were concentrated into regions between ice dendrites forming a microscopic pattern of high- and low-particle-density regions. X-ray scattering indicates that the particles in the high-density regions were so closely packed as to be touching. However, the arrangement of the particles does not conform to that predicted by standard interparticle pair potentials, suggesting that the particle packing induced by freezing differs from that formed during equilibrium densification processes.

We report experiments on soap film configurations in a triangular prism for which the shape factor can be changed continuously. Two stable configurations can be observed for a range of the shape factor $h$, being the prism-height/edge-length ratio. A hysteretic behavior is found, due to the occurence of another local minima in the free energy. Contrary to a common belief, soap films can be trapped in a particular configuration being different from a global surface minimization. This metastability can be evidenced from a geometrical model based on idealized structures. Depending on the configuration, the transition is either first or second order, providing clues on the structural relaxations taking place into three-dimensional foams, such as T1 rearrangements.

The rheological behavior of 100-nm-thick polystyrene films cast from various solvents was examined using an electric field to weakly perturb the free surface of the polymer melt. The effective viscosity and residual stresses of the as-spun films are seen to strongly depend on the properties of the casting solvent and the solvent quality. Both effects are explained in terms of the coil dimension at the solvent-polymer composition at which the film vitrifies. The more compact chains in a near-$\Theta$-solvent are less entangled and less deformed when quenched to the dry melt compared to the more swollen chains in an athermal solution. Despite chain conformations that are further from equilibrium for the $\Theta$-solvent cast chains, these films have reduced stored stresses compared to the chains cast in films from athermal solvents. A more detailed analysis of the data suggests that the formation of a surface-near region with more strongly deformed chains during spin coating. Since thermal equilibration of spin-cast high-molecular-weight films is unpractical, solvent vapor annealing was used to equilibrate films on timescale of a few hours.

It has recently been reported that even single-celled organisms appear to be “indecisive” or “contemplative” when confronted with an obstacle. When the amoeboid organism Physarum plasmodium encounters the chemical repellent quinine during migration along a narrow agar lane, it stops for a period of time (typically several hours) and then suddenly begins to move again. When movement resumes, three distinct types of behavior are observed: The plasmodium continues forward, turns back, or migrates in both directions simultaneously. Here, we develop a continuum mathematical model of the cell dynamics of contemplative amoeboid movement. Our model incorporates the dynamics of the mass flow of the protoplasmic sol, in relation to the generation of pressure based on the autocatalytic kinetics of pseudopod formation and retraction (mainly, sol-gel conversion accompanying actin-myosin dynamics). The biological justification of the model is tested by comparing with experimentally measured spatiotemporal profiles of the cell thickness. The experimentally observed types of behavior are reproduced in simulations based on our model, and the core logic of the modeled behavior is clarified by means of nonlinear dynamics. An on-off transition between the refractory and activated states of the chemical reactivity that takes place at the leading edge of the plasmodium plays a key role in the emergence of contemplative behavior.

Many motile eukaryotic cells determine their direction by measuring external chemical gradients through the binding of ligands to membrane bound receptors. This process is limited by fluctuations arising from the binding process and from the diffusion of the ligand molecules. Here, we apply estimation-theoretic methods to determine the physical limits of gradient sensing for cells that are noncircular and for cells that have an internal bias. Specifically, we derive theoretical expressions for the accuracy of gradient sensing in elliptical cells. This accuracy for highly elliptical cells can significantly deviate from the gradient sensing limits derived for circular cells. Furthermore, we find that a cell cannot improve its sensing of the gradient steepness and direction simultaneously by elongating its cell body. Finally, we derive a lower bound on the accuracy of gradient sensing for cells that possess an internal bias and compare our analytical results with recent experimental findings.

We study the statistics of intervals $\tau$ between ventricular premature complexes (VPCs) in 24-h electrocardiogram records obtained from PhysioNet data source. We find that the long-term memory inherent in the heartbeat intervals leads to power laws in the probability density function $P(\tau )$ between VPCs for $\tau >6$ s. As a consequence, the probability $W(t,\Delta t)$ that at least one VPC will occur within the next time interval $\Delta t$, if the last VPC occurred $t$ time units intervals ago, decays by a power law of $t$. Based on these results, we suggest a method to obtain a priori information about the occurrence of the next VPC, and how to predict it. We think that usage of this a priori information could be useful for the improvement of the algorithms in healthcare monitoring devices with alarm facilities.

We asymptotically calculate the spatially averaged mean first passage time (MFPT) of a diffusing channel protein in a finite membrane patch containing a small absorbing anchor site. Different two-dimensional membrane geometries are considered including a circular, a square-shaped, a rectangular, and a cylindrical domain. The asymptotic expressions are found to be in excellent agreement with results from Monte Carlo simulations if the radius of the diffusing protein is sufficiently small. For a larger radius, a simple correction to the asymptotic expressions is proposed. We show that the average MFPT for a circle and a square-shaped domain of the same area are approximately equal as long as the anchor site is close to the center of the domain. We also discuss how the average MFPT depends on the aspect ratio of a rectangular and a cylindrical domain. Among such domains with a fixed area, a minimal MFPT is obtained for the square-shaped domain.

Quantum escapes of two particles with Coulomb interactions from a confined one-dimensional region to a semi-infinite lead are discussed by using the probability of finding all particles within the confined region, that is, the survival probability, in comparison with free particles. By taking into account the quantum effects of two identical particles, such as the Pauli exclusion principle, it is shown analytically that for two identical free fermions (bosons), the survival probability decays asymptotically in power $~$$t^{-10}$ ($~$$t^{-6}$) as a function of time $t$, although it decays in power $~$$t^{-3}$ for one free particle. On the other hand, for two particles with attractive Coulomb interactions it is shown numerically that the survival probability decays in power $~$$t^{-3}$ after a long time. Moreover, for two particles with repulsive Coulomb interactions it decays exponentially in time $~$$\exp \hspace{0.5em}(-\alpha t)$ with a constant $\alpha$, which is almost independent of the initial energy of particles.

A system of coupled oscillators may include inactive elements that have lost spontaneous oscillatory activity for some reason, such as aging and accidental damages. Following previous papers devoted to the case of global coupling, here the discussion is centered around what happens in a large ring of locally coupled oscillators, some of which are inactivated. In particular, it is shown that the critical ratio of inactive oscillators at which the system makes a transition to quiescence approaches unity algebraically as the system size tends to infinity. It is also shown that under some conditions, the system’s phase coherence is enhanced by intensifying quenched disorder originating from random assignments of inactive sites on the ring.

Dynamics of two Chua circuits, mutually coupled via conjugate variables, have been explored both numerically and experimentally. When the two autonomous systems were placed in the oscillatory regime the conjugate coupling provoked suppression of oscillations (amplitude death) in both systems. In contrast, if the two autonomous systems were placed in quiescent (fixed-point) states, then the effect of conjugate coupling was to generate oscillatory behavior (rhythmogenesis) in both systems. These phenomena of amplitude death and rhythmogenesis were found to persist for identical as well as nonidentical systems. It was also realized that the dynamics of the coupled systems can be regulated efficiently by varying the magnitude of conjugate coupling.

Plane Poiseuille flow of a rarefied gas, which flows horizontally in the presence of strong gravitation, is studied based on the Boltzmann equation. Applying the asymptotic analysis for a small variation in the flow direction [Y. Sone, Molecular Gas Dynamics (Birkhäuser, 2007)], the two-dimensional problem is reduced to a one-dimensional problem, as in the case of a Poiseuille flow in the absence of gravitation, and the solution is obtained in a semianalytical form. The reduced one-dimensional problem is solved numerically for a hard sphere molecular gas over a wide range of the gas-rarefaction degree and the gravitational strength. The presence of gravitation reduces the mass flow rate, and the effect of gravitation is significant for large Knudsen numbers. To verify the validity of the asymptotic solution, a two-dimensional problem of a flow through a long channel is directly solved numerically, and the validity of the asymptotic solution is confirmed.

Macroscopic properties of granular materials are important in modeling a variety of flow and transport phenomena in many fields of science. Determination of these parameters has always been an issue among both researchers and engineers, mainly in view of tortuosity and permeability. This paper presents analytical functions for the tortuosity and permeability of monosized sphere arrays based on a volume averaging approach and eliminates some ambiguities by modification of the original representative elementary volume model. Veracity of the proposed formulations has been illustrated through comparisons with the latest available results on the subject. Good agreement is found.

This work studies the electron quantum states, as determined by the Dirac equation, in the field of electrostatic and electromagnetic waves in a plasma. We discuss the main differences with respect to the vacuum case, and the assumptions under which the vacuum Volkov solutions can be adapted to a plasma. The case of ultrashort electromagnetic wave pulses is also discussed. We also consider the electron states in the field of an electron plasma wave. Modified Volkov solutions of the Dirac equation can also be found. For electron plasma waves such that the phase velocity becomes close to the speed of light, these solutions are exact. Finally, we consider electron states in the field of two waves in a plasma, with relevance to the mixed case where one of the waves is electrostatic and the other is electromagnetic.

We obtain exact traveling wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with variable coefficients and polynomial Kerr nonlinearity of an arbitrarily high order. Exact solutions, given in terms of Jacobi elliptic functions, are presented for the special cases of cubic-quintic and septic models. We demonstrate that the widely used method for finding exact solutions in terms of Jacobi elliptic functions is not applicable to the nonlinear Schrödinger equation with saturable nonlinearity.

We propose a mechanism for soliton creation from resonantly excited localized waves $\text{via}$ supratransmission in band gaps of nonlinear lattices. A nonlinear localized wave, which is formed by and vibrates around an impurity with an intrinsic frequency, is found to undergo a local resonance when subject to an external forcing. Under the resonance, an instability develops that leads to the efficient emission of solitons at a much lower rate than that in uniform lattices with no impurity.

There has been a long-standing argument about Pendry's suggestion that a plane harmonic evanescent (surface) wave along the interface between free space and a slab of $\varepsilon =-1$, $\mu =-1$ double-negative (DNG) medium will emerge on the far side with recovery of phase and amplitude. While this is possible, it is subject to parameter restrictions. This work generalizes previous work and now gives analytical criteria for when to expect such a recovery in a Smith-Kroll DNG medium. Basically this requires, among other things, a relatively narrow bandwidth and relatively small transverse-mode component. There also is a very strong dependence on the ratio of slabwidth to plasma wavelength.

We propose a method to generate statistically similar reconstructions of two-phase media. As with previous work, we initially characterize the microstructure of the material using two-point correlation functions (a subset of spatial correlation functions) and then generate numerical reconstructions using a simulated annealing method that preserves the geometric relationships of the material’s phase of interest. However, in contrast to earlier contributions that consider reconstructions composed of discrete arrays of pixels or voxels alone, we generate reconstructions based on assemblies of continuous, three-dimensional, interpenetrating objects. The result is a continuum description of the material microstructure (as opposed to a discretized or pixelated description), capable of efficiently representing large disparities in scale. Different reconstruction methods are considered based on distinct combinations of two-point correlation functions of varying degrees of complexity. The quality of the reconstruction methods are evaluated by comparing the total pore fraction, specific surface area of the percolating cluster, pore fraction of the percolating cluster, tortuosity, and permeability of the reconstructions to those of a set of reference assemblies. Elsewhere it has been proposed that two-phase media could be statistically reproduced with only two spatial correlation functions: the two-point probability function (the probability that two points lie within the same phase) and the lineal path function (the probability that a line between two points lies entirely within the same phase). We find that methods employing the two-point probability function and lineal path function are improved if the percolating cluster volume is also considered in the reconstruction. However, to reproduce more complicated geometric assemblies, we find it necessary to employ the two-point probability, two-point cluster, and lineal path function in addition to the percolating cluster volume to produce a generally accurate statistical reconstruction.

A lattice Boltzmann method on nonuniform quadtree grids is proposed. Our method employs the interpolation-supplemented lattice Boltzmann model. The advantages of the quadtree grid are preserved by using linear interpolation instead of quadratic interpolation to complete the streaming step in the lattice Boltzmann method. The back-and-forth error compensation and correction (BFECC) method is used to improve the accuracy, so that the second-order accuracy of the conventional lattice Boltzmann method is maintained. Several numerical cases, including a BFECC streaming test, lid-driven cavity flow, and flow over an asymmetrically placed cylinder in a channel, are carried out to demonstrate the accuracy and efficiency of our method.

In this Brief Report we study both experimentally and numerically the intermittent behavior taking place near the boundary of the synchronous time scales of chaotic oscillators being in the regime of time scale synchronization. We have shown that the observed type of the intermittent behavior should be classified as the ring intermittency.