We study the behavior of two spheres that settle along their line of center in a yield stress fluid that “ages:” a Laponite suspension. In such a fluid, the fluid flow behind a falling single particle can either exhibit a negative wake, i.e., an upward motion, or not, according to the stress exerted by the particle on the fluid. We show that, if their initial separation distance is smaller than 15 radii, two identical particles cluster whatever the wake’s structure. In addition, in the conditions within which a negative wake is observed, we evidence an unexpected lateral motion of the spheres.

Spectral analysis of heart rate sequences is commonly used to investigate neuroauthonomic control of heart rate by means of two indexes, the low and the high frequency power. For tilt test data of normal subjects we compare the spectral indexes with new indexes defined within the framework of symbolic analysis. We define two classes of binary words of length 4: the first class is related to “acceleration” of heart rate and the second class to “stationary behavior.” The new indexes measure the change in frequency of the two classes before and after the tilt. Data analysis of 13 normal subjects shows that the behavior of the new indexes is in agreement with that of spectral ones.

The projection operator method developed by Mori involves the essential assumption that chaotic motion is successfully divided into a coherent motion and a fluctuating one. We investigate the validity of the assumption using the Kuramoto-Sivashinsky equation as a model equation of chaotic systems. It has been found that the assumption is reasonable for both long wave modes and short wave modes. We have also evaluated a value of the eddy viscosity as 9.0 by extracting the nonlinear term from the coherent part. This value is consistent with the former estimates with other methods.

We consider finite-amplitude Kelvin waves on an inviscid vortex assuming that the vortex core has infinitesimal thickness. By numerically solving the governing Biot-Savart equation of motion, we study how the frequency of the Kelvin waves and the velocity of the perturbed ring depend on the Kelvin wave amplitude. In particular, we show that, if the amplitude of the Kelvin waves is sufficiently large, the perturbed vortex ring moves backwards.

We study in detail the damped sine-Gordon equation, driven by two ac forces (one is added as a parametric perturbation and the other one in an additive way), as an example of soliton ratchets. By means of a collective coordinate approach we derive an analytical expression for the average velocity of the soliton, which allows us to show that this mechanism of transport requires certain relationships both between the frequencies and between the initial phases of the two ac forces. The control of the velocity by the damping coefficient and parameters of the ac forces is also presented and discussed. All these results are subsequently checked by means of simulations for the driven and damped sine-Gordon equation that we have studied.

Elasticity theory calculations predict the number $N$ of depressions that appear at the surface of a spherical thin shell submitted to an external isotropic pressure. Using a model that mainly considers curvature deformations, we show that $N$ depends on the relative volume variation and on an adimensional parameter that takes into account both the relative spontaneous curvature and the relative thickness of the shell. Equilibrium configurations show single depression $(N=1)$ for small volume variations, then $N$ increases, at maximum up to 6, before decreasing more abruptly due to steric constraints, down to $N=1$ again for maximal volume variations. These static predictions are consistent with previously published experimental observations.

We propose a decoupling process performed in scale-free networks to enhance the synchronizability of the network, together with preserving the scale-free structure. Simulation results show that the decoupling process can effectively promote the network synchronizability, which is measured in terms of eigenratio of the coupling matrix. Moreover, we investigate the correlation between some important structural properties and the collective synchronization, and find that the maximum vertex betweenness seems to be the most strongly correlated with the synchronizability among the major structural features considered. We explain the effect of the decoupling process from a viewpoint of coupling information transmission. Our work provides some evidence that the dynamics of synchronization is related to that of information or vehicle traffic. Because of the low cost in modifying the coupling network, the decoupling process may have potential applications.

We prove the finite-time collapse of a system of $N$ classical fields, which are described by $N$ coupled nonlinear Schrödinger equations. We derive the conditions under which all of the fields experiences this finite-time collapse. Finally, for two-dimensional systems, we derive constraints on the number of particles associated with each field that are necessary to prevent collapse.

We use a relatively simple continuum model to investigate the effects of dielectric inhomogeneity within confined liquid-crystal cells. Specifically, we consider, in planar, cylindrical, and spherical geometries, the stability of a nematic-isotropic interface subject to an applied voltage when the nematic liquid crystal has a positive dielectric anisotropy. Depending on the magnitude of this voltage, the temperature, and the geometry of the cell, the nematic region may shrink until the material is completely isotropic within the cell, grow until the nematic phase fills the cell, or, in certain geometries, coexist with the isotropic phase. For planar geometry, no coexistence is found, but we are able to give analytical expressions for the critical voltage for an electric-field-induced phase transition as well as the critical wetting layer thickness for arbitrary applied voltage. In cells with cylindrical and spherical geometries, however, locally stable nematic-isotropic coexistence is predicted, the thickness of the nematic region being controllable by alteration of the applied voltage.

We find in a model system of thermotropic liquid crystals that the translational diffusion coefficient parallel to the director $D_{\Vert }$ first increases and then decreases as temperature drops through the nematic phase, and this reversal occurs where the smectic order parameter of the underlying inherent structures becomes significant. We argue, based on an energy landscape analysis, that the coupling between orientational and translational order can play a role in inducing the nonmonotonic temperature behavior of $D_{\Vert }$. Such a view is likely to form the foundation of a theoretical framework to explain the anisotropic translation diffusion.

Experiments involving vibrating pastes before drying were performed for the purposes of controlling the crack patterns that appear in the drying process. These experiments revealed a transition in the direction of lamellar cracks from perpendicular to parallel when compared with the direction of the initial external vibration as the solid volume fraction of the paste is decreased. This result suggests a transition in the memory in paste, which is visually represented as morphological changes in the crack pattern. Given that the memory in paste represents the flow pattern induced by the initial external vibration, it should then be possible to control and design various crack patterns, such as cellular, lamellar, radial, ring, spiral, and others.

The quantum-resonant evolution of the mean kinetic energy (MKE) of the kicked particle is studied in detail on different time scales for general periodic kicking potentials. It is shown that the asymptotic time behavior of a wave-packet MKE is typically a linear growth with bounded fluctuations having a simple number-theoretical origin. For a large class of wave packets, the MKE is shown to be exactly the superposition of its asymptotic behavior and transient logarithmic corrections. Both fluctuations and transients can be significant for not too large times but they may vanish identically under some conditions. In the case of incoherent mixtures of plane waves, it is shown that the MKE never exhibits asymptotic fluctuations but transients usually occur.

Constructing a minimal vertex cover of a graph can be seen as a prototype for a combinatorial optimization problem under hard constraints. In this paper, we develop and analyze message-passing techniques, namely, warning and survey propagation, which serve as efficient heuristic algorithms for solving these computational hard problems. We show also, how previously obtained results on the typical-case behavior of vertex covers of random graphs can be recovered starting from the message-passing equations, and how they can be extended.

Analytical tools are applied to investigate piecewise linear coupled map lattices in terms of probabilistic cellular automata. The so-called disorder condition of probabilistic cellular automata is closely related with attracting sets in coupled map lattices. The importance of this condition for the suppression of phase transitions is illustrated by spatially one-dimensional systems. Invariant densities and temporal correlations are calculated explicitly. Ising type phase transitions are found for one-dimensional coupled map lattices acting on repelling sets and for a spatially two-dimensional Miller-Huse-like system with stable long time dynamics. Critical exponents are calculated within a finite size scaling approach. The relevance of detailed balance of the resulting probabilistic cellular automaton for the critical behavior is pointed out.

Dependence of the damping rate of the oscillations of the dust particles levitating in the sheath on the plasma parameters is investigated both theoretically and experimentally. Significant deviations of the damping rate from the values predicted by the Epstein formula are found in the experiment. The delayed charging effect is applied for the theoretical explanation of the experimental results. Qualitative agreement between the theoretical and experimental data is obtained.

This paper summarizes the present understanding of the processes leading to precursor column formation in cylindrical wire arrays on the $1\mathrm{MA}$ MAGPIE generator at Imperial College London. Direct experimental measurements of the diameter variation during the collapse and formation phase of the precursor column are presented, along with soft x-ray emission, and quantitative radiography. In addition, data from twisted cylindrical arrays are presented which give additional information on the behavior of coronal plasma generated in wire array $z$ pinches. Three stages in precursor column formation are identifiable from the data: broad initial density profile, rapid contraction to small diameter, and slow expansion after formation. The correlation of emission to column diameter variation indicates the contraction phase is a nonlinear collapse resulting from the increasing on-axis density and radiative cooling rate. The variation in the minimum diameter is measured for several array materials, and data show good agreement with a pressure balance model. Comparison of column expansion rates to analytical models allows an estimate of column temperature variation, and estimates of the current in the column are also made. Formation data are in good agreement with both fluid and kinetic modeling, but highlight the need to include collisionless flow in the early time behavior.

High-order harmonic generation due to the interaction of a short ultrarelativistic laser pulse with overdense plasma is studied analytically and numerically. On the basis of the ultrarelativistic similarity theory we show that the high-order harmonic spectrum is universal, i.e., it does not depend on the interaction details. The spectrum includes the power-law part $I_n\propto n^{-8∕3}$ for $n<\sqrt{8\alpha }{\gamma }_{\max }^3$, followed by exponential decay. Here ${\gamma }_{\max }$ is the largest relativistic $\gamma$ factor of the plasma surface and $\alpha$ is the second derivative of the surface velocity at this moment. The high-order harmonic cutoff at $\propto {\gamma }_{\max }^3$ is parametrically larger than the $4{\gamma }_{\max }^2$ predicted by the simple “oscillating mirror” model based on the Doppler effect. The cornerstone of our theory is the new physical phenomenon: spikes in the relativistic $\gamma$ factor of the plasma surface. These spikes define the high-order harmonic spectrum and lead to attosecond pulses in the reflected radiation.

We present a further theoretical extension to the kinetic-theory-based formulation of the lattice Boltzmann method of Shan et al. [J. Fluid Mech. 550, 413 (2006)]. In addition to the higher-order projection of the equilibrium distribution function and a sufficiently accurate Gauss-Hermite quadrature in the original formulation, a regularization procedure is introduced in this paper. This procedure ensures a consistent order of accuracy control over the nonequilibrium contributions in the Galerkin sense. Using this formulation, we construct a specific lattice Boltzmann model that accurately incorporates up to third-order hydrodynamic moments. Numerical evidence demonstrates that the extended model overcomes some major defects existing in conventionally known lattice Boltzmann models, so that fluid flows at finite Knudsen number Kn can be more quantitatively simulated. Results from force-driven Poiseuille flow simulations predict the Knudsen’s minimum and the asymptotic behavior of flow flux at large Kn.

In recent years, lattice Boltzmann methods have been increasingly used to simulate rarefied gas flows in microscale and nanoscale devices. This is partly due to the fact that the method is computationally efficient, particularly when compared to solution techniques such as the direct simulation Monte Carlo approach. However, lattice Boltzmann models developed for rarefied gas flows have difficulty in capturing the nonlinear relationship between the shear stress and strain rate within the Knudsen layer. As a consequence, these models are equivalent to slip-flow solutions of the Navier-Stokes equations. In this paper, we propose an effective mean-free path to address the Knudsen layer effect, so that the capabilities of lattice Boltzmann methods can be extended beyond the slip-flow regime. The model has been applied to rarefied shear-driven and pressure-driven flows between parallel plates at Knudsen numbers between 0.01 and 1. Our results show that the proposed approach significantly improves the near-wall accuracy of the lattice Boltzmann method and provides a computationally economic solution technique over a wide range of Knudsen numbers.