In many models for binary particulate systems, the relative motion between two particle species is modeled by diffusion. Recently, two-equation models have been used to improve diffusion models. While two-equation models are significant improvements to diffusion models and are applicable in modeling dilute systems, they are still theoretically inadequate for dense systems. This inadequacy directly results from the assumption that the species interaction forces in the two momentum equations sum to zero. In fact, the sum of the two forces is not zero but the divergence of an interspecies stress [Zhang, Ma, and Rauenzahn, Phys. Rev. Lett. 97, 048301 (2006)]. Introduction of this interspecies stress amends the inadequacy in two-equation models. The main objective of the present paper is to examine the importance of this newly introduced interspecies stress relative to other known stresses in the system. For this purpose we numerically simulate the simplest possible granular system. The interspecies stress is of the same order of magnitude as other stresses for dense systems. Additionally, we also examine properties of the species interaction force under different conditions.

The emergence of very stable traveling intrinsic localized modes (ILMs) locked to a uniform driver is demonstrated in a discrete electrical transmission line. The speed of these traveling ILMs is tunable by the driver amplitude and frequency. It is found to be quite sensitive to the ratio of intersite to on-site nonlinearity. The number of traveling ILMs can also be selected via the driving conditions and appears to be the result of a spatiotemporal pattern selection process.

A parallel quantum electron and nuclei wave packet computer code, LZH-DICP, has been developed to study laser-atom-molecule interaction in the nonperturbative regime with attosecond resolution. The nonlinear phenomena occurring in that regime can be studied with the code in a rigorous way by numerically solving the time-dependent Schrödinger equation of electrons and nuclei. Time propagation of the wave functions is performed using a split-operator approach, and based on a sine discrete variable representation. Photoelectron spectra for hydrogen and kinetic-energy spectra for molecular hydrogen ion in linearly polarized laser fields are calculated using a flux operator scheme, which testifies to the validity and the high efficiency of LZH-DICP.

There is growing interest in studying the role of connectivity patterns in brain functions. In recent years, functional brain networks were found to exhibit small-world properties during different brain states. In previous studies, time-independent networks were recovered from long time periods of brain activity. In this paper, we propose an approach, the event-related networks, that allows one to characterize the dynamical evolution of functional brain networks in time-frequency space. We illustrate this approach by characterizing connectivity patterns in magnetoencephalographic signals recorded during a visual stimulus paradigm. When compared with equivalent random and regular networks, the results reveal that functional connectivity varies with time and frequency during the processing of the stimulus, while maintaining a small-world structure. This approach may provide insights into the connectivity of other complex and spatially extended nonstationary systems.

It is well known that an activity expansion of the grand canonical partition function works well for attractive interactions, but poorly for repulsive interactions, such as occur between atoms and molecules. The virial expansion of the canonical partition function shows just the opposite behavior. This poses a problem for applications that involve both types of interactions, such as occur in the outer layers of low-mass stars. We show that it is possible to obtain expansions for repulsive systems that convert the poorly performing Mayer activity expansion into a series of rational polynomials that converge uniformly to the virial expansion. In the current work we limit our discussion to the second virial approximation. In contrast to the Mayer activity expansion, the activity expansion presented herein converges for both attractive and repulsive systems.

Reversible reaction-diffusion systems display anomalous dynamics characterized by a power-law relaxation toward stationarity. In this paper we study in the aging regime the nonequilibrium dynamical properties of some model systems with reversible reactions. Starting from the exact Langevin equations describing these models, we derive expressions for two-time correlation and autoresponse functions and obtain a simple aging behavior for these quantities. The autoresponse function is thereby found to depend on the specific nature of the chosen perturbation of the system.

The potential energy surface of a model discotic liquid crystal is investigated across mesophases as a function of temperature by characterizing the local potential energy minima. The average depth of the minima sampled by the system gradually grows as orientational order increases through the discotic-nematic phase upon cooling, while it remains fairly constant in the isotropic phase for isochoric temperature variation. The high-temperature Arrhenius behavior of the single-particle orientational correlation times is found to break down at a temperature that marks the onset of exploration of deeper potential energy minima. The structural features of the minima reveal an interplay between orientational and translational order, in particular, when the parent phase is discotic-nematic. The local minima then exhibit short-range columns that tend to have local hexagonal packing. The present study and recent work on calamitic liquid crystals [D. Chakrabarti and B. Bagchi, Proc. Natl. Acad. Sci. U.S.A. 103, 7217 (2006)] together reveal a striking similarity between thermotropic liquid crystals and supercooled liquids in the exploration of the energy landscape and the breakdown of Arrhenius behavior for relaxation times.

We examine how intense optical beams can penetrate deeply into highly absorbing media by a nonlinear, photobleaching process. The role of stimulated recovery to the dye ground state can be important and is delineated. This analysis of nonlinear absorption processes is applicable in general to situations where chromophores are irradiated, for instance, in biology. We examine the implications for the bending of cantilevers made of heavily dye-loaded nematic photosolids, that is nematic glasses and elastomers that have large mechanical reactions to light. In particular we describe the bending of cantilevers sufficiently absorbing that they would not bend if Beer’s law were applicable. We quantify the role of optically generated heat in determining the mechanical response and conclude that in general it is minor in importance compared with optical effects.

A system consisting of two map-based neurons coupled through reciprocal excitatory or inhibitory chemical synapses is discussed. After a brief explanation of the basic mechanism behind generation and synchronization of bursts, parameter space is explored to determine less obvious but biologically meaningful regimes and effects. Among them, we show how excitatory synapses without any delays may induce antiphase synchronization; that a synapse may change its character from excitatory to inhibitory and vice versa by changing its conductance, without any change in reversal potential; and that small variations in the synaptic threshold may result in drastic changes in the synchronization of spikes within bursts. Finally we show how the synchronization effects found in the two-neuron system carry over to larger networks.

In this paper, the results of laboratory investigation about the flow behind the sphere in the range of $150<\mathrm{Re}<300$, where very interesting physical phenomenon occurs, are presented. After a first stationary transition where the flow breaks the axisymmetry, very controlled experiments allow one to define a threshold for the second transition from stationary to unstable flow, which includes three-dimensional peristaltic oscillations of the two trailing vortices prior to hairpins shedding. The scenario has been proposed to explain the hairpin formation, as pieces of a counter-rotating longitudinal vortex. Hairpin shedding is suggested to be the result of oscillations, which are powerful enough, and reconnection of the trailing vortices.

An investigation of the chaotic properties of nonequilibrium atomic systems under planar shear and planar elongational flows is carried out for a constant pressure and temperature ensemble, with the combined use of a Gaussian thermostat and a Nosé-Hoover integral feedback mechanism for pressure conservation. A comparison with Lyapunov spectra of atomic systems under the same flows and at constant volume and temperature shows that, regardless of whether the underlying algorithm describing the flow is symplectic, the degrees of freedom associated with the barostat have no overall influence on chaoticity and the general conjugate pairing properties are independent of the ensemble. Finally, the dimension of the strange attractor onto which the phase space collapses is found not to be significantly altered by the presence of the Nosé-Hoover barostatting mechanism.

We study the stability of a two-component Bose-Einstein condensate (BEC) in the parameter regime in which its classical counterpart has regular motion. The stability is characterized by the fidelity for both the same and different initial states. We study as initial states the Fock states with definite numbers of atoms in each component of the BEC. It is found that for some initial times the two Fock states with all the atoms in the same component of the BEC are more stable than Fock states with atoms distributed in the two components. An experimental scheme is discussed, in which the fidelity can be measured in a direct way.

An exact identity for nonlinear sound wave propagation in one-dimensional media is shown to apply under a wide variety of conditions. The evidence suggests that this is true whenever there is a single input and output channel on each side of the medium, which can generally be achieved using monochromatic filters. It is shown mathematically that the identity cannot be derived from this condition and the known symmetries of the system. The question of what hidden symmetries in the system lead to the identity, and whether it applies even more generally to light waves, remains unresolved.

In this paper we present axisymmetric nonlinear simulations of magnetized Ekman and Stewartson layers in a magnetized Taylor-Couette flow with a centrifugally stable angular-momentum profile and with a magnetic Reynolds number below the threshold of magnetorotational instability. The magnetic field is found to inhibit the Ekman suction. The width of the Ekman layer is reduced with increased magnetic field normal to the end plate. A uniformly rotating region forms near the outer cylinder. A strong magnetic field leads to a steady Stewartson layer emanating from the junction between differentially rotating rings at the endcaps. The Stewartson layer becomes thinner with larger Reynolds number and penetrates deeper into the bulk flow with stronger magnetic field and larger Reynolds number. However, at Reynolds number larger than a critical value $\sim 600$, axisymmetric, and perhaps also nonaxisymmetric, instabilities occur and result in a less prominent Stewartson layer that extends less far from the boundary.

Although time-periodic fluid flows sometimes produce mixing via Lagrangian chaos, the additional contribution to mixing caused by nonperiodicity has not been quantified experimentally. Here, we do so for a quasi-two-dimensional flow generated by electromagnetic forcing. Several distinct measures of mixing are found to vary continuously with the Reynolds number, with no evident change in magnitude or slope at the onset of nonperiodicity. Furthermore, the scaled probability distributions of the mean Lyapunov exponent have the same form in the periodic and nonperiodic flow states.

The electric microfield distribution (MFD) at a neutral point is studied for two-component (TCP) electron-ion plasmas using molecular-dynamics simulation and theoretical models. The particles are treated within classical statistical mechanics using an electron-ion Coulomb potential regularized at distances less than the de Broglie length to take into account quantum-diffraction effects. Corrections to the potential-of-mean-force exponential (PMFEX) approximation recently proposed for the MFD at an impurity ion in a strongly coupled TCP [Nersisyan et al., Phys. Rev. E 72, 036403 (2005)] are obtained and discussed. This has been done by a generalization of the standard Baranger-Mozer and renormalized cluster expansion techniques originally developed for the one-component plasmas to the TCPs. The results from this theoretical model are compared with those from molecular-dynamics simulations. In particular, for a strongly coupled TCP with an ionic charge $Z>5$ the agreement with numerical simulations is excellent. For still increasing coupling we furthermore found that the PMFEX scheme becomes insufficient to predict the MFD at a neutral point, while its improved version quite well agrees with the simulations.

The thermal confinement time of a magnetized fusion plasma is essentially determined by turbulent heat conduction across the equilibrium magnetic field. To achieve the study of turbulent thermal diffusivities, Vlasov gyrokinetic description of the magnetically confined plasmas is now commonly adopted, and offers the advantage over fluid models (MHD, gyrofluid) to take into account nonlinear resonant wave-particle interactions which may impact significantly the predicted turbulent transport. Nevertheless kinetic codes require a huge amount of computer resources and this constitutes the main drawback of this approach. A unifying approach is to consider the water-bag representation of the statistical distribution function because it allows us to keep the underlying kinetic features of the problem, while reducing the Vlasov kinetic model into a set of hydrodynamic equations, resulting in a numerical cost comparable to that needed for solving multifluid models. The present paper addresses the gyro-water-bag model derived as a water-bag-like weak solution of the Vlasov gyrokinetic models. We propose a quasilinear analysis of this model to retrieve transport coefficients allowing us to estimate turbulent thermal diffusivities without computing the full fluctuations. We next derive another self-consistent quasilinear model, suitable for numerical simulation, that we approximate by means of discontinuous Galerkin methods.

The Bell-Evans-Polanyi principle that is valid for a chemical reaction that proceeds along the reaction coordinate over the transition state is extended to molecular dynamics trajectories that in general do not cross the dividing surface between the initial and the final local minima at the exact transition state. Our molecular dynamics Bell-Evans-Polanyi principle states that low energy molecular dynamics trajectories are more likely to cross into the basin of attraction of a low energy local minimum than high energy trajectories. In the context of global optimization schemes based on molecular dynamics our molecular dynamics Bell-Evans-Polanyi principle implies that using trajectories that have an energy that is only somewhat higher than the energy necessary to overcome the barriers lead fastest to the global minimum of funnellike energy landscapes.

In two independent articles, Escudier and Presti [J. Non-Newtonian Fluid Mech. 62, 291 (1996)] and Peixinho et al. [J. Non-Newtonian Fluid Mech. 128, 172 (2005)] studied experimentally the flow structure of a yield stress fluid in a cylindrical pipe. It was observed that the mean, i.e., time-averaged, velocity profiles were axisymmetric in the laminar and turbulent regimes, and presented an increasing asymmetry with increasing Reynolds number in the transitional regime. The present paper provides a three-dimensional description of this asymmetry from axial velocity profiles measurements at three axial positions and different azimuthal positions. The observed transitional flow suggests the existence of a robust nonlinear coherent structure characterized by two weakly modulated counter-rotating longitudinal vortices. This new state mediates the transition between laminar and turbulent flow.

We investigated the photonic crystal structure inside iridescent scales of the weevil Lamprocyphus augustus. By combining a high-resolution structure analysis technique based on sequential focused ion beam milling and scanning electron microscopy imaging with theoretical modeling and photonic band-structure calculations, we discovered a natural three-dimensional photonic structure with a diamond-based crystal lattice operating at visible wavelengths. Moreover, we found that within individual scales, the diamond-based structure is assembled in the form of differently oriented single-crystalline micrometer-sized pixels with only selected lattice planes facing the scales’ top surface. A comparison of results obtained from optical microreflectance measurements with photonic band-structure calculations reveals that it is this sophisticated microassembly of the diamond-based crystal lattice that lends Lamprocyphus augustus its macroscopically near angle-independent green coloration.