A single-sided structure left-handed metamaterial (LHM), of which the symmetric paired split-ring resonators are connected directly through cut wires, is discussed in this paper. This connected single-sided LHM can exhibit a low loss and broad negative refraction passband. Good agreement of the retrieved result and the simulated result verify the above conclusion by comparison with the in-plane case and the off-plane case [T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 93, 107402 (2004)].

The dynamics of a network model of astrocytes coupled by gap junctions is investigated. Calcium dynamics of the single cell is described by the biophysical model comprising the set of three nonlinear differential equations. Intercellular dynamics is provided by the diffusion of inositol 1,4,5-trisphosphate $\left({\mathrm{IP}}_3\right)$ through gap junctions between neighboring astrocytes. It is found that the diffusion induces the appearance of spontaneous activity patterns in the network. Stability of the network steady state is analyzed. It is proved that the increase of the diffusion coefficient above a certain critical value yields the generation of low-amplitude subthreshold oscillatory signals in a certain frequency range. It is shown that such spontaneous oscillations can facilitate calcium pulse generation and provide a certain time scale in astrocyte signaling.

The effective-medium theory of transport in disordered systems, whose basis is the replacement of spatial disorder by temporal memory, is extended in several practical directions. Restricting attention to a one-dimensional system with bond disorder for specificity, a transformation procedure is developed to deduce explicit expressions for the memory functions from given distribution functions characterizing the system disorder. It is shown how to use the memory functions in the Laplace domain forms in which they first appear, and in the time domain forms which are obtained via numerical inversion algorithms, to address time evolution of the system beyond the asymptotic domain of large times normally treated. An analytic but approximate procedure is provided to obtain the memories, in addition to the inversion algorithm. Good agreement of effective-medium theory predictions with numerically computed exact results is found for all time ranges for the distributions used except near the percolation limit, as expected. The use of ensemble averages is studied for normal as well as correlation observables. The effect of size on effective-medium theory is explored and it is shown that, even in the asymptotic limit, finite-size corrections develop to the well-known harmonic mean prescription for finding the effective rate. A percolation threshold is shown to arise even in one dimension for finite (but not infinite) systems at a concentration of broken bonds related to the system size. Spatially long-range transfer rates are shown to emerge naturally as a consequence of the replacement of spatial disorder by temporal memories, in spite of the fact that the original rates possess nearest neighbor character. Pausing time distributions in continuous-time random walks corresponding to the effective-medium memories are calculated.

We consider the dynamic behavior in driven phase transitions dominated either by attachment-detachment or by surface diffusion mass transport mechanisms. As the driving force increases, we numerically demonstrate for both cases that the spatiotemporal faceted structure of the surface undergoes a sequential transition from slow coarsening turning to accelerated coarsening followed by fixed length scale structures before finally becoming spatiotemporally chaotic. For the attachment-detachment dominated phase transition problem we compare in the accelerated coarsening regime the simulation results with an intrinsic dynamical system governing the leading-order piecewise-affine dynamic surface (PADS), which can be obtained through a matched asymptotic analysis. The PADS predicts the numerically observed coarsening law for the growth in time of the characteristic morphological length scale ${\mathcal{L}}_{\mathcal{M}}$. In particular we determine the prefactor of the scaling law which allows for quantitative predictions necessary for any use of the theory in preparing patterned surfaces through modifications of the driving force.

The drift and diffusion of a few interacting, overdamped Brownian particles in a tilted periodic potential are studied analytically and numerically. Both quantities exhibit a complex multipeaked structure as a function of the equilibrium interparticle separation. Upon variation of the interaction strength, both drift and diffusion may exhibit a nonmonotonic, resonancelike behavior.

The hydrodynamic modes and the velocity autocorrelation functions for a dilute sheared inelastic fluid are analyzed using an expansion in the parameter $ϵ={(1-e)}^{1∕2}$, where $e$ is the coefficient of restitution. It is shown that the hydrodynamic modes for a sheared inelastic fluid are very different from those for an elastic fluid in the long-wave limit, since energy is not a conserved variable when the wavelength of perturbations is larger than the “conduction length.” In an inelastic fluid under shear, there are three coupled modes, the mass and the momenta in the plane of shear, which have a decay rate proportional to $k^{2∕3}$ in the limit $k\to 0$, if the wave vector has a component along the flow direction. When the wave vector is aligned along the gradient-vorticity plane, we find that the scaling of the growth rate is similar to that for an elastic fluid. The Fourier transforms of the velocity autocorrelation functions are calculated for a steady shear flow correct to leading order in an expansion in $ϵ$. The time dependence of the autocorrelation function in the long-time limit is obtained by estimating the integral of the Fourier transform over wave number space. It is found that the autocorrelation functions for the velocity in the flow and gradient directions decay proportional to $t^{-5∕2}$ in two dimensions and $t^{-15∕4}$ in three dimensions. In the vorticity direction, the decay of the autocorrelation function is proportional to $t^{-3}$ in two dimensions and $t^{-7∕2}$ in three dimensions.

The effect of correlations on the viscosity of a dilute sheared inelastic fluid is analyzed using the ring-kinetic equation for the two-particle correlation function. The leading-order contribution to the stress in an expansion in $ϵ={(1-e)}^{1∕2}$ is calculated, and it is shown that the leading-order viscosity is identical to that obtained from the Green-Kubo formula, provided the stress autocorrelation function in a sheared steady state is used in the Green-Kubo formula. A systemmatic extension of this to higher orders is also formulated, and the higher-order contributions to the stress from the ring-kinetic equation are determined in terms of the terms in the Chapman-Enskog solution for the Boltzmann equation. The series is resummed analytically to obtain a renormalized stress equation. The most dominant contributions to the two-particle correlation function are products of the eigenvectors of the conserved hydrodynamic modes of the two correlated particles. In Part I, it was shown that the long-time tails of the velocity autocorrelation function are not present in a sheared fluid. Using those results, we show that correlations do not cause a divergence in the transport coefficients; the viscosity is not divergent in two dimensions, and the Burnett coefficients are not divergent in three dimensions. The equations for three-particle and higher correlations are analyzed diagrammatically. It is found that the contributions due to the three-particle and higher correlation functions to the renormalized viscosity are smaller than those due to the two-particle distribution function in the limit $ϵ\to 0$. This implies that the most dominant correlation effects are due to the two-particle correlations.

A density functional formalism is applied to investigate the wetting behavior of Ne adsorbed on planar substrates. The study is performed over the complete range of temperatures spanned from the triple point $T_t$ up to the critical one $T_c$. For this purpose, an effective attractive pair potential was built on the basis of a separation procedure. This approach yields a good description of properties of the liquid-vapor interface at coexistence in the whole range of temperatures $T_t⩽T⩽T_c$. The adsorption of Ne on alkali metals and the alkaline-earth metal Mg is analyzed. This sequence of substrates exhibit increasing attractive strength leading to a variety of wetting situations throughout the interval $T_t\leftrightarrow T_c$. A comparison with experimental data and other microscopic calculations is done. The predictions of a simple model are discussed. For $\mathrm{Ne}∕\mathrm{Rb}$ we were able to resolve prewetting lines. Results obtained from a density functional are reported for $\mathrm{Ne}∕\mathrm{K}$ and $\mathrm{Ne}∕\mathrm{Mg}$. In the case of the latter system the interesting behavior occurs close to $T_t$. According to our results, Ne wets surfaces of Na and Li, and this statement is in agreement with the whole picture of the analyzed substrates.

Minimization of free energy is used to calculate the equilibrium vertical rise and meniscus shape of a liquid column between two closely spaced, parallel planar surfaces that are inert and immobile. States of minimum free energy are found using standard variational principles, which lead not only to an Euler-Lagrange differential equation for the meniscus shape and elevation, but also to the boundary conditions at the three-phase junction where the liquid meniscus intersects the solid walls. The analysis shows that the classical Young-Dupré equation for the thermodynamic contact angle is valid at the three-phase junction, as already shown for sessile drops with or without the influence of a gravitational field. Integration of the Euler-Lagrange equation shows that a generalized Laplace-Young (LY) equation first proposed by O’Brien, Craig, and Peyton [J. Colloid Interface Sci. 26, 500 (1968)] gives an exact prediction of the mean elevation of the meniscus at any wall separation, whereas the classical LY equation for the elevation of the midpoint of the meniscus is accurate only when the separation approaches zero or infinity. When both walls are identical, the meniscus is symmetric about the midpoint, and the midpoint elevation is a more traditional and convenient measure of capillary rise than the mean elevation. Therefore, for this symmetric system a different equation is fitted to numerical predictions of the midpoint elevation and is shown to give excellent agreement for contact angles between 15° and 160° and wall separations up to $30\mathrm{mm}$. When the walls have dissimilar surface properties, the meniscus generally assumes an asymmetric shape, and significant elevation of the liquid column can occur even when one of the walls has a contact angle significantly greater than 90°. The height of the capillary rise depends on the spacing between the walls and also on the difference in contact angles at the two surfaces. When the contact angle at one wall is greater than 90° but the contact angle at the other wall is less than 90°, the meniscus can have an inflection point separating a region of positive curvature from a region of negative curvature, the inflection point being pinned at zero height. However, this condition arises only when the spacing between the walls exceeds a threshold value that depends on the difference in contact angles.

Molecular dynamics simulations of spherical nanoparticles (NPs) in a nematogenic matrix of soft spherocylinders (SSCs) with equal NP diameter and SSC length were performed. The NPs were found to be dispersed in the isotropic SSC matrix. At higher pressure, the NP-SSC mixture demixed into a NP-poor nematic phase and a NP-rich isotropic phase over most of the composition range investigated. However, at low NP concentrations a single-phase nematic with dispersed NPs was observed, while at very high NP concentration no nematic phase was observed. When the NP-SSC interactions were changed to promote homeotropic anchoring, the matrix-induced interaction between NPs in the isotropic SSC matrix exhibited strong intermediate-range repulsion that was expected to result in even greater dispersion of NPs. However, many-body effects appear to dominate NP-NP interactions in the isotropic SSC matrix with homeotropic anchoring even at the lowest NP concentration investigated, resulting in suppression of the intermediate range repulsion leading to aggregation of the NPs.

We present a thermodynamically guided, low-noise, time-scale-bridging, and pertinently efficient strategy for the dynamic simulation of microscopic models for complex fluids. The systematic coarse-graining method is exemplified for low-molecular polymeric systems subjected to homogeneous flow fields. We use established concepts of nonequilibrium thermodynamics and an alternating Monte Carlo-molecular-dynamics iteration scheme in order to obtain the model equations for the slow variables. For chosen flow situations of interest, the established model predicts structural as well as material functions beyond the regime of linear response. As a by-product, we present steady-state simulation results for polymers in general flow situations, including simple, planar, and yet unexplored equibiaxial elongation. The method is simple to implement and allows for the calculation of time-dependent behavior through quantities readily available from nonequilibrium steady states.

We use a long, all-atom molecular-dynamics (MD) simulation combined with theoretical modeling to investigate the dynamics of selected lipid atoms and lipid molecules in a hydrated diyristoyl-phosphatidylcholine lipid bilayer. From the analysis of a $0.1\mu \mathrm{s}$ MD trajectory, we find that the time evolution of the mean-square displacement, $⟨{\left[\delta r\left(t\right)\right]}^2⟩$, of lipid atoms and molecules exhibits three well-separated dynamical regions: (i) ballistic, with $⟨{\left[\delta r\left(t\right)\right]}^2⟩\sim t^2$ for $t\lesssim 10\mathrm{fs}$; (ii) subdiffusive, with $⟨{\left[\delta r\left(t\right)\right]}^2⟩\sim t^{\beta }$ with $\beta <1$ for $10\mathrm{ps}\lesssim t\lesssim 10\mathrm{ns}$; and (iii) Fickian diffusion, with $⟨{\left[\delta r\left(t\right)\right]}^2⟩\sim t$ for $t\gtrsim 30\mathrm{ns}$. We propose a memory-function approach for calculating $⟨{\left[\delta r\left(t\right)\right]}^2⟩$ over the entire time range extending from the ballistic to the Fickian diffusion regimes. The results are in very good agreement with the ones from the MD simulations. We also examine the implications of the presence of the subdiffusive dynamics of lipids on the self-intermediate scattering function and the incoherent dynamic structure factor measured in neutron-scattering experiments.

We study a spatial two-strategy (cooperation and defection) prisoner’s dilemma game with two types ($A$ and $B$) of players located on the sites of a square lattice. The evolution of strategy distribution is governed by iterated strategy adoption from a randomly selected neighbor with a probability depending on the payoff difference and also on the type of the neighbor. The strategy adoption probability is reduced by a prefactor $(w<1)$ from the players of type $B$. We consider the competition between two opposite effects when increasing the number of neighbors ($k=4$, 8, and 24). Within a range of the portion of influential players (type $A$) the inhomogeneous activity in strategy transfer yields a relevant increase (dependent on $w$) in the density of cooperators. The noise dependence of this phenomenon is also discussed by evaluating phase diagrams.

Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy.

We studied the dynamics of a single sonoluminescing bubble (SBSL) in a liquid hammer device. In particular, we investigated the phosphoric acid–xenon system, in which pulses up to four orders of magnitude brighter than SBSL in water systems (about ${10}^{12}$ photons per pulse) have been previously reported [Chakravarty et al., Phys. Rev. E 69, 066317 (2004)]. We used stroboscopic photography and a Mie scattering technique in order to measure the radius evolution of the bubbles. Under adequate conditions we may position a bubble at the bottom of the tube (cavity) and a second bubble trapped at the middle of the tube (upper bubble). During its collapse, the cavity produces the compression of the liquid column. This compression drives impulsively the dynamics of the upper bubble. Our measurements reveal that the observed light emissions produced by the upper bubble are generated at its second collapse. We employed a simple numerical model to investigate the conditions that occur during the upper bubble collapse. We found good agreement between numerical and experimental values for the light intensity (fluence) and light pulse widths. Results from the model show that the light emission is increased mainly due to an increase in noble gas ambient radius and not because the maximum temperature increases. Even for the brightest pulses obtained ($2\times {10}^{13}$ photons, about $20\mathrm{W}$ of peak power) the maximum temperatures computed for the upper bubble are always lower than $20000\mathrm{K}$.

The interaction between microbubbles through pressure pulses has been studied to show that it can be a source of cavitation noise. A recent report demonstrated that the acoustic noise generated by a shrimp originates from the collapse of a cavitation bubble produced when the shrimp closes its snapper claw. The recorded acoustic signal contains a broadband noise that consists of positive and negative pulses, but a theoretical model for single bubbles fails to reproduce the negative ones. Using a nonlinear multibubble model, we have shown here that the negative pulses can be explained by considering the interaction of microbubbles formed after the cavitation bubble has collapsed and fragmented: Positive pulses produced at the collapse of the microbubbles hit and impulsively compress neighboring microbubbles to generate reflected pulses whose amplitudes are negative. Discussing the details of the noise generation process, we have found that no negative pulses are generated if the internal pressure of the reflecting bubble is very high when hit by a positive pulse.

We employ the Los Alamos suite of atomic physics codes to model the inner-shell x-ray emission spectrum of xenon and compare results with those obtained via high-resolution x-ray spectroscopy of xenon clusters irradiated by $30\mathrm{fs}$ Ti:Sapphire laser pulses. We find that the commonly employed configuration-average approximation breaks down and significant spin-orbit splitting necessitates a detailed level accounting. We reproduce an interesting spectral trend for a series of experimental spectra taken with varying pulse energy for fixed pulse duration. To simulate the experimental measurements at increasing beam energies, we find that spectral modeling requires an increased hot electron fraction, but decreased atomic density and bulk electron temperature. We believe these latter conditions to be a result of partial cluster destruction due to the increased energy in the laser prepulse.

We investigate the time average mean-square displacement $\overline{{\delta }^2}\mathbf{\left(}x\left(t\right)\mathbf{\right)}={\int }_0^{t-\Delta }{[x(t^{\prime }+\Delta )-x\left(t^{\prime }\right)]}^{2}d{t}^{\prime }∕(t-\Delta )$ for fractional Brownian-Langevin motion where $x\left(t\right)$ is the stochastic trajectory and $\Delta$ is the lag time. Unlike the previously investigated continuous-time random-walk model, $\overline{{\delta }^2}$ converges to the ensemble average $⟨x^2⟩\sim t^{2H}$ in the long measurement time limit. The convergence to ergodic behavior is slow, however, and surprisingly the Hurst exponent $H=\frac{3}{4}$ marks the critical point of the speed of convergence. When $H<\frac{3}{4}$, the ergodicity breaking parameter $E_B={\mathbf{[}⟨[\overline{{\delta }^2}\mathbf{\left(}x\right(t\left)\mathbf{\right)}\mathbf{]}}^2⟩-{⟨\overline{{\delta }^2}\mathbf{\left(}x\right(t\left)\mathbf{\right)}⟩}^2\mathbf{]}/{⟨\overline{{\delta }^2}\mathbf{\left(}x\right(t\left)\mathbf{\right)}⟩}^2\sim k\left(H\right)\Delta t^{-1}$, when $H=\frac{3}{4}$, $E_B\sim \left(\frac{9}{16}\right)\left(\ln t\right)\Delta t^{-1}$, and when $\frac{3}{4}<H<1$, $E_B\sim k\left(H\right){\Delta }^{4-4H}{t}^{4H-4}$. In the ballistic limit $H\to 1$ ergodicity is broken and $E_B\sim 2$. The critical point $H=\frac{3}{4}$ is marked by the divergence of the coefficient $k\left(H\right)$. Fractional Brownian motion as a model for recent experiments of subdiffusion of mRNA in the cell is briefly discussed, and a comparison with the continuous-time random-walk model is made.

We derive a fluctuation theorem for generalized work distributions, related to bijective mappings of the phase spaces of two physical systems, and use it to derive a two-sided constraint maximum likelihood estimator of their free-energy difference which uses samples from the equilibrium configurations of both systems. As an application, we evaluate the chemical potential of a dense Lennard-Jones fluid and study the construction and performance of suitable maps.

We make a phenomenological model of optical two-beam interaction in a model planar liquid crystal cell. The liquid crystal is subject to homeotropic anchoring at the cell walls, is surrounded by thin photosensitive layers, and is subject to a variable potential across the cell. These systems are often known as liquid crystal photorefractive systems. The interference between the two obliquely incident beams causes a time-independent periodic modulation in electric field intensity in the direction transverse to the cell normal. Our model includes this field phenomenologically by supposing an effect on the electric potential at the cell walls. The transverse periodic surface potential causes spatially periodic departures from a pure homeotropic texture. The texture modulation acts as a grating for the incident light. The incident light is both directly transmitted and also subject to diffraction. The lowest order diffracted beams correspond to energy exchange between the beams. We find that the degree of energy exchange can be strongly sensitive to the mean angle of incidence, the angle between the beams, and the imposed potential across the cell. We use the model to speculate about what factors optimize nonlinear optical interaction in liquid crystalline photorefractive systems.