We present the results of Monte Carlo simulations of hard spheroids of revolution of different elongations. Both prolate and oblate shapes are examined. A systematic study of the bridge function $b(1,2)$, and direct comparison with the indirect correlation function $\gamma (1,2)=h(1,2)-c(1,2)$ at densities spanning the isotropic fluid range, allow us to evaluate the accuracy of various proposed closure relations for integral equations.

Bulk electroconvection pertains to flow induced by the action of a mean electric field upon the residual space charge in the macroscopic regions of a locally quasielectroneutral strong electrolyte. For a long time, controversy has existed in the literature as to whether quiescent electric conduction from such an electrolyte into a uniform charge-selective solid, such as a metal electrode or ion exchange membrane, is stable with respect to bulk electroconvection. While it was recently claimed that bulk electroconvective instability could not occur, this claim pertained to an aqueous, low-molecular-weight electrolyte characterized by an order-unity electroconvection Péclet number. In this paper, we show that the bulk electroconvection model transforms into the leaky dielectric model in the limit of infinitely large Péclet number. For the leaky dielectric model, conduction of the above-mentioned type is unstable, and so it is in the bulk electroconvection model for sufficiently large Péclet numbers. Such instability is sensitive to the ratio of the diffusivity of the cations to the anions. For infinite Péclet number, the case with equal ionic diffusivities is a bifurcation point separating stable and unstable regimes at the low-current limit. Further, for a cation-selective solid, when the Péclet number is finite and the anions are much more diffusive than the cations, an unreported bulk electroconvective instability is possible at low current. At higher currents and large Péclet numbers, we found that the system is unstable for all cation-to-anion diffusivity ratios, but passes from a monotonic instability to an oscillatory one as this ratio passes through unity.

Molecular crowding occurs when the density of interacting molecules in some reaction system is sufficient to create deviations from traditional mass-action models of chemistry in diffusive systems. While there is a great deal of theory on the influence of molecular crowding on biochemistry in vivo, the effects are highly dependent on specific assumptions about the shapes, volumes, and diffusion properties of the components of an individual system and are thus difficult to predict from first principles. In this study, we use lattice Monte Carlo simulations to examine the effects on a reaction system for two limiting cases of the diffusion behavior of inert crowding agents. In cells, inert molecules might diffuse throughout a solute along with the reactant species by passive diffusion or may be anchored at fixed positions within the solute. We investigate the relative contributions of the two models to crowding effects by examining moving inert particles versus stationery inert particles on the kinetics of a heterodimer assembly system. The two models of inert crowding agents resulted in highly divergent effects on the reactant system. Stationary particles exhibited a bimodal response in the reaction rate curve that was a function of copy number and spatial arrangement and which accelerated the process at conditions not unlike those found in cellular environments. On the other hand, moving inert particles created a well mixed background that had no effect on the reaction process even under extremely compacted conditions. These results may have applications in developing more realistic simulations of reaction chemistry in crowded environments such as living cells.

The density oscillator is a simple system that exhibits self-sustained oscillation. It alternately exhibits up and down flow through a pipe which connects two containers filled with fluids of different densities. However, the mechanism of the flow reversal has not yet been fully understood. From the detailed measurements, we have found that flow reversal begins with an intrusion of fluid, which is followed by rapid growth. This process is definitely sensitive to the viscosities of the fluids, and as a consequence, the critical heights leading to flow reversal are clearly viscosity dependent. These experimental results are explained by a simple model, derived by considering forces acting on a unit volume element located at the tip of the intrusion. Using this model, we can successfully explain the mechanism of flow reversal, which is the most essential process in a density oscillator.

We present the complete set of symmetric and antisymmetric (edge and corner) surface modes in finite one- and two-dimensional arrays of waveguides. We provide classification of the modes based on the anti-continuum limit, study their stability and bifurcations, and discuss relation between surface and bulk modes. We put forward existence of surface breathers, which represent two-frequency modes localized about the array edges.

We derive an exact propagation scheme for nonlinear Schrödinger equations. This scheme is entirely analogous to the propagation of linear Schrödinger equations. We accomplish this by defining a special operator whose algebraic properties ensure the correct propagation. As applications, we provide a simple proof of a recent conjecture regarding higher-order integrators for the Gross-Pitaevskii equation, extend it to multicomponent equations, and to a new class of integrators.

By applying the three-dimensional total internal reflection velocimetry (3D-TIRV) technique to freely suspended micron-sized fluorescent particles, we are able to simultaneously observe the three-dimensional anisotropic hindered diffusion for values of the gap-size-to-radius ratio much less than one. We demonstrate that the 3D-TIRV can be used to accurately track freely suspended $1.5\text{−}\mathrm{\mu }\mathrm{m}$ radius particles. The displacement measurements reveal that the hindered diffusion coefficients are in close agreement with the theoretical values predicted by the asymptotic solutions of Brenner [Chem. Eng. Sci. 16, 242 (1961)] and Goldman et al. [Chem. Eng. Sci. 22, 637 (1967)] for gap-size-to-radius ratio much less than one, while hindered diffusion anisotropicity is simultaneously observed in all data sets.

We present the noise-free escape of a chain of linearly interacting units from a metastable state over a cubic on-site potential barrier. The underlying dynamics is conservative and purely deterministic. The mutual interplay between nonlinearity and harmonic interactions causes an initially uniform lattice state to become unstable, leading to an energy redistribution with strong localization. As a result, a spontaneously emerging localized mode grows into a critical nucleus. By surpassing this transition state, the nonlinear chain manages a self-organized, deterministic barrier crossing. Most strikingly, these noise-free, collective nonlinear escape events proceed generally by far faster than transitions assisted by thermal noise when the ratio between the average energy supplied per unit in the chain and the potential barrier energy assumes small values.

We study the generalized diffusion of a tagged particle in a one-dimensional fluid of hard-point particles. The dynamics of a single particle in its nonuniform, nondeterministic environment is assumed known. On eliminating suitably defined transients from the exact solution, we find a universal form for the tagged particle dynamics when written in terms of stretched space and time, appearing as the classical telegrapher’s equation.

We report the results of an experimental study of the static and dynamic properties of long wavelength concentration fluctuations in a mixture of glycerol and water undergoing free diffusion. The shadowgraph method was used to measure both the mean-squared amplitude and the temporal correlation function of the fluctuations for wave vectors so small as to be inaccessible to dynamic light scattering. For a fluid with a stabilizing vertical concentration gradient, the fluctuations are predicted to have a decay rate that increases with decreasing wave vector $q$, for wave vectors below a cutoff wave vector $q_C$, determined by gravity and the fluid properties. This behavior is caused by buoyant forces acting on the fluctuations. We find that for wave vectors above $\sim q_C$, the decay rate does vary in the normal diffusive manner as $D{q}^2$, where $D$ is the mass diffusion coefficient. Furthermore, for $q\lesssim q_C$ we find that longer wavelength fluctuations decay more rapidly than do shorter wavelength fluctuations, i.e., the behavior is nondiffusive, as predicted.

Ellipsometry is exquisitely sensitive to density variations across a fluid-fluid interface. The coefficient of ellipticity at the interface between water and a series of nonpolar and polar oils is the opposite sign to that predicted for an interface roughened by thermal capillary waves. For pure hydrocarbons, the coefficient of ellipticity is correlated with the refractive index of the oil, but is largely independent of the molecular architecture of the oil phase, ruling out molecular alignment at the interface as the major cause of the deviation from the capillary-wave model. The introduction of a “drying” layer between the oil and water can explain the experimental data. The thickness of the drying layer, modeled as a slab with a relative permittivity of unity, was only $0.3–0.4\mathrm{\AA }$, which is close to that expected simply from the hard sphere repulsion of a hydrocarbon surface. For polar oils, the coefficient of ellipticity decreases as the interfacial tension decreases, consistent with the reduction in thickness of the hard-sphere exclusion region on account of the formation of hydrogen bonds to water.

We study ultrathin films of 8CB in planar anchoring on a $\mathrm{Mo}{\mathrm{S}}_2$ inorganic substrate. We evidence an anchoring breakage for $60\text{−}\mathrm{nm}$-thick films, in favor of the homeotropic anchoring at the air interface. This allows one to determine the $8\mathrm{CB}\text{−}\mathrm{Mo}{\mathrm{S}}_2$ smectic anchoring energy. We then demonstrate for films thinner than $60\mathrm{nm}$ that, under the homeotropic bulk, an intermediate film remains in planar anchoring, associated with a melting of the smectic layers close to the substrate. Such a melting could be general for planar or tilted anchorings and we show that, for strong anchorings, the anchoring energy can be driven by the deformations of this intermediate nematic film.

The stability of the dynamical states characterized by a uniform firing rate (splay states) is analyzed in a network of globally coupled leaky integrate-and-fire neurons. This is done by reducing the set of differential equations to a map that is investigated in the limit of large network size. We show that the stability of the splay state depends crucially on the ratio between the pulse width and the interspike interval. More precisely, the spectrum of Floquet exponents turns out to consist of three components: (i) one that coincides with the predictions of the mean-field analysis [Abbott and van Vreesvijk, Phys. Rev. E 48, 1483 (1993)], (ii) a component measuring the instability of “finite-frequency” modes, (iii) a number of “isolated” eigenvalues that are connected to the characteristics of the single pulse and may give rise to strong instabilities (the Floquet exponent being proportional to the network size). Finally, as a side result, we find that the splay state can be stable even for inhibitory coupling.

There has been an increasing interest in properties of complex networks, such as small-world property, power-law degree distribution, and network transitivity which seem to be common to many real world networks. In this study, a useful community detection method based on non-negative matrix factorization (NMF) technique is presented. Based on a popular modular function, a proper feature matrix from diffusion kernel and NMF algorithm, the presented method can detect an appropriate number of fuzzy communities in which a node may belong to more than one community. The distinguished characteristic of the method is its capability of quantifying how much a node belongs to a community. The quantification provides an absolute membership degree for each node to each community which can be employed to uncover fuzzy community structure. The computational results of the method on artificial and real networks confirm its ability.

We analyze the time resolved spike statistics of a solitary and two mutually interacting chaotic semiconductor lasers whose chaos is characterized by apparently random, short intensity spikes. Repulsion between two successive spikes is observed, resulting in a refractory period, which is largest at laser threshold. For time intervals between spikes greater than the refractory period, the distribution of the intervals follows a Poisson distribution. The spiking pattern is highly periodic over time windows corresponding to the optical length of the external cavity, with a slow change of the spiking pattern as time increases. When zero-lag synchronization between two lasers is established, the statistics of the nearly perfectly matched spikes are not altered. The similarity of these features to those found in complex interacting neural networks, suggests the use of laser systems as simpler physical models for neural networks.

We observed that Faraday waves are parametrically generated on a free surface of superfluid ${}^4\mathrm{He}$ when a sample cell is vibrated vertically. Standing-wave patterns appear on the surface, and their frequencies are one-half the driving frequency. We observed clear threshold amplitudes of the vibration for the instability. The difference in the threshold between the superfluid and the normal fluid is explained by a wall damping.

We demonstrate that thermal convection in a rapidly rotating spherical shell may produce zonal flows outside the tangent cylinder that consist of multiple alternating jets drifting towards the interior. A quasigeostrophic model that in model space is located between the classical annulus and the spherical shell, has been constructed. In this generalized annulus model we allow for terms in the Ekman correction to the flow that are usually neglected. It is shown that these terms may create observable effects at low Ekman numbers. Some of the remaining differences between the two-dimensional (2D) and 3D model may be explained by the missing heat transport along the rotation axis of the 2D model. The 2D model makes it possible to show that the occurrence of jet drift requires a significant radial dependence of the $\beta$ parameter. In addition, the relatively low numerical costs of the 2D model allow extensive parameter studies. For an increasing rotation rate and fixed moderate thermal driving, the 2D model predicts (i) an increased zonal flow strength, (ii) an increased number of jets related to Rhines length scale, and (iii) an inward drift of the center jets. For an increasing thermal driving and fixed rotation rate, the solutions of the 2D model develop stronger zonal flows with a reduced number of still faster drifting jets. The jet drift is ultimately converted into fluctuations of a couple of steady jets as the center region outside the tangent cylinder is being cleared of jets. These solutions, that display reduced Ekman layer effects, resemble solutions obtained with stress-free boundary conditions.

Many punctuated phenomena in nature are claimed [e.g., by the theory of self-organized criticality (SOC)] to be power-law distributed. In our experiments on a three-dimensional pile of long-grained rice, we find that by only changing the boundary condition of the system, we switch from such power-law-distributed avalanche sizes to quasiperiodic system-spanning avalanches. Conversely, by removing ledges the incidence of system-spanning avalanches is significantly reduced. This may offer a perspective on new avalanche prevention schemes. In addition, our findings may help to explain why the archetype of SOC, the sandpile, was found to have power-law-distributed avalanches in some experiments, while in other experiments quasiperiodic system-spanning avalanches were found.

The effective interactions between model proteins of various shapes are computed by means of Monte Carlo simulations. In particular, we determine how the modification of the excluded volume architecture influences both entropic and purely electrostatic ion-mediated forces between proteins. We find that interprotein interactions are strongly affected by protein shape, which results in a high decrease of electrostatic screening for typical active site geometries. Effective interactions are then closer to the direct Coulombic interactions, and both affinity and selectivity are enhanced by several orders of magnitude.

We explore the percolation threshold shift as short-range correlations are introduced and systematically varied in binary composites. Two complementary representations of the correlations are developed in terms of the distribution of phase bonds or, alternatively, using a set of appropriate short-range order parameters. In either case, systematic exploration of the correlation space reveals a boundary that separates percolating from nonpercolating structures and permits empirical equations that identify the location of the threshold for systems of arbitrary short-range correlation states. Two- and three-dimensional site lattices with two-body correlations, as well as a two-dimensional hexagonal bond network with three-body correlations, are explored. The approach presented here should be generalizable to more complex correlation states, including higher-order and longer-range correlations.