Microscale models of foam structure traditionally incorporate a balance between bubble pressures and surface tension forces associated with curvature of bubble films. In particular, models for flowing foam microrheology have assumed this balance is maintained under the action of some externally imposed motion. Recently, however, a dynamic model for foam structure has been proposed, the viscous froth model, which balances the net effect of bubble pressures and surface tension to viscous dissipation forces: this permits the description of fast-flowing foam. This contribution examines the behavior of the viscous froth model when applied to a paradigm problem with a particularly simple geometry: namely, a two-dimensional bubble “lens.” The lens consists of a channel partly filled by a bubble (known as the “lens bubble”) which contacts one channel wall. An additional film (known as the “spanning film”) connects to this bubble spanning the distance from the opposite channel wall. This simple structure can be set in motion and deformed out of equilibrium by applying a pressure across the spanning film: a rich dynamical behavior results. Solutions for the lens structure steadily propagating along the channel can be computed by the viscous froth model. Perturbation solutions are obtained in the limit of a lens structure with weak applied pressures, while numerical solutions are available for higher pressures. These steadily propagating solutions suggest that small lenses move faster than large ones, while both small and large lens bubbles are quite resistant to deformation, at least for weak applied back pressures. As the applied back pressure grows, the structure with the small lens bubble remains relatively stiff, while that with the large lens bubble becomes much more compliant. However, with even further increases in the applied back pressure, a critical pressure appears to exist for which the steady-state structure loses stability and unsteady-state numerical simulations show it breaks up by route of a topological transformation.

We employ self-consistent mean-field theory to study the phase behavior and the microstructural sizes of $AB$ diblock copolymers in the presence of a neutral solvent $S_1$ and a slightly B-selective solvent $S_2$. In particular, the effects of copolymer volume fraction ${\overline{\varphi }}_C$, the solvent ratio, and the immiscibility parameter between two solvents ${\chi }_{S_1{S}_2}$, are examined. We find that increasing ${\chi }_{S_1{S}_2}$ not only enlarges the ordered microphase region in the concentrated solutions, but also induces a less concentrated homogeneous solution to form an ordered structure and even undergo a macrophase separation. This is due to the fact that increasing ${\chi }_{S_1{S}_2}$ enhances the preferentially of $S_1$ for A and $S_2$ for B and, thereafter, the effective segregation between A and B. Hence, we observe that the structural length results obtained by varying ${\chi }_{S_1{S}_2}$ resemble a consequence of varying the solvent selectivity in the diblock copolymer solutions when only one solvent is added. For example, when ${\chi }_{S_1{S}_2}$ is small, the domain spacing decreases with decreasing ${\overline{\varphi }}_C$ while at larger values of ${\chi }_{S_1{S}_2}$, it first shows a decreasing trend and then an increasing behavior with decreasing ${\overline{\varphi }}_C$.

We propose a method for electrophoretic separation of DNA in which adsorbed polymers are driven over a disordered two-dimensional substrate which contains attractive sites for the polymers. Using simulations of a model for long polymer chains, we show that the mobility increases with polymer length, in contrast to gel electrophoresis techniques, and that separation can be achieved for a range of length scales. We demonstrate that the separation mechanism relies on steric interactions between polymer segments, which prevent substrate disorder sites from trapping more than one DNA segment each. Since thermal activation does not play a significant role in determining the polymer mobility, band broadening due to diffusion can be avoided in our separation method.

We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of structural constraints. We also introduce an algorithm for generating maximally random weighted networks with arbitrary $P(k,s)$ to be used as null models. The application of our measures to real networks reveals the importance of weights in a correct understanding and modeling of these heterogeneous systems.

In this paper, we propose a susceptible-infected model with identical infectivity, in which, at every time step, each node can only contact a constant number of neighbors. We implemented this model on scale-free networks, and found that the infected population grows in an exponential form with the time scale proportional to the spreading rate. Furthermore, by numerical simulation, we demonstrated that the targeted immunization of the present model is much less efficient than that of the standard susceptible-infected model. Finally, we investigate a fast spreading strategy when only local information is available. Different from the extensively studied path-finding strategy, the strategy preferring small-degree nodes is more efficient than that preferring large-degree nodes. Our results indicate the existence of an essential relationship between network traffic and network epidemic on scale-free networks.

The effect of drainage front morphology on gaseous diffusion through partially saturated porous media is analyzed using the lattice Boltzmann method (LBM). Flow regimes for immiscible displacement in porous media have been characterized as stable displacement, capillary fingering, and viscous fingering. The dominance of a flow regime is associated with the relative magnitudes of gravity, viscous, and capillary forces, quantifiable via the Bond number Bo, capillary number Ca, and their difference, $\mathrm{Bo}-\mathrm{Ca}$. Forced drainage from an initially saturated two-dimensional (2D) porous medium was simulated and the resulting flow patterns were analyzed and compared with theoretical predictions and experimental results. The LBM simulations reproduced expected flow morphologies for a range of drainage velocities and gravitational forces (i.e., a range of capillary and Bond numbers). Furthermore, measures of drainage front width as a function of the dimensionless difference $\mathrm{Bo}-\mathrm{Ca}$ correspond well with scaling laws derived from percolation theory. Effects of flow morphology on residual fluid entrapment and gaseous diffusion were assessed by running LBM diffusion simulations through the partially saturated domain for a range of water contents. The effective diffusion coefficient as a function of water content was estimated for three regimes: stable drainage front, capillary fingering, and viscous fingering. Significant reductions in gaseous diffusion coefficient were found for viscous fingering relative to stable displacement, and to a lesser extent for capillary fingering, indicating that wetting phase distribution with a high degree of fingering in the 2D domain severely restricts connectivity of gas diffusion pathways through the medium. The study lends support for the use of LBM in design and management of fluids in porous media under variable gravity, and enhances the understanding of the role of dynamic fluid behavior on macroscopic transport properties of partially saturated porous media.

Self-organized separation of charged-dust species in two-dimensional dusty plasmas is studied by means of molecular-dynamics simulation. The multispecies dust grains, interacting through a screened Coulomb potential with a long-range attractive component, are confined by an external quadratic potential and subjected to a radially outward ion drag force. It is found that, in general, the species are spatially separated by bandlike dust-free (or void) regions, and grains of the same species tend to populate a common shell. At large ion drag and/or large plasma screening, a central disklike void as well as concentric bandlike voids separating the different species appear. Because of the outward drag and the attractive component of the dust-dust interaction forces, highly asymmetrical states consisting of species-separated dust clumps can also exist despite the fact that all the forces are either radial or central.

The chaotic synchronization in $n$-dimensional large map networks with local coupling and their size stabilities in the node number $N\to \infty$ are studied analytically and numerically. The analytical results show that the chaotic synchronization is stable for $N\to \infty$ in the presence of the external driving or global coupling. The numerical calculations show that, as the driving or global interaction strength increases from zero, the network states have the whole route: spatiotemporal chaotic state $\to$ cluster chaotic synchronous state $\to$ complete chaotic synchronous state $\to$ spatiotemporal pattern $\to$ spatiotemporal chaotic state.

We determine all families of Markovian three-state lattice gases with pair interaction and a single local conservation law. One such family of models is an asymmetric exclusion process where particles exist in two different nonconserved states. We derive conditions on the transition rates between the two states such that the shock has a particularly simple structure with minimal intrinsic shock width and random walk dynamics. We calculate the drift velocity and diffusion coefficient of the shock.

Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see, e.g., B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature 418, 171 (2002)] and B. Kirkup and M. A. Riley [Nature 428, 412 (2004)]. Through analytical methods supported by numerical simulations, we address this issue by studying the properties of a paradigmatic non-spatial three-species stochastic system, namely, the “rock-paper-scissors” or cyclic Lotka-Volterra model. While the deterministic approach (rate equations) predicts the coexistence of the species resulting in regular (yet neutrally stable) oscillations of the population densities, we demonstrate that fluctuations arising in the system with a finite number of agents drastically alter this picture and are responsible for extinction: After long enough time, two of the three species die out. As main findings we provide analytic estimates and numerical computation of the extinction probability at a given time. We also discuss the implications of our results for a broad class of competing population systems.

In this study, the integral equation method proposed recently by Sarkisov [J. Chem. Phys. 114, 9496 (2001).], which has proved accurate for continuous potentials, is extended successfully to the hard sphere potential plus an attractive Yukawa tail. By comparing the results of thermodynamic properties, including the liquid-vapor phase diagram, with available simulation data, it is found that this method remains reliable for this class of models of interaction often used in colloid science.

We examine some characteristic properties of reaction-diffusion processes of the $A+A\to 0$ type on scale-free networks. Due to the inhomogeneity of the structure of the substrate, as compared to usual lattices, we focus on the characteristics of the nodes where the annihilations occur. We show that at early times the majority of these events take place on low-connectivity nodes, while as time advances the process moves towards the high-connectivity nodes, the so-called hubs. This pattern remarkably accelerates the annihilation of the particles, and it is in agreement with earlier predictions that the rates of reaction-diffusion processes on scale-free networks are much faster than the equivalent ones on lattice systems.

Models of the convergence of opinion in social systems have been the subject of considerable recent attention in the physics literature. These models divide into two classes, those in which individuals form their beliefs based on the opinions of their neighbors in a social network of personal acquaintances, and those in which, conversely, network connections form between individuals of similar beliefs. While both of these processes can give rise to realistic levels of agreement between acquaintances, practical experience suggests that opinion formation in the real world is not a result of one process or the other, but a combination of the two. Here we present a simple model of this combination, with a single parameter controlling the balance of the two processes. We find that the model undergoes a continuous phase transition as this parameter is varied, from a regime in which opinions are arbitrarily diverse to one in which most individuals hold the same opinion.

The irradiance diffraction profile of a straight edge is given as a Taylor series in powers of the distance from the geometrical shadow boundary to any point in the profile for monochromatic radiation. The coefficients of the series, which are obtained as simple analytic expressions, are proportional to the real part of a complex number whose phase cycles through a complete period every eight terms in the series. Integration of this series over a Planck distribution of radiation yields the power series for the Planck profile; this derived series has a finite radius of convergence. The asymptotic series for the Planck profile far from the shadow boundary and beyond the radius of convergence of its power series is obtained by analytic continuation of the power series with the aid of a Barnes type of integral representation.

The dynamic structure factor, vorticity and entropy density dynamic correlation functions are measured for stochastic rotation dynamics (SRD), a particle based algorithm for fluctuating fluids. This allows us to obtain unbiased values for the longitudinal transport coefficients such as thermal diffusivity and bulk viscosity. The results are in good agreement with earlier numerical and theoretical results, and it is shown for the first time that the bulk viscosity is indeed zero for this algorithm. In addition, corrections to the self-diffusion coefficient and shear viscosity arising from the breakdown of the molecular chaos approximation at small mean free paths are analyzed. In addition to deriving the form of the leading correlation corrections to these transport coefficients, the probabilities that two and three particles remain collision partners for consecutive time steps are derived analytically in the limit of small mean free path. The results of this paper verify that we have an excellent understanding of the SRD algorithm at the kinetic level and that analytic expressions for the transport coefficients derived elsewhere do indeed provide a very accurate description of the SRD fluid.

We revisit the sandpile model with “sticky” grains introduced by Mohanty and Dhar [Phys. Rev. Lett. 89, 104303 (2002)] whose scaling properties were claimed to be generically in the universality class of directed percolation for both isotropic and directed models. While for directed models this conclusion is unquestionable, for isotropic models we present strong evidence that the asymptotic scaling in the self-organized regime (in which a stationary critical state exists in the limit of slow driving and vanishing dissipation rate) is, like other stochastic sandpiles, generically in the Manna universality class. This conclusion is drawn from extensive Monte Carlo simulations, and is strengthened by the analysis of the Langevin equations (proposed by the same authors to account for this problem), argued to converge upon coarse-graining to the well-established set of Langevin equations for the Manna class.

We propose an adaptation of the osmotic stress technique for determining equations of state of colloids covered by polymer films. We describe here the case of silica particles covered by 6 or 7 layers of polyelectrolyte multilayers. The establishment of a pressure-distance curve allows the interpretation of colloidal interactions over more than four orders of magnitude in pressure. This large range allows a clear separation between three distinct regimes: layer compression, brush extension and at very low pressures a regime of weak repulsion. The physical origins of the regimes are discussed and described by models of colloidal interactions.

Cholesteric liquid crystals (CLC) selectively reflect light when the helical pitch is of the order of the wavelength of the incident beam propagating along the helix axis. The wavelength bandwidth, related to the optical anisotropy, is typically limited to a few tens of nanometers in the visible part of the spectrum, which is insufficient for applications such as white-or-black polarizer-free reflective displays and smart windows for the control of the solar light and heat. A way to make cholesteric films reflecting in a broad wavelength band consists in associating various cholesteric pitches in the same film. In this work, it is shown how a study by confocal micro Raman spectrometry mapping makes it possible to have access to information accounting for the local organization of CLCs in the case of graded pitch materials. These investigations will be correlated to the optical response and the transverse microstructure of the CLC material as investigated by transmission electron microscopy. An accurate analysis of the vibrational behavior evolution of the $\mathrm{C}\mathrm{O}$ can be correlated to the evolution of the populations of the chiral and achiral groups in the case of the interdiffusion of two CLC substances with various stoechiometries. Besides an easy measurement of the Raman spectrum gives the opportunity to quantify the relative ratio of the mesogenic species and thus to go up by a simple way to the pitch of the helical structure.

We investigate feedback control of the cooperative dynamics of two coupled neural oscillators that is induced merely by external noise. The interacting neurons are modeled as FitzHugh-Nagumo systems with parameter values at which no autonomous oscillations occur, and each unit is forced by its own source of random fluctuations. Application of delayed feedback to only one of two subsystems is shown to be able to change coherence and time scales of noise-induced oscillations either in the given subsystem, or globally. It is also able to induce or to suppress stochastic synchronization under certain conditions.