The effect of convection on horizontally propagating fronts arising in the acid-catalyzed reaction of chlorite and tetrathionate ions is investigated experimentally in vertically oriented narrow reaction vessels of various heights. A stable finger develops which can be characterized by its mixing length defined as the standard deviation of the average front profile. The mixing length scales with the height of the reaction vessel, and the scaling law has been determined for three different chemical compositions.

We extend the quasiergodic model proposed as an alternative version of the Antonov isothermal model [L. Velazquez and F. Guzman, Phys. Rev. E 68, 066116 (2003)] by including the incidence of a mass spectrum. We propose an iterative procedure inspired by the Newton-Raphson method to solve the resulting nonlinear structure equations. As an example of application, we assume the existence of a mass spectrum with a standard Salpeter form, $dN=Cdm∕m^{\alpha }$. We analyze consequences of this realistic ingredient on the system thermodynamical behavior and perform a quantitative description of the mass segregation effect.

We study the effects of random partnerships, introduced to interaction or replacement networks, on the evolution of cooperation in spatial game theory on a square lattice. For the spatial prisoner dilemma game, we show that, compared with the case without random partnership, cooperation can be enhanced regardless of whether a random partnership is introduced to an interaction or replacement network. Specifically, the enhancement of cooperation is strongest in the limit of zero randomness. We show explicitly that the cooperator frequency is a decreasing function of randomness, and the cooperation eventually vanishes once the randomness is strong enough. For the spatial snow drift game, we find that the enhancement of cooperation occurs only when a random partnership is introduced to an interaction network.

We study two-dimensional $q$-state random-bond Potts models for both $q=8$ and $q=5$ with a linearly varying temperature. By applying a successive Monte Carlo renormalization group procedure, both the static and dynamic critical exponents are obtained for randomness amplitudes (the strong to weak coupling ratio) of $r_0=3$, 10, 15, and 20. The correlation length exponent $\nu$ increases with disorder from less than to larger than unity and this variation is justified by the good collapse of the specific heat near the critical region. The specific heat exponent is obtained by the usual hyperscaling relation $\alpha =2-d\nu$ and thus indicates no possibility of the activated dynamic scaling. Both $r_0$ and $q$ have effects on the critical dynamics of the disordered systems, which can be seen from variations of the rate exponent, the hysteresis exponent, and the dynamic critical exponent. Implications of these results are discussed.

An integral-equation approach is developed to study interfacial properties of anisotropic fluids with planar spins in the presence of an external magnetic field. The approach is based on the coupled set of the Lovett-Mou-Buff-Wertheim integro-differential equation for the inhomogeneous anisotropic one-particle density and the Ornstein-Zernike equation for the orientationally dependent two-particle correlation functions. Using the proposed inhomogeneous angle-harmonics expansion formalism we show that these integral equations can be reduced to a much simpler form similar to that inherent for a system of isotropic fluids. The interfacial orientationally dependent direct correlation function can be consistently constructed by means of a nonlinear interpolation via its values obtained in the coexisting anisotropic bulk phases. A soft mean spherical approximation is employed for the closure relation. This has allowed us to solve the complicated integral equations in the situation when both spatial inhomogeneity and orientational anisotropy are present simultaneously. The approach introduced is applied to an $XY$ fluid model with ferromagnetic spin interactions. As a result, the density-orientation and magnetization profiles at the liquid-vapor interfaces are calculated in a wide range of temperatures up to subcritical regions. The influence of the external field on the microscopic structure of the interfaces and the surface tension is also analyzed in detail.

We use x-ray photon correlation spectroscopy to investigate the dynamics of a high-volume-fraction emulsion creaming under gravity. The dodecane-in-water emulsion has interfaces stabilized solely by colloidal particles (silica). The samples were observed soon after mixing: as the emulsion becomes compact we discern two regimes of aging with a crossover between them. The young emulsion has faster dynamics associated with creaming in a crowded environment accompanied by local rearrangements. The dynamics slow down for the older emulsion, although our studies show that motion is associated with large intermittent events. The relaxation rate, as seen from the intensity autocorrelation function, depends linearly on the wave vector at all times; however, the exponent associated with the line shape changes from 1.5 for young samples to less than 1 as the emulsion ages. The combination of ballisticlike dynamics, an exponent that drops below 1, and large intermittent fluctuations has not been reported before to our knowledge.

Three-dimensional interface patterns are common in condensed matter, whose dynamical behavior is still deserving clarification. The dynamics of cellular patterns formed at the concave solid-liquid interface during directional solidification in a cylinder of a transparent alloy is studied by means of bright-field live imaging. For each pulling velocity, in situ observation shows that the asymptotic cellular pattern, which establishes with time, is characterized by the continuous birth of a large number of cells at a circular source of morphological instability on the periphery, the sustained collective gliding of the whole cellular array down the interface slope, and the elimination of coarse cells at the central sink. This very peculiar dynamics is the specific signature of the cell advection imposed by interface curvature for the concave situation in three-dimensional solidification. It follows from the comparison between experimental cell gliding and pure slope advection that an additional mechanism of pattern advection is active. It is attributed to fluid flow interaction, estimated on the basis of the Forth and Wheeler traveling wave equations.

We study the conformation of polyelectrolyte-surfactant complexes in the presence of monovalent salt. A simple model for the formation of these structures is presented in the framework of the Debye-Hückel-Bjerrum-Manning and Flory theories, with the hydrophobic interactions between the hydrocarbon tails of surfactant molecules treated in the spirit of van der Waals theory as an effective attraction. The extension of the polyelectrolyte-surfactant complexes is analyzed as a function of the salt concentration and a discrete conformational transition between a compact globule and an elongated coil is found, in agreement with experimental results for the unfolding transition of a DNA-cationic surfactant complex.

The velocity and the adenosine triphosphate (ATP) hydrolysis rate of the molecular motor kinesin are studied using a general network representation for the motor, which incorporates both the energetics of ATP hydrolysis and the experimentally observed separation of time scales between chemical and mechanical transitions. Both the motor velocity and its hydrolysis rate can be expressed as superpositions of excess fluxes for the directed cycles (or dicycles) of the network. The sign of these dicycle excess fluxes depends only on two thermodynamic control parameters as provided by the load force $F$ and the chemical energy $\Delta \mu$ released during the hydrolysis of a single ATP molecule. In contrast, both the motor velocity and its hydrolysis rate depend, in general, on the load force $F$ as well as on the three concentrations of ATP, adenosine diphosphate (ADP), and inorganic phosphate (P), separately. Thus, in order to represent the different operation modes of the motor in the $(F,\Delta \mu )$ plane, one has to specify two concentrations such as the product concentrations [ADP] and [P]. As a result, we find four different operation modes corresponding to the four possible combinations of ATP hydrolysis or synthesis with forward or backward mechanical steps. Our operation diagram implies in particular that backward steps are coupled to ATP hydrolysis for sufficiently large ATP concentrations, but to ATP synthesis for sufficiently large ADP and/or P concentrations.

We study the effect of random inhomogeneous connections on a continuous field description of neural tissue. We focus on a regime in which persistent random fluctuations in activity arise spontaneously in the absence of either time-varying or spatially inhomogeneous input. While present in real tissue and network models of discrete neurons, such behavior has not been reported in continuum models of this type. The activity contains frequencies similar to those seen experimentally. We consider a power-law envelope $r^{-\alpha }$ for the inhomogeneity and present evidence that the statistical coherence (a measure of two-point correlation) rapidly percolates across the system as $\alpha$ is reduced below ${\alpha }_c\approx 1,2$ in one and two dimensions, respectively.

From simulations of two-dimensional inverse energy cascading turbulence, we show that points with low acceleration values are predominantly advected by the local fluid velocity. The fluid velocity $\mathbf{u}$ in the global frame and the fluid velocity $\mathbf{\xi }$ in the frame moving with a low-acceleration point are approximately statistically independent. This property remains valid in high-acceleration regions but only in the direction of the local acceleration vector. In the perpendicular direction, the acceleration velocity ${\mathbf{V}}_a=\mathbf{u}-\mathbf{\xi }$ is approximately independent of $\mathbf{\xi }$ everywhere. These statistical independences constitute our formulation of the sweeping decorrelation hypothesis for two-dimensional inverse energy cascading turbulence.

We show that a topological investigation of the phase space of a semiconductor ring laser can be used to devise switching schemes which are alternative to optical pulse injection of counterpropagating light. To provide physical insight in these switching mechanisms, a full bifurcation analysis and an investigation of the topology is performed on a two-dimensional asymptotic model. Numerical simulations confirm the topological predictions.

In a one-component plasma constituted by electrons with a uniform positive background, the correlations are studied in the framework of the Singwi, Tosi, Land, and Sjölander (STLS) model. The local-field corrections (LFCs) are calculated with electron density ranging from ${10}^{19}\text{to}{10}^{26}{\mathrm{cm}}^{-3}$ and with a temperature of ${10}^4\mathrm{K}$. Then, a dielectric formalism is used to deduce the potential energy of a positive test charge (a proton) imbedded in the electron medium. A significant departure of this potential from the random phase approximation (RPA) one has been found. In particular, as the density increases, the discrepancy between the two potentials grows up to reach a maximum correlated to the maximum of the electron coupling parameter. In addition, it is found that in both high and low density limits, the STLS and RPA approaches yield similar results. On the other hand, the effect of the LFC on the electrical conductivity is also estimated in hydrogen plasmas.

The ionization degree and equation of state of dense xenon plasma were calculated by using self-consistent fluid variational theory for temperature of $4–30\mathrm{kK}$ and density of $0.01–8.5\mathrm{g}∕{\mathrm{cm}}^3$. The dense fluid xenon will be ionized at high pressures and temperatures. The ionization energy of xenon will be lowered due to the interactions among all particles of Xe, ${\mathrm{Xe}}^{+}$, ${\mathrm{Xe}}^{2+}$, and $e$. The ionization degree is obtained from nonideal ionization equilibrium, taking into account the correlative contributions to the chemical potential which is determined self-consistently by the free energy function. The composition of xenon has been calculated with given densities and temperatures in the region of partial ionization. The calculated results show a pressure softening regime at the onset of ionization. Comparison is performed with available shock-wave experiments and other theoretical calculations.

Rules for the transformation of time parameters in relativistic Langevin equations are derived and discussed. In particular, it is shown that, if a coordinate-time-parametrized process approaches the relativistic Jüttner-Maxwell distribution, the associated proper-time-parametrized process converges to a modified momentum distribution, differing by a factor proportional to the inverse energy.

We introduce a framework based on the percolation idea to investigate the relaxation under zero-temperature Glauber and outflow dynamics on $L\times L$ square and triangular lattices. This helps us to understand the appearance of a double time regime in the survival probability. We show that the first, short-time, regime corresponds to relaxation through droplets and the second, long-time, regime corresponds to relaxation through stripes. For both dynamics the probability that the system becomes ordered through droplets (which indicates fast relaxation) is about $2∕3$.

We present a confocal microscopy study of $1.55\mu \mathrm{m}$ monodisperse silica hard spheres as they sediment and crystallize at the bottom wall of a container. If the particles sediment onto a feature less flat wall, the two bottom layers crystallize simultaneously and layerwise growth follows. If the wall is replaced by a hexagonal template, only layerwise growth occurs. Our results complement earlier numerical simulations and experiments on other colloidal systems.

DNA is an ideal candidate to organize matter on the nanoscale, primarily due to the specificity and complexity of DNA based interactions. Recent advances in this direction include the self-assembly of colloidal crystals using DNA grafted particles. In this paper we theoretically study the self-assembly of DNA-caged particles. These nanoblocks combine DNA grafted particles with more complicated purely DNA based constructs. Geometrically the nanoblock is a sphere (DNA grafted particle) inscribed inside a polyhedron (DNA cage). The faces of the DNA cage are open, and the edges are made from double stranded DNA. The cage vertices are modified DNA junctions. We calculate the equilibriuim yield of self-assembled, tetrahedrally caged particles, and discuss their stability with respect to alternative structures. The experimental feasability of the method is discussed. To conclude we indicate the usefulness of DNA-caged particles as nanoblocks in a hierarchical self-assembly strategy.