The critical behavior of the contact process (CP) in disordered and periodic binary two-dimensional (2D) lattices is investigated numerically by means of Monte Carlo simulations as well as via an analytical approximation and standard mean field theory. Phase-separation lines calculated numerically are found to agree well with analytical predictions around the homogeneous point. For the disordered case, values of static scaling exponents obtained via quasistationary simulations are found to change with disorder strength. In particular, the finite-size scaling exponent of the density of infected sites approaches a value consistent with the existence of an infinite-randomness fixed point as conjectured before for the $2D$ disordered CP. At the same time, both dynamical and static scaling exponents are found to coincide with the values established for the homogeneous case thus confirming that the contact process in a heterogeneous environment belongs to the directed percolation universality class.

Oscillatory zoning, i.e., self-formation of spatial quasiperiodic oscillations in the composition of solid growing from aqueous solution, is analyzed theoretically. Keeping in mind systems like $(\mathrm{Ba},\mathrm{Sr})\mathrm{S}{\mathrm{O}}_4$, we propose a one-dimensional model that takes into account the nonideality of the solid solution and the system asymmetry, in particular, reflecting itself in different solubilities for such systems. Based on a linear stability analysis, different parameter regions can be identified. Even an ideal solution with a sufficiently large asymmetry can display oscillatory zoning. Numerical simulations complement the linear stability analysis as well as the qualitative consideration of the instability development and reveal the nature of the limit cycles.

In planar nematic electrohydrodynamic convection (EHC), a microscopic liquid crystal cell is driven by a homogeneous ac electric field, which, if strong enough, causes the fluid to destabilize into a regular pattern-forming state. We consider asymmetric electric fields $E\left(t\right)=E(t+T)\ne -E(t+T∕2)$, which leads to the possibility of three different types of instabilities at onset: conductive, dielectric, and subharmonic. The first two are already well known as they are easily produced when the system is driven by symmetric electric fields; the third can only occur when the electric field symmetry is broken. We present theoretical results on EHC using linear stability analysis and Floquet theory. We consider rigid and free boundary conditions, extending the model to two Fourier modes in the vertical plane, the inclusion of flexoelectricity, and using standard (nematic electric conductivity ${\sigma }_a>0$ and dielectric anisotorpy ${ϵ}_a<0$) and nonstandard $({\sigma }_a<0)$ material parameters. We make full use of a three-dimensional linear model where two mutually perpendicular planar wave numbers $q$ and $p$ can be varied. Our results show that there is a qualitative difference between the boundary conditions used, which is also dependent on how many vertical Fourier modes were used in the model. We have obtained threshold values favoring oblique rolls in subharmonic and dielectric regimes in parameter space. For the nonstandard EHC parameter values, both conduction and subharmonic regimes disappear and only the dielectric threshold exists.

We reveal experimentally a mechanism that alters the critical behavior of a Hopf bifurcation substantially due to the presence of imperfections of the reflection symmetry in a hydrodynamic system. The onset of rotating waves in Taylor vortex flow, which is widely considered as a “classical” example for a Hopf bifurcation in hydrodynamics, is investigated primarily by transient response experiments. While wavy vortex flow is not influenced by such (unavoidable) experimental imperfections, the critical behavior of the axially subharmonic rotating wave with wavy outflow boundaries, also called the small-jet mode, is qualitatively altered. Experimental evidence is provided that the modified critical behavior at the Hopf bifurcation is associated with imperfections of the reflection symmetry of the Taylor-Couette setup. The experimental results on Hopf bifurcation are discussed in the context of a cusp-Hopf bifurcation model recently proposed by Harlim and Langford [Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, 2547 (2007)] and compared to experimental results on imperfect pitchfork bifurcation in small-aspect ratio Taylor-Couette flow.

We model a reaction-diffusion-convection system which comprises a liquid drop containing solutes that undergo an Oregonator reaction producing chemical waves. The reactants are taken to have surfactant properties so that the variation in their concentrations induces Marangoni flows at the drop interface which lead to a displacement of the drop. We discuss the mechanism by which the chemical-mechanical coupling leads to drop motion and the way in which the net displacement of the drop depends on the strength of the surfactant action. The equations of motion are solved using a lattice Boltzmann approach.

We consider the capillary absorption of liquid metal droplets by carbon nanotubes using molecular dynamics simulations and the steady-state flow model due to Marmur [A. Marmur, J. Colloid Interface Sci. 122, 209 (1988)]. We find an exact solution to Marmur’s evolution equation for the height of the absorbed liquid column as a function of time, and show that this reproduces the dynamics observed in the simulations well. The simulations show that the flow of the metal exhibits a large degree of slippage at the tube walls, with slip lengths of up to $10\mathrm{nm}$ depending on the wettability of the nanotube. The results support the use of the Lucas-Washburn approach for modeling capillary absorption at the nanoscale.

A simple method, previously used to calculate the equilibrium concentration of dimers adsorbed on a Bethe lattice as a function of the dimer activity, is generalized to solve the problem of a Bethe lattice in contact with a reservoir containing a mixture of molecules. The molecules may have arbitrary sizes and shapes consistent with the geometry of the lattice and the molecules do not interact with one another except for the hard-core restriction that two molecules cannot touch the same site. We obtain a set of simultaneous nonlinear equations, one equation for each species of molecule, which determines the equilibrium concentration of each type of molecule as a function of the (arbitrary) activities of the various species. Surprisingly, regardless of the number of species, the equilibrium concentrations are given explicitly in terms of the solution of a single equation in one unknown which can be solved numerically, if need be. Some numerical examples show that increasing the activity of one species need not necessarily decrease the equilibrium concentration of all other species. We also calculate the adsorption isotherm of an “annealed” Bethe lattice consisting of two types of sites which differently influence the activity of an adsorbed molecule. We prove that if the reservoir contains a finite number of molecular species, regions of two different polymer densities cannot simultaneously exist on the lattice. The widely used Guggenheim theory of mixtures, which can also be construed as a theory of adsorption, assumes for simplicity that the molecules in the mixture are composed of elementary units, which occupy sites of a lattice of coordination number $q$. Guggenheim’s analysis relies on approximate combinatorial formulas which become exact on a Bethe lattice of the same coordination number, as we show in an appendix. Our analysis involves no combinatorics and relies only on recognizing the statistical independence of certain quantities. Despite the nominal equivalence of the two approaches, the easily visualized properties of the Bethe lattice enable one to solve some apparently difficult problems by quite elementary methods.

We study the thermostatistical fluctuations of a single Delrin monomer on a granular lattice of dimer particles using both experiment and simulation. The goal is to examine the collision frequency, energy injection, and sidewall effects on a single second-layer particle in a bilayer granular gas experiment. Non-Gaussian velocity statistics are observed for the single particle of the top layer and result from the presence of defects in the first layer. These deviations are not directly due to the presence of the boundary wall, since the form of velocity distributions is quite spatially homogeneous, but are the consequence of the presence of a few mobile defects in the first layer.

Improvement of energy-conversion efficiency from laser to proton beam is demonstrated by particle simulations in a laser-foil interaction. When an intense short-pulse laser illuminates the thin-foil target, the foil electrons are accelerated around the target by the ponderomotive force. The hot electrons generate a strong electric field, which accelerates the foil protons, and the proton beam is generated. In this paper a multihole thin-foil target is proposed in order to increase the energy-conversion efficiency from laser to protons. The multiholes transpiercing the foil target help to enhance the laser-proton energy-conversion efficiency significantly. Particle-in-cell 2.5-dimensional ($x$, $y$, $v_x$, $v_y$, $v_z$) simulations present that the total laser-proton energy-conversion efficiency becomes 9.3% for the multihole target, though the energy-conversion efficiency is 1.5% for a plain thin-foil target. The maximum proton energy is $10.0\mathrm{MeV}$ for the multihole target and is $3.14\mathrm{MeV}$ for the plain target. The transpiercing multihole target serves as a new method to increase the energy-conversion efficiency from laser to ions.

We present experimental results on relaxation dynamics of $\lambda$-DNA and T4 polymer molecules toward a steady state in elongation flow. Strong critical slowing down (similar to the well-known effect in continuous phase transitions) in polymer relaxation near the coil-stretch transition (CST) is quantitatively investigated and found to be in good accord with predictions. For polymers with a small number of Kuhn segments the maximum of the relaxation time vs the strain rate provides precise information about the location of the CST and serves as its criterion.

In this paper we extend the branching aftershock sequence model to study the role of missing data at short times and small amplitudes after a mainshock. We apply this model, which contains three parameters characterizing the missing data, to the magnitude and temporal statistics of four aftershock sequences in California. We find that the observed time-dependent deviations of the frequency-magnitude scaling from the Gutenberg-Richter power law dependency can be described quantitatively by the model. We also show that, for the same set of parameters, the model is able to explain quantitatively the observed magnitude-dependent deviations of the temporal decay of aftershocks from Omori’s law. In addition, we show that the same sets of data can also reproduce quite well the various functional forms of the probability density functions of the return times between consecutive events with magnitudes above a prescribed threshold, as well as the violation of scaling at short and intermediate time scales.

Collision statistics of hard-core systems (thermal and dissipative) is investigated through the velocity-correlation distributions after $n$ collisions of a tagged hard-core particle: These quantities provide information on the velocity correlations for a given number of collisions. We obtain exact results for arbitrary dimension for the velocity-correlation distribution after the first collision as well as for the velocity-correlation function after an infinite number of collisions. For Gaussian velocity distributions, we show that the decay of the first-collision velocity-correlation distribution for negative argument is always exponential in any dimension; the decay rate is then a function of the mass and the coefficient of restitution. For granular gases, where deviations from Gaussian are relevant, expressions including Sonine corrections are also derived for the velocity-correlation distribution and a comparison with a direct simulation Monte Carlo (DSMC) shows accurate agreement with theoretical results. We emphasize that these quantities can be easily obtained in simulations and most likely also in experiments: therefore they could be an efficient probe of the local environment and of the degree of inelasticity of the collisions.

We present a systematic study of dynamical heterogeneity in a model for permanent gels upon approaching the gelation threshold. We find that the fluctuations of the self-intermediate scattering function are increasing functions of time, reaching a plateau whose value, at large length scales, coincides with the mean cluster size and diverges at the percolation threshold. Another measure of dynamical heterogeneities—i.e., the fluctuations of the self-overlap—displays instead a peak and decays to zero at long times. The peak, however, also scales as the mean cluster size. Arguments are given for this difference in the long-time behavior. We also find that the non-Gaussian parameter reaches a plateau in the long-time limit. The value of the plateau of the non-Gaussian parameter, which is connected to the fluctuations of diffusivity of clusters, increases with the volume fraction and remains finite at the percolation threshold.

In a recent paper we introduced two Potts-like models in three dimensions, which share the following properties: (A) One of the ice rules is always fulfilled (in particular also at infinite temperature, $\beta =0$). (B) Both ice rules hold for ground-state configurations. This allowed for an efficient calculation of the residual entropy of ice I (ordinary ice) by means of multicanonical simulations. Here we present the thermodynamics of these models in more details. Despite their similarities with Potts models, no sign of a disorder-order phase transition is found.

The Lynden-Bell statistics has been proposed to explain common features among galaxies, which are not in thermal equilibrium. The statistics is not successful to reproduce energy distribution in the one-dimensional self-gravitating sheet model except for initial states near the virial equilibrium. The breakdown is caused by dynamically accelerated high-energy sheets, and hence a modified statistics is examined by focusing on low-energy sheets in order to clarify validity of the basic idea of the Lynden-Bell statistics. The modification improves agreement between the theoretical and numerical energy distributions in a wide interval of the initial virial ratio.

We investigate the transport mechanism of a small hydrophobic solute molecule across two types of fluid interfaces, (i) an interface between two immiscible liquids and (ii) a surfactant-covered liquid-liquid interface. These systems are modeled by coarse-grained molecular dynamics simulations. It is demonstrated that the dynamics of the solute molecule near the interface significantly deviates from Markovian Brownian motion. Specifically, the correlation time of the random force acting on the solute strongly depends on the distance between the solute and the interface and increases by two orders of magnitude within a very narrow (less than $1\mathrm{nm}$ wide) region near the interface. The slow fluctuations of the random force in this narrow region are caused by capillary waves. The region location and width are determined by interface protrusions caused by attraction between the solute and the hydrophobic phase. We use results of molecular dynamics simulations to develop a stochastic model for the coupled solute-interface dynamics and estimate the rate of the solute transport across the interface. The observed phenomenon appears to be a general feature of mass transport across fluid or flexible membranes. The coupling between the solute transport and the interface fluctuations is the strongest in areas corresponding to a large free energy gradient or near a free energy barrier for the solute transport. This suggests a strong influence of the coupled solute-interface dynamics on the rate of mass transfer across interfaces.

The dielectric strength is shown to increase and the relaxation frequency to decrease for a large temperature range up to a certain value of the electric field in the smectic-$A^{*}$ phase. This behavior contrasts to that observed in a conventional smectic-$A^{*}$, but can be explained in terms of de Vries scenerio. On assuming the reorientation of the molecular dipoles with electric field to be of the Langevin type in the de Vries smectic-$A^{*}$, we find that around $1300\text{molecules}$, corresponding to a minimum correlation length of ${\xi }_{\perp }\approx 45\mathrm{nm}$ in a single layer cooperatively respond to the applied field.

We report effects of polyethylene glycol (PEG, molecular weight of $35\mathrm{kDa}$) on microtubule (MT) bundling and pattern formation. Without PEG, polymerizing tubulin solutions of a few mg/ml that are initially subjected to a field that aligns MTs can spontaneously form striated birefringence patterns. These patterns form through MT alignment, bundling, and coordinated bundle buckling. With increasing PEG concentrations, solutions form progressively weaker patterns. At a sufficiently high PEG concentration ($\sim 0.5\%$ by weight), the samples maintain a nearly uniform birefringence (i.e., no pattern) and laterally contract at a later stage. Concomitantly, on a microscopic level, the network of dispersed MTs that accompany the bundles in pure solutions disappear and the bundles become more distinct. We attribute the weakening of the pattern to the loss of the dispersed MT network, which is required to mediate the coordination of bundle buckling. We propose that the loss of the dispersed network and the enhanced bundling result from PEG associated osmotic forces that drive MTs together and osmotic torques that facilitate their bundling. Similarly, we attribute the lateral contraction of the samples to osmotic torques that tend to align crossing bundles in the network.

We study the scaling of two-dimensional crack roughness using large scale beam lattice systems. Our results indicate that the crack roughness obtained using beam lattice systems does not exhibit anomalous scaling in sharp contrast to the simulation results obtained using scalar fuse lattices. The local and global roughness exponents (${\zeta }_{\mathrm{loc}}$ and $\zeta$, respectively) are equal to each other, and the two-dimensional crack roughness exponent is estimated to be ${\zeta }_{\mathrm{loc}}=\zeta =0.64\pm 0.02$. Removal of overhangs (jumps) in the crack profiles eliminates even the minute differences between the local and global roughness exponents. Furthermore, removing these jumps in the crack profile completely eliminates the multiscaling observed in other studies. We find that the probability density distribution $p\left[\Delta h\left(l\right)\right]$ of the height differences $\Delta h\left(l\right)=[h(x+l)-h\left(x\right)]$ of the crack profile obtained after removing the jumps in the profiles follows a Gaussian distribution even for small window sizes $\left(l\right)$.

Multiagent models have been used in many contexts to study generic collective behavior. Similarly, complex networks have become very popular because of the diversity of growth rules giving rise to scale-free behavior. Here we study adaptive networks where the agents trade “wealth” when they are linked together while links can appear and disappear according to the wealth of the corresponding agents; thus the agents influence the network dynamics and vice versa. Our framework generalizes a multiagent model of Bouchaud and Mézard [Physica A 282, 536 (2000)], and leads to a steady state with fluctuating connectivities. The system spontaneously self-organizes into a critical state where the wealth distribution has a fat tail and the network is scale free; in addition, network heterogeneities lead to enhanced wealth condensation.