We investigated the scaling of the hydrodynamic velocity fluctuations and self-diffusion in the sedimentation of monodispersed spherical particles via direct numerical simulations using the smoothed profile method over a moderate range of volume fractions $(0.01\le \varphi \le 0.12)$. Hydrodynamic velocity fluctuations are visible at large Peclet numbers (Pe), and they scale as ${(\varphi L/a)}^{1/2}$ at low volume fractions ($\varphi \le 0.04$). Their characteristics become independent of volume fraction at moderate volume fractions ($0.06\le \varphi \le 0.12$). Both vertical and horizontal self-diffusion coefficients scale as ${(L/a)}^{3/2}{\varphi }^{1/2}$ at low volume fractions. At moderate volume fractions, the vertical diffusion scales as ${(L/a)}^{3/2}{\varphi }^{-1/2}$; in contrast, the horizontal diffusion is saturated with respect to volume fraction. The diffusion anisotropy increases with increasing Pe and saturates at high Pe values. The saturated value remains unchanged at low volume fractions, whereas further increase in the volume fraction decreases this anisotropy. The reduction of this anisotropy is attributed to the ${\varphi }^{-1/2}$ scaling of the vertical relaxation time at moderate volume fractions; however, the horizontal relaxation time is independent of the volume fraction at this regime.

We investigate the effects of the range of adsorption potential on the equilibrium behavior of a single polymer chain end-attached to a solid surface. The exact analytical theory for ideal lattice chains interacting with a planar surface via a box potential of depth $U$ and width $W$ is presented and compared to continuum model results and to Monte Carlo (MC) simulations using the pruned-enriched Rosenbluth method for self-avoiding chains on a simple cubic lattice. We show that the critical value $U_c$ corresponding to the adsorption transition scales as $W^{-1/\nu }$, where the exponent $\nu =1/2$ for ideal chains and $\nu \approx 3/5$ for self-avoiding walks. Lattice corrections for finite $W$ are incorporated in the analytical prediction of the ideal chain theory $U_c\approx \left(\frac{{\pi }^2}{24}\right){(W+1/2)}^{-2}$ and in the best-fit equation for the MC simulation data $U_c=0.585{(W+1/2)}^{-5/3}$. Tail, loop, and train distributions at the critical point are evaluated by MC simulations for $1\le W\le 10$ and compared to analytical results for ideal chains and with scaling theory predictions. The behavior of a self-avoiding chain is remarkably close to that of an ideal chain in several aspects. We demonstrate that the bound fraction $\theta$ and the related properties of finite ideal and self-avoiding chains can be presented in a universal reduced form: $\theta (N,U,W)=\theta (N{U}_c,U/U_c)$. By utilizing precise estimations of the critical points we investigate the chain length dependence of the ratio of the normal and lateral components of the gyration radius. Contrary to common expectations this ratio attains a limiting universal value $\langle R_{g\perp }^2\rangle /\langle R_{g\parallel }^2\rangle =0.320\pm 0.003$ only at $N\sim 5000$. Finite-$N$ corrections for this ratio turn out to be of the opposite sign for $W=1$ and for $W\ge 2$. We also study the $N$ dependence of the apparent crossover exponent ${\varphi }_{\mathrm{eff}}\left(N\right)$. Strong corrections to scaling of order $N^{-0.5}$ are observed, and the extrapolated value $\varphi =0.483\pm 0.003$ is found for all values of $W$. The strong correction to scaling effects found here explain why for smaller values of $N$, as used in most previous work, misleadingly large values of ${\varphi }_{\mathrm{eff}}\left(N\right)$ were identified as the asymptotic value for the crossover exponent.

In the study of the evolution of cooperation, resource limitations are usually assumed just to provide a finite population size. Recently, however, it has been pointed out that resource limitation may also generate dynamical payoffs able to modify the original structure of the games. Here we study analytically a phase transition from a homogeneous population of defectors when resources are abundant to the survival of unconditional cooperators when resources reduce below a threshold. To this end, we introduce a model of simple agents, with no memory or ability of recognition, interacting in well-mixed populations. The result might shed light on the role played by resource constraints on the origin of multicellularity.

We investigate the properties of the threshold contact process (TCP), a process showing an absorbing-state phase transition with infinitely many absorbing states, on random complex networks. The finite-size scaling exponents characterizing the transition are obtained in a heterogeneous mean-field (HMF) approximation and compared with extensive simulations, particularly in the case of heterogeneous scale-free networks. We observe that the TCP exhibits the same critical properties as the contact process, which undergoes an absorbing-state phase transition to a single absorbing state. The accordance among the critical exponents of different models and networks leads to conjecture that the critical behavior of the contact process in a HMF theory is a universal feature of absorbing-state phase transitions in complex networks, depending only on the locality of the interactions and independent of the number of absorbing states. The conditions for the applicability of the conjecture are discussed considering a parallel with the susceptible-infected-susceptible epidemic spreading model, which in fact belongs to a different universality class in complex networks.

We study numerically the photon emission from a semiconductor microcavity containing $N\ge 2$ quantum wells under the influence of a periodic external forcing. The emission is determined by the interplay between external forcing and internal interaction between the wells. While the external forcing synchronizes the periodic motion, the internal interaction destroys it. The nonlinear term of the Hamiltonian supports the synchronization. The numerical results show a jump of the photon intensity to very large values at a certain critical value of the external forcing when the number of quantum wells is not too large. We discuss the dynamics of the system across this transition.

The multiplicity of stable convection patterns in a rotating spherical fluid shell heated from the inner boundary and driven by a central gravity field is presented. These solution branches that arise as rotating waves (RWs) are traced for varying Rayleigh number while their symmetry, stability, and bifurcations are studied. At increased Rayleigh numbers all the RWs undergo transitions to modulated rotating waves (MRWs) which are classified by their spatiotemporal symmetry. The generation of a third frequency for some of the MRWs is accompanied by a further loss of symmetry. Eventually a variety of MRWs, three-frequency solutions, and chaotic saddles and attractors control the dynamics for higher Rayleigh numbers.

We comprehensively analyze the emergence of anomalous statistics in the context of the random relaxation (RARE) model [Eliazar and Metzler, J. Chem. Phys. 137, 234106 (2012)], a recently introduced versatile model of random relaxations in random environments. The RARE model considers excitations scattered randomly across a metric space around a reaction center. The excitations react randomly with the center, the reaction rates depending on the excitations’ distances from this center. Relaxation occurs upon the first reaction between an excitation and the center. Addressing both the relaxation time and the relaxation range, we explore when these random variables display anomalous statistics, namely, heavy tails at zero and at infinity that manifest, respectively, exceptionally high occurrence probabilities of very small and very large outliers. A cohesive set of closed-form analytic results is established, determining precisely when such anomalous statistics emerge.

When the equations that govern the dynamics of a random field are nonlinear, the field can develop with time non-Gaussian statistics even if its initial condition is Gaussian. Here, we provide a general framework for calculating the effect of the underlying nonlinear dynamics on the relative densities of maxima and minima of a two-dimensional field. Using this simple geometrical probe, we can identify the size of the non-Gaussian contributions in the random field, or alternatively the magnitude of the nonlinear terms in the underlying equations of motion. We demonstrate our approach by applying it to an initially Gaussian field that evolves according to the deterministic KPZ equation, which models surface growth and shock dynamics.

Confined granular fluids, placed in a shallow box that is vibrated vertically, can achieve homogeneous stationary states due to energy injection mechanisms that take place throughout the system. These states can be stable even at high densities and inelasticities allowing for a detailed analysis of the hydrodynamic modes that govern the dynamics of granular fluids. By analyzing the decay of the time correlation functions it is shown that there is a crossover from a quasielastic regime in which energy evolves as a slow mode to an inelastic regime with energy slaved to the other conserved fields. The two regimes have well differentiated transport properties and in the inelastic regime the dynamics can be described by a reduced hydrodynamics with modified longitudinal viscosity and sound speed. The crossover between the two regimes takes place at a wave vector that is proportional to the inelasticity. A two-dimensional granular model, with collisions that mimic the energy transfers that take place in a confined system, is studied by means of microscopic simulations. The results show excellent agreement with the theoretical framework and allow validation of hydrodynamiclike models.

A multicomponent lattice Boltzmann scheme is used to investigate the surface coating of substrates with two topographical features by a gravity-driven thin liquid film. The considered topographies are $\mathsf{U}$- and $\mathsf{V}$-shaped grooves and mounds. For the case of substrates with two grooves, our results indicate that for each of the grooves there is a critical width such that if the groove width is larger than the critical width, the groove can be coated successfully. The critical width of each groove depends on the capillary number, the contact angle, the geometry, and the depth of that groove. The second groove critical width depends on, in addition, the geometry and the depth of the first groove; for two grooves with the same geometries and depths, it is at least equal to that of the first groove. If the second groove width lies between the critical widths, the second groove still can be coated successfully on the condition that the distance between the grooves is considered larger than a critical distance. For considered contact angles and capillary numbers our results indicate that the critical distance is a convex function of the capillary number and the contact angle. Our study also reveals similar results for the case of substrates with a mound and a groove.

We study smectic-liquid-crystal order in a cell with a heterogeneous substrate imposing surface random positional and orientational pinnings. Proposing a minimal random elastic model, we demonstrate that, for a thick cell, the smectic state without a rubbed substrate is always unstable at long scales and, for weak random pinning, is replaced by a smectic glass state. We compute the statistics of the associated substrate-driven distortions and the characteristic smectic domain size on the heterogeneous substrate and in the bulk. We find that for weak disorder, the system exhibits a three-dimensional temperature-controlled phase transition between a weakly and strongly pinned smectic glass states akin to the Cardy-Ostlund phase transition. We explore experimental implications of the predicted phenomenology and suggest that it provides a plausible explanation for the experimental observations on polarized light microscopy and x-ray scattering.

We describe the stable existence of quasi-one-dimensional solutions of the two-dimensional cubic-quintic complex Ginzburg-Landau equation for a large range of the bifurcation parameter. By quasi-one-dimensional (quasi-1D) in the present context, we mean solutions of fixed shape in one spatial dimension that are simultaneously fully extended and space filling in a second direction. This class of stable solutions arises for parameter values for which simultaneously other classes of solutions are at least locally stable: the zero solution, 2D fixed shape dissipative solitons, or 2D azimuthally symmetric or asymmetric exploding dissipative solitons. We show that quasi-1D solutions can form stable compound states with 2D stationary dissipative solitons or with azimuthally symmetric exploding dissipative solitons. In addition, we find stable breathing quasi-1D solutions near the transition to collapse. The analogy of several features of the work presented here to recent experimental results on convection by Miranda and Burguete [Phys. Rev. E 78, 046305 (2008); Phys. Rev. E 79, 046201 (2009)] is elucidated.

Nanoconfined liquid behavior is highly dependent on boundary and bulk factors. In this paper, we use a hybrid simulation method to investigate the variations of the velocity profile, temperature profile, slip length, and Kapitza length in nano-Poiseuille flows. They are determined by liquid behavior under the combined effect of boundary factors of solid-liquid bonding strength and surface roughness and bulk factors of the pressure gradient, maximum liquid velocity, flow rate, and dissipation heat. On the one hand, diverse variations of the profiles depend on the bulk factors. On the other hand, the boundary conditions of velocity slip and temperature jump, both strongly correlated to boundary factors, can significantly modify the velocity and temperature profiles. Based on this understanding, we find an explicitly local minimum value of the average temperature difference between liquid and solid when varying boundary and bulk factors lead to opposite influences. Moreover, we find that the Kapitza length varies as a power function of slip length and the index number depends on surface roughness but not on flow constraint. The results imply that by appropriately modifying the boundary and bulk factors, the confined liquid behavior is largely controllable.

Sand dunes are often covered by vegetation and biogenic crusts. Despite their significant role in dune stabilization, biogenic crusts have rarely been considered in model studies of dune dynamics. Using a simple model, we study the existence and stability ranges of different dune-cover states along gradients of rainfall and wind power. Two ranges of alternative stable states are identified: fixed crusted dunes and fixed vegetated dunes at low wind power; and fixed vegetated dunes and active dunes at high wind power. These results suggest a crossover between two different forms of desertification.

A Brownian refrigerator with the cold and hot reservoirs alternating along a space coordinate is established. The heat flux couples with the movement of the Brownian particles due to an external force in the spatially asymmetric but periodic potential. After using the Arrhenius factor to describe the behaviors of the forward and backward jumps of the particles, the expressions for coefficient of performance (COP) and cooling rate are derived analytically. Then, through maximizing the product of conversion efficiency and heat flux flowing out, a new upper bound only depending on the temperature ratio of the cold and hot reservoirs is found numerically in the reversible situation, and it is a little larger than the so-called Curzon and Ahlborn COP ${\varepsilon }_{\mathrm{CA}}=\left(1/\sqrt{1-\tau }\right)-1$. After considering the irreversible factor owing to the kinetic energy change of the moving particles, we find the optimized COP is smaller than ${\varepsilon }_{\mathrm{CA}}$ and the external force even does negative work on the Brownian particles when they jump from a cold to hot reservoir.

The phase diagram of the two- and three-state Potts model with infinite-range interactions in the external field is analyzed by studying the partition function zeros in the complex field plane. The tricritical point of the three-state model is observed as the approach of the zeros to the real axis at the nonzero field value. Different regimes, involving several first- and second-order transitions of the complicated phase diagram of the three-state model, are identified from the scaling properties of the zeros closest to the real axis. The critical exponents related to the tricritical point and the Yang-Lee edge singularity are well reproduced. Calculations are extended to the negative fields, where the exact implicit expression for the transition line is derived.

We examine the dynamics of two-dimensional colloidal systems using numerical simulations of a system with a drive applied to a thin region in the middle of the sample to produce a local shear. For a monodisperse colloidal assembly, we find a well-defined decoupling transition separating a regime of elastic motion from a plastic phase where the driven particles break away or decouple from the bulk particles and produce a shear band. For a bidisperse assembly, the onset of a bulk disordering transition coincides with the broadening of the shear band. We identify several distinct dynamical regimes that are correlated with features in the velocity-force curves. As a function of bidispersity, the decoupling force shows a nonmonotonic behavior associated with features in the noise fluctuations, power spectra, and bulk velocity profiles. When pinning is added in the bulk, we find that the shear band regions can become more localized, causing a decoupling of the driven particles from the bulk particles. For a system with thermal noise and no pinning, the shear band region becomes more extended and the average velocity of the driven particles drops at the thermal disordering transition of the bulk system.

Interfacial roughening denotes the nonequilibrium process by which an initially flat interface reaches its equilibrium state, characterized by the presence of thermally excited capillary waves. Roughening of fluid interfaces has been first analyzed by Flekkoy and Rothman [Phys. Rev. Lett. 75, 260 (1995)], where the dynamic scaling exponents in the weakly damped case in two dimensions were found to agree with the Kardar-Parisi-Zhang universality class. We extend this work by taking into account also the strong-damping regime and perform extensive fluctuating hydrodynamics simulations in two dimensions using the Lattice Boltzmann method. We show that the dynamic scaling behavior is different in the weakly and strongly damped case.

Nonlinear evolution of three-dimensional strained islands or quantum dots in heteroepitaxial thin films is studied via a continuum elasticity model and both perturbation analysis of the system and numerical simulations of the corresponding nonlinear dynamic equation governing the film morphological profile. Three regimes of island array evolution are identified and examined, including a film instability regime at early stage, a nonlinear coarsening regime at intermediate times, and the crossover to a saturated asymptotic state, with detailed behavior depending on film-substrate misfit strains but not qualitatively on finite system sizes. The phenomenon of island array stabilization, which corresponds to the formation of steady but nonordered arrays of strained quantum dots, occurs at later time for smaller misfit strain. It is found to be controlled by the strength of film-substrate wetting interaction which would constrain the valley-to-peak mass transport and hence the growth of island height, and also determined by the effect of elastic interaction between surface islands and the high-order strain energy of individual islands at late evolution stage. The results are compared to previous experimental and theoretical studies on quantum dot coarsening and stabilization.