We show that the statistics of a turbulent passive scalar at scales larger than the pumping may exhibit multiscaling due to a weaker mechanism than the presence of statistical conservation laws. We develop a general formalism to give explicit predictions for the large scale scaling exponents in the case of the Kraichnan model and discuss their geometric origin at small and large scale.

We study the effects of degree-degree correlations on the success of cooperation in an evolutionary prisoner’s dilemma played on a random network. When degree-degree correlations are not present, the standardized variance of the network’s degree distribution has been shown to be an accurate analytical measure of network heterogeneity that can be used to predict the success of cooperation. In this paper, we use a local-mechanism interpretation of standardized variance to give a generalization to graphs with degree-degree correlations. Two distinct mechanisms are shown to influence cooperation levels on these types of networks. The first is an intrinsic measurement of base-line heterogeneity coming from the network’s degree distribution. The second is the increase in heterogeneity coming from the degree-degree correlations present in the network. A strong linear relationship is found between these two parameters and the average cooperation level in an evolutionary prisoner’s dilemma on a network.

Given a large and complex network, we would like to find the partition of this network into a small number of clusters. This question has been addressed in many different ways. In a previous paper, we proposed a deterministic framework for an optimal partition of a network as well as the associated algorithms. In this paper, we extend this framework to a probabilistic setting, in which each node has a certain probability of belonging to a certain cluster. Two classes of numerical algorithms for such a probabilistic network partition are presented and tested. Application to three representative examples is discussed.

We study the localization properties of eigenvectors of the Google matrix, generated both from the world wide web and from the Albert-Barabási model of networks. We establish the emergence of a delocalization phase for the PageRank vector when network parameters are changed. For networks with localized PageRank, eigenvalues of the matrix in the complex plane with a modulus above a certain threshold correspond to localized eigenfunctions while eigenvalues below this threshold are associated with delocalized relaxation modes. We argue that, for networks with delocalized PageRank, the efficiency of information retrieval by Google-type search is strongly affected since the PageRank values have no clear hierarchical structure in this case.

A hybrid lattice Boltzmann method (LBM) for binary mixtures based on the free-energy approach is proposed. Nonideal terms of the pressure tensor are included as a body force in the LBM kinetic equations, used to simulate the continuity and Navier-Stokes equations. The convection-diffusion equation is studied by finite-difference methods. Differential operators are discretized in order to reduce the magnitude of spurious velocities. The algorithm has been shown to be stable and reproducing the correct equilibrium behavior in simple test configurations and to be Galilean invariant. Spurious velocities can be reduced by approximately an order of magnitude with respect to standard discretization procedure.

We examine the ordering behavior of the ferromagnetic Ising lattice model defined on a surface with a constant negative curvature. Small-sized ferromagnetic domains are observed to exist at temperatures far greater than the critical temperature, at which the inner-core region of the lattice undergoes a mean-field phase transition. The survival of short-range order at such high temperatures can be attributed to strong boundary-spin contributions to the ordering mechanism as a result of which boundary effects remain active even within the thermodynamic limit. Our results are consistent with the previous finding of disorder-free Griffiths phase that is stable at temperatures lower than the mean-field critical temperature.

A generalization of the functional form of the anchoring energy of a nematic liquid crystal in contact with a structured surface is proposed. The structured surface is represented by side-chain polymer, containing only aliphatic or aliphatic and mesogenic side groups, deposited as a thin alignment film onto a solid substrate. The basic assumption in the model developed in the present work is that the coupling between the polymer side groups and the nematic liquid crystal molecules is responsible for the elastic deformation and compression of the orienting groups taking place in the alignment film. We show that in the limit of small deformations, the surface energy is the same as the one given by the Rapini-Papoular approximation. In this limit, the effective anchoring strength is weak and is due to the elastic deformation of the orienting side groups, which is proportional to the inverse of the length of the aliphatic groups and the length of the linkage group of the mesogens, respectively. In the limit of large deformation, however, the term accounting the film compression is predominant which results in a nonzero torque facilitating the relaxation process of an imposed deformation when the applied electric field is switched off. Good agreement is found between the prediction of our model and the experimental data of the anchoring energy of a nematic liquid crystal aligned by means of Langmuir-Blodgett monolayers of fatty acids as a function of the length of their alkyl chains.

Steady dynamics of coupled conductance-based integrate-and-fire neuronal networks in the limit of small fluctuations is studied via the equilibrium states of a Fokker-Planck equation. An asymptotic approximation for the membrane-potential probability density function is derived and the corresponding gain curves are found. Validity conditions are discussed for the Fokker-Planck description and verified via direct numerical simulations.

The propagation of extreme events in space is analyzed for a class of dynamical systems giving rise to spatiotemporal chaos. It is shown that this process can be mapped into a generalized random walk, whereby the mean square displacement increases linearly in time and there is a nonvanishing probability for jumps beyond first neighbors. The relative roles of the local dynamics and of the spatial coupling are identified.

Laser-induced fluorescence of two-photon excited $8p$, $9p$, $J=0,2$ and $5f$, $6f$, $J=2$ levels in neutral xenon has been investigated in the pressure regime between 4 and 120 Pa. Radiative lifetimes and collisional deactivation rates have been deduced especially for the $5f{\left[3/2\right]}_2$, $5f{\left[5/2\right]}_2$, and $8p{\left[1/2\right]}_0$ levels using the Stern-Volmer approach. The spontaneous lifetimes for $5f{\left[3/2\right]}_2$, $5f{\left[5/2\right]}_2$, and $8p{\left[1/2\right]}_0$ levels are 94, 78, and 207 ns, respectively. These lifetimes have been calculated also by applying extended multiconfiguration Dirac-Fock wave functions and are found in agreement with experiment within $10–25\%$.

Depth dependence of vertical plunging force in granular medium is studied experimentally by measuring the slow-pushing force of different size and shape objects intruding vertically into a granular bed. It is found that all of the force curves of fully immersed intruders have concave-to-convex transition. The depth dependence of the force turns from supralinear to sublinear. By studying the properties of the inflection point of the concave-convex transition, we find that the plunging force at inflection point is proportional to intruder’s volume, and the inflection point occurs when the intruder is fully buried to a level around twice its diameter. Testing by plunging a long cylinder, which is always partially immersed, we find no inflection point in this case, which verifies that the inflection of the plunging force is related to the filled-in loose granules on top of the intruder. The slowdown of the increasing rate of the force is, therefore, not a result of sidewall support proposed by previous researchers.

The microstructure of coagulated colloidal particles, for which the interparticle potential is described by the Derjaguin-Landau-Verweg-Overbeek theory, is strongly influenced by the particles’ surface potential. Depending on its value, the resulting microstructures are either more “homogeneous” or more “heterogeneous,” at equal volume fractions. An adequate quantification of a structure’s degree of heterogeneity (DOH), however, does not yet exist. In this work, methods to quantify and thus classify the DOH of microstructures are investigated and compared. Three methods are evaluated using particle packings generated by Brownian dynamics simulations: (1) the pore size distribution, (2) the density-fluctuation method, and (3) the Voronoi volume distribution. Each method provides a scalar measure, either via a parameter in a fit function or an integral, which correlates with the heterogeneity of the microstructure and which thus allows to quantitatively capture the DOH of a granular material. An analysis of the differences in the density fluctuations between two structures additionally allows for a detailed determination of the length scale on which differences in heterogeneity are most pronounced.

Small organisms (e.g., bacteria) and artificial microswimmers move due to a combination of active swimming and passive Brownian motion. Considering a simplified linear three-sphere swimmer, we study how the swimmer size regulates the interplay between self-driven and diffusive behavior at low Reynolds number. Starting from the Kirkwood-Smoluchowski equation and its corresponding Langevin equation, we derive formulas for the orientation correlation time, the mean velocity and the mean-square displacement in three space dimensions. The validity of the analytical results is illustrated through numerical simulations. Tuning the swimmer parameters to values that are typical of bacteria, we find three characteristic regimes: (i) Brownian motion at small times, (ii) quasiballistic behavior at intermediate time scales, and (iii) quasidiffusive behavior at large times due to noise-induced rotation. Our analytical results can be useful for a better quantitative understanding of optimal foraging strategies in bacterial systems, and they can help to construct more efficient artificial microswimmers in fluctuating fluids.

The concept of information mobility in complex networks is introduced on the basis of a stochastic process taking place in the network. The transition matrix for this process represents the probability that the information arising at a given node is transferred to a target one. We use the fractional powers of this transition matrix to investigate the stochastic process at fractional time intervals. The mobility coefficient is then introduced on the basis of the trace of these fractional powers of the stochastic matrix. The fractional time at which a network diffuses 50% of the information contained in its nodes $\left(1/k_{50}\right)$ is also introduced. We then show that the scale-free random networks display a better spread of information than the non-scale-free ones. We study 38 real-world networks and analyze their performance in spreading information from their nodes. We find that some real-world networks perform even better than the scale-free networks with the same average degree and we point out some of the structural parameters that make this possible.

A three-dimensional model of laminar flow in microchannels is numerically analyzed incorporating surface roughness effects as characterized by fractal geometry. The Weierstrass-Mandelbrot function is proposed to characterize the multiscale self-affine roughness. The effects of Reynolds number, relative roughness, and fractal dimension on laminar flow are all investigated and discussed. The results indicate that unlike flow in smooth microchannels, the Poiseuille number in rough microchannels increases linearly with the Reynolds number, Re, and is larger than what is typically observed in smooth channels. For these situations, the flow over surfaces with high relative roughness induces recirculation and flow separation, which play an important role in single-phase pressure drop. More specifically, surfaces with the larger fractal dimensions yield more frequent variations in the surface profile, which result in a significantly larger incremental pressure loss, even though at the same relative roughness. The accuracy of the predicted Poiseuille number as calculated by the present model is verified using experimental data available in the literature.

We investigate three-dimensional magnetohydrodynamics turbulence in the presence of velocity and magnetic shear (i.e., with both a large-scale shear flow and a nonuniform magnetic field). By assuming a turbulence driven by an external forcing with both helical and nonhelical spectra, we investigate the combined effect of these two shears on turbulence intensity and turbulent transport represented by turbulent diffusivities (turbulent viscosity, $\alpha$ and $\beta$ effect) in Reynolds-averaged equations. We show that turbulent transport (turbulent viscosity and diffusivity) is quenched by a strong flow shear and a strong magnetic field. For a weak flow shear, we further show that the magnetic shear increases the turbulence intensity while decreasing the turbulent transport. In the presence of a strong flow shear, the effect of the magnetic shear is found to oppose the effect of flow shear (which reduces turbulence due to shear stabilization) by enhancing turbulence and transport, thereby weakening the strong quenching by flow shear stabilization. In the case of a strong magnetic field (compared to flow shear), magnetic shear increases turbulence intensity and quenches turbulent transport.

The social networks that infectious diseases spread along are typically clustered. Because of the close relation between percolation and epidemic spread, the behavior of percolation in such networks gives insight into infectious disease dynamics. A number of authors have studied percolation or epidemics in clustered networks, but the networks often contain preferential contacts in high degree nodes. We introduce a class of random clustered networks and a class of random unclustered networks with the same preferential mixing. Percolation in the clustered networks reduces the component sizes and increases the epidemic threshold compared to the unclustered networks.

We investigate a model of transportation networks with nonlinear elements which may represent local shortage of resources. Frustrations arise from competition for resources. When the initial resources are uniform, different regimes with discrete fractions of satisfied nodes are observed, resembling the Devil’s staircase. We demonstrate how functional recursions are converted to simple recursions of probabilities. Behaviors similar to those in the vertex cover or close packing problems are found. When the initial resources are bimodally distributed, increases in the fraction of rich nodes induce a glassy transition, entering an algorithmically hard regime.

Aging is always present, tailoring our interactions with others, and postulating a finite lifespan during which we are able to exercise them. We consider the prisoner’s dilemma game on a square lattice and examine how quenched age distributions and different aging protocols influence the evolution of cooperation when taking the life experience and knowledge accumulation into account as time passes. In agreement with previous studies, we find that a quenched assignment of age to players, introducing heterogeneity to the game, substantially promotes cooperative behavior. Introduction of aging and subsequent death as a coevolutionary process may act detrimental on cooperation but enhances it efficiently if the offspring of individuals that have successfully passed their strategy is considered newborn. We study resulting age distributions of players and show that the heterogeneity is vital—yet insufficient—for explaining the observed differences in cooperator abundance on the spatial grid. The unexpected increment of cooperation levels can be explained by a dynamical effect that has a highly selective impact on the propagation of cooperator and defector states.

The dynamics of red blood cells (RBCs) in simple shear flow was studied using a theoretical approach based on three variables: a shape parameter, the inclination angle $\theta$, and phase angle $\varphi$ of the membrane rotation. At high shear rate and low viscosity contrast of internal fluid, RBCs exhibit tank-treading motion, where $\varphi$ rotates with swinging oscillation of shape and $\theta$. At low shear rate, tumbling motion occurs and $\theta$ rotates. In the middle region between these two phases, it is found that synchronized rotation of $\varphi$ and $\theta$ with integer ratios of the frequencies occurs in addition to intermittent rotation. These dynamics are robust to the modification of the potential of the RBC shape and membrane rotation. Our results agree well with recent experiments.