We study numerically the spectrum and eigenstate properties of the Google matrix of various examples of directed networks such as vocabulary networks of dictionaries and university World Wide Web networks. The spectra have gapless structure in the vicinity of the maximal eigenvalue for Google damping parameter $\alpha$ equal to unity. The vocabulary networks have relatively homogeneous spectral density, while university networks have pronounced spectral structures which change from one university to another, reflecting specific properties of the networks. We also determine specific properties of eigenstates of the Google matrix, including the PageRank. The fidelity of the PageRank is proposed as a characterization of its stability.

Rheology of a dilute suspension of liquid-filled elastic capsules in linear shear flow is studied by three-dimensional numerical simulations using a front-tracking method. This study is motivated by a recent discovery that a suspension of viscous vesicles exhibits a shear viscosity minimum when the vesicles undergo an unsteady vacillating-breathing dynamics at the threshold of a transition between the tank-treading and tumbling motions. Here we consider capsules of spherical resting shape for which only a steady tank-treading motion is observed. A comprehensive analysis of the suspension rheology is presented over a broad range of viscosity ratio (ratio of internal-to-external fluid viscosity), shear rate (or, capillary number), and capsule surface-area dilatation. We find a result that the capsule suspension exhibits a shear viscosity minimum at moderate values of the viscosity ratio, and high capillary numbers, even when the capsules are in a steady tank-treading motion. It is further observed that the shear viscosity minimum exists for capsules with area-dilating membranes but not for those with nearly incompressible membranes. Nontrivial results are also observed for the normal stress differences which are shown to decrease with increasing capillary number at high viscosity ratios. Such nontrivial results neither can be predicted by the small-deformation theory nor can be explained by the capsule geometry alone. Physical mechanisms underlying these results are studied by decomposing the particle stress tensor into a contribution due to the elastic stresses in the capsule membrane and a contribution due to the viscosity differences between the internal and suspending fluids. It is shown that the elastic contribution is shear-thinning, but the viscous contribution is shear thickening. The coupling between the capsule geometry and the elastic and viscous contributions is analyzed to explain the observed trends in the bulk rheology.

We study the evolution of cooperation in spatial public goods games with four competing strategies: cooperators, defectors, punishing cooperators, and punishing defectors. To explore the robustness of the cooperation-promoting effect of costly punishment, besides the usual strategy adoption dynamics we also apply strategy mutations. As expected, frequent mutations create kind of well-mixed conditions, which support the spreading of defectors. However, when the mutation rate is small, the final stationary state does not significantly differ from the state of the mutation-free model, independently of the values of the punishment fine and cost. Nevertheless, the mutation rate affects the relaxation dynamics. Rare mutations can largely accelerate the spreading of costly punishment. This is due to the fact that the presence of defectors breaks the balance of power between both cooperative strategies, which leads to a different kind of dynamics.

In this paper, we investigate the non-Markovian heat transfer between a weakly damped harmonic oscillator (system) and a thermal bath. When the system is initially in a thermal state and not correlated with the environment, the mean energy of the system always first increases, then oscillates, and finally reaches equilibrium with the bath, no matter what the initial temperature of the system is. Moreover, the heat transfer between the system and the bath can be controlled by fast bang-bang modulation. This modulation does work on the system, and temporarily inverts the direction of heat flow. In this case, the common sense that heat always transfers from hot to cold does not hold any more. At the long time scale, a new dynamic equilibrium is established between the system and the bath. At this equilibrium, the energy of the system can be either higher or lower than its normal equilibrium value. A comprehensive analysis of the relationship between the dynamic equilibrium and the parameters of the modulation as well as the environment is presented.

We present the temperature dependence of $\alpha$-relaxation times of 13 glass formers determined from broadband dielectric spectroscopy, also including data from aging measurements. The data sets partly cover relaxation-time ranges of up to 16 decades enabling a critical test of the validity of model predictions. For this purpose, the data are provided for electronic download. Here we employ these results to test the applicability of the Vogel-Fulcher-Tammann equation and a recently proposed new approach that was demonstrated to provide superior fits of a vast collection of viscosity data.

We report the appearance of a spatially segregated state in a microsphere as a result of cooperation between actin filaments and giant DNA molecules. When the coexisting actin concentration is high enough, DNA molecules are excluded toward the surface by forming an assembly with actin filaments. With a decrease in the actin concentration, actin filaments tend to dissolve within the sphere whereas DNA molecules remain to be excluded onto the surface. When the actin concentration becomes still lower, DNA molecules dissolve within the sphere by avoiding surface attachment. We interpret these experimental trends by introducing the concept of an “exclusion zone” for actin filaments within a microsphere.

The blood clotting enzyme thrombin converts fibrinogen molecules into fibrin monomers which polymerize to form a fibrous three-dimensional gel. The concentration of thrombin affects the architecture of the resulting gel, in particular, a higher concentration of thrombin produces a gel with more branch points per unit volume and with shorter fiber segments between branch points. We propose a mechanism by which fibrin branching can occur and show that this mechanism can lead to dependence of the gel’s structure (at the time of gelation) on the rate at which monomer is supplied. A higher rate of monomer supply leads to a gel with a higher branch concentration and with shorter fiber segments between branch points. The origin of this dependence is explained.

We study the existence and stability of synchronous solutions in a continuum field of nonlocally coupled identical phase oscillators with distance-dependent propagation delays. We present a comprehensive stability diagram in the parameter space of the system. From the numerical results, a heuristic synchronization condition is suggested and an analytic relation for the marginal stability curve is obtained. We also provide an expression in the form of a scaling relation that closely follows the marginal stability curve over the complete range of the nonlocality parameter.

We use scaling arguments and coarse-grained Monte Carlo simulations to study the fluctuation-mediated interactions between a pair of adhesion sites of a bilayer membrane and a supporting surface. We find that the potential of mean force is an infinitely long range attractive potential that grows logarithmically with the pair distance $r$: $\varphi \left(\vec{r}\right)/k_{B}T=c\text{ln}r$, where the constant $c=2$ and $c=1$ for nonstressed and stressed membranes, respectively. When, in addition to excluded volume repulsion, the membrane also interacts with the underlying surface through a height-dependent attractive potential, the potential $\varphi \left(\vec{r}\right)$ is screened at large pair distances.

We investigate the wetting behavior of liquid droplets on rough hydrophobic substrates for the case of droplets that are of comparable size to the surface asperities. Using a simple three-dimensional analytical free-energy model, we have shown in a recent letter [M. Gross, F. Varnik, and D. Raabe, EPL 88, 26002 (2009)] that, in addition to the well-known Cassie-Baxter and Wenzel states, there exists a further metastable wetting state where the droplet is immersed into the texture to a finite depth, yet not touching the bottom of the substrate. Due to this new state, a quasistatically evaporating droplet can be saved from going over to the Wenzel state and instead remains close to the top of the surface. In the present paper, we give an in-depth account of the droplet behavior based on the results of extensive computer simulations and an improved theoretical model. In particular, we show that releasing the assumption that the droplet is pinned at the outer edges of the pillars improves the analytical results for larger droplets. Interestingly, all qualitative aspects, such as the existence of an intermediate minimum and the “reentrant transition,” remain unchanged. We also give a detailed description of the evaporation process for droplets of varying sizes. Our results point out the role of droplet size for superhydrophobicity and give hints for achieving the desired wetting properties of technically produced materials.

We present a study of thermotropic smectic liquid crystal films in aqueous environment. Macroscopic freely suspended films in water with a size up to $7.4\times 15{\text{mm}}^2$ were prepared with the help of a surfactant, which ensures a strong homeotropic anchoring at liquid crystal/water interfaces. The films were studied by optical microscopy and ellipsometry. Attention was paid to the stability and the thinning transitions which occurred at temperatures above the bulk smectic-$A$-isotropic transition temperature. In addition, we investigated the formation and rupture kinetics of thin smectic membranes separating water droplets in microfluidic devices. Besides possible applications in discrete microfluidics, smectic films in aqueous environment may expand the general range of possible studies of freely suspended smectic films.

Slowing down of the relaxation of the fluctuations around equilibrium is investigated both by stochastic simulations and by analysis of master equation of reversible reaction networks consisting of reactions between a pair of resource and the corresponding high-energy product that works as a catalyst for another resource-product reaction. As the number of molecules $N$ is decreased, the relaxation time to equilibrium is prolonged due to the deficiency of catalysts, as demonstrated by the amplification compared to that by the continuum limit. This amplification ratio of the relaxation time is represented by a scaling function as $h=N\text{exp}\left(-\beta V\right)$, and it becomes prominent as $N$ becomes less than a critical value $h\sim 1$, where $\beta$ is the inverse temperature and $V$ is the energy required to the transformation from resources to the corresponding products.

We use the damage spreading method to investigate the spectra of connected spin avalanches in the exponential networks and the scale-free networks with antiferromagnetically coupled spins. The results suggest that the avalanche spectra are characterized by the same statistics as the degree distribution in their home networks. Further, the obtained mean range $Z$ of an avalanche, i.e., the maximal distance reached by an avalanche from the damaged site, scales with the avalanche size $s$ as $Z/N^{\beta }=f\left(s/N^{\alpha }\right)$, where $\alpha =0.5$ and $\beta =0.33$. These values are true for both kinds of networks for the number $M$ of nodes to which new nodes are attached between 4 and 10; a check for $M=25$ confirms these values as well.

We study the splitting of regular square lattices subject to stochastic intermittent flows. Various flow patterns are produced by different groupings of the nodes, based on their random alternation between two possible states. The resulting flows on the lattices decrease with the number of groups according to a power law. By Monte Carlo simulations we reveal how the time span until the occurrence of a splitting depends on the flow patterns. Increasing the flow fluctuation frequency shortens this time span, which reaches a minimum before rising again due to inertia effects incorporated in the model. The size of the largest connected component after the splitting is rather independent of the flow fluctuation frequency but slightly decreases with the link capacities. Our findings carry important implications for real-world networks, such as electric power grids with a large share of renewable intermittent energy sources.

We study the spatiotemporal patterns in coupled circle maps on a small-world network. This system shows a rich phase diagram with several interesting phases. In particular, we make a detailed study of transition from clustered phase to spatiotemporal chaos. In the clustered state, observed at smaller coupling values, some sites stay close to the fixed point forever while others explore a larger part of the phase space. For stronger coupling, there is a transition to spatiotemporal chaos where no site stays close to fixed point forever. We study this transition as a dynamic phase transition. Persistence acts as a good order parameter for this transition. We find that this transition is continuous. We also briefly discuss other phases observed in this system.

Enhancing the synchronization of dynamical networks is of great interest to those designing and analyzing many man-made and natural systems. In this work, we investigate how network topology can be evolved to improve this property through the rewiring of edges. A computational tool called NETEVO performs this task using a simulated annealing metaheuristic. In contrast to other work which considers topological attributes when assessing current performance, we instead take a dynamical approach using simulated output from the system to direct the evolution of the network. Resultant topologies are analyzed using standard network measures, $B$ matrices, and motif distributions. These uncover the convergence of many similar features for all our networks, highlighting also significant differences between those evolved using topological rather than dynamical performance measures.

Two-component liquid-liquid Poiseuille flow through a circular pipe with a “Y junction” has been investigated theoretically, but few experimental studies exist. Here we report a simple microfluidic two-component flow measurement in a capillary tube with magnetic-resonance imaging (MRI). Velocity mapping of both liquids has been achieved using spin-echo pure phase encoding techniques combined with chemical shift imaging. Images of $32\times 32\mu {\text{m}}^2$ resolution were obtained for a channel of circular cross section (internal radius $R=400\mu \text{m}$). The results are in agreement with the theoretical prediction of liquid-liquid flow. This report is to validate theoretical liquid-liquid Poiseuille velocity distribution predictions with a high-resolution MRI method. This MRI method is shown to be a versatile tool for the study of multicomponent flow in microfluidic systems.

The dynamics of microcapsules in steady shear flow were studied using a theoretical approach based on three variables: the Taylor deformation parameter ${\alpha }_D$, the inclination angle $\theta$, and the phase angle $\varphi$ of the membrane rotation. It is found that the dynamic phase diagram shows a remarkable change with an increase in the ratio of the membrane shear and bending elasticities. A fluid vesicle (no shear elasticity) exhibits three dynamic modes: (i) tank treading at low viscosity ${\eta }_{\text{in}}$ of internal fluid (${\alpha }_D$ and $\theta$ relaxes to constant values), (ii) tumbling (TB) at high ${\eta }_{\text{in}}$ ($\theta$ rotates), and (iii) swinging (SW) at middle ${\eta }_{\text{in}}$ and high shear rates $\dot{\gamma }$ ($\theta$ oscillates). All of three modes are accompanied by a membrane $\left(\varphi \right)$ rotation. For microcapsules with low shear elasticity, the TB phase with no $\varphi$ rotation and the coexistence phase of SW and TB motions are induced by the energy barrier of $\varphi$ rotation. Synchronization of $\varphi$ rotation with TB rotation or SW oscillation occurs with integer ratios of rotational frequencies. At high shear elasticity, where a saddle point in the energy potential disappears, intermediate phases vanish and either $\varphi$ or $\theta$ rotation occurs. This phase behavior agrees with recent simulation results of microcapsules with low bending elasticity.