The interaction between a nanoprobe and a liquid surface is studied. The surface deformation depends on physical and geometric parameters, which are depicted by employing three dimensionless parameters: Bond number $B_o$, modified Hamaker number $H_a$, and dimensionless separation distance $D^{*}$. The evolution of the deformation is described by a strongly nonlinear partial differential equation, which is solved by means of numerical methods. The dynamic analysis of the liquid profile points out the existence of a critical distance $D_{\min }^{*}$, below which the irreversible wetting process of the nanoprobe happens. For $D^{*}\ge D_{\min }^{*}$, the numerical results show the existence of two deformation profiles, one stable and another unstable from the energetic point of view. Different deformation length-scales, characterizing the stable liquid equilibrium interface, define the near- and the far-field deformation zones, where self-similar profiles are found. Finally, our results allow us to provide simple relationships between the parameters, which leads to determine the optimal conditions when performing atomic force microscope measurements over liquids.

Networks of fast-spiking interneurons are crucial for the generation of neural oscillations in the brain. Here we study the synchronous behavior of interneuronal networks that are coupled by delayed inhibitory and fast electrical synapses. We find that both coupling modes play a crucial role by the synchronization of the network. In addition, delayed inhibitory synapses affect the emerging oscillatory patterns. By increasing the inhibitory synaptic delay, we observe a transition from regular to mixed oscillatory patterns at a critical value. We also examine how the unreliability of inhibitory synapses influences the emergence of synchronization and the oscillatory patterns. We find that low levels of reliability tend to destroy synchronization and, moreover, that interneuronal networks with long inhibitory synaptic delays require a minimal level of reliability for the mixed oscillatory pattern to be maintained.

Tachycardia and fibrillation are potentially fatal arrhythmias associated with the formation of rotating spiral waves in the heart. Presently, the termination of these types of arrhythmia is achieved by use of antitachycardia pacing or cardioversion. However, these techniques have serious drawbacks, in that they either have limited application or produce undesirable side effects. Low-energy far-field stimulation has recently been proposed as a superior therapy. This proposed therapeutic method would exploit the phenomenon in which the application of low-energy far-field shocks induces a large number of activation sites (“virtual electrodes”) in tissue. It has been found that the formation of such sites can lead to the termination of undesired states in the heart and the restoration of normal beating. In this study we investigate a particular aspect of this method. Here we seek to determine how the activation site density depends on the applied electric field through in vitro experiments carried out on neonatal rat cardiac tissue cultures. The results indicate that the activation site density increases exponentially as a function of the intracellular conductivity and the level of cell isotropy. Additionally, we report numerical results obtained from bidomain simulations of the Beeler-Reuter model that are quantitatively consistent with our experimental results. Also, we derive an intuitive analytical framework that describes the activation site density and provides useful information for determining the ratio of longitudinal to transverse conductivity in a cardiac tissue culture. The results obtained here should be useful in the development of an actual therapeutic method based on low-energy far-field pacing. In addition, they provide a deeper understanding of the intrinsic properties of cardiac cells.

The effects of bond randomness on the universality aspects of the simple cubic lattice ferromagnetic Blume-Capel model are discussed. The system is studied numerically in both its first- and second-order phase transition regimes by a comprehensive finite-size scaling analysis. We find that our data for the second-order phase transition, emerging under random bonds from the second-order regime of the pure model, are compatible with the universality class of the 3d random Ising model. Furthermore, we find evidence that the second-order transition emerging under bond randomness from the first-order regime of the pure model belongs to a new and distinctive universality class. The first finding reinforces the scenario of a single universality class for the 3d Ising model with the three well-known types of quenched uncorrelated disorder (bond randomness, site and bond dilution). The second amounts to a strong violation of the universality principle of critical phenomena. For this case of the ex-first-order 3d Blume-Capel model, we find sharp differences from the critical behaviors, emerging under randomness, in the cases of the ex-first-order transitions of the corresponding weak and strong first-order transitions in the 3d three-state and four-state Potts models.

In the lateral confinement of a flat microfluidic channel, monodisperse emulsion droplets spontaneously self-organize in a variety of topologically different packings. The explicit construction of mechanically equilibrated arrangements of effectively two-dimensional congruent droplet shapes reveals the existence of multiple mechanical equilibria depending on channel width $W$, droplet area $A_d$, and volume fraction $\phi$ of the dispersed phase. The corresponding boundaries of local or global stability are summarized in a packing diagram for congruent droplet shapes in terms of the dimensionless channel width $w=W/\sqrt{A_d}$ and $\phi$. In agreement with experimental results, an increasingly strong hysteresis of the transition between single-row and two-row packings is observed during changes of $w$ above a threshold volume fraction of ${\phi }^{*}\simeq 0.813$.

Colloidosomes are created in the laboratory from a Pickering emulsion of water droplets in oil. The colloidosomes have approximately the same diameter and by choosing (hairy) particles of different diameters it is possible to control the particle density on the droplets. The experiment is performed at room temperature. The radial distribution function of the assembly of (primary) particles on the water droplet is measured in the laboratory and in a computer experiment of a fluid model of particles with pairwise interactions on the surface of a sphere.

Here we present a range-limited approach to centrality measures in both nonweighted and weighted directed complex networks. We introduce an efficient method that generates for every node and every edge its betweenness centrality based on shortest paths of lengths not longer than $\ell =1,...,L$ in the case of nonweighted networks, and for weighted networks the corresponding quantities based on minimum weight paths with path weights not larger than $w_{\ell }=\ell \Delta$, $\ell =1,2...,L=R/\Delta$. These measures provide a systematic description on the positioning importance of a node (edge) with respect to its network neighborhoods one step out, two steps out, etc., up to and including the whole network. They are more informative than traditional centrality measures, as network transport typically happens on all length scales, from transport to nearest neighbors to the farthest reaches of the network. We show that range-limited centralities obey universal scaling laws for large nonweighted networks. As the computation of traditional centrality measures is costly, this scaling behavior can be exploited to efficiently estimate centralities of nodes and edges for all ranges, including the traditional ones. The scaling behavior can also be exploited to show that the ranking top list of nodes (edges) based on their range-limited centralities quickly freezes as a function of the range, and hence the diameter-range top list can be efficiently predicted. We also show how to estimate the typical largest node-to-node distance for a network of $N$ nodes, exploiting the afore-mentioned scaling behavior. These observations were made on model networks and on a large social network inferred from cell-phone trace logs ($\sim$$5.5\times {10}^6$ nodes and $\sim$$2.7\times {10}^7$ edges). Finally, we apply these concepts to efficiently detect the vulnerability backbone of a network (defined as the smallest percolating cluster of the highest betweenness nodes and edges) and illustrate the importance of weight-based centrality measures in weighted networks in detecting such backbones.

“Voting with feet” describes the prominent social phenomenon that people tend to move away from deteriorating neighborhoods and search for and join prosperous groups. To quantify the role this kind of expectation-driven migration plays in the evolution of cooperation, here we study a simple yet effective model of cooperation based on spatial public goods games. The population structure is characterized by a square lattice with some nodes being left empty. Individuals have expectations toward their current habitats. Dissatisfied players, whose expectation is not met after interacting with all directly connected neighbors, tend to abstain from the groups of low quality by moving away and explore the physical niches of avail. How fast interaction happens relatively to selection is regulated by the time-scale ratio of game interaction to natural selection. Under strong selection, simulation results show that cooperation is greatly improved for either low, moderate, or high expectations compared to whenever the expectation-driven migration is absent. Further explorations reveal that neither too high nor too low but rather a combination of moderate expectations and rapid interaction establishes cooperation for a moderate public goods enhancement factor. There exists an optimal interval of expectation level most favoring the evolution of cooperation as the required time-scale ratio is minimized.

The study of real-world communication systems via complex network models has greatly expanded our understanding on how information flows, even in completely decentralized architectures such as mobile wireless networks. Nonetheless, static network models cannot capture the time-varying aspects and, therefore, various temporal metrics have been introduced. In this paper, we investigate the robustness of time-varying networks under various failures and intelligent attacks. We adopt a methodology to evaluate the impact of such events on the network connectivity by employing temporal metrics in order to select and remove nodes based on how critical they are considered for the network. We also define the temporal robustness range, a new metric that quantifies the disruption caused by an attack strategy to a given temporal network. Our results show that in real-world networks, where some nodes are more dominant than others, temporal connectivity is significantly more affected by intelligent attacks than by random failures. Moreover, different intelligent attack strategies have a similar effect on the robustness: even small subsets of highly connected nodes act as a bottleneck in the temporal information flow, becoming critical weak points of the entire system. Additionally, the same nodes are the most important across a range of different importance metrics, expressing the correlation between highly connected nodes and those that trigger most of the changes in the optimal information spreading. Contrarily, we show that in randomly generated networks, where all the nodes have similar properties, random errors and intelligent attacks exhibit similar behavior. These conclusions may help us in design of more robust systems and fault-tolerant network architectures.

We study families of open chaotic maps that classically share the same asymptotic properties—forward and backward trapped sets, repeller dimensions, and escape rate—but differ in their short time behavior. When these maps are quantized we find that the fine details of the distribution of resonances and the corresponding eigenfunctions are sensitive to the initial shape and size of the openings. We study phase space localization of the resonances with respect to the repeller and find strong delocalization effects when the area of the openings is smaller than $\hslash$.

Self-gravitating systems, such as globular clusters or elliptical galaxies, are the prototypes of many-body systems with long-range interactions, and should be the natural arena in which to test theoretical predictions on the statistical behavior of long-range-interacting systems. Systems of classical self-gravitating particles can be studied with the standard tools of equilibrium statistical mechanics, provided the potential is regularized at small length scales and the system is confined in a box. The confinement condition looks rather unphysical in general, so that it is natural to ask whether what we learn with these studies is relevant to real self-gravitating systems. In order to provide an answer to this question, we consider a basic, simple, yet effective model of globular clusters: the King model. This model describes a self-consistently confined system, without the need of any external box, but the stationary state is a nonthermal one. In particular, we consider the King model with a short-distance cutoff on the interactions, and we discuss how such a cutoff affects the caloric curve, i.e., the relation between temperature and energy. We find that the cutoff stabilizes a low-energy phase, which is absent in the King model without cutoff; the caloric curve of the model with cutoff turns out to be very similar to that of previously studied confined and regularized models, but for the absence of a high-energy gaslike phase. We briefly discuss the possible phenomenological as well as theoretical implications of these results.

We study the transport of granular matter through a staircaselike array of $K$ vertically vibrated compartments. Given a constant inflow rate $Q<Q_{\text{cr}}\left(K\right)$ into the top compartment, a continuous particle flow establishes itself along the entire length of the system. However, as soon as $Q$ grows beyond the critical value $Q_{\text{cr}}\left(K\right)$ the particles form a cluster and the flow comes to a halt. Interestingly, this clustering is preceded by a subcritical warning signal: for $Q$ values just below $Q_{\text{cr}}\left(K\right)$ the density profile along the conveyor belt spontaneously develops a pattern in which the compartments are alternatingly densely and sparsely populated. In a previous paper [Kanellopoulos and van der Weele, Int. J. Bifurcation Chaos 21, 2305 (2011)] this pattern was shown to be the result of a period-doubling bifurcation. The present paper aims at unravelling the physical mechanism that lies at the basis of the pattern formation. To this end we study the continuum version of the same system, replacing the compartment number $k=1,...,K$ by a continuous variable $x$. The dynamics of the system is now described (instead of by $K$ coupled ordinary differential equations) by a single partial differential equation of the Fokker-Planck type, with a drift and a diffusive term that both depend on the density. The drift term turns out to be responsible for the subcritical density oscillations, thereby paving the way for the eventual clustering which sets in when the diffusion coefficient becomes negative. The observed sequence of events in the granular transport system is thus explained as an interplay between drift and (anti)diffusion.

We have adopted an ensemble Monte Carlo simulation method to systematically verify two physical driving mechanisms responsible for overcharging which refers to the adsorption of an effective charge onto a like-charged planar surface around the point of zero charge within the primitive model of mixed electrolytes with varying salt concentrations. One is electrostatic in character dominated by dielectric images and the other is purely entropic in origin by ionic size asymmetry effects, of which the former has never been reported both theoretically and experimentally and the latter could be interpreted satisfactorily in terms of available theoretical approaches. The electrostatically driven mechanism is found to critically depend on the ionic sizes while the entropically driven mechanism occurs with almost the same efficiency in a relative wide range of surface charge density. Depending on the delicate interplay between charge and steric correlations, the two distinct driving mechanisms may cooperatively give rise to a more pronounced overcharging process.

We study group chasing and escaping between three species. In our model, one species acts as a group of chasers for another species and acts as a group of targets for the third species. When a particle is caught by a target, the particle becomes a new chaser. Although the ratio of three species is changed, the total number of particles is conserved. When particles move randomly, the numbers of the three species change periodically but no species seems to become extinct. If particles escape from the nearest chaser and chase the nearest target, the extinction of a species occurs. The extinction induces that of the second species and finally only one species survives.

Using amplitude equations, we show that groups of identical nanomechanical resonators, interacting with a common mode of a cavity microwave field, synchronize to form a single mechanical mode which couples to the cavity with a strength dependent on the squared sum of the individual mechanical-microwave couplings. Classically this system is dominated by periodic behavior which, when analyzed using amplitude equations, can be shown to exhibit multistability. In contrast, groups of sufficiently dissimilar nanomechanical oscillators may lose synchronization and oscillate out of phase at significantly higher amplitudes. Further, the method by which synchronization is lost resembles that for large amplitude forcing which is not of the Kuramoto form.

The Rayleigh equation $\frac{3}{2}\dot{R}+R\ddot{R}+p{\rho }^{-1}=0$ with initial conditions $R\left(0\right)=R_0$, $\dot{R}\left(0\right)=0$ models the collapse of an empty spherical bubble of radius $R\left(T\right)$ in an ideal, infinite liquid with far-field pressure $p$ and density $\rho$. The solution for $r\equiv R/R_0$ as a function of time $t\equiv T/T_{\mathrm{c}}$, where $R\left(T_{\mathrm{c}}\right)\equiv 0$, is independent of $R_0$, $p$, and $\rho$. While no closed-form expression for $r\left(t\right)$ is known, we find that $r_0\left(t\right)={(1-t^2)}^{2/5}$ approximates $r\left(t\right)$ with an error below 1$\%$. A systematic development in orders of $t^2$ further yields the 0.001$\%$ approximation $r_{*}\left(t\right)=r_0\left(t\right)[1-a_1{\mathrm{Li}}_{2.21}\left(t^2\right)]$, where $a_1\approx -0.01832099$ is a constant and Li is the polylogarithm. The usefulness of these approximations is demonstrated by comparison to high-precision cavitation data obtained in microgravity.

Microscale slender swimmers are frequently encountered in nature and are now used in microrobotic applications. The swimming mechanism examined in this paper is based on small transverse axisymmetric traveling wave deformations of a cylindrical long shell. The thin-shelled device is assumed to be inextensible at the middle surface and extensible at the surface wetted by the fluid. Assuming low-Reynolds-number hydrodynamics, an analytical solution is derived for waves of small amplitudes compared with the cylinder diameter. We show that swimming velocity increases with ${\beta }_1$ (the ratio of cylinder radius to wavelength) and that swimming velocity is linearly dependent on wave propagation velocity, increasing to leading order with the square of the ratio of wave amplitude to wavelength ${\beta }_2$ and decreasing with the wall thickness. A fourth-order correction in ${\beta }_2$ was also calculated and was found to have a negative effect on the swimming velocity. The results for a shell of negligible-wall thickness were compared with Taylor's solution for an inextensible two-dimensional flat membrane undergoing a waving motion and Felderhof's results [Phys. Fluids 22, 113604 (2010)] for an unbounded flow field and negligible-wall thickness. We show that Taylor's analytic solution is a particular limiting case of the present solution, assuming zero wall thickness and infinite values of ${\beta }_1$. The present mechanism was also compared with Taylor's well known solutions of waving planar and helical circular tails. We show that the present approach yields higher velocities as ${\beta }_1$ increases, whereas, the opposite occurs for waving tails. Indeed, in the region where ${\beta }_1>15$, the present approach yields velocities nearly as fast as Taylor's helical waving tail while consuming less power and with a design that is considerably more compact. In this regime, the axisymmetric swimmer is twice as fast as Taylor's planar-tail swimmer for an additional investment of only one-third of the power. Experiments were conducted using a macroscale autonomous model immersed in highly viscous silicone fluid. We outlined how the proposed mechanism was realized to propel an elongated, yet finite, swimmer. Measured data demonstrate the effects of wave velocity and wavelength on swimming speed, showing good agreement with analytical results.

The problem of a two-layer system consisting of a horizontal liquid layer in contact with its own vapor is considered. The liquid layer is bounded by a rigid wall from below, and phase change can occur at the interface. The flow of the vapor phase is driven by a constant pressure gradient in the streamwise direction. We have taken into account the effects of buoyancy, thermocapillarity, evaporation, and the dynamics of the vapor phase. A full linear stability analysis is performed using a Chebyshev spectral method. The influences of evaporation effect and the interfacial shear on the Rayleigh instability and the Marangoni instability have been studied. The results show that both the evaporation and the interfacial shear play important roles in the stability of the system.

We predict theoretically that linear magnetic permeability induces nonlinear absorption (NA) of an electric field in lossy metamaterials (MMs) with Kerr-type nonlinear polarization even when the imaginary part of the nonlinear polarization is absent. The nonlinear magnetic susceptibility, if it exists and although it may be real, enhances or reduces the NA of the electric field, depending on the relative values of the electric and magnetic losses. In particular, it is shown that the NA effect can be tuned by the figure of merit (FOM) of the MM: generally, MMs with a better FOM have a weaker NA effect. Moreover, the nonlinear coefficient can also be enhanced greatly due to the combined effect of the linear losses and the nonlinear magnetization of MMs. The control of the tunable NA and nonlinear coefficients by the structural parameters of MMs is also discussed.