Communities of vertices within a giant network such as the World Wide Web are likely to be vastly smaller than the network itself. However, Fortunato and Barthélemy have proved that modularity maximization algorithms for community detection may fail to resolve communities with fewer than $\sqrt{L/2}$ edges, where $L$ is the number of edges in the entire network. This resolution limit leads modularity maximization algorithms to have notoriously poor accuracy on many real networks. Fortunato and Barthélemy’s argument can be extended to networks with weighted edges as well, and we derive this corollary argument. We conclude that weighted modularity algorithms may fail to resolve communities with less than $\sqrt{W\epsilon /2}$ total edge weight, where $W$ is the total edge weight in the network and $\epsilon$ is the maximum weight of an intercommunity edge. If $\epsilon$ is small, then small communities can be resolved. Given a weighted or unweighted network, we describe how to derive new edge weights in order to achieve a low $\epsilon$, we modify the Clauset, Newman, and Moore (CNM) community detection algorithm to maximize weighted modularity, and we show that the resulting algorithm has greatly improved accuracy. In experiments with an emerging community standard benchmark, we find that our simple CNM variant is competitive with the most accurate community detection methods yet proposed.

The mechanical behavior of an ensemble of athermal fibers forming a nonbonded network subjected to triaxial compression is studied using a numerical model. The response exhibits a power law dependence of stress on the dilatation strain and hysteresis upon loading and unloading. A stable hysteresis loop results after the first loading and unloading cycle. In the early stages of compaction, strain energy is associated primarily with the bending of fibers, while at higher densities, it is stored primarily in the axial deformation mode. It is shown that the exponent of the power law, and the partition of energy in the axial and bending modes depends on the ratio of the bending to axial stiffness of the fibers. Accounting for interfiber friction does not change the functional form of the stress-strain relationship or the exponent. The central feature that distinguishes the mechanics of this system from that of bonded random networks is the relative sliding at contacts and the ensuing fiber rearrangements. We show that suppressing sliding leads to a much stiffer response. The results indicate that the value of the exponent of the stress-strain power law is determined not only by fiber bending and the formation of new contacts, but also by the relative sliding and axial deformation of fibers.

We consider a delayed susceptible-infected-recovered epidemic model on an uncorrelated complex network and address the effect of time lag on the shape and multiple waves of epidemic curves. We show that when the transmission rate is above a threshold, a large delay can cause multiple waves with larger amplitudes in the second and subsequent waves.

For a broad range of single-seed contagion processes acting on generalized random networks, we derive a unifying analytic expression for the possibility of global spreading events in a straightforward, physically intuitive fashion. Our reasoning lays bare a direct mechanical understanding of an archetypal spreading phenomena that is not evident in circuitous extant mathematical approaches.

Coarse-graining model is a promising way to analyze and visualize large-scale networks. The coarse-grained networks are required to preserve statistical properties as well as the dynamic behaviors of the initial networks. Some methods have been proposed and found effective in undirected networks, while the study on coarse-graining directed networks lacks of consideration. In this paper we proposed a path-based coarse-graining (PCG) method to coarse grain the directed networks. Performing the linear stability analysis of synchronization and numerical simulation of the Kuramoto model on four kinds of directed networks, including tree networks and variants of Barabási-Albert networks, Watts-Strogatz networks, and Erdös-Rényi networks, we find our method can effectively preserve the network synchronizability.

We investigate the route to exploding dissipative solitons in the complex cubic-quintic Ginzburg-Landau equation, as the bifurcation parameter, the distance from linear onset, is increased. We find for a large class of initial conditions the sequence: stationary localized solutions, oscillatory localized solutions with one frequency, oscillatory localized solutions with two frequencies, and exploding localized solutions. The transition between localized solutions with one and with two frequencies, respectively, is analyzed in detail. It is found to correspond to a forward Hopf bifurcation for these localized solutions as the bifurcation parameter is increased. In addition, we make use of power spectra to characterize all time-dependent states. On the basis of all information available, we conclude that the sequence oscillatory localized solutions with one frequency, oscillatory localized solutions with two frequencies, and exploding dissipative solitons can be interpreted as the analog of the Ruelle-Takens-Newhouse route to chaos for spatially localized solutions.

In this paper, a series of numerical simulations was performed to investigate the pumping performance of electro-osmotic micropumps containing electrode arrays patterned on the upper and lower sides of a microchannel. The simulations have been analyzed with a linear electro-osmotic model based upon the Debye-Hückel theory of the double layer. The potential drop across the diffuse layer is assumed to be less than 25 mV ($k_{B}T/e$), and there is a linear response between the surface charge and the voltage drop across the double layer. The double layer is not resolved but is lumped into effective parameters that are imported from the Debye-Hückel and Stern layers. We examined the effects of the relative positioning of the electrodes in the opposing arrays (i.e., symmetrical or staggered), and the phase lag and the angular frequency of the alternating current (ac) signals applied to the electrodes within the two arrays. A critical height of the microchannel was observed, below which the interactions of the applied electrical potentials on the walls became significant. The optimum pumping effect was obtained when the electrode arrays were symmetrical to one another around the centerline of the channel and were activated by ac potentials with a 0° phase shift. The corresponding angular frequency of the maximum pumping velocity for different phase shifts of the applied ac signals was also determined. Overall, the simulation results presented in this paper provide a useful insight into the optimal design parameters and operating conditions for micropumps containing two arrays of microelectrodes on the microchannel walls.

We simulate the response of a corrugated plasma channel to an ultrashort laser pulse in two dimensions with the goal of demonstrating the production of terahertz frequency electromagnetic modes. Corrugated channels support electromagnetic modes that have a Floquet-type dispersion relation and thus consist of a sum of spatial harmonics with subluminal phase velocities. This allows the possibility of phase matching between the ponderomotive potential associated with the laser pulse and the electromagnetic modes of the channel. Since the bandwidth of an ultrashort pulse includes terahertz frequencies, significant excitation of terahertz radiation is possible. Here we consider realistic density profiles to obtain predictions of the terahertz power output and mode structure for a channel with periodic boundary conditions. We then estimate pulse depletion effects from our simulation results. The fraction of laser energy converted to terahertz is independent of laser pulse energy in the linear regime, and we find it to be around 1%. Extrapolating to a pulse energy of 0.5 J gives a terahertz power output of 6 mJ with a pulse depletion length of less than 20 cm.

Time-periodic solitons of the parametrically driven damped nonlinear Schrödinger equation are obtained as solutions of the boundary-value problem on a two-dimensional spatiotemporal domain. We follow the transformation of the periodic solitons as the strength of the driver is varied. The resulting bifurcation diagrams provide a natural explanation for the overall form and details of the attractor chart compiled previously via direct numerical simulations. In particular, the diagrams confirm the occurrence of the period-doubling transition to temporal chaos for small values of dissipation and the absence of such transitions for larger dampings. This difference in the soliton’s response to the increasing driving strength can be traced to the difference in the radiation frequencies in the two cases. Finally, we relate the soliton’s temporal chaos to the homoclinic bifurcation.

Stationary and oscillatory bound states, or complexes, of the damped-driven solitons are numerically path-followed in the parameter space. We compile a chart of the two-soliton attractors, complementing the one-soliton attractor chart.

The prisoner’s dilemma (PD) game is a simple model for understanding cooperative patterns in complex systems. Here, we study a PD game problem in scale-free networks containing hierarchically organized modules and controllable shortcuts connecting separated hubs. We find that cooperator clusters exhibit a percolation transition in the parameter space $(p,b)$, where $p$ is the occupation probability of shortcuts and $b$ is the temptation payoff in the PD game. The cluster size distribution follows a power law at the transition point. Such a critical behavior, resulting from the combined effect of stochastic processes in the PD game and the heterogeneity of complex network structure, illustrates diversities arising in social relationships and in forming cooperator groups in real-world systems.

The concept of “random loose packing” (RLP) has evolved through extensive study of loose packings of spheres, which has resulted in an accepted definition as the loosest packing that can be obtained by pouring grains. We extend this consideration to packings of nonspherical grains (ellipsoids) formed by slow settling in a viscous liquid, and perform a detailed analysis of the structural properties of the resulting packings. We find that as in the case of spheres the loosest ellipsoid packings are generated for grains with high interparticle friction. However, unlike spheres, these packings cannot be considered random as they have a significant degree of orientational ordering that increases with the grain’s aspect ratio. This demonstrates that applying sedimentation or pouring techniques that have become part of the commonly held definition of RLP, will not generate random packings of ellipsoids. The consequences for the accepted definition of RLP and its applicability to nonspherical grains is discussed.

Using an atomic force microscope (AFM) we confined a smectic-A liquid crystal (LC) between a flat glass plate and a 10-μm glass sphere attached to the free end of the AFM cantilever. Both surfaces were treated with a surfactant that induces normal alignment of the LC molecules. We measured the force $F$ acting on the cantilever while varying the plate-sphere distance $D$ with subnanometer precision. For $D$ < 50 nm, the force was periodically oscillating and decayed as $D$ was increased. Analyzing the force in the framework of a simple model of elastic deformation of the smectic layers, we have evaluated the undeformed layer thickness $a_0$ and compressibility modulus $B$. Compared to other techniques used to determine $a_0$ and $B$, AFM measurements are faster and require a much smaller amount (microliters) of LC. Moreover, they are based on purely mechanical deformations of the LC structure and do not require any static or radiative electromagnetic field.

Nematic and smectic liquid crystals were introduced into μm-scale gaps between plates coated with polymer films nanoimprinted with parallel arrays of rectangular channels. Overlaying the channels on the two plates close enough at a slight angle produces a mosaic of alternating planar and homeotropic alignments and hybrid alignment, showing that complex liquid-crystal orientation patterns can be achieved by combining two simple topographic patterns. These alignment patterns are attributed to spatial variation of surface roughness and 3D topographic structure created by a sufficient proximity of the two patterns.

The three-dimensional structure and the mechanical properties of a $\beta$-connectin fragment from human cardiac muscle, belonging to the $I$ band, from $I_{27}$ to $I_{34}$, were investigated by small-angle x-ray scattering (SAXS) and single-molecule force spectroscopy (SMFS). This molecule presents an entropic elasticity behavior, associated to globular domain unfolding, that has been widely studied in the last 10 years. In addition, atomic force microscopy based SMFS experiments suggest that this molecule has an additional elastic regime, for low forces, probably associated to tertiary structure remodeling. From a structural point of view, this behavior is a mark of the fact that the eight domains in the $I_{27}$-$I_{34}$ fragment are not independent and they organize in solution, assuming a well-defined three-dimensional structure. This hypothesis has been confirmed by SAXS scattering, both on a diluted and a concentrated sample. Two different models were used to fit the SAXS curves: one assuming a globular shape and one corresponding to an elongated conformation, both coupled with a Coulomb repulsion potential to take into account the protein-protein interaction. Due to the predominance of the structure factor, the effective shape of the protein in solution could not be clearly disclosed. By performing SMFS by atomic force microscopy, mechanical unfolding properties were investigated. Typical sawtooth profiles were obtained and the rupture force of each unfolding domain was estimated. By fitting a wormlike chain model to each peak of the sawtooth profile, the entropic elasticity of octamer was described.

A laminated ablator is explored as an alternative concept for stabilizing the ablative Rayleigh-Taylor instability which develops in inertial fusion targets. Experiments measuring the growth of the Rayleigh-Taylor instability of laminated planar foils are reported. Consistent with both theory and simulations, a significant reduction of the perturbation growth is experimentally observed for laminated ablators in comparison to what is observed for classical uniform ablators. Such an enhanced hydrodynamic stability opens opportunities for the design of high-gain inertial fusion targets.

Capillary attraction between identical millimeter-sized spheres floating at a liquid-air interface and the resulting aggregation are investigated at low Reynolds number. We show that the measured capillary forces between two spheres as a function of distance can be described by expressions obtained using the Nicolson approximation at low Bond numbers for far greater particle sizes than previously assumed. We find that viscous hydrodynamic interactions between the spheres needs to be included to describe the dynamics close to contact. We then consider the aggregates formed when a third sphere is added after the initial two spheres are already in contact. In this case, we find that linear superposition of capillary forces describes the observed approach qualitatively but not quantitatively. Further, we observe an angular dependence of the structure due to a rapid decrease of capillary force with distance of separation, which has a tendency to align the particles before contact. When the three particles come into contact, they may preserve their shape or rearrange to form an equilateral triangle cluster—the lowest-energy state—depending on the competition between attraction between particles and friction. Using these observations, we demonstrate that a linear particle chain can be built from frictional particles with capillary attraction.

A free-energy functional that contains both the symmetry-conserved and symmetry-broken parts of the direct pair correlation function has been used to investigate the freezing of a system of hard spheres into crystalline and amorphous structures. The freezing parameters for fluid-crystal transition have been found to be in very good agreement with the results found from simulations. We considered amorphous structures found from molecular dynamics simulations at packing fractions $\eta$ lower than the glass close packing fraction ${\eta }_J$ and investigated their stability compared to that of a homogeneous fluid. The existence of a free-energy minimum corresponding to a density distribution of overlapping Gaussians centered around an amorphous lattice depicts a deeply supercooled state with a heterogeneous density profile.

The two-point correlation measured on a thin section can be used to derive the probability density of the radii of a population of penetrable spheres. The geometrical, transport, and deformation properties of samples derived by this method compare well with the properties of the digitized real sample and of the samples generated by the standard grain reconstruction method.

An off-lattice automaton for modeling pedestrian dynamics is presented. Pedestrians are represented by disks with variable radius that evolve following predefined rules. The key feature of our approach is that although positions and velocities are continuous, forces do not need to be calculated. This has the advantage that it allows using a larger time step than in force-based models. The room evacuation problem and circular racetrack simulations quantitatively reproduce the available experimental data, both for the specific flow rate and for the fundamental diagram of pedestrian traffic with an outstanding performance. In this last case, the variation of two free parameters ($r_{\min }$ and $r_{\max }$) of the model accounts for the great variety of experimental fundamental diagrams reported in the literature. Moreover, this variety can be interpreted in terms of these model parameters.