We study a modified version of a model previously proposed by Jackson and Wolinsky to account for communication of information and allocation of goods in socioeconomic networks. In the model, the utility function of each node is given by a weighted sum of contributions from all accessible nodes. The weights, parametrized by the variable $\delta$, decrease with distance. We introduce a growth mechanism where new nodes attach to the existing network preferentially by utility. By increasing $\delta$, the network structure evolves from a power-law to an exponential degree distribution, passing through a regime characterized by shorter average path length, lower degree assortativity, and higher central point dominance. In the second part of the paper we compare different network structures in terms of the average utility received by each node. We show that power-law networks provide higher average utility than Poisson random networks. This provides a possible justification for the ubiquitousness of scale-free networks in the real world.

We study the dispersion of heavy particle sets, triangle and tetrahedron, in an isotropic and incompressible three-dimensional turbulent flow. The turbulent velocity field is generated using kinematic simulation, which allows us to vary the inertial range and to reach large values of the Reynolds numbers. We study the time evolution of the parameters characterizing the geometry, the size and shape of the triangle and tetrahedron. The Lagrangian correlations of the sets’ size, area or volume, are also studied. Different initial separations between particles, inertial ranges, Stokes numbers, and particle drift velocities are considered. We found that the Reynolds number has no effect on the shape evolution of the triangle and tetrahedron provided that the initial distance between the particles is larger than the Kolmogorov length scale.

The non-Bragg resonance of surface water waves is investigated, both theoretically and experimentally, in a trough with square-wave corrugated sidewalls. Unlike the familiar Bragg resonances, the non-Bragg resonances occur far from the edges of the Brillouin zone and open additional forbidden bands. The experimental observations confirm the existence of these resonances, and the measurements for the transmission properties showing both Bragg and non-Bragg band gaps agree fairly well with the theoretical predictions obtained by the plane-wave expansion method. It is shown that both Bragg and non-Bragg resonances highly depend on the symmetry of the corrugations on the opposite sidewall. As the relative shift between the two corrugations increases from zero to the half period of the corrugations, the Bragg gap shrinks and vanishes, but the non-Bragg gap varies in the opposite way, reaching its maximum, which is impressively wide and much more efficient in reflecting water waves.

This paper gives numerical examples showing that non-self-similar collapse can occur in the motion of four point vortices on a sphere. It is found when the four-vortex problem is integrable, in which the moment of vorticity vector is zero. The non-self-similar collapse has significant properties. It is partial in the sense that three of the four point vortices collapse to one point in finite time and the other one moves to the antipodal position to the collapse point. Moreover, it is robust with respect to perturbation of the initial configuration as long as the system remains integrable.

Operator-difference multilayer schemes for solving the time-dependent Schrödinger equation up to sixth order of accuracy in the time step are presented. Reduced schemes for solving a set of coupled time-dependent Schrödinger equations with respect to the hyper-radial variable are devised using expansion of a wave packet over the set of appropriate basis angular functions. Further discretization of the resulting problem is realized by means of the finite-element method. The convergence of the expansion with respect to the number of basis functions and the efficiency of the numerical schemes are demonstrated in the exactly solvable model of an electric-field-driven two-dimensional oscillator (or a charged particle in a constant uniform magnetic field), in which we explicitly observed an effect of the periodical focusing and defocusing of the probability density flux.

Crystalline assemblages of identical subunits packed together and elastically bent in the form of a torus have been found in the past ten years in a variety of systems of surprisingly different nature, such as viral capsids, self-assembled monolayers, and carbon nanomaterials. In this Rapid Communication we analyze the structural properties of toroidal crystals and provide a unified description based on the elastic theory of defects in curved geometries. We find ground states characterized by the presence of fivefold disclinations on the exterior of the torus and sevenfold disclinations in the interior. The number of excess disclinations is controlled primarily by the aspect ratio of the torus, suggesting a mechanism for creating toroidal templates with precisely controlled valency via functionalization of the defect sites.

We consider the motion of an overdamped particle in a periodic potential lacking spatial symmetry under the influence of symmetric, white, Lévy noise, being a minimal setup for a “Lévy ratchet.” Due to the nonthermal character of the Lévy noise, the particle exhibits a motion with a preferred direction even in the absence of whatever additional time-dependent forces. The examination of the Lévy ratchet has to be based on the characteristics of directionality which are different from typically used measures such as mean current and the dispersion of particle positions, since these become inappropriate when the moments of the noise diverge. To overcome this problem, we discuss robust measures of directionality of transport such as the position of the median of the particle displacement distribution characterizing the group velocity and the interquantile distance giving the measure of the distribution width. Moreover, we analyze the behavior of splitting probabilities for leaving an interval of a given length, unveiling qualitative differences between the noises with Lévy indices below and above unity.

The dynamics of a number of experimental systems can be described as thermally activated escape out of a metastable state over a potential barrier, whose height is being constantly reduced in time by an increasing external force. In such systems, one can distinguish two loading regimes: for slow loading, the distribution of the force values at which escape occurs is a monotonically decreasing function, while for fast loading, the escape-force distribution has a maximum at some nonzero force value. In this work, an approximate relation between the most probable escape force and the first two moments thereof is derived for fast loading, and the expression for the first two force moments vs loading rate is obtained for slow loading. Then, for a special but physically well-motivated functional form of the escape rate, the most probable escape force is found analytically as a function of the loading rate. The high accuracy of these expressions is confirmed by comparing them with numerical results for realistic parameter values.

The avalanche behavior of gravitationally forced granular layers on a rough inclined plane is investigated experimentally for different materials and for a variety of grain shapes ranging from spherical beads to highly anisotropic particles with dendritic shape. We measure the front velocity, area, and height of many avalanches and correlate the motion with the area and height. We also measure the avalanche profiles for several example cases. As the shape irregularity of the grains is increased, there is a dramatic qualitative change in avalanche properties. For rough nonspherical grains, avalanches are faster, bigger, and overturning in the sense that individual particles have down-slope speeds $u_p$ that exceed the front speed $u_f$ as compared with avalanches of spherical glass beads that are quantitatively slower and smaller and where particles always travel slower than the front speed. There is a linear increase of three quantities: (i) dimensionless avalanche height, (ii) ratio of particle to front speed, and (iii) the growth rate of avalanche speed with increasing avalanche size with increasing $\tan {\theta }_r$ where ${\theta }_r$ is the bulk angle of repose, or with increasing ${\beta }_P$, the slope of the depth averaged flow rule, where both ${\theta }_r$ and ${\beta }_P$ reflect the grain shape irregularity. These relations provide a tool for predicting important dynamical properties of avalanches as a function of grain shape irregularity. A relatively simple depth-averaged theoretical description captures some important elements of the avalanche motion, notably the existence of two regimes of this motion.

We show that the dynamics of supercooled liquids, analyzed from computer simulations of the binary mixture Lennard-Jones system, can be described in terms of a continuous-time random walk (CTRW). The required discretization comes from mapping the dynamics on transitions between metabasins. This yields a quantitative link between the elementary step and the full structural relaxation. The analysis involves a verification of the CTRW conditions as well as a quantitative test of the predictions. The wave-vector dependence of the relaxation time and the degree of nonexponentiality can be expressed in terms of the first moments of the waiting time distribution.

We report an analysis of the thickness dependence of the liquid-to-hexatic phase transition in a quasi-two-dimensional hard-sphere colloid system as the confining wall separation changes from 1 to 1.6 hard-sphere diameters. In our theoretical evaluation, we study the bifurcation of solutions to the integral equation for the pair correlation function. Our study predicts that at small wall separation the liquid-to-hexatic phase transition is continuous and that it occurs at lower density than the liquid-to-crystal phase transition density, in agreement with the predictions for a strictly two-dimensional system obtained from the Kosterlitz-Thouless-Halperin-Nelson-Young theory. At larger wall separation (larger than about 1.4 hard-sphere diameters), the liquid-to-hexatic phase transition density is predicted to occur at higher density than the liquid-to-crystal phase transition.

Changes in a cell’s external or internal conditions are usually reflected in the concentrations of the relevant transcription factors. These proteins in turn modulate the expression levels of the genes under their control and sometimes need to perform nontrivial computations that integrate several inputs and affect multiple genes. At the same time, the activities of the regulated genes would fluctuate even if the inputs were held fixed, as a consequence of the intrinsic noise in the system, and such noise must fundamentally limit the reliability of any genetic computation. Here we use information theory to formalize the notion of information transmission in simple genetic regulatory elements in the presence of physically realistic noise sources. The dependence of this “channel capacity” on noise parameters, cooperativity and cost of making signaling molecules is explored systematically. We find that, in the range of parameters probed by recent in vivo measurements, capacities higher than one bit should be achievable. It is of course generally accepted that gene regulatory elements must, in order to function properly, have a capacity of at least one bit. The central point of our analysis is the demonstration that simple physical models of noisy gene transcription, with realistic parameters, can indeed achieve this capacity: it was not self-evident that this should be so. We also demonstrate that capacities significantly greater than one bit are possible, so that transcriptional regulation need not be limited to simple “on-off” components. The question whether real systems actually exploit this richer possibility is beyond the scope of this investigation.

Dynamin is a ubiquitous GTPase that tubulates lipid bilayers and is implicated in many membrane severing processes in eukaryotic cells. Setting the grounds for a better understanding of this biological function, we develop a generalized hydrodynamics description of the conformational change of large dynamin-membrane tubes, taking into account GTP consumption as a free-energy source. On observable time scales, dissipation is dominated by an effective dynamin-membrane friction and the deformation field of the tube has a simple diffusive behavior, which could be tested experimentally. A more involved, semimicroscopic model yields complete predictions for the dynamics of the tube and possibly accounts for contradictory experimental results concerning its change of conformation as well as for plectonemic supercoiling.

An effective potential for longitudinal interactions between adjacent protofilaments in a microtubule is introduced. Our proposed interaction potential is a periodic and continuous function of the offset between two protofilaments, which also incorporates the bending energy of protofilaments. This potential produces the results of atomistic simulations. Further, using the potential, a Monte Carlo simulation gives results for the skew angles of observed structures that are in good agreement with experiments.

A flow state consisting of two oppositely traveling waves (TWs) with oscillating amplitudes has been found in the counter-rotating Taylor-Couette system by full numerical simulations. This structure bifurcates out of axially standing waves that are nonlinear superpositions of left- and right-handed spiral vortex waves with equal time-independent amplitudes. Beyond a critical driving, the two spiral TW modes start to oscillate in counterphase due to a Hopf bifurcation. The trigger for this bifurcation is provided by a nonlinearly excited mode of different symmetry than the spiral TWs. A three-mode coupled amplitude equation model is presented that captures this bifurcation scenario. The mode-coupling between two symmetry degenerate critical modes and a nonlinearly excited one that is contained in the model can be expected to occur in other structure-forming systems as well.

We present a method for detecting communities in bipartite networks. Based on an extension of the $k$-clique community detection algorithm, we demonstrate how modular structure in bipartite networks presents itself as overlapping bicliques. If bipartite information is available, the biclique community detection algorithm retains all of the advantages of the $k$-clique algorithm, but avoids discarding important structural information when performing a one-mode projection of the network. Further, the biclique community detection algorithm provides a level of flexibility by incorporating independent clique thresholds for each of the nonoverlapping node sets in the bipartite network.

Extending a semiconductor laser by means of an external resonator providing a weak optical feedback causes high-dimensional chaotic fluctuations of the light intensity. Adding a second resonator with different round-trip time may turn these fluctuations into more ordered oscillations or even lead back to a stable steady-state operation. The stability range of periodic or continuous wave solutions can be increased by adding a third resonator to the system. This stabilizing effect of multicavities is shown experimentally and theoretically using numerical simulations based on an extended Lang-Kobayashi model and corresponding linear stability analysis of continuous wave solutions.

We consider the two classes of exothermic chemical wave fronts, propagating toward a stable or an unstable steady state. The hydrodynamic equations for stream velocity, temperature, and concentrations are solved numerically for increasing values of the reaction heat. For a critical value of the heat release, we find a transition between a chemical front, whose speed depends on the chemical dynamics, and a generic flame, whose speed is entirely determined by heat release. We derive an analytical expression of the flame speed from the invariants of the hydrodynamic equations. This result substantiates macroscopic approaches widely used in combustion, in which the chemical models include only simplified reaction mechanisms.