Two types of measurement are presented that relate molecular events to macroscopic behavior of F-actin networks. First, shear modulus is measured by oscillating an embedded microbead. Second, a microbead is translated at constant rate and transitions in the resisting force are observed. The loading rate dependence of the force at the transitions is similar to that of the molecular unbinding force, suggesting that they share a common origin. Reversibility tests of shear modulus provide further evidence that strain softening of F-actin networks is caused by force-induced rupture of cross-links.

We predict an abrupt observable transition, on the basis of numerical studies, of hantavirus infection in terrain characterized by spatially dependent environmental resources. The underlying framework of the analysis is that of Fisher equations with an internal degree of freedom, the state of infection. The unexpected prediction is of the sudden disappearance of refugia of infection in spite of the existence of supercritical (favorable) food resources, brought about by reduction of their spatial extent. Numerical results are presented and a theoretical explanation is provided on analytic grounds on the basis of the competition of diffusion of rodents carrying the hantavirus and nonlinearity present in the resource interactions.

The identification of motifs—subgraphs that appear significantly more often in a particular network than in an ensemble of randomized networks—has become a ubiquitous method for uncovering potentially important subunits within networks drawn from a wide variety of fields. We find that the most common algorithms used to generate the ensemble from the real network change subgraph counts in a highly correlated manner, such that one subgraph’s status as a motif may not be independent from the statuses of the other subgraphs. We demonstrate this effect for the problem of three- and four-node motif identification in the transcriptional regulatory networks of E. coli and S. cerevisiae in which randomized networks are generated via an edge-swapping algorithm. We find strong correlations among subgraph counts; for three-node subgraphs these correlations are easily interpreted, and we present an information-theoretic tool that may be used to identify correlations among subgraphs of any size. Our results suggest that single-feature statistics such as $Z$ scores that implicitly assume independence among subgraph counts constitute an insufficient summary of the network.

Inverse Chladni patterns, i.e., grains collecting at the antinodes of a resonating plate, are traditionally believed to occur only when the particles are small enough to be carried along by the ambient air. We now show—theoretically and numerically—that air currents are not the only mechanism leading to inverse patterns: When the acceleration of the resonating plate does not exceed $g$, particles will always roll to the antinodes, irrespective of their size, even in the absence of air. We also explain why this effect has hitherto escaped detection in standard Chladni experiments.

Motivated by the mycologic situation, Dorosz and collaborators considered a modification of the totally asymmetric exclusion process, including the probabilities of injection and of death. In the case of the backward-ordered sequential dynamics with the death probability larger than the critical value, the average particle density in the stationary state was erroneously reported to equal the injection probability. Correcting the error, we find that the average density is given by the death probability rather than the injection probability.

In soft matter systems the local displacement field can be accessed directly by video microscopy enabling one to compute local strain fields and hence the elastic moduli in these systems using a coarse-graining procedure. We study this process in detail for a simple triangular, harmonic lattice in two dimensions. Coarse-graining local strains obtained from particle configurations in a Monte Carlo simulation generates nontrivial, nonlocal strain correlations (susceptibilities). These may be understood within a generalized, Landau-type elastic Hamiltonian containing up to quartic terms in strain gradients [K. Franzrahe et al., Phys. Rev. E 78, 026106 (2008)]. In order to demonstrate the versatility of the analysis of these correlations and to make our calculations directly relevant for experiments on colloidal solids, we systematically study various parameters such as the choice of statistical ensemble, presence of external pressure and boundary conditions. Crucially, we show that special care needs to be taken for an accurate application of our results to actual experiments, where the analyzed area is embedded within a larger system, to which it is mechanically coupled. Apart from the smooth, affine strain fields, the coarse-graining procedure also gives rise to a noise field $\left(\chi \right)$ made up of nonaffine displacements. Several properties of $\chi$ may be rationalized for the harmonic solid using a simple “cell model” calculation. Furthermore the scaling behavior of the probability distribution of the noise field $\left(\chi \right)$ is studied. We find that for any inverse temperature $\beta$, spring constant $f$, density $\rho$ and coarse-graining length $\Lambda$ the probability distribution can be obtained from a master curve of the scaling variable $\mathcal{X}=\chi \beta f/\rho {\Lambda }^2$.

We explore the self-organization dynamics of a set of entities by considering the interactions that affect the different subgroups conforming the whole. To this end, we employ the widespread example of coagulation kinetics, and characterize which interaction types lead to consensus formation and which do not, as well as the corresponding different macroscopic patterns. The crucial technical point is extending the usual one species coagulation dynamics to the two species one. This is achieved by means of introducing explicitly solvable kernels which have a clear physical meaning. The corresponding solutions are calculated in the long time limit, in which consensus may or may not be reached. The lack of consensus is characterized by means of scaling limits of the solutions. The possible applications of our results to some topics in which consensus reaching is fundamental, such as collective animal motion and opinion spreading dynamics, are also outlined.

Gravity-driven flow of concentrated suspensions (solid volume fraction $\varphi >0.50$) of non-Brownian spherical particles through a channel contraction at low Reynolds number is studied experimentally. The abrupt change in the flow area at the contraction forms distinct shear-rate regions having different fluid pressures, which are related to the concept of particle pressure. A model involving particle pressure variation coupled to a Darcy-like behavior for the fluid captures the phenomenon of “self-filtration,” in which the effluent material has lower solid fraction than the input suspension. For $\varphi \doteq {\varphi }_{crit}\approx 0.58$, under added load from a weighted piston, the flow periodically alternates between fast and slow motions.

We study thermal transport in a chain of coupled atoms, which can vibrate in longitudinal as well as transverse directions. The particles interact through anharmonic potentials upto cubic order. The problem is treated quantum mechanically. We first calculate the phonon frequencies self-consistently taking into account the anharmonic interactions. We show that for all the modes, frequencies must have linear dispersion with wave vector $q$ for small $q$ irrespective of their bare dispersions. We then calculate the phonon relaxation rates ${\Gamma }_i\left(q\right)$, where $i$ is the polarization index of the mode, in a self-consistent approximation based on second-order perturbation diagrams. We find that the relaxation rate for the longitudinal phonon, ${\Gamma }_x\left(q\right)\propto q^{3/2}$, while that for the transverse phonon ${\Gamma }_y\left(q\right)\propto q^2$. The consequence of these results on the thermal conductivity $\kappa \left(N\right)$ of a chain of $N$ particles is that $\kappa \left(N\right)\propto N^{1/2}$.

Nanoparticle agglomeration in a quiescent fluid is simulated by solving the Langevin equations of motion of a set of interacting monomers in the continuum regime. Monomers interact via a radial rapidly decaying intermonomer potential. The morphology of generated clusters is analyzed through their fractal dimension $d_f$ and the cluster coordination number. The time evolution of the cluster fractal dimension is linked to the dynamics of two populations: small $\left(k\le 15\right)$ and large $\left(k>15\right)$ clusters. At early times monomer-cluster agglomeration is the dominant agglomeration mechanism $\left(d_f=2.25\right)$, whereas at late times cluster-cluster agglomeration dominates $\left(d_f=1.56\right)$. Clusters are found to be compact (mean coordination number of $\sim 5$), tubular, and elongated. The local compact structure of the aggregates is attributed to the isotropy of the interaction potential, which allows rearrangement of bonded monomers, whereas the large-scale tubular structure is attributed to its relatively short attractive range. The cluster translational diffusion coefficient is determined to be inversely proportional to the cluster mass and the (per-unit-mass) friction coefficient of an isolated monomer, a consequence of the neglect of monomer shielding in a cluster. Clusters generated by unshielded Langevin equations are referred to as ideal clusters because the surface area accessible to the underlying fluid is found to be the sum of the accessible surface areas of the isolated monomers. Similarly, ideal clusters do not have, on average, a preferential orientation. The decrease in the numbers of clusters with time and a few collision kernel elements are evaluated and compared to analytical expressions.

In the vapor-liquid-solid (VLS) nanowire growth, nanowires can be constructed utilizing the difference in the mechanism of crystallization between the vapor-solid (VS) process (outside the solvent droplet) and the VLS process (inside the droplet). We performed a series of separate molecular dynamics simulations for a VLS system and a VS system under equivalent nonequilibrium conditions to clarify the different mechanisms of the solid growth process in both systems and to understand how a liquid substance can catalyze the solidification. The detailed observation of the chemical potential distribution during the steady solid growth state clearly outlines the processes that limit the growth rate. We found that the most dominant process limiting the growth rate is mass transport in the solvent liquid. We also show numerically and analytically that the mass transport rate is proportional to the diffusion constant and also to the solubility of in the solvent, and that a high solubility in the solvent can almost compensate for the disadvantage of a small diffusion constant. Although remarkable catalytic effect by the solvent at least in the linear nonequilibrium region could not be observed, our results suggest that the VLS process would catalyze the solid growth using liquid substance with higher solubility or in a nonlinear nonequilibrium state.

We use the torsional angles of the protein chain as generalized coordinates in the canonical formalism, derive canonical equations of motion, and investigate the coordinate dependence of the kinetic energy expressed in terms of the canonical momenta. We use the formalism to compute the normal-frequency distributions of the $\alpha$ helix and the $\beta$ sheet, under the assumption that they are stabilized purely through hydrogen bonding. In addition, we obtain the free-energy relations of the $\alpha$ helix, the $\beta$ sheet, and the random coil of a 15-residue polyalanine. Interestingly, our results predict a phase transition from an $\alpha$ helix to a $\beta$ sheet at a critical temperature.

We argue that protein loops can be described by topological domain-wall solitons that interpolate between ground states which are the $\alpha$ helices and $\beta$ strands. We present an energy function that realizes loops as soliton solutions to its equation of motion, and apply these solitons to model a number of biologically active proteins including 1VII, 2RB8, and 3EBX (Protein Data Bank codes). In all the examples that we have considered we are able to numerically construct soliton solutions that reproduce secondary structural motifs such as $\alpha$-helix-loop-$\alpha$-helix and $\beta$-sheet-loop-$\beta$-sheet with an overall root-mean-square-distance accuracy of around $1.0\text{Å}$ or less for the central $\alpha$-carbons, i.e., close to the limits of current experimental accuracy.

The transition of a counter-chemotactic particle flow from a free-flow state to a jammed state in a quasi-one-dimensional path is investigated. One of the characteristic features of such a flow is that the constituent particles spontaneously form a cluster that blocks the path, called a path-blocking cluster (PBC), and causes a jammed state when the particle density is greater than a threshold value. Near the threshold value, the PBC occasionally collapses on itself to recover the free flow. In other words, the time evolution of the size of the PBC governs the flux of a counter-chemotactic flow. In this Rapid Communication, on the basis of numerical results of a stochastic cellular automata (SCA) model, we introduce a Langevin equation model for the size evolution of the PBC that reproduces the qualitative characteristics of the SCA model. The results suggest that the emergence of the jammed state in a quasi-one-dimensional counterflow is caused by a saddle-node bifurcation.

The use of dyadic interaction between agents, in combination with homophily (the principle that “likes attract”) in the Axelrod model for the study of cultural dissemination, has two important problems: the prediction of monoculture in large societies and an extremely narrow window of noise levels in which diversity with local convergence is obtained. Recently, the inclusion of social influence has proven to overcome them [A. Flache and M. W. Macy, e-print arXiv:0808.2710]. Here, we extend the Axelrod model with social influence interaction for the study of mass media effects through the inclusion of a superagent which acts over the whole system and has non-null overlap with each agent of the society. The dependence with different parameters as the initial social diversity, size effects, mass media strength, and noise is outlined. Our results might be relevant in several socioeconomic contexts and for the study of the emergence of collective behavior in complex social systems.

We explore the noiseless Burgers dynamics in the inviscid limit, the so-called “adhesion model” in cosmology, in a regime where (almost) all the fluid particles are embedded within pointlike massive halos. Following previous works, we focus our investigations on a “geometrical” model, where the matter evolution within the shock manifold is defined from a geometrical construction. This hypothesis is at variance with the assumption that the usual continuity equation holds but, in the inviscid limit, both models agree in the regular regions. Taking advantage of the formulation of the dynamics of this “geometrical model” in terms of Legendre transforms and convex hulls, we study the evolution with time of the distribution of matter and the associated partitions of the Lagrangian and Eulerian spaces. We describe how the halo mass distribution derives from a triangulation in Lagrangian space, while the dual Voronoi-like tessellation in Eulerian space gives the boundaries of empty regions with shock nodes at their vertices. We then emphasize that this dynamics actually leads to halo fragmentations for space dimensions greater or equal to 2 (for the inviscid limit studied in this paper). This is most easily seen from the properties of the Lagrangian-space triangulation and we illustrate this process in the two-dimensional (2D) case. In particular, we explain how pointlike halos only merge through three-body collisions while two-body collisions always give rise to two new massive shock nodes (in 2D). This generalizes to higher dimensions and we briefly illustrate the three-dimensional case. This leads to a specific picture for the continuous formation of massive halos through successive halo fragmentations and mergings.

We have experimentally studied the impact of an initially planar axisymmetric vortex ring, incident at an oblique angle, upon a gravity-induced interface separating two fluids of differing densities. After impact, the vortex ring was found to exhibit a variety of subsequent trajectories, which we organize according to both the incidence angle, ${\theta }_i$, and the interface strength, defined as the ratio of the Atwood and Froude numbers, $A/F$. For grazing incidence angles $\left({\theta }_i\gtrsim 70°\right)$ vortices either penetrate or reflect from the interface, depending on whether the interface is weak or strong. In some cases, reflected vortices execute damped oscillations before finally disintegrating. For smaller incidence angles $\left({\theta }_i\lesssim 70°\right)$ vortices penetrate the interface. When there is a strong interface, these vortices are observed to curve back up toward the interface. When there is a weak interface, these vortices are observed to refract downward, away from the interface. The critical interface strength below which vortex ring refraction is observed is given by ${\text{log}}_{10}\left(A/F\right)=-2.38\pm 0.05$.

The aim of the paper is the study of dynamo action using a simple nonlinear model in the framework of magnetohydrodynamic turbulence. The nonlinear behavior of the system is described by using a shell model for velocity field and magnetic field fluctuations, modified for the magnetic field at the largest scale by a term describing a supercritical pitchfork bifurcation. Turbulent fluctuations generate a dynamical situation where the large-scale magnetic field jumps between two states which represent the opposite polarities of the magnetic field. Despite its simplicity, the model has the capability to describe a long time series of reversals from which we infer results about the statistics of persistence times and scaling laws of cancellations between opposite polarities for different magnetic diffusivity coefficients. These properties of the model are compared with real paleomagnetic data, thus revealing the origin of long-range correlations in the process.

The stability of a thermally stratified liquid metal flow is considered numerically. The flow is driven by a rotating magnetic field in a cylinder heated from above and cooled from below. The stable thermal stratification turns out to destabilize the flow. This is explained by the fact that a stable stratification suppresses the secondary meridional flow, thus indirectly enhancing the primary rotation. The instability in the form of Taylor-Görtler rolls is consequently promoted. These rolls can only be excited by finite disturbances in the isothermal flow. A sufficiently strong thermal stratification transforms this nonlinear bypass instability into a linear one reducing, thus, the critical value of the magnetic driving force. A weaker temperature gradient delays the linear instability but makes the bypass transition more likely. We quantify the non-normal and nonlinear components of this transition by direct numerical simulation of the flow response to noise. It is observed that the flow sensitivity to finite disturbances increases considerably under the action of a stable thermal stratification. The capabilities of the random forcing approach to identify disconnected coherent states in a general case are discussed.