The properties of the anisotropic random sequential adsorption (RSA) of objects of various shapes on a two-dimensional triangular lattice are studied numerically by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding lattice steps, whereby the first step determines the orientation of the object. Anisotropy is introduced by positing unequal probabilities for orientation of depositing objects along different directions of the lattice. This probability is equal $p$ or $(1-p)/2$, depending on whether the randomly chosen orientation is horizontal or not, respectively. Approach of the coverage $\theta \left(t\right)$ to the jamming limit ${\theta }_{\text{jam}}$ is found to be exponential ${\theta }_{\text{jam}}-\theta \left(t\right)\propto \exp (-t/\sigma )$, for all probabilities $p$. It was shown that the relaxation time $\sigma$ increases with the degree of anisotropy in the case of elongated and asymmetrical shapes. However, for rounded and symmetrical shapes, values of $\sigma$ and ${\theta }_{\text{jam}}$ are not affected by the presence of anisotropy. We finally analyze the properties of the anisotropic RSA of polydisperse mixtures of $k$-mers. Strong dependencies of the parameter $\sigma$ and the jamming coverage ${\theta }_{\text{jam}}$ on the degree of anisotropy are obtained. It is found that anisotropic constraints lead to the increased contribution of the longer $k$-mers in the total coverage fraction of the mixture.

The tubelike cages of stiff polymers in entangled solutions have been shown to exhibit characteristic spatial heterogeneities. We explain these observations by a systematic theory generalizing previous work by Morse [Phys. Rev. E 63, 031502 (2001)]. With a local version of the binary collision approximation, the distribution of confinement strengths is calculated, and the magnitude and the distribution function of tube radius fluctuations are predicted. Our main result is a unique scaling function for the tube radius distribution, in good agreement with experimental and simulation data.

A system of equations describing motion of dust particles in gas discharge plasma is formulated. This system is developed for a monolayer of dust particles with an account of dust particle charge fluctuations and features of the discharge near-electrode layer. Molecular dynamics simulation of the dust particles system is performed. A mechanism of dust particle average kinetic energy increase is suggested on the basis of theoretical analysis of the simulation results. It is shown that heating of dust particles' vertical motion is initiated by forced oscillations caused by the dust particles' charge fluctuations. The process of energy transfer from vertical to horizontal motion is based on the phenomenon of the parametric resonance. The combination of parametric and forced resonances explains the abnormally high values of the dust particles' kinetic energy. Estimates of frequency, amplitude, and kinetic energy of dust particles are close to the experimental values.

We consider the mass-dependent aggregation process $(k+1)X\to X$, given a fixed number of unit mass particles in the initial state. One cluster is chosen proportional to its mass and is merged into one, either with $k$ neighbors in one dimension, or—in the well-mixed case—with $k$ other clusters picked randomly. We find the same combinatorial exact solutions for the probability to find any given configuration of particles on a ring or line, and in the well-mixed case. The mass distribution of a single cluster exhibits scaling laws and the finite-size scaling form is given. The relation to the classical sum kernel of irreversible aggregation is discussed.

We investigate colloid-facilitated contaminant advection in strongly heterogeneous geological medium with fractal properties. Transport regimes and asymptotic behavior at large distances are studied for different relationships between sorption parameters and characteristics of percolation medium. Crossover times between transport regimes are determined.

The discrete-time version of totally asymmetric simple-exclusion process (TASEP) on a finite one-dimensional lattice is studied with the periodic boundary condition. Each particle at a site hops to the next site with probability $0⩽p⩽1$ if the next site is empty. This condition can be rephrased by the condition that the number $n$ of vacant sites between the particle and the next particle is positive. Then the average velocity is given by a product of the hopping probability $p$ and the probability that $n⩾1$. By mapping the TASEP to another driven diffusive system called the zero-range process, it is proved that the distribution function of vacant sites in the stationary state is exactly given by a factorized form. We define $k$-particle velocity correlation function as the expectation value of a product of velocities of $k$ particles in the stationary distribution. It is shown that it does not depend on positions of $k$ particles on a circle but depends only on the number $k$. We give explicit expressions for all velocity correlation functions using the Gauss hypergeometric functions. Covariance of velocities of two particles is studied in detail, and we show that velocities become independent asymptotically in the thermodynamic limit.

The time reversal of stochastic diffusion processes is revisited with emphasis on the physical meaning of the time-reversed drift and the noise prescription in the case of multiplicative noise. The local kinematics and mechanics of free diffusion are linked to the hydrodynamic description. These properties also provide an interpretation of the Pope-Ching formula for the steady-state probability density function along with a geometric interpretation of the fluctuation-dissipation relation. Finally, the statistics of the local entropy production rate of diffusion are discussed in the light of local diffusion properties, and a stochastic differential equation for entropy production is obtained using the Girsanov theorem for reversed diffusion. The results are illustrated for the Ornstein-Uhlenbeck process.

The phase-field model of Echebarria, Folch, Karma, and Plapp [Phys. Rev. E 70, 061604 (2004)] is extended to the case of rapid solidification in which local nonequilibrium phenomena occur in the bulk phases and within the diffuse solid-liquid interface. Such an extension leads to the fully hyperbolic system of equations given by the atomic diffusion equation and the phase-field equation of motion. This model is applied to the problem of solute trapping, which is accompanied by the entrapment of solute atoms beyond chemical equilibrium by a rapidly moving interface. The model predicts the beginning of complete solute trapping and diffusionless solidification at a finite solidification velocity equal to the diffusion speed in bulk liquid.

We generalize the belief-propagation algorithm to sparse random networks with arbitrary distributions of motifs (triangles, loops, etc.). Each vertex in these networks belongs to a given set of motifs (generalization of the configuration model). These networks can be treated as sparse uncorrelated hypergraphs in which hyperedges represent motifs. Here a hypergraph is a generalization of a graph, where a hyperedge can connect any number of vertices. These uncorrelated hypergraphs are treelike (hypertrees), which crucially simplifies the problem and allows us to apply the belief-propagation algorithm to these loopy networks with arbitrary motifs. As natural examples, we consider motifs in the form of finite loops and cliques. We apply the belief-propagation algorithm to the ferromagnetic Ising model with pairwise interactions on the resulting random networks and obtain an exact solution of this model. We find an exact critical temperature of the ferromagnetic phase transition and demonstrate that with increasing the clustering coefficient and the loop size, the critical temperature increases compared to ordinary treelike complex networks. However, weak clustering does not change the critical behavior qualitatively. Our solution also gives the birth point of the giant connected component in these loopy networks.

We generate maximally random jammed (MRJ) packings of the four nontiling Platonic solids (tetrahedra, octahedra, dodecahedra, and icosahedra) using the adaptive-shrinking-cell method [S. Torquato and Y. Jiao, Phys. Rev. E 80, 041104 (2009)]. Such packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid. The MRJ packing fractions for tetrahedra, octahedra, dodecahedra, and icosahedra are, respectively, $0.763\pm 0.005$, $0.697\pm 0.005$, $0.716\pm 0.002$, and $0.707\pm 0.002$. We find that as the number of facets of the particles increases, the translational order in the packings increases while the orientational order decreases. Moreover, we show that the MRJ packings are hyperuniform (i.e., their infinite-wavelength local-number-density fluctuations vanish) and possess quasi-long-range pair correlations that decay asymptotically with scaling $r^{-4}$. This provides further evidence that hyperuniform quasi-long-range correlations are a universal feature of MRJ packings of frictionless particles of general shape. However, unlike MRJ packings of ellipsoids, superballs, and superellipsoids, which are hypostatic, MRJ packings of the nontiling Platonic solids are isostatic. We provide a rationale for the organizing principle that the MRJ packing fractions for nonspherical particles with sufficiently small asphericities exceed the corresponding value for spheres ($\sim$0.64). We also discuss how the shape and symmetry of a polyhedron particle affects its MRJ packing fraction.

In a granular solid, mechanical equilibrium requires a delicate balance of forces at the disordered grain scale. To understand how macroscopic rigidity can emerge in this amorphous solid, it is crucial that we understand how Newton’s laws pass from the disordered grain scale to the laboratory scale. In this work, we introduce an exact discrete calculus, in which Newton’s laws appear as differential relations at the scale of a single grain. Using this calculus, we introduce gauge variables that describe identically force- and torque-balanced configurations. In a first, intrinsic formulation, we use the topology of the contact network, but not its geometry. In a second, extrinsic formulation, we introduce geometry with the Delaunay triangulation. These formulations show, with exact methods, how topology and geometry in a disordered medium are related by constraints. In particular, we derive Airy’s expression for a divergence-free, symmetric stress tensor in two and three dimensions.

We study the morphology and dynamics of craterlike structures formed when free-falling, randomly oriented, elongated particles bounce off a flat surface in a single particle scattering mode. The origin of a sharply defined rim with its associated structure, the factors determining the rim diameter, and the scaling of the diameter with impact velocity are examined. The probability distribution of rebounding particle ranges is calculated for a particular example and shown to provide a precursor description of structure formation.

The hydrodynamic properties of rigid fractal aggregates have been investigated by considering their motion in shear flow in the Stokesian dynamics approach. Due to the high fluid viscosity and small particle inertia of colloidal systems, the total force and torque applied to the aggregate reach equilibrium values in a short time. Obtaining equilibrating motions for a number of independent samples, one can extract the average hydrodynamic characteristics of the given fractal aggregates. Despite the geometry of these objects being essentially disordered, the average drag-force distributions for aggregates show symmetric patterns. Moreover, these distributions collapse on a single master curve, characteristic of the nature of the aggregates, provided the positions of the particles are rescaled with the geometric radius of gyration. This result can be used to explain the reason why the stress acting on an aggregate and moments of the forces acting on contact points between particles follow power-law behaviors with the aggregate size. Moreover, the values of the exponents can be explained. As a consequence, considering cohesive force typical for colloidal particles, we find that even aggregates smaller than a few dozen particles must experience restructuring when typical shear flow is applied.

The denaturation transition which takes place in circular DNA is analyzed by extending the Poland-Scheraga (PS) model to include the winding degrees of freedom. We consider the case of a homopolymer whereby the winding number of the double-stranded helix, released by a loop denaturation, is absorbed by supercoils. We find that as in the case of linear DNA, the order of the transition is determined by the loop exponent $c$. However the first-order transition displayed by the PS model for $c>2$ in linear DNA is replaced by a continuous transition with arbitrarily high order as $c$ approaches 2, while the second-order transition found in the linear case in the regime $1<c⩽2$ disappears. In addition, our analysis reveals that melting under fixed linking number is a condensation transition, where the condensate is a macroscopic loop which appears above the critical temperature.

Epidemic outbreaks have been shown to be closely related to the rendezvous-induced transmission of infection, which is caused by casual contact with infected individuals in public gatherings. To investigate rendezvous effects in the spread of infectious diseases, we propose an epidemic model on metapopulation networks bipartite-divided into two sets of location and rendezvous nodes. At a given transition rate ${\gamma }_{k{k}^{\prime }}^p$, each individual transfers from location $k$ to rendezvous $p$ (where rendezvous-induced disease incidence occurs) and thereafter moves to location $k^{\prime }$. We find that the eigenstructure of a transition-rate-dependent matrix determines the epidemic threshold condition. Both analytical and numerical results show that rendezvous-induced transmission accelerates the progress of infectious diseases, implying the significance of outbreak control measures including prevention of public gatherings or decentralization of a large-scale rendezvous into downsized ones.

Recently an alternative approach to the determination of dynamic correlation lengths ξ for supercooled liquids, based on the properties of the slow (picosecond) vibrational dynamics, was carried out [Hong, Novikov, and Sokolov, Phys. Rev. E 83, 061508 (2011)]. Although these vibrational measurements are typically conducted well below the glass transition temperature, the liquid is frozen at $T_g$, whereby structural correlations, density variations, etc., manifested at low temperatures as spatial fluctuations of local elastic constants, can be related to a dynamic heterogeneity length scale for the liquid state. We compare ξ from this method to values calculated using an approximation to the four-point dynamic susceptibility. For 26 different materials we find good correlation between the two measures; moreover, the pressure dependences are consistent within the large experimental error. However, ξ from Boson peak measurements above $T_g$ have a different, and unrealistic, temperature dependence.

Despite its importance for rumors or innovations propagation, peer-to-peer collaboration, social networking, or marketing, the dynamics of information spreading is not well understood. Since the diffusion depends on the heterogeneous patterns of human behavior and is driven by the participants’ decisions, its propagation dynamics shows surprising properties not explained by traditional epidemic or contagion models. Here we present a detailed analysis of our study of real viral marketing campaigns where tracking the propagation of a controlled message allowed us to analyze the structure and dynamics of a diffusion graph involving over 31 000 individuals. We found that information spreading displays a non-Markovian branching dynamics that can be modeled by a two-step Bellman-Harris branching process that generalizes the static models known in the literature and incorporates the high variability of human behavior. It explains accurately all the features of information propagation under the “tipping point” and can be used for prediction and management of viral information spreading processes.

The international trade network (ITN) has received renewed multidisciplinary interest due to recent advances in network theory. However, it is still unclear whether a network approach conveys additional, nontrivial information with respect to traditional international-economics analyses that describe world trade only in terms of local (first-order) properties. In this and in a companion paper, we employ a recently proposed randomization method to assess in detail the role that local properties have in shaping higher-order patterns of the ITN in all its possible representations (binary or weighted, directed or undirected, aggregated or disaggregated by commodity) and across several years. Here we show that, remarkably, the properties of all binary projections of the network can be completely traced back to the degree sequence, which is therefore maximally informative. Our results imply that explaining the observed degree sequence of the ITN, which has not received particular attention in economic theory, should instead become one the main focuses of models of trade.

Based on the misleading expectation that weighted network properties always offer a more complete description than purely topological ones, current economic models of the International Trade Network (ITN) generally aim at explaining local weighted properties, not local binary ones. Here we complement our analysis of the binary projections of the ITN by considering its weighted representations. We show that, unlike the binary case, all possible weighted representations of the ITN (directed and undirected, aggregated and disaggregated) cannot be traced back to local country-specific properties, which are therefore of limited informativeness. Our two papers show that traditional macroeconomic approaches systematically fail to capture the key properties of the ITN. In the binary case, they do not focus on the degree sequence and hence cannot characterize or replicate higher-order properties. In the weighted case, they generally focus on the strength sequence, but the knowledge of the latter is not enough in order to understand or reproduce indirect effects.

Kelvin-Helmholtz instability (KHI) driven by velocity shear is a generator of waves found away from the vicinity of the velocity-shear layers since the fast-mode waves radiated from the surface perturbation can propagate away from the transition layer. Thus the nonlinear evolution associated with KHI is not confined near the velocity-shear layer. To understand the physical processes in multiple velocity-shear layers, the interactions between two KHIs at a pair of tangential discontinuities are studied by two-dimensional magnetohydrodynamic simulations. It is shown that the interactions between two neighboring velocity-shear layers are dominated by the propagation of the fast-mode waves radiated from KHIs in a nonuniform medium. That is, the fast-mode Mach number of the surface waves $M_{Fy}$, a key factor of the nonlinear evolution of KHI, will vary with the nonuniform background plasma velocity due to the existence of two neighboring velocity-shear layers. As long as the $M_{Fy}$ observed in the plasma rest frame across the neighboring velocity-shear layer is larger than one, newly formed fast-mode Mach-cone-like (MCL) plane waves generated by the fast-mode waves can be found in this region. As results of the interactions of two KHIs, reflection and distortion of the MCL plane waves generate the turbulence and increase the plasma temperature, which provide possible mechanisms of heating and accelerating local plasma between two neighboring velocity-shear layers.