A one-dimensional system of particles is examined in which even numbered particles are bound to adjacent even particles by harmonic spring forces, while odd particles are free. Even and odd particles collide elastically. This is a momentum conserving modification of the famous “ding-a-ling” model. Molecular-dynamics simulations are carried out and the current power spectra are obtained. The energy current power spectrum has zero slope at low frequencies. This implies that the thermal conductivity $\kappa$ is finite and independent of system length $L$, for $L$ sufficiently large. Steady-state simulations provide further evidence that $\kappa$ is independent of $L$ at large values of $L$. The relevance of this result to the proof by Prosen and Campbell that momentum conservation with nonvanishing pressure implies an infinite thermal conductivity is discussed.

We computationally investigate the dependence of the rheology of dense sheared granular mixtures on their particle size distribution. We consider the simplest case of a binary mixture of two different sized particles where the fraction of large particles is varied from one simulation to the next while the total solid mass is kept constant. We find that the variation of the rheology with the particle size distribution depends on the boundary conditions. For example, under constant pressure conditions the effective friction coefficient ${\mu }^{\ast }$ (the ratio between shear and pressure stresses at the boundary) increases mildly with the average particle size. On the other hand, under constant volume conditions, ${\mu }^{\ast }$ has a nonmonotonic dependence on the average particle size that is related to the proximity of the system solid fraction to the maximum packing fraction. Somewhat surprisingly, then, ${\mu }^{\ast }$ scales with a dimensionless shear rate (a generalized inertial number) in the same way for either boundary condition. We show that, for our system of relatively hard spheres, these relationships are governed largely by the ratio between average collision times and mean-free-path times, also independent of boundary conditions.

We have formulated the problem of generating dense packings of nonoverlapping, nontiling nonspherical particles within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem called the adaptive-shrinking cell (ASC) formulation [S. Torquato and Y. Jiao, Phys. Rev. E 80, 041104 (2009)]. Because the objective function and impenetrability constraints can be exactly linearized for sphere packings with a size distribution in $d$-dimensional Euclidean space ${\mathbb{R}}^d$, it is most suitable and natural to solve the corresponding ASC optimization problem using sequential-linear-programming (SLP) techniques. We implement an SLP solution to produce robustly a wide spectrum of jammed sphere packings in ${\mathbb{R}}^d$ for $d=2$, 3, 4, 5, and 6 with a diversity of disorder and densities up to the respective maximal densities. A novel feature of this deterministic algorithm is that it can produce a broad range of inherent structures (locally maximally dense and mechanically stable packings), besides the usual disordered ones (such as the maximally random jammed state), with very small computational cost compared to that of the best known packing algorithms by tuning the radius of the influence sphere. For example, in three dimensions, we show that it can produce with high probability a variety of strictly jammed packings with a packing density anywhere in the wide range [0.6, 0.7408…], where $\pi /\sqrt{18}=0.7408\dots$ corresponds to the density of the densest packing. We also apply the algorithm to generate various disordered packings as well as the maximally dense packings for $d=2$, 4, 5, and 6. Our jammed sphere packings are characterized and compared to the corresponding packings generated by the well-known Lubachevsky-Stillinger (LS) molecular-dynamics packing algorithm. Compared to the LS procedure, our SLP protocol is able to ensure that the final packings are truly jammed, produces disordered jammed packings with anomalously low densities, and is appreciably more robust and computationally faster at generating maximally dense packings, especially as the space dimension increases.

In the present work, we develop a systematic examination of the existence, stability, and dynamical properties of a discrete breather at the interface between a diatomic and a monoatomic granular chain. We remarkably find that such an “interface breather” is more robust than its bulk diatomic counterpart throughout the gap of the linear spectrum. The latter linear spectral gap needs to exist for the breather state to arise and the relevant spectral conditions are discussed. We illustrate the minimal excitation conditions under which such an interface breather can be “nucleated” and analyze its apparently weak interaction with regular highly nonlinear solitary waveforms.

We discuss, with the aid of numerical calculations based on a Landau–de Gennes theory, the stabilization of a blue phase in chiral liquid crystals by introducing a guest component. Our argument is based on a common speculation that cores of disclination lines with higher free-energy density are replaced by the guest component. We assume that the guest component forms sharp interfaces with the liquid crystal (strong segregation). We show that, by a suitable choice of materials with small interfacial tension, a guest component of volume fraction less than 10% drastically increases the temperature range of thermodynamic stability of a blue phase, in agreement with experiments [Kikuchi et al., Nature Mater. 1, 64 (2002)].

We report measurements of the temperature dependences of the splay $\left(K_{11}\right)$ and bend $\left(K_{33}\right)$ elastic constants of several homologues and a binary mixutre of disulfide bridged symmetric dimers made of alkoxy cyanobiphenyl monomeric units. All of them have an even number $m$ of carbon and sulfur atoms in the linking chain and expected to have linear conformations. Both $K_{11}$ and $K_{33}$ alternate depending on the parity of x which is the number of carbon atoms in the alkyl chain of a monomer. We will refer to this as ‘odd-even' effect. This effect, occurs near the nematic-isotropic transition temperature. $T_{\text{NI}}$, but monotonically decrease with $m$ at lower temperatures. We argue that these results imply large rotational fluctuations of the two halves of the dimers about the S-S bond giving rise to average bent conformations near $T_{\text{NI}}$. At lower temperatures those conformations which can adapt better to the given curvature deformation in the medium are favored.

A high-pressure chamber was designed to study crumpling beyond the power-law regime. Preceded by a smooth transition, the crumpled ball that characterizes the high-pressure state contains less than 50% air and exhibits separate ordered domains. All data for different sheet thicknesses, sizes, and numbers were found to collapse to a master line when using volume ratio and pressure as the plotting parameters, which suggests the existence of a scaling relation. Based on these findings, we deduced a bundled-layer model that could consistently explain six outstanding properties at both low and high pressures. This successful union of theory and experiment has strong bearings on other soft-matter systems where similar changes in mechanical response are also linked to reorganization of structure.

Quantitative evidence that establishes the existence of the hairpin vortex state (HVS) [T. Itano and S. C. Generalis, Phys. Rev. Lett. 102, 114501 (2009)] in plane Couette flow (PCF) is provided in this work. The evidence presented in this paper shows that the HVS can be obtained via homotopy from a flow with a simple geometrical configuration, namely, the laterally heated flow (LHF). Although the early stages of bifurcations of LHF have been previously investigated, our linear stability analysis reveals that the root in the LHF yields multiple branches via symmetry breaking. These branches connect to the PCF manifold as steady nonlinear amplitude solutions. Moreover, we show that the HVS has a direct bifurcation route to the Rayleigh-Bénard convection.

We report large-scale (${10}^7$ atoms in an 85-nm-wide container) molecular dynamics simulations of collapse of nanoscopic (5–12 nm in diameter) voids in liquid argon. During the collapse the pressure on the liquid side decreases, and this decrease propagates into liquid at the speed of sound. Despite the nonuniform profile of pressure in the liquid the solutions of the Rayleigh-Plesset equation compares well to the measured evolution of the radius of the void and the velocity of the interface. Evaporation of liquid into the void does not affect the dynamics appreciably.

Nonlinear propagation characteristics are investigated theoretically in a one-dimensional photonic band-gap structure doped with a nonlinear indefinite metamaterial defect for five distinct frequency intervals. It is found from the electric field distribution that there exists the bright gap solitonlike when the nonlinear indefinite metamaterial defect is a cut-off medium, while the dark gap solitonlike can appear in the nonlinear never cut-off defect layer. It is also found that there exists corresponding bistable lateral shift the properties of which are strongly dependent on the permittivity and permeability of nonlinear indefinite metamaterials. Moreover, in contrast to the switch-down threshold value, the switch-up threshold value is more sensitive to the incident frequency.

Dissipative particle dynamics (DPD) is a mesoscopic simulation method that describes “clusters” of molecules as a single numerical particle. DPD is a very effective method but it introduces numerical artifacts through the coarse-graining procedure, such as particle ordering in the near-wall region. These artifacts can result in nonphysical phenomena during a simulation of a polymer tethered to the wall undergoing shear flow: polymer sticking and overextension for higher shear rates. In this paper we report that a version of DPD with a so-called solidification boundary formulation and conservative-force interactions based on the equation of state allows to reduce number density fluctuations in near-wall region significantly.

The aim of this study is to investigate a wave dynamics and a size scaling of avalanches which were created by the mathematical model [J. Černák, Phys. Rev. E 65, 046141 (2002)]. Numerical simulations were carried out on a two-dimensional lattice $L\times L$ in which two constant thresholds $E_c^I=4$ and $E_c^{II}>E_c^I$ were randomly distributed. The density of sites $c$ of the thresholds $E_c^{II}$ and threshold $E_c^{II}$ are parameters of the model. Autocorrelations of avalanche size waves, Hurst exponents, avalanche structures, and avalanche size moments were determined for several densities $c$ and thresholds $E_c^{II}$. The results show correlated avalanche size waves and multifractal scaling of avalanche sizes not only for specific conditions, densities $c=0.0,1.0$ and thresholds $8\le E_c^{II}\le 32$, in which relaxation rules were precisely balanced, but also for more general conditions, densities $0.0<c<1.0$ and thresholds $8\le E_c^{II}\le 32$, in which relaxation rules were unbalanced. The results suggest that the hypothesis of a precise relaxation balance could be a specific case of a more general rule.

Extensive Monte Carlo simulations were carried out to investigate the nature of the ordering transition of a model of adsorbed self-assembled rigid rods on the bonds of a square lattice [Tavares et al., Phys. Rev. E 79, 021505 (2009)]. The polydisperse rods undergo a continuous ordering transition that is found to be in the two-dimensional Ising universality class, as in models where the rods are monodisperse. This finding is in sharp contrast with the recent claim that equilibrium polydispersity changes the nature of the phase transition in this class of models [López et al., Phys. Rev. E 80, 040105(R) (2009)].

Proteins involved in homologous recombination such as RecA and hRad51 polymerize on single- and double-stranded DNA according to a nucleation-growth kinetics, which can be monitored by single-molecule in vitro assays. The basic models currently used to extract biochemical rates rely on ensemble averages and are typically based on an underlying process of bidirectional polymerization, in contrast with the often observed anisotropic polymerization of similar proteins. For these reasons, if one considers single-molecule experiments, the available models are useful to understand observations only in some regimes. In particular, recent experiments have highlighted a steplike polymerization kinetics. The classical model of one-dimensional nucleation growth, the Kolmogorov-Avrami-Mehl-Johnson (KAMJ) model, predicts the correct polymerization kinetics only in some regimes and fails to predict the steplike behavior. This work illustrates by simulations and analytical arguments the limitation of applicability of the KAMJ description and proposes a minimal model for the statistics of the steps based on the so-called stick-breaking stochastic process. We argue that this insight might be useful to extract information on the time and length scales involved in the polymerization kinetics.

A record-breaking temperature is the highest or lowest temperature at a station since the period of time considered began. The temperatures at a station constitute a time series. After the removal of daily and annual periodicities, the primary considerations are trends (i.e., global warming) and long-range correlations. We first carry out Monte Carlo simulations to determine the influence of trends and long-range correlations on record-breaking statistics. We take a time series that is a Gaussian white noise and give the classic record-breaking theory results for an independent and identically distributed process. We then carry out simulations to determine the influence of long-range correlations and linear temperature trends. For the range of fractional Gaussian noises that are observed to be applicable to temperature time series, the influence on the record-breaking statistics is less than 10%. We next superimpose a linear trend on a Gaussian white noise and extend the theory to include the effect of an additive trend. We determine the ratios of the number of maximum to the number of minimum record-breaking temperatures. We find the single governing parameter to be the ratio of the temperature change per year to the standard deviation of the underlying white noise. To test our approach, we consider a 30 yr record of temperatures at the Mauna Loa Observatory for 1977–2006. We determine the temperature trends by direct measurements and use our simulations to infer trends from the number of record-breaking temperatures. The two approaches give values that are in good agreement. We find that the warming trend is primarily due to an increase in the (overnight) minimum temperatures, while the maximum (daytime) temperatures are approximately constant.

This paper describes a method for implementing surface reaction kinetics in lattice Boltzmann simulations. The interpolated boundary conditions are capable of simulating surface reactions and dissolution at both stationary and moving solid-fluid and fluid-fluid interfaces. Results obtained with the boundary conditions are compared to analytical solutions for first-order and constant-flux kinetic surface reactions in a one-dimensional half space, as well as to the analytical solution for evaporation from the surface of a cylinder. Excellent agreement between analytical and simulated results is obtained for a wide range of diffusivities, lattice velocities, and surface reaction rates. The boundary model’s ability to represent dissolution in binary fluid mixtures is demonstrated by modeling diffusion from a rising bubble and dissolution of a droplet near a flat plate.

We derive exact analytic expressions for the distributions of eigenvalues and singular values for the product of an arbitrary number of independent rectangular Gaussian random matrices in the limit of large matrix dimensions. We show that they both have power–law behavior at zero and determine the corresponding powers. We also propose a heuristic form of finite size corrections to these expressions which very well approximates the distributions for matrices of finite dimensions.

Starting from a master equation, we derive the evolution equation for the size distribution of elements in an evolving system, where each element can grow, divide into two, and produce new elements. We then probe general solutions of the evolution equation, to obtain such skew distributions as power-law, log-normal, and Weibull distributions, depending on the growth or division and production. Specifically, repeated production of elements of uniform size leads to power-law distributions, whereas production of elements with the size distributed according to the current distribution as well as no production of new elements results in log-normal distributions. Finally, division into two, or binary fission, bears Weibull distributions. Numerical simulations are also carried out, confirming the validity of the obtained solutions.

We present an approach of topology biased random walks for undirected networks. We focus on a one-parameter family of biases, and by using a formal analogy with perturbation theory in quantum mechanics we investigate the features of biased random walks. This analogy is extended through the use of parametric equations of motion to study the features of random walks vs parameter values. Furthermore, we show an analysis of the spectral gap maximum associated with the value of the second eigenvalue of the transition matrix related to the relaxation rate to the stationary state. Applications of these studies allow ad hoc algorithms for the exploration of complex networks and their communities.

Cascade dynamics on networks are usually analyzed statically to determine existence criteria for cascades. Here, the Watts model of threshold dynamics on random Erdős-Rényi networks is analyzed to determine the dynamic time evolution of cascades. The network is assumed to have a specific finite number of nodes $n$ and is not assumed to be treelike. All combinations of threshold $\varphi$, network average nodal degree $z$, and seed sizes $\left|S\right|$ from a single node up are included. The analysis permits study of network size effects and increased clustering coefficient. Several size effects not found by infinite network theory are predicted by the analysis and confirmed by simulations. In the region of $\varphi$ and $z$ where a single node can start a cascade, cascades are expanding, in the sense that each step flips a larger group than the previous step did. We show that this region extends to larger values of $z$ than predicted by infinite network analyses. In the region where larger seeds are needed (size proportional to $n$), cascades begin by contracting: at the outset, each step flips fewer nodes than the previous step, but eventually the process reverses and becomes expanding. A critical mass that grows during the cascade beyond an easily-calculated threshold is identified as the cause of this reversal.