This paper investigates the equilibrium behavior of broadly studied synchronization dynamics of coupled systems, among which shared information is delayed. The underlying relationship is established between graph structures and the largest amount of delay the dynamics can withstand without losing stability. In particular, based on Cartesian product of graphs, we present the rules and limitations for synthesizing the graphs of large-scale systems that can remain stable for as large delays as possible. Examples are provided to demonstrate the results.

The conventional momentum-exchange method (CME) is verified to be accurate for the stationary boundary by Mei et al. [Phys. Rev. E 65, 041203 (2002)], but it might be inaccurate when the boundary is moving in the lattice Boltzmann simulations. A lattice-type-dependent momentum-exchange method (LME) is presented to evaluate the hydrodynamic force on moving boundaries, in which the additional momenta induced by the type-changing lattices are well considered. LME preserves the superior features of CME, such as reliability, simplicity, and parallelism. Without any interpolation and integration, the algorithm is independent of boundary geometries, and therefore, efficient in computation and easy to be implemented in both two and three dimensions. A series of cylinder sedimentations are simulated to illustrate the accuracy and robustness of LME, and the results are in excellent agreement with those by the arbitrary Lagrangian-Eulerian technique (ALE). The lateral migrations of a particle are also investigated in the simulations of a neutrally buoyant cylinder in a Poiseuille flow, and consistent with the Segré-Silberberg effect.

Paying attention to the difference of density of states, $\Delta \ln g\left(E\right)\equiv \ln g(E+\Delta E)-\ln g\left(E\right)$, we study the convergence of the Wang-Landau method. We show that this quantity is a good estimator to discuss the errors of convergence and refer to the $1/t$ algorithm. We also examine the behavior of the first-order transition with this difference of density of states in connection with Maxwell's equal area rule. A general procedure to judge the order of transition is given.

We study the mean turnaround time of a Brownian needle in a narrow planar strip. When the needle is only slightly shorter than the width of the strip, the computation becomes a nonstandard narrow escape problem. We develop a boundary layer method, based on a conformal mapping of cusplike narrow straits, to obtain an explicit asymptotic approximation to the mean turnaround time. Our result suggests that two-dimensional domains lying between parallel walls may play a significant role in DNA repair.

The Husimi distribution provides for a coarse-grained representation of the phase-space distribution of a quantum system, which may be used to track the growth of entropy of the system. We present a general and systematic method of solving the Husimi equation of motion for an isolated quantum system, and we construct a coarse-grained Hamiltonian whose expectation value is exactly conserved. As an application, we numerically solve the Husimi equation of motion for two-dimensional Yang-Mills quantum mechanics (the x-y model) and calculate the time evolution of the coarse-grained entropy of a highly excited state. We show that the coarse-grained entropy saturates to a value that coincides with the microcanonical entropy corresponding to the energy of the system.

We study the critical short-time dynamical behavior of a one-dimensional model where diffusive individuals can infect a static population upon contact. The model presents an absorbing phase transition from an active to an inactive state. Previous calculations of the critical exponents based on quasistationary quantities have indicated an unusual crossover from the directed percolation to the diffusive contact process universality classes. Here we show that the critical exponents governing the slow short-time dynamic evolution of several relevant quantities, including the order parameter, its relative fluctuations, and correlation function, reinforce the lack of universality in this model. Accurate estimates show that the critical exponents are distinct in the regimes of low and high recovery rates.

A phase-separation front will leave in its wake a phase-separated morphology that differs markedly from homogeneous phase-separation morphologies. For a purely diffusive system such a front, moving with constant velocity, will generate very regular, nonequilibrium structures. We present here a numerical study of these fronts using a lattice Boltzmann method. In two dimensions these structures are regular stripes or droplet arrays. In general the kind and orientation of the selected morphology and the size of the domains depends on the speed of the front as well as the composition of the material overtaken by the phase-separation front. We present a survey of morphologies as a function of these two parameters. We show that the resulting morphologies are initial condition dependent. We then examine which of the potential morphologies is the most stable. An analytical analysis for symmetrical compositions predicts the transition point from orthogonal to parallel stripes.

The mechanics of fiber bundles has been widely studied in the literature, and fiber bundle models in particular have provided a wealth of useful analytical and numerical results for modeling ordinary materials. These models, however, are inadequate to treat bioinspired nanostructured materials, where hierarchy, multiscale, and complex properties play a decisive role in determining the overall mechanical characteristics. Here, we develop an ad hoc hierarchical theory designed to tackle these complex architectures, thus allowing the determination of the strength of macroscopic hierarchical materials from the properties of their constituents at the nanoscale. The roles of finite size, twisting angle, and friction are also included. Size effects on the statistical distribution of fiber strengths naturally emerge without invoking best-fit or unknown parameters. A comparison between the developed theory and various experimental results on synthetic and natural materials yields considerable agreement.

While degree correlations are known to play a crucial role for spreading phenomena in networks, their impact on the propagation speed has hardly been understood. Here we investigate a tunable spreading model on scale-free networks and show that the propagation becomes slow in positively (negatively) correlated networks if nodes with a high connectivity locally accelerate (decelerate) the propagation. Examining the efficient paths offers a coherent explanation for this result, while the $k$-core decomposition reveals the dependence of the nodal spreading efficiency on the correlation. Our findings should open new pathways to delicately control real-world spreading processes.

The evanescent wave field outside an optical resonator is typically strongly directional when the shape deviates even very slightly from being perfectly circular or spherical. In this Rapid Communication we show that the tunneling mechanism underlying escape from such weakly deformed resonators can lead to emission patterns that look quite different to the corresponding internal mode. A direct short-wavelength analysis is not possible because the required complex ray data cannot be found due to the presence of natural boundaries. We show, however, that an approach based on perturbative approximation of the ray families successfully describes this phenomenon. In appropriate limits, the emission pattern allows one effectively to perform a direct observation of solutions of the one-dimensional Schrödinger equation in the complex plane.

Human dynamics is known to be inhomogeneous and bursty but the detailed understanding of the role of human factors in bursty dynamics is still lacking. In order to investigate their role we devise an agent-based model, where an agent in an uncertain situation tries to reduce the uncertainty by communicating with information providers while having to wait time for responses. Here the waiting time can be considered as cost. We show that the optimal choice of the waiting time under uncertainty gives rise to the bursty dynamics, characterized by the heavy tailed distribution of optimal waiting time. We find that in all cases the efficiency for communication is relevant to the scaling behavior of the optimal waiting time distribution. On the other hand, the cost turns out in some cases to be irrelevant depending on the degree of uncertainty and efficiency.

In this paper we present a model describing susceptible-infected-susceptible-type epidemics spreading on a dynamic contact network with random link activation and deletion where link activation can be locally constrained. We use and adapt an improved effective degree compartmental modeling framework recently proposed by Lindquist et al. [J. Math Biol. 62, 143 (2010)] and Marceau et al. [Phys. Rev. E 82, 036116 (2010)]. The resulting set of ordinary differential equations (ODEs) is solved numerically, and results are compared to those obtained using individual-based stochastic network simulation. We show that the ODEs display excellent agreement with simulation for the evolution of both the disease and the network and are able to accurately capture the epidemic threshold for a wide range of parameters. We also present an analytical $R_0$ calculation for the dynamic network model and show that, depending on the relative time scales of the network evolution and disease transmission, two limiting cases are recovered: (i) the static network case when network evolution is slow and (ii) homogeneous random mixing when the network evolution is rapid. We also use our threshold calculation to highlight the dangers of relying on local stability analysis when predicting epidemic outbreaks on evolving networks.

We report an algorithm of constructing linear and nonlinear potentials in the two-dimensional Gross-Pitaevskii equation subject to given boundary conditions, which allow for exact analytic solutions. The obtained solutions represent superfluid flows in inhomogeneous Bose-Einstein condensates. The method is based on the combination of the similarity reduction of the two-dimensional Gross-Pitaevskii equation to the one-dimensional nonlinear Schrödinger equation, the latter allowing for exact solutions, with the conformal mapping of the given domain, where the flow is considered, to a half space. The stability of the obtained flows is addressed. A number of stable and physically relevant examples are described.

We present a discrete-element method (DEM) model to simulate the mechanical behavior of sea ice in response to ocean waves. The interaction of ocean waves and sea ice potentially can lead to the fracture and fragmentation of sea ice depending on the wave amplitude and period. The fracture behavior of sea ice explicitly is modeled by a DEM method where sea ice is modeled by densely packed spherical particles with finite sizes. These particles are bonded together at their contact points through mechanical bonds that can sustain both tensile and compressive forces and moments. Fracturing naturally can be represented by the sequential breaking of mechanical bonds. For a given amplitude and period of incident ocean waves, the model provides information for the spatial distribution and time evolution of stress and microfractures and the fragment size distribution. We demonstrate that the fraction of broken bonds $\alpha$ increases with increasing wave amplitude. In contrast, the ice fragment size $l$ decreases with increasing amplitude. This information is important for the understanding of the breakup of individual ice floes and floe fragment size.

The percolation behavior of aligned rigid rods of length $k$ ($k$mers) on two-dimensional square lattices has been studied by numerical simulations and finite-size scaling analysis. The $k$mers, containing $k$ identical units (each one occupying a lattice site), were irreversibly deposited along one of the directions of the lattice. The process was monitored by following the probability $R_{L,k}\left(p\right)$ that a lattice composed of $L\times L$ sites percolates at a concentration $p$ of sites occupied by particles of size $k$. The results, obtained for $k$ ranging from 1 to 14, show that (i) the percolation threshold exhibits a decreasing function when it is plotted as a function of the $k$mer size; (ii) for any value of $k$ ($k>1$), the percolation threshold is higher for aligned rods than for rods isotropically deposited; (iii) the phase transition occurring in the system belongs to the standard random percolation universality class regardless of the value of $k$ considered; and (iv) in the case of aligned $k$mers, the intersection points of the curves of $R_{L,k}\left(p\right)$ for different system sizes exhibit nonuniversal critical behavior, varying continuously with changes in the $k$mer size. This behavior is completely different to that observed for the isotropic case, where the crossing point of the curves of $R_{L,k}\left(p\right)$ do not modify their numerical value as $k$ is increased.

We investigate the directed random walk on hierarchic trees. Two cases are investigated: random variables on deterministic trees with a continuous branching, and random variables on the trees constructed through the random branching process. We derive renormalization group (partial differential) equations for the branching models with binomial, Poisson, and compound Poisson distributions of random variables on the links of a tree. These renormalization group equations are a new class of reaction-diffusion equations in one dimension.

The luminescence parameters of laser-induced bubble in the presence of an acoustic field in water are studied. A comparison is made between parameters such as bubble radius, interior temperature, and pressure of the bubble induced by laser and an acoustic field influenced by different driving pressure amplitudes. It is found that the bubble volume induced by laser at the collapse instant is more than 10${}^6$ times larger than the one induced by an acoustic field. It is also noticed, by increasing the driving pressure amplitude, the bubble radius decreases in both cases, however, the bubble interior pressure and temperature increase.

The free decay of a strong flow of liquid sodium (at Reynolds number defined via the maximal mean velocity and the radius of the channel cross section up to $\mathrm{Re}\approx 3\times {10}^6$ and the corresponding magnetic Reynolds number up to $\mathrm{Rm}\approx 30$) generated by the sudden stop of a rapidly rotating toroidal channel is studied experimentally. The toroidal and poloidal components of velocity are measured using a potential probe. We describe the onset of motion, the evolution of strongly anisotropic fluctuations, and the homogenization and decay of turbulence in the final period. We analyze the statistical characteristics of velocity fields in relation to the behavior of effective magnetic diffusivity estimated from measurements of the phase shift between the induced and applied magnetic fields. For the late (self-similar) decay of turbulent flow, turbulent viscosity is shown to be dependent on the root-mean-square velocity pulsations and can be expressed as ${\nu }_t\sim \nu {\mathrm{Re}}^{1.3}$. The behavior of turbulent magnetic diffusivity depends on the magnetic Reynolds number defined in terms of the root-mean-square velocity pulsations. At low magnetic Reynolds numbers (${\mathrm{Rm}}_{\mathrm{rms}}<1$), turbulent magnetic diffusivity grows rapidly with increasing velocity pulsations (${\eta }_t\sim \eta {\mathrm{Rm}}_{\mathrm{rms}}^2$). If the magnetic Reynolds number exceeds unity, the behavior of turbulent magnetic diffusivity becomes similar to the behavior of turbulent viscosity. The highest values of turbulent magnetic diffusivity are achieved at the end of braking, which corresponds to the transient stage of a strongly anisotropic turbulent flow in which the poloidal velocity oscillations prevail.

We demonstrate the effectiveness of a statistical potential (SP) in the description of fermions in a worm-algorithm path-integral Monte Carlo simulation of a few ${}^3$He atoms floating on a ${}^4$He layer adsorbed on graphite. The SP in this work yields successful results, as manifested by the clusterization of ${}^3$He, and by the observation that the ${}^3$He atoms float on the surface of ${}^4$He. We display the positions of the particles in 3D coordinate space, which reveal clusterization of the ${}^3$He component. The correlation functions are also presented, which give further evidence for the clusterization.