We consider signed networks in which connections or edges can be either positive (friendship, trust, alliance) or negative (dislike, distrust, conflict). Early literature in graph theory theorized that such networks should display “structural balance,” meaning that certain configurations of positive and negative edges are favored and others are disfavored. Here we propose two measures of balance in signed networks based on the established notions of weak and strong balance, and we compare their performance on a range of tasks with each other and with previously proposed measures. In particular, we ask whether real-world signed networks are significantly balanced by these measures compared to an appropriate null model, finding that indeed they are, by all the measures studied. We also test our ability to predict unknown signs in otherwise known networks by maximizing balance. In a series of cross-validation tests we find that our measures are able to predict signs substantially better than chance.

Experiments have shown that self-propelled particles can slide along the surface of a circular obstacle without becoming trapped over long times. Using simulations and theory, we study the impact of boundary conditions on the diffusive transport of active particles in an obstacle lattice. We find that particle dynamics with sliding boundary conditions result in large diffusivities even at high obstacle density, unlike classical specular reflection. These dynamics are very well described by a model based on run-and-tumble particles with microscopically derived reorientation functions arising from obstacle-induced tumbles. This model, however, fails to describe fine structure in the diffusivity at high obstacle density predicted by simulations for pusherlike collisions. Using a simple deterministic model, we show that this structure results from particles being guided by the lattice. Our results thus show how nonclassical surface scattering introduces a dependence on the lattice geometry at high densities. We discuss implications for the study of bacteria in complex environments.

The kinetics of Ostwald ripening of solid domains in the liquid phase of one-component systems in two dimensions is investigated numerically via the phase field crystal model. The simulations, which are performed systematically as a function of volume fraction of the solid phase, show that dynamical scaling is reached during late times, and the growth law is in good agreement with the classical theory of Lifshitz, Slyozov, and Wagner (LSW), i.e., $\overline{R}\sim t^{1/3}$, an indication that domain growth is mediated by the long-range interdomain diffusion of atoms. In contrast to the LSW theory, however, the domain size distribution is symmetric, and can be fit with a Gaussian. The investigation of the topological domain structure, through the Voronoi tessellation of the domains' centers of mass shows that both the Lewis law and the Aboav–Weaire law of two-dimensional cellular patterns are satisfied, implying that the kinetics proceed such that the conformational entropy of the domain-containing Voronoi cells is maximized. These results are in very good agreement with an earlier experimental study of a phase-separating phospholipid-cholesterol Langmuir film.

We investigate the dependency of the magnitude of heat transfer in a convection cell as a function of its inclination by means of experiments and simulations. The study is performed with a working fluid of large Prandtl number, $\mathrm{Pr}\simeq 480$, and at Rayleigh numbers $\mathrm{Ra}\simeq {10}^8$ and $\mathrm{Ra}\simeq 5\times {10}^8$ in a quasi-two-dimensional rectangular cell with unit aspect ratio. By changing the inclination angle $\left(\beta \right)$ of the convection cell, the character of the flow can be changed from moderately turbulent, for $\beta =0^{\circ }$, to laminar and steady at $\beta ={90}^{\circ }$. The global heat transfer is found to be insensitive to the drastic reduction of turbulent intensity, with maximal relative variations of the order of $20\%$ at $\mathrm{Ra}\simeq {10}^8$ and $10\%$ at $\mathrm{Ra}\simeq 5\times {10}^8$, while the Reynolds number, based on the global root-mean-square velocity, is strongly affected with a decay of more than $85\%$ occurring in the laminar regime. We show that the intensity of the heat flux in the turbulent regime can be only weakly enhanced by establishing a large-scale circulation flow by means of small inclinations. However, in the laminar regime the heat is transported solely by a slow large-scale circulation flow which exhibits large correlations between the velocity and temperature fields. For inclination angles close to the transition regime in-between the turbulentlike and laminar state, a quasiperiodic heat-flow bursting phenomenon is observed.

The kinetic theory of electric fluctuations in a collisional weakly ionized dusty plasma is formulated with due regard to the grain charging dynamics. The correlation functions of electron and ion density are obtained by considering their collisions with neutrals described within the Bhatnagar-Gross-Krook model. The electron density correlation spectra in isothermal and nonisothermal plasma are calculated for various values of grain density, grain size, and ion collisionality.

An efficient numerical method for determining the spectral characteristics and spatial distribution of the field of a spheroidal whispering-gallery-mode (WGM) resonator interacting with a dielectric nanoparticle is presented. The developed approach is based on a combination of $T$-matrix formalism applied to a single resonator with a dipole approximation for the field of the nanoparticle. The method is illustrated by computation of the scattered field of the resonator-particle system illuminated by an incident field in the form of a single WGM mode of TE or TM polarization mimicking the excitation of the resonances by a tapered fiber. Our calculations show that even a very small (less than 0.1%) deviation of the resonator's shape from an ideal sphere renders spherical approximation invalid. They also confirm that analytical resonant approximation for spheroidal resonators developed previously gives a reasonable qualitative description of the spectral characteristics of the resonator-particle system. It was found, however, that corrections to the resonant approximation are significant enough for realistic nominally spherical resonators to be taken into account for accurate analysis of the experimental data.

Imaging techniques are essential tools for inquiring a number of properties from different materials. Liquid crystals are often investigated via optical and image processing methods. In spite of that, considerably less attention has been paid to the problem of extracting physical properties of liquid crystals directly from textures images of these materials. Here we present an approach that combines two physics-inspired image quantifiers (permutation entropy and statistical complexity) with machine learning techniques for extracting physical properties of nematic and cholesteric liquid crystals directly from their textures images. We demonstrate the usefulness and accuracy of our approach in a series of applications involving simulated and experimental textures, in which physical properties of these materials (namely: average order parameter, sample temperature, and cholesteric pitch length) are predicted with significant precision. Finally, we believe our approach can be useful in more complex liquid crystal experiments as well as for probing physical properties of other materials that are investigated via imaging techniques.

Inspired by one-dimensional light-particle systems, the dynamics of a non-Hamiltonian system with long-range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the thermodynamic limit by a Vlasov equation that does possess stable stationary solutions. This implies that on a macroscopic scale the molecular dynamics evolves on a slow timescale that diverges with the system size. At the single-particle level, the evolution is driven by incoherent interaction between the particles, which may be effectively modeled by a noise, leading to a Brownian-like dynamics of the momentum. Because this self-generated diffusion process depends on the particle distribution, the associated Fokker-Planck equation is nonlinear, and a subdiffusive behavior of the momentum fluctuations emerges, in agreement with numerics.

We use an efficient method that eases the daunting task of simulating dynamics in spin systems with long-range interaction. Our Monte Carlo simulations of the long-range Ising model for the nonequilibrium phase ordering dynamics in two spatial dimensions perform significantly faster than the standard Metropolis approach and considerably more efficiently than the kinetic Monte Carlo method. Importantly, this enables us to establish agreement with the theoretical prediction for the time dependence of domain growth, in contrast to previous numerical studies. This method can easily be generalized to applications in other systems.

We study the mixing of active swimmers. Two different types of swimmers (modeled as particles) are placed initially in two boxes with an interconnection between them. The mixing of swimmers happens as they move with their own self-propelled forces. The self-propelled force is constant and the direction of the exerted thrust is governed by the neighboring swimmers. Overall mixing of the swimmers depends on the magnitude of the exerted thrust, the initial packing fraction, and the activity level. Different nonequilibrium states are also identified depending on the exerted thrust and the initial packing fraction of the swimmers.

We study fragment size distributions after crushing single and many particles under uniaxial compression inside a cylindrical container by means of numerical simulations. Under the assumption that breaking goes through the bulk of the particle we obtain the size distributions of fragments for both cases after large displacements. For the single-particle crushing, this fragmentation mechanism produces a log-normal size distribution, which deviates from the power-law distribution of fragment sizes for the packed bed. We show that as the breaking process evolves, a power-law dependency on the displacement is present for the single grain, while for the many-grains system, the distribution converges to a steady state. We further investigate the force networks and the average coordination number as a function of the particle size, which gives information about the origin of the power-law distributions for the granular assembly under uniaxial compression.

The column collapse experiment is a simplified version of the complex granular flows observed in both natural and industrial contexts. Due to its simple setup and rich behavior, the column collapse has been studied experimentally and numerically by several authors. The purpose of the analyses presented in this paper is to verify whether some of the results presented in these publications are affected by grain-size effects. In order to do so, we simulate two-dimensional granular columns by means of a discrete-element method, i.e., contact dynamics. Specifically, we study the influence of the grain size, as compared to the system size, on the resultant deposit geometry and collapse duration. We show that (i) some of the previously published results may be affected by grain-size effects, (ii) in order to avoid these effects, the system-size to grain-size ratio must be larger than 75 for short columns and larger than 50 for tall columns, and (iii) the quantities that are the most affected by grain-size effects are the column mobility and the collapse duration. Our findings serve as a tool for comparing results obtained by different researchers and draw guidelines on the number of grains that must be used in order to avoid grain-size effects.

A lattice Boltzmann model for compressible flows on standard lattices is developed and analyzed. A consistent two-population thermal lattice Boltzmann is used which allows a variable Prandtl number and a variable adiabatic exponent, and appropriate correction terms are introduced into the kinetic equations to compensate for deviations in the hydrodynamic limit. Using the concept of a shifted lattice, the model is extended to supersonic flows involving shock waves, and the shock-vortex interaction problem is simulated to show the accuracy of the proposed model. Numerical results demonstrate that the proposed model is a viable candidate for compressible flow simulations.

The concept of transport mediated through the dynamics of “jumping” particles is used to develop an iterative method for obtaining steady-state solutions to the nonlocal transport equation in two dimensions. The technique is self-adjoint and capable of correctly treating spatially nonuniform, asymmetric systems. An appropriate reduced version of the iteration method is used to compare with results obtained with a self-adjoint one-dimensional transport matrix approach [Maggs and Morales, Phys. Rev. E 94, 053302 (2016)]. The transport “jump” probability distribution functions are based on Lévy α-stable distributions. The technique can handle the entire Lévy α-parameter range from one (Lorentz distributions) to two (Gaussian distributions). Cases with $\alpha =2$ (standard diffusion) are used to establish the validity of the iterative method. The capabilities of the iterative method are demonstrated by presenting examples from systems with various source configurations, boundary shapes, boundary conditions, and spatial variations in parameters.

A multiphase lattice Boltzmann method is developed to simulate immiscible three-phase flows with contact-line dynamics. In this method, the immiscible three-phase flow is modeled by a multiple-relaxation-time color-gradient model, which not only allows for a full range of interfacial tensions but also can produce viscosity-independent results especially when the fluid-surface interactions are considered. To achieve the desired contact angles, a weighted contact angle model is utilized to obtain a relatively smooth transition of contact angle for each fluid, which is enforced through a geometrical wetting condition. This method is first validated by simulations of a Janus droplet resting on a surface for various contact angles and fluid properties and dynamic capillary filling of ternary fluids with different viscosity ratios. It is then used to simulate a Janus droplet on a substrate subject to Poiseuille flow. Results show that the droplet may undergo three typical modes, namely, two stable deformation modes and breakup mode, which depend not only on the inlet velocity but also on the fluid viscosity. The terminal velocity of moving droplet increases linearly with the inlet velocity in both stable modes only when three fluids do not differ much in their viscosities.

This work proposes a simulation technique that can be used to compute the thermal interaction between a rarefied gas and an atomically rough nanopore. A standard pore geometry, the slit pore, is used to derive the correct version of the cosine law in case the wall consists out of individual atoms. Having the correct cosine law drastically reduces the computational cost of calculating the gas-wall pair interaction in the rarefied gas regime since it is no longer necessary to consider a fully flexible crystal lattice. By considering only a small modification of the Lowe-Andersen thermostat, a well-known simulation technique that uses diffusive gas-heatbath collisions, we show how it can be used to incorporate lattice flexibility even if the wall is modeled as a rigid lattice.

Modularity maximization using greedy algorithms continues to be a popular approach toward community detection in graphs, even after various better forming algorithms have been proposed. Apart from its clear mechanism and ease of implementation, this approach is persistently popular because, presumably, its risk of algorithmic failure is not well understood. This Rapid Communication provides insight into this issue by estimating the algorithmic performance limit of the stochastic block model inference using modularity maximization. This is achieved by counting the number of metastable states under a local update rule. Our results offer a quantitative insight into the level of sparsity at which a greedy algorithm typically fails.

In this work we consider the nonequilibrium mechanical and magnetic work performed on a one-dimensional compressible Ising model. In the harmonic approximation we easily integrate the mechanical degrees of freedom of the model, and the resulting effective Hamiltonian depends on two external parameters, the magnetic field and the force applied along the chain. As the model is exactly soluble in one dimension we can determine the free energy difference between two arbitrary thermodynamic states of the system. We show the validity of the Jarzynski equality, which relates the free energy difference between two thermodynamic states of the system and the average work performed by external agents in a finite time, through nonequilibrium paths between the same thermodynamic states. We have found that the Jarzynski theorem remains valid for all the values of the rate of variation of the magnetic field and the mechanical force applied to the system.

We study the random deposition model with power-law distributed noise and rare-event dominated fluctuation. In this model instead of particles with unit sizes, rods with variable lengths are deposited onto the substrate. The length of each rod is chosen from a power-law distribution $P\left(l\right)\sim l^{-(\mu +1)}$, and the site at which each rod is deposited is chosen randomly. The results show that for $\mu <{\mu }_{\mathit{c}}=3$ the log-log diagram of roughness, $W\left(t\right)$, versus deposition time, $t$, increases as a step function, where the roughness in each interval acts as $W_{\mathrm{loc}}\left(t\right)\approx t^{{\beta }_{\mathrm{loc}}}$. The local growth exponent, ${\beta }_{\mathrm{loc}}$, is zero for $\mu =1$. By increasing the $\mu$ exponent, the value of ${\beta }_{\mathrm{loc}}$ is increased. It tends to the growth exponent of the random distribution model with Gaussian noise, $\beta =1/2$, at ${\mu }_{\mathit{c}}=3$. The fractal analysis of the height fluctuations for this model was performed by multifractal detrended fluctuation analysis algorithm. The results show multiaffinity behavior for the height fluctuations at $\mu <{\mu }_{\mathit{c}}$ and the multiaffinity strength is greater for smaller values of the $\mu$ exponent.

We study numerically the aging properties of the two-dimensional Ising model with quenched disorder considered in our recent paper [Phys. Rev. E 95, 062136 (2017)], where frustration can be tuned by varying the fraction of antiferromagnetic interactions. Specifically, we focus on the scaling properties of the autocorrelation and linear response functions after a quench of the model to a low temperature. We find that the interplay between equilibrium and aging occurs differently in the various regions of the phase diagram of the model. When the quench is made into the ferromagnetic phase the two-time quantities are made by the sum of an equilibrium and an aging part, whereas in the paramagnetic phase these parts combine in a multiplicative way. Scaling forms are shown to be obeyed with good accuracy, and the corresponding exponents and scaling functions are determined and discussed in the framework of what is known in clean and disordered systems.