We consider the diffusion of new products in social networks, where consumers who adopt the product can later “recover” and stop influencing others to adopt the product. We show that the diffusion is not described by the susceptible-infected-recovered (SIR) model, but rather by a new model, the Bass-SIR model, which combines the Bass model for diffusion of new products with the SIR model for epidemics. The phase transition of consumers from nonadopters to adopters is described by a nonstandard Kolmogorov-Johnson-Mehl-Avrami model, in which clusters growth is limited by adopters' recovery. Therefore, diffusion in the Bass-SIR model only depends on the local structure of the social network, but not on the average distance between consumers. Consequently, unlike the SIR model, a small-worlds structure has a negligible effect on the diffusion. Moreover, unlike the SIR model, there is no threshold value above which the diffusion will peter out. Surprisingly, diffusion on scale-free networks is nearly identical to that on Cartesian ones.

Inspired by gecko adhesion in humid environments, a modified Kendall's model is established in order to investigate the effect of relative humidity on the interfacial peeling behavior of a thin film adhering on a rigid substrate. When the humidity is less than 90%, a monolayer of water molecules adsorbed on the substrate surface induces a strong disjoining pressure at the interface. As a result, the steady-state peel-off force between the thin film and substrate is significantly enhanced. When the humidity is greater than 90%, water molecules condense into water droplets. Four different peeling models are established on this occasion, depending on the surface wettability of the film and substrate. It is found that the steady-state peel-off force is influenced by the water meniscus in a complicated manner, which is either enhanced or reduced by the water capillarity comparing to that predicted by the classical Kendall's model, i.e., a dry peeling model. It should be noted that, at the vicinity of the wetting transition, the peel-off force of the four models can be reduced to an identical one, which means the four peeling models can transit from one to another continuously. The present model, as an extension of the classical Kendall's one, should be useful not only for understanding gecko adhesion in humid environments, but also for analyzing interface behaviors of a film-substrate system in real applications.

The granular Leidenfrost effect [B. Meerson, et al., Phys. Rev. Lett. 91, 024301 (2003); P. Eshuis et al., Phys. Rev. Lett. 95, 258001 (2005)] is the levitation of a mass of granular matter when a wall below the grains is vibrated, giving rise to a hot granular gas below the cluster. We find by simulation that for a range of parameters the system is bistable: the levitated cluster can occasionally break and give rise to two clusters and a hot granular gas above and below. We use techniques from the theory of rare events to compute the mean transition time for breaking to occur. This requires the introduction of a two-component reaction coordinate.

Here we show the effect of the thermal conductivity of the substrate on the evaporation process of small droplets. We deposited small droplets on the order of $100–500 \mu \mathrm{m}$ in diameter on four different substrates with different thermal conductivities and surface properties, and we measured the evaporation time. Also, a numerical model that describes this process was developed to include thermal effects inside the droplet and heat transfer from the substrate. Our model considers the entire time of evaporation including the pinned and depinned stages. This model uses a new approach for the contact line behavior. It uses experimental results to define the movement of the contact line as a function of the contact angle.

We propose a method of determination of the dust particle spatial distribution in dust clouds that form in three-dimensional (3D) complex plasmas under microgravity conditions. The method utilizes the data obtained during the 3D scanning of a cloud, and it provides reasonably good accuracy. Based on this method, we investigate the particle density in a dust cloud realized in gas discharge plasma in the PK-3 Plus setup onboard the International Space Station. We find that the treated dust clouds are both anisotropic and inhomogeneous. One can isolate two regimes in which a stationary dust cloud can be observed. At low pressures, the particle density decreases monotonically with the increase of the distance from the discharge center; at higher pressures, the density distribution has a shallow minimum. Regardless of the regime, we detect a cusp of the distribution at the void boundary and a slowly varying density at larger distances (in the foot region). A theoretical interpretation of the obtained results is developed that leads to reasonable estimates of the densities for both the cusp and the foot. The modified ionization equation of state, which allows for violation of the local quasineutrality in the cusp region, predicts the spatial distributions of ion and electron densities to be measured in future experiments.

We consider the problem of an overdamped Brownian particle moving in multiscale potential with $N+1$ characteristic length scales: the macroscale and $N$ separated microscales. We show that the coarse-grained dynamics is given by an overdamped Langevin equation with respect to the free energy and with a space-dependent diffusion tensor, the calculation of which requires the solution of $N$ fully coupled Poisson equations. We study in detail the structure of the bifurcation diagram for one-dimensional problems, and we show that the multiscale structure in the potential leads to hysteresis effects and to noise-induced transitions. Furthermore, we obtain an explicit formula for the effective diffusion coefficient for a self-similar separable potential, and we investigate the limit of infinitely many small scales.

We study the coevolution of culture and cooperation by combining the Axelrod model of cultural dissemination with a spatial public goods game, incorporating both noise and social influence. Both participation and cooperation in public goods games are conditional on cultural similarity. We find that a larger “scope of cultural possibilities” in the model leads to the survival of cooperation, when noise is not present, and a higher probability of a multicultural state evolving, for low noise rates. High noise rates, however, lead to both rapid extinction of cooperation and collapse into cultural “anomie,” in which stable cultural regions fail to form. These results suggest that cultural diversity can actually be beneficial for the evolution of cooperation, but that cultural information needs to be transmitted accurately in order to maintain both coherent cultural groups and cooperation.

We explore the electrostatic properties of poly-$N$-isopropyl acrylamide microgels in dilute, quasi-de-ionized dispersions and show that the apparent net charge of these thermosensitive microgels is an increasing function of their size, the size being conveniently varied by temperature. Our experimental results obtained in a combination of light scattering, conductivity, and mobility experiments are consistent with those obtained in Poisson-Boltzmann cell model calculations, effectively indicating that upon shrinking the number of counterions entrapped within the microgels increases. Remarkably, this behavior shows that the electrostatic energy per particle remains constant upon swelling or deswelling the microgel, resulting in a square root dependence of the net charge on the particle radius.

We present a numerical study of the spatial correlations of a quasi-two-dimensional granular fluid kept in a nonstatic steady state via vertical shaking. The simulations explore a wide range of vertical accelerations, restitution coefficients, and packing fractions, always staying below the crystallization limit. From the simulations we obtain the relevant pair distribution functions (PDFs), and effective potentials for the interparticle interaction are extracted from these PDFs via the Ornstein-Zernike equation with the Percus-Yevick closure. The correlations in the granular structures originating from these effective potentials are checked against the originating PDF using standard Monte Carlo simulations, and we find in general an excellent agreement. The resulting effective potentials show an increase of the spatial correlation at contact with the decreasing values of the restitution coefficient, and a tendency of the potentials to display deeper wells for more dissipative dynamics. A general exception to this trend appears for a range of values of the forcing, which depends on the restitution coefficient, but not on the density, where resonant bouncing increases correlations, resulting in deeper potential wells. The nature of these resonances is explored and shown to be the result of synchronization in the parabolic flights of the particles.

In this article, we study granular avalanches when external mechanical vibrations are applied. We identify conditions of flow arrest and compare with the ones classically observed for nonvibrating granular flows down inclines [Phys. Fluids 11, 542 (1999)]. We propose an empirical law to describe the thickness of the deposits with the inclination angle and the vibration intensity. The link between the surface velocity and the depth of the flow highlights a competition between gravity and vibrations induced flows. We identify two distinct regimes: (a) gravity-driven flows at large angles where vibrations do not modify dynamical properties but the deposits (scaling laws in this regime are in agreement with the literature for nonvibrating granular flows) and (b) vibrations-driven flows at small angles where no flow is possible without applied vibrations (in this last regime, the flow behavior can be properly described by a vibration induced activated process). We show, in this study, that granular flows down inclined planes can be finely tuned by external mechanical vibrations.

In a two-dimensional (2D) dusty plasma composed of superparamagnetic, charged dust grains and immersed in an external magnetic field $\mathbf{B}$, the grains interact via both Yukawa and magnetic dipole-dipole potentials. Because the grains' magnetic dipole moments are induced by $\mathbf{B}$, the dipole moments all lie along $\mathbf{B}$. When $\mathbf{B}$ is tilted with respect to the normal to the dust layer, the interaction between the grains becomes anisotropic. In our previous paper [Hartmann et al., Phys. Rev. E 89, 043102 (2014)], we studied the character of waves in such a system, confined strictly to two dimensions, without any spatial extension in the direction perpendicular to the layer. We analyzed how the dispersion of waves depends on the direction of propagation and the relative strengths of the magnetic dipole and Yukawa potentials. In this paper, we consider a more realistic quasi-2D system where the grains are confined by an external potential and can undergo small oscillations perpendicular to the layer. We analyze the effect of the strength of the confining potential on the in-plane correlations and on the wave propagation. In addition to the in-plane compressional and transverse waves, there now appears an out-of-plane transverse wave generated by the oscillation of the grains in the confining potential. The theoretical approach uses the quasi-localized charge approximation paralleled by molecular dynamics simulations.

In a recent paper [Phys. Rev. E 92, 012123 (2015)], a modified $d$-dimensional ${\mathrm{\Phi }}^4$ model was investigated that differs from the standard one in that the ${\mathrm{\Phi }}^4$ term was replaced by a nonlocal one with a potential $u(\mathit{x}-{\mathit{x}}^{\prime })$ that depends on a parameter $\sigma$ and decays exponentially as $|\mathit{x}-{\mathit{x}}^{\prime }|\to \infty$ on a scale ${\left|m\right|}^{-1}<\infty$. The authors claim the upper critical dimension of this model to be $d_{\sigma }=4+2\sigma$. Performing a one-loop calculation, they arrive at expansions in powers of ${\epsilon }_{\sigma }=d_{\sigma }-d$ for critical exponents such as $\eta$ and related ones to $O\left({\epsilon }_{\sigma }\right)$ whose $O\left({\epsilon }_{\sigma }\right)$ coefficients depend on $\sigma$ and the ratio $w=m^2/{\mathrm{\Lambda }}^2$, where $\mathrm{\Lambda }$ is the uv cutoff. It is shown that these claims are unfounded and based on misjudgments and an ill-conceived renormalization-group calculation.

We study the problem to infer the ground state of a spin-glass Hamiltonian using data from another Hamiltonian with interactions disturbed by noise from the original Hamiltonian, motivated by the ground-state inference in quantum annealing on a noisy device. It is shown that the average Hamming distance between the inferred spin configuration and the true ground state is minimized when the temperature of the noisy system is kept at a finite value, and not at zero temperature. We present a spin-glass generalization of a well-established result that the ground state of a purely ferromagnetic Hamiltonian is best inferred at a finite temperature in the sense of smallest Hamming distance when the original ferromagnetic interactions are disturbed by noise. We use the numerical transfer-matrix method to establish the existence of an optimal finite temperature in one- and two-dimensional systems. Our numerical results are supported by mean-field calculations, which give an explicit expression of the optimal temperature to infer the spin-glass ground state as a function of variances of the distributions of the original interactions and the noise. The mean-field prediction is in qualitative agreement with numerical data. Implications on postprocessing of quantum annealing on a noisy device are discussed.

We study level statistics in ensembles of integrable $N\times N$ matrices linear in a real parameter $x$. The matrix $H\left(x\right)$ is considered integrable if it has a prescribed number $n>1$ of linearly independent commuting partners $H^i\left(x\right)$ (integrals of motion) $\left[H\left(x\right),H^i\left(x\right)\right]=0$, $\left[H^i\left(x\right),H^j\left(x\right)\right]=0$, for all $x$. In a recent work [Phys. Rev. E 93, 052114 (2016)], we developed a basis-independent construction of $H\left(x\right)$ for any $n$ from which we derived the probability density function, thereby determining how to choose a typical integrable matrix from the ensemble. Here, we find that typical integrable matrices have Poisson statistics in the $N\to \infty$ limit provided $n$ scales at least as $logN$; otherwise, they exhibit level repulsion. Exceptions to the Poisson case occur at isolated coupling values $x=x_0$ or when correlations are introduced between typically independent matrix parameters. However, level statistics cross over to Poisson at $O\left(N^{-0.5}\right)$ deviations from these exceptions, indicating that non-Poissonian statistics characterize only subsets of measure zero in the parameter space. Furthermore, we present strong numerical evidence that ensembles of integrable matrices are stationary and ergodic with respect to nearest-neighbor level statistics.

We investigate common-noise-induced synchronization between two identical networks of coupled phase oscillators exhibiting fully locked collective oscillations. Using the collective phase description method for fully locked oscillators, we demonstrate that two noninteracting networks of coupled phase oscillators can exhibit in-phase synchronization between the networks when driven by weak common noise. We derive the Lyapunov exponent characterizing the relaxation time for synchronization and develop a method of obtaining the optimal input pattern of common noise to achieve fast synchronization. We illustrate the theory using three representative networks with heterogeneous, global, and local coupling. The theoretical results are validated by direct numerical simulations.

We present an analysis of two-dimensional (2D) matter-wave solitons, governed by the pseudospinor system of Gross-Pitaevskii equations with self- and cross attraction, which includes the spin-orbit coupling (SOC) in the general Rashba-Dresselhaus form, and, separately, the Rashba coupling and the Zeeman splitting. Families of semivortex (SV) and mixed-mode (MM) solitons are constructed, which exist and are stable in free space, as the SOC terms prevent the onset of the critical collapse and create the otherwise missing ground states in the form of the solitons. The Dresselhaus SOC produces a destructive effect on the vortex solitons, while the Zeeman term tends to convert the MM states into the SV ones, which eventually suffer delocalization. Existence domains and stability boundaries are identified for the soliton families. For physically relevant parameters of the SOC system, the number of atoms in the 2D solitons is limited by $\sim 1.5\times {10}^4$. The results are obtained by means of combined analytical and numerical methods.

Random heteropolymers are a minimal description of biopolymers and can provide a theoretical framework to the investigate the formation of loops in biophysical experiments. The looping probability as a function of polymer length was observed to display in some biopolymers, like chromosomes in cell nuclei or long RNA chains, anomalous scaling exponents. Combining a two-state model with self-adjusting simulated-tempering calculations, we calculate numerically the looping properties of several realizations of the random interactions within the chain. We find a continuous set of exponents upon varying the temperature, which arises from finite-size effects and is amplified by the disorder of the interactions. We suggest that this could provide a simple explanation for the anomalous scaling exponents found in experiments. In addition, our results have important implications notably for the study of chromosome folding as they show that scaling exponents cannot be the sole criteria for testing hypothesis-driven models of chromosome architecture.

Recent experiments have demonstrated that dynein motors exhibit catch bonding behavior, in which the unbinding rate of a single dynein decreases with increasing force, for a certain range of force. Motivated by these experiments, we study the effect of catch bonding on unidirectional transport properties of cellular cargo carried by multiple dynein motors. We introduce a threshold force bond deformation (TFBD) model, consistent with the experiments, wherein catch bonding sets in beyond a critical applied load force. We find catch bonding can result in dramatic changes in the transport properties, which are in sharp contrast to kinesin-driven unidirectional transport, where catch bonding is absent. We predict that under certain conditions, the average velocity of the cellular cargo can actually increase as applied load is increased. We characterize the transport properties in terms of a velocity profile plot in the parameter space of the catch bond strength and the stall force of the motor. This plot yields predictions that may be experimentally accessed by suitable modifications of motor transport and binding properties.

Density waves are characteristic for fluidized beds and affect measurements on liquidlike dynamics in fluidized granular media. Here the intensity autocorrelation function as obtainable with diffusing-wave spectroscopy is derived in the presence of density waves. The predictions by the derived form of the intensity autocorrelation function match experimental observations from a gas-fluidized bed. The model suggests separability of the contribution from density waves from the contribution by microscopic scatterer displacement to the decay of correlation and thus paves the way for characterizing microscopic particle motions using diffusing-wave spectroscopy as well as heterogeneities in fluidized granular media.