An extension of the random sequential adsorption model has been proposed recently, motivated by the coverage of oil droplets by DNA-functionalized colloidal particles. Particles arrive to a flat substrate with a uniform flux $F$ but they can only adsorb on patches. Patches diffuse on the substrate with a diffusion coefficient $D$ if they are free and they remain immobile when attached to an adsorbed particle. The adsorption is considered irreversible and particles cannot adsorb on top of each other. Thus, the system reaches a jammed state, consisting of a monolayer where no more particles can adsorb. We performed Monte Carlo simulations to study the adsorption kinetics and jammed-state morphology on a one-dimensional lattice. We show that, while the time-dependence of the coverage depends on $F$ and $D$, the jammed-state coverage depends solely on the ratio $F/D$. This result is grasped by a simple mean-field calculation. We also report two different regimes for the functional dependence of the jammed-state coverage on the size of the particles, for low and high density of patches.

In this paper we present a method for obtaining the WKB approximation for non-separable multidimensional potentials. At its leading order one has to solve the classical Hamilton-Jacobi equation with zero energy for which a very efficient method is proposed. The essence of this method lies in the recognition that in the vicinity to the potential minimum the solution of Schrödinger equation has to approach that of coupled harmonic oscillators. Quantum corrections to the semiclassical result are then obtained very easily and to an arbitrarily high order. The method is applied to the calculation of the tunneling splitting and tunneling lifetime. We show that classical turning points are part of the dynamical problem; they could not be determined simply from looking at the form of the potential, but are obtained from the solution of the pertinent equations of motion.

The two-step contagion model is a simple toy model for understanding pandemic outbreaks that occur in the real world. The model takes into account that a susceptible person either gets immediately infected or weakened when getting into contact with an infectious one. As the number of weakened people increases, they eventually can become infected in a short time period and a pandemic outbreak occurs. The time required to reach such a pandemic outbreak allows for intervention and is often called golden time. Understanding the size-dependence of the golden time is useful for controlling pandemic outbreak. Using an approach based on a nonlinear mapping, here we find that there exist two types of golden times in the two-step contagion model, which scale as $O\left(N^{1/3}\right)$ and $O\left(N^{\zeta }\right)$ with the system size $N$ on Erdős-Rényi networks, where the measured $\zeta$ is slightly larger than $1/4$. They are distinguished by the initial number of infected nodes, $o\left(N\right)$ and $O\left(N\right)$, respectively. While the exponent $1/3$ of the $N$-dependence of the golden time is universal even in other models showing discontinuous transitions induced by cascading dynamics, the measured $\zeta$ exponents are all close to $1/4$ but show model-dependence. It remains open whether or not $\zeta$ reduces to $1/4$ in the asymptotically large-$N$ limit. Our method can be applied to several models showing a hybrid percolation transition and gives insight into the origin of the two golden times.

We investigate the liquid state structure of the two-dimensional model introduced by Barkan et al. [Phys. Rev. Lett. 113, 098304 (2014)], which exhibits quasicrystalline and other unusual solid phases, focusing on the radial distribution function $g\left(r\right)$ and its asymptotic decay $r\to \infty$. For this particular model system, we find that as the density is increased there is a structural crossover from damped oscillatory asymptotic decay with one wavelength to damped oscillatory asymptotic decay with another distinct wavelength. The ratio of these wavelengths is $\approx 1.932$. Following the locus in the phase diagram of this structural crossover leads directly to the region where quasicrystals are found. We argue that identifying and following such a crossover line in the phase diagram towards higher densities where the solid phase(s) occur is a good strategy for finding quasicrystals in a wide variety of systems. We also show how the pole analysis of the asymptotic decay of equilibrium fluid correlations is intimately connected with the nonequilibrium growth or decay of small-amplitude density fluctuations in a bulk fluid.

Aqueous foams are an important model system that displays coarsening dynamics. Coarsening in dispersions and foams is well understood in the dilute and dry limits, where the gas fraction tends to zero and one, respectively. However, foams are known to undergo a jamming transition from a fluidlike to a solidlike state at an intermediate gas fraction ${\varphi }_c$. Much less is known about coarsening dynamics in wet foams near jamming, and the link to mechanical response, if any, remains poorly understood. Here we probe coarsening and mechanical response using numerical simulations of a variant of the Durian bubble model for wet foams. As in other coarsening systems we find a steady state scaling regime with an associated particle size distribution. We relate the time rate of evolution of the coarsening process to the wetness of the foam and identify a characteristic coarsening time that diverges approaching jamming. We further probe mechanical response of the system to strain while undergoing coarsening. There are two competing timescales, namely the coarsening time and the mechanical relaxation time. We relate these to the evolution of the elastic response and the mechanical structure.

The classic self-similar solutions of the nonstationary compressible Euler equations obtained for a blast-wave propagation (Sedov, Taylor, and von Neumann), a shock-wave implosion (Guderley, Landau, and Stanyukovich), or an impulsive loading of a planar target (von Hoerner, Häfele, and Zel’dovich) have all been derived for a polytropic ideal gas. None of them can be generalized for a fluid with an arbitrary equation of state (EOS), such as the van der Waals EOS of a non-ideal-gas or a three-term EOS of a condensed material. We demonstrate here that the Noh accretion-shock problem is an exception. Its self-similar solutions exist in cylindrical and spherical geometry for fluids and materials with an arbitrary EOS. Such solutions for finite accretion-shock strength and nonuniform inflow velocity are constructed semianalytically with a model three-term equation of state that includes cold, thermal ion (lattice), and thermal electron contributions to the pressure and internal energy. Examples are presented for aluminum and copper. Other material- and EOS-specific semianalytic solutions of the Noh problem can be easily constructed using the same method for any material that in the pressure range of interest can be approximated as a dissipation-free fluid with an arbitrary equation of state.

Ultraslow diffusion (i.e., logarithmic diffusion) has been extensively studied theoretically but has hardly been observed empirically. In this paper, first, we find the ultraslow-like diffusion of the time series of word counts of already popular words by analyzing three different nationwide language databases: (i) newspaper articles (Japanese), (ii) blog articles (Japanese), and (iii) page views of Wikipedia (English, French, Chinese, and Japanese). Second, we use theoretical analysis to show that this diffusion is basically explained by the random walk model with the power-law forgetting with the exponent $\beta \approx 0.5$, which is related to the fractional Langevin equation. The exponent $\beta$ characterizes the speed of forgetting and $\beta \approx 0.5$ corresponds to (i) the border (or thresholds) between the stationary and the nonstationary and (ii) the right-in-the-middle dynamics between the IID noise for $\beta =1$ and the normal random walk for $\beta =0$. Third, the generative model of the time series of word counts of already popular words, which is a kind of Poisson process with the Poisson parameter sampled by the above-mentioned random walk model, can almost reproduce not only the empirical mean-squared displacement but also the power spectrum density and the probability density function.

We study the nonconservative earthquake model on random spatial networks. The spatial networks are composed of sites on a two-dimensional (2D) plane which are connected locally. Differently from a regular lattice, the locations of sites are modeled in the way that sites are randomly placed on the plane. Using the same connectivity degree as a 2D lattice, however, the spatial network cannot exhibit critical earthquake behavior. Mimicking long range energy transfer, the connection radius is increased and the connectivity degree of the spatial network is increased. Then we show that the model exhibits self-organized criticality. The mechanism of the structural effect is presented. The spatial network includes many modules when connectivity degree is very small. The effect of modular structure on the avalanche dynamics is to limit the spreading of avalanches in the whole network. When the connectivity degree is larger, the long range energy transfer can overcome the effect of local modularity and criticality can be reached.

We analyze two alterations of the standard susceptible-infected-susceptible (SIS) dynamics that preserve the central properties of spontaneous healing and infection capacity of a vertex increasing unlimitedly with its degree. All models have the same epidemic thresholds in mean-field theories but depending on the network properties, simulations yield a dual scenario, in which the epidemic thresholds of the modified SIS models can be either dramatically altered or remain unchanged in comparison with the standard dynamics. For uncorrelated synthetic networks having a power-law degree distribution with exponent $\gamma <5/2$, the SIS dynamics are robust exhibiting essentially the same outcomes for all investigated models. A threshold in better agreement with the heterogeneous rather than quenched mean-field theory is observed in the modified dynamics for exponent $\gamma >5/2$. Differences are more remarkable for $\gamma >3$, where a finite threshold is found in the modified models in contrast with the vanishing threshold of the original one. This duality is elucidated in terms of epidemic lifespan on star graphs. We verify that the activation of the modified SIS models is triggered in the innermost component of the network given by a $k$-core decomposition for $\gamma <3$ while it happens only for $\gamma <5/2$ in the standard model. For $\gamma >3$, the activation in the modified dynamics is collective involving essentially the whole network while it is triggered by hubs in the standard SIS. The duality also appears in the finite-size scaling of the critical quantities where mean-field behaviors are observed for the modified but not for the original dynamics. Our results feed the discussions about the most proper conceptions of epidemic models to describe real systems and the choices of the most suitable theoretical approaches to deal with these models.

For the investigation of cell-cell interaction in general and for neural communication and future applications of neural networks, a controllable and well-defined network structure is crucial. We here propose the implementation of an acoustically driven system for tunable and deliberate stimulation and manipulation of cell growth on a chip. This piezoelectric chip allows us to generate a checkerboard-like standing surface acoustic wave pattern coupled to a fluid layer in a microfluidic chamber on top. Such a dynamically induced patterning lattice is shown to allow for the active positioning of the neurons and subsequent guided neurite outgrowth, thus finally overcoming the limitations of static approaches. After thorough characterization of the resulting tunable potential landscape, we successfully demonstrate cell adhesion and even growth of the such positioned cells within the well-defined pressure nodes. We demonstrate neuron growth at predetermined positions and observe a subsequent neurite outgrowth, even being correlated with the artificial potential landscape. For the very delicate and sensitive primary neural cells, this is a change of paradigm! Our experimental findings give us confidence that our hybrid lab-on-a-chip system in the near future will allow researchers to study cell-cell interaction of primary neurons. If scaled to a true network level, it will enable us to control and study how neural networks connect, interact, and communicate.

The number of precise conductance measurements in nanopores is quickly growing. To clarify the dominant mechanisms at play and facilitate the characterization of such systems for which there is still no clear consensus, we propose an analytical approach to the ionic conductance in nanopores that takes into account (i) electro-osmotic effects, (ii) flow slip at the pore surface for hydrophobic nanopores, (iii) a component of the surface charge density that is modulated by the reservoir $p\mathrm{H}$ and salt concentration $c_s$ using a simple charge regulation model, and (iv) a fixed surface charge density that is unaffected by $p\mathrm{H}$ and $c_s$. Limiting cases are explored for various ranges of salt concentration and our formula is used to fit conductance experiments found in the literature for carbon nanotubes. This approach permits us to catalog the different possible transport regimes and propose an explanation for the wide variety of currently known experimental behavior for the conductance versus $c_s$.

Fingering instabilities of a miscible interface between two fluids in a gravitational field can develop due to adverse density gradients as in the well-known Rayleigh-Taylor (RT) and double-diffusive (DD) instabilities. In the absence of differential diffusion, the mixing rate and the onset time of the RT instability developing when a denser solution of a given solute A overlies a less dense solution of a solute B are respectively proportional and inversely proportional to the initial density difference $\mathrm{\Delta }{\rho }_0$ between the two superposed layers. We show here both experimentally and theoretically for porous media flows that when the mechanisms of RT and DD instabilities are combined, the properties of the convective growth of the fingers are controlled by the dynamic density jump $\mathrm{\Delta }{\rho }_m$ of the nonmonotonic density profile induced by the differential diffusion effects. In particular, the onset time and mixing rate can be controlled by varying the ratio of the diffusion coefficients of the solutes.

It has been shown recently that the Coulomb part of electromagnetic interactions is more important than the transverse propagation waves for the near-field enhancement of heat transfer between metal objects at a distance of order nanometers. Here we present a theory focusing solely on the Coulomb potential between electrons hopping among tight-binding sites. When the relevant systems are reduced to very small geometry, for example, a single site, the enhancement is much higher compared to a collection of them packed within a distance of a few $\text{Å}$. We credit this to the screening effect. This result may be useful in designing metal-based metamaterials to enhance heat transfer much higher.

The adsorption of particles diffusing in a half space bounded by the substrate and irreversibly sticking to the substrate upon contacts is investigated. We show that when absorbing particles are planar disks diffusing in the three-dimensional half space, the coverage approaches its saturated “jamming” value as $t^{-1}$ in the large time limit (generally as $t^{-1/(d-1)}$ when the substrate is $d$ dimensional and $d>1$, and as $e^{-t/ln\left(t\right)}$ when $d=1$). We also analyze the asymptotic behavior when particles are spherical and when particles are planar aligned squares.

A one-dimensional linear autonomous system coupled to a generic stationary nonequilibrium fluctuating bath can exhibit resonant response when its damped oscillation period matches some characteristic bath's relaxation time. This condition justifies invoking the stochastic resonance paradigm, even if it can be achieved more easily by tuning the system to the bath and not vice versa, as is usually the case. The simple nature of the mechanism numerically investigated here suggests a number of interesting applications for instance in the context of (1) energy harvesting from random ambient vibrations, (2) activated barrier crossing through a saddle point, or (3) an unstable limit cycle.

In systems with long-range interactions, since energy is a nonadditive quantity, ensemble inequivalence can arise: it is possible that different statistical ensembles lead to different equilibrium descriptions, even in the thermodynamic limit. The microcanonical ensemble should be considered the physically correct equilibrium distribution as long as the system is isolated. The canonical ensemble, on the other hand, can always be defined mathematically, but it is quite natural to wonder to which physical situations it does correspond. We show numerically and, in some cases, analytically that the equilibrium properties of a generalized Hamiltonian mean-field model in which ensemble inequivalence is present are correctly described by the canonical distribution in (at least) two different scenarios: (a) when the system is coupled via local interactions to a large reservoir (even if the reservoir shows, in turn, ensemble inequivalence), and (b) when the mean-field interaction between a small part of a system and the rest of it is weakened by some kind of screening.

We determine the frequency-dependent response characteristics of a quantum system to a driven Caldeira-Leggett bath. The bath degrees of freedom are explicitly driven by an external time-dependent force, in addition to the direct time-dependent forcing of the system itself. After general considerations of driven Caldeira-Leggett baths, we consider the Rubin model of a chain of quantum particles coupled by linear springs as an important model of a quantum dissipative system. We show that in the presence of time-dependent driving of the chain, this model can be mapped to a quantum system which couples to a driven Caldeira-Leggett bath. The effect of the bath driving is captured by a time-dependent force on the central system, which is, in principle, non-Markovian in nature. We study two specific examples, the exactly solvable case of a harmonic potential and a quantum two-state system for which we assume a weak system-bath coupling. We evaluate the dynamical response to a periodic driving of the system and the bath. The dynamic susceptibility is shown to be altered qualitatively by the bath drive: The dispersive part is enhanced at low frequencies and acquires a maximum at zero frequency. The absorptive part develops a shoulder-like behavior in this frequency regime. These features seem to be generic for quantum systems in a driven Caldeira-Leggett bath.

Synchronization of coupled oscillators is a ubiquitous phenomenon, occurring in topics ranging from biology and physics to social networks and technology. A fundamental and long-time goal in the study of synchronization has been to find low-order descriptions of complex oscillator networks and their collective dynamics. However, for the Kuramoto model, the most widely used model of coupled oscillators, this goal has remained surprisingly challenging, in particular for finite-size networks. Here, we propose a model reduction framework that effectively captures synchronization behavior in complex network topologies. This framework generalizes a collective coordinates approach for all-to-all networks [G. A. Gottwald, Chaos 25, 053111 (2015)] by incorporating the graph Laplacian matrix in the collective coordinates. We first derive low dimensional evolution equations for both clustered and nonclustered oscillator networks. We then demonstrate in numerical simulations for Erdős-Rényi networks that the collective coordinates capture the synchronization behavior in both finite-size networks as well as in the thermodynamic limit, even in the presence of interacting clusters.

The totally asymmetric simple exclusion process (TASEP) is a paradigmatic stochastic model for nonequilibrium physics, and has been successfully applied to describe active transport of molecular motors along cytoskeletal filaments. Building on this simple model, we consider a two-lane lattice-gas model that couples directed transport (TASEP) to diffusive motion in a semiclosed geometry, and simultaneously accounts for spontaneous growth and particle-induced shrinkage of the system's size. This particular extension of the TASEP is motivated by the question of how active transport and diffusion might influence length regulation in confined systems. Surprisingly, we find that the size of our intrinsically stochastic system exhibits robust temporal patterns over a broad range of growth rates. More specifically, when particle diffusion is slow relative to the shrinkage dynamics, we observe quasiperiodic changes in length. We provide an intuitive explanation for the occurrence of these self-organized temporal patterns, which is based on the imbalance between the diffusion and shrinkage speed in the confined geometry. Finally, we formulate an effective theory for the oscillatory regime, which explains the origin of the oscillations and correctly predicts the dependence of key quantities, such as the oscillation frequency, on the growth rate.

A polydisperse granular gas made of inelastic and rough hard disks is considered. Focus is laid on the kinetic-theory derivation of the partial energy production rates and the total cooling rate as functions of the partial densities and temperatures (both translational and rotational) and of the parameters of the mixture (masses, diameters, moments of inertia, and mutual coefficients of normal and tangential restitution). The results are applied to the homogeneous cooling state of the system and the associated nonequipartition of energy among the different components and degrees of freedom. It is found that disks typically present a stronger rotational-translational nonequipartition but a weaker component-component nonequipartition than spheres. A noteworthy “mimicry” effect is unveiled, according to which a polydisperse gas of disks having common values of the coefficient of restitution and of the reduced moment of inertia can be made indistinguishable from a monodisperse gas in what concerns the degree of rotational-translational energy nonequipartition. This effect requires the mass of a disk of component $i$ to be approximately proportional to $2{\sigma }_i+\langle \sigma \rangle$, where ${\sigma }_i$ is the diameter of the disk and $\langle \sigma \rangle$ is the mean diameter.