Understanding microbial biofilm growth is important to public health because biofilms are a leading cause of persistent clinical infections. In this paper, we develop a thin-film model for microbial biofilm growth on a solid substratum to which it adheres strongly. We model biofilms as two-phase viscous fluid mixtures of living cells and extracellular fluid. The model explicitly tracks the movement, depletion, and uptake of nutrients and incorporates cell proliferation via a nutrient-dependent source term. Notably, our thin-film reduction is two dimensional and includes the vertical dependence of cell volume fraction. Numerical solutions show that this vertical dependence is weak for biologically feasible parameters, reinforcing results from previous models in which this dependence was neglected. We exploit this weak dependence by writing and solving a simplified one-dimensional model that is computationally more efficient than the full model. We use both the one- and two-dimensional models to predict how model parameters affect expansion speed and biofilm thickness. This analysis reveals that expansion speed depends on cell proliferation, nutrient availability, cell-cell adhesion on the upper surface, and slip on the biofilm-substratum interface. Our numerical solutions provide a means to qualitatively distinguish between the extensional flow and lubrication regimes, and quantitative predictions that can be tested in future experiments.

In a recent work [Bret, EPL 135, 35001 (2021)], quantum electrodynamic (QED) effects were evaluated for the two-stream instability. It pertains to the growth of perturbations with a wave vector oriented along the flow in a collisionless counter-streaming system. Here, the analysis is extended to every possible orientation of the wave vector. The previous result for the two-stream instability is recovered, and it is proved that, even within the framework of a three-dimensional (3D) analysis, this instability remains fundamentally 1D even when accounting for QED effects. The filamentation instability, found for wave vectors normal to the flow, is weakly affected by QED corrections. As in the classical case, its growth rate saturates at large $k_{\perp }$. The saturation value is found independent of QED corrections. Also, the smallest unstable $k_{\perp }$ is independent of QED corrections. Surprisingly, unstable modes found for oblique wave vectors do not follow the same pattern. For some, QED corrections do reduce the growth rate. But, for others, the same corrections increase the growth rate instead. The possibility for QED effects to play a role in unmagnetized systems is evaluated. Pair production resulting from $\gamma$ emission by particles oscillating in the exponentially growing fields is not accounted for.

In this paper, an analytical solution of a linear nonlocal Poisson-Boltzmann equation (NPBE) test model with multiple charges in a spherical solute region surrounded by a water spherical shell is derived as a single series of Legendre polynomials and modified spherical Bessel functions. The classic Kirkwood ball model is then shown to be a special case of the NPBE test model so that its analytical solution is regained from a double series of associated Legendre polynomials (derived by Kirkwood in 1934) to a new single series of Legendre polynomials, sharply reducing its computational cost. As an application of these series solutions, a comparison study is done to demonstrate the differences between the Kirkwood and NPBE test models.

From the exact solution of the stochastic telegrapher's equation, Fourier plane-wave-like modes are introduced. Then the time evolution of the plane-wave modes are analyzed when the absorption of energy in the telegrapher's equation has strong time fluctuations. We demonstrate that fluctuations in the loss of energy introduce a localized gap with a size that depends on the correlation timescale of the fluctuations. We prove that for a large time correlation the gap is strongly reduced, which means that there is delocalization in the plane-wave modes with respect to the plane waves in the ordinary telegrapher's equation. This result is of relevance in the study of the transport of electromagnetic waves in a conducting medium, and sheds light on the functional role of the fluctuations in the loss of energy in the telegrapher's dynamics.

Fixed-energy sandpile (FES) models, introduced to understand the self-organized criticality, show a continuous phase transition between absorbing and active phases. In this work, we study the dynamics of the deterministic FES models on random networks. We observe that close to absorbing transition the density of active nodes oscillates and nodes topple in synchrony. The deterministic toppling rule and the small-world property of random networks lead to the emergence of sustained oscillations. The amplitude of oscillations becomes larger with increasing the value of network randomness. The bifurcation diagram for the density of active nodes is obtained. We use the activity-dependent rewiring rule and show that the interplay between the network structure and the FES dynamics leads to the emergence of a bistable region with a first-order transition between the absorbing and active states. Furthermore during the rewiring, the ordered activation pattern of the nodes is broken, which causes the oscillations to disappear.

How ecosystems maintain stability is an active area of research. Inspired by applications of random matrix theory in nuclear physics, May showed decades ago that in an ecosystem model with many randomly interacting species, increasing species diversity decreases the stability of the ecosystem. There have since been many additions to May's efforts, one being an improved understanding the effect of mutualistic, competitive, or predator-prey-like correlations between pairs of species. Here we extend a random matrix technique developed in the context of spin-glass theory to study the effect of high-order correlations among species interactions. The resulting analytically solvable models include next-to-nearest-neighbor correlations in the species interaction network, such as the enemy of my enemy is my friend, as well as higher-order correlations. We find qualitative differences from May and others' models, including nonmonotonic diversity-stability relationships. Furthermore, inclusion of particular next-to-nearest-neighbor correlations in predator-prey as opposed to mutualist-competitive networks causes the former to transition to being more stable at higher species diversity. We discuss potential applicability of our results to microbiota engineering and to the ecology of interpredator interactions, such as cub predation between lions and hyenas as well as companionship between humans and dogs.

We investigate simple models of a monodisperse system of soft, frictionless disks flowing through a two-dimensional microchannel in the presence of a single or a double constriction using Brownian dynamics simulation. After a transient time, a stationary state is observed with an increase in particle density before the constriction and a depletion after it. For a constriction width to particle diameter ratio of less than 3, the mean particle velocity is reduced compared to the unimpeded flow and it falls to zero for ratios of less than 1. At low temperatures, the particle mean velocity may vary nonmonotonically with the constriction width. The associated intermittent behavior is due to the formation of small arches of particles with a finite lifetime. The distribution of the interparticle exit times rises rapidly at short times followed by an exponential decay with a large characteristic time, while the cascade size distribution displays prominent peaks for specific cluster sizes. Although the dependence of the mean velocity on the separation of two constrictions is not simple, the mean flow velocity of a system with a single constriction provides an upper envelope for the system with two constrictions. We also examine the orientation of the leading pair of particles in front of the constriction(s). With a single constriction in the intermittent regime, there is a strong preference for the leading pair to be orientated perpendicular to the flow. When two constrictions are present, orientations parallel to the flow are much more likely at the second constriction.

The evolution of structural defects during phase transition is of great significance to the understanding of the mechanism of solid-liquid transition. However, the current research on topological defects still uses the pair-correlation function and the orientational order correlation function, so it is difficult to quantify the detailed changes of structural defects locally. In this paper, the local volume fraction is proposed as a key parameter to accurately quantify the variation of structural defects. The experimental results indicate that the evolution of structural defects in the particle system is caused by the decrease of local volume fraction, so the critical value of phase transition could be determined by the minimum local volume fraction ${\varphi }_{\min }$. Furthermore, according to the evolution law of structural defects, it can be deduced that the phase transition is continuous, which is consistent with the Kosterlitz-Thouless-Halperin-Nelson-Young theory. Therefore, the quantitative analysis of structural defects by using local volume fraction can help make the mechanism of solid-liquid phase transformation clearer.

We have inferred the energy distribution of trapped ions in an electron beam ion trap (EBIT) from simulations of the spatial distribution of ${\mathrm{Fe}}^{13+}$ ions and a comparison with measured visible light images of the ion cloud. We simulated the cloud of ${\mathrm{Fe}}^{13+}$ ions by computing ion trajectories in the EBIT for different ion energy distributions used to initialize the trajectories. We then performed a least-squares fit to infer the ion energy distribution that best reproduced the measured ion cloud. These best-fit distributions were typically non-Maxwellian. For electron beam energies of 395–475 eV and electron beam currents of 1–9 mA, we find that the average ion energy is in the range of 10–300 eV. We also find that the average ion energy increases with increasing beam current approximately as $\langle E\rangle \approx 25I_{\mathrm{e}}\mathrm{eV}$, where $I_{\mathrm{e}}$ is the electron beam current in mA. We have also compared our results to Maxwell-Boltzmann-distribution ion clouds. We find that our best-fit non-thermal distributions have an $\langle E\rangle$ that is less than half that of the $T$ from the best-fit Maxwell-Boltzmann distributions $(\langle E\rangle /q)/T=0.41\pm 0.05$.

In this work, a lattice Boltzmann (LB) model based on the phase-field method is proposed for simulating large density ratio two-phase flows. An improved multiple-relaxation-time (MRT) LB equation is first developed to solve the conserved Allen-Cahn (AC) equation. By utilizing a nondiagonal relaxation matrix and modifying the equilibrium distribution function and discrete source term, the conserved AC equation can be correctly recovered by the proposed MRT LB equation with no deviation term. Therefore, the calculations of the temporal derivative term in the previous LB models are successfully avoided. Numerical tests demonstrate that satisfactory accuracy can be achieved by the present model to solve the conserved AC equation. What is more, the discrete force term of the MRT LB equation for the incompressible Navier-Stokes equations is also simplified and modified in the present work. An alternative scheme to calculate the gradient terms of the order parameter involved in the discrete force term through the nonequilibrium part of the distribution function is also developed. To validate the ability of the present LB model for simulating large density ratio two-phase flows, series of benchmarks, including two-phase Poiseuille flow, droplet impacting on thin liquid film, and planar Taylor bubble are simulated. It is found that the results predicted by the present LB model agree well with the analytical, numerical, and experimental results.

When a randomness is introduced at the level of real matrix elements, depending on its particular realization, a pair of eigenvalues can appear as real or form a complex conjugate pair. We show that in the limit of large matrix size the density of such real eigenvalues is proportional to the square root of the asymptotic density of complex eigenvalues continuated to the real line. This relation allows one to calculate the real densities up to a normalization constant, which is then applied to various examples, including heavy-tailed ensembles and adjacency matrices of sparse random regular graphs.

We investigate the local elastic properties of polystyrene doped with ${\mathrm{SiO}}_2$ nanoparticles by analyzing the local density fluctuations. The density fluctuations were established from coarse-grained molecular dynamics simulations performed with the MARTINI force field. A significant increase in polystyrene stiffness was revealed within a characteristic range of 1.4 nm from the nanoparticle, while polystyrene density saturates to the bulk value at significantly shorter distances. The enhancement of the local elastic properties of the polymer was attributed to the effect of nonaffine deformations at the length scale below 1 nm, which was further confirmed through the random matrix model with variable strength of disorder.

We describe analytically, and simulate numerically, traveling waves with oscillatory tails in a bistable, piecewise-linear reaction-diffusion-advection system of the FitzHugh-Nagumo type with linear cross-diffusion and cross-advection terms of opposite signs. We explore the dynamics of two wave types, namely, solitary pulses and their infinite sequences, i.e., periodic wave trains. The effects of cross diffusion and cross advection on wave profiles and speed of propagation are analyzed. For pulses, in the speed diagram splitting of a curve into several branches occurs, corresponding to different waves (wave branching). For wave trains, in the dispersion relation diagram there are oscillatory curves and the discontinuous curve of an isola with two branches. The corresponding wave trains have symmetric or asymmetric profiles. Numerical simulations show that for large values of the period there exist two wave trains, which come closer and closer together and are subject to fusion into one when the value of the period is decreasing. Other types of waves are also briefly discussed.

A molecular model describing the effective anchoring energy of a liquid crystal (LC) system, composed of 4-$n$-pentyl-$4^{\prime }$-cyanobiphenyl (5CB) molecules deposited on a photosensitive azobenzene layer consisting of 6Az10PVA molecules, is proposed. This model takes into account the interaction between the surface polarization in the LC phase and the surface electric field, arising from the surface charge density. Within the framework of this molecular model, the mechanism responsible for the anchoring transition in the LC phase from homeotropic to planar alignment and vice versa, caused by trans-cis and cis-trans conformational changes in the monolayer 6Az10PVA after laser radiation, is described. It is shown that using experimental data for the voltage across the $\text{6Az10PVA}+\text{5CB}$ film, obtained by the surface potential technique, the charge separation during the conformational changing, caused by the laser irradiation, may lead to an anchoring transition induced by trans-cis-trans isomerization in the photosensitive azobenzene monolayer. The calculated values of the isothermal surface pressure diagram $\pi \text{−}A$ showed that the surface area $A$ per LC molecule is noticeably higher for the cis configuration, which reflects a less efficient packaging than in the trans state.

It has recently been shown that altering the shape of the metastable and unstable branches of an equation of state (EOS) can substantially improve the numerical accuracy of liquid and vapor densities in the pseudopotential lattice Boltzmann method [Peng et al., Phys. Rev. E 101, 063309 (2020)]. We found that this approach reduces stability of the method in nonequilibrium conditions and is unstable for bubbles at low reduced temperatures. Here we present an improved method for altering the shape of the metastable and unstable branches of the EOS which remains stable for both equilibrium and nonequilibrium situations and has no issues with bubbles. We also performed a detailed study of the stability of the methods for a droplet impact on a liquid film for reduced temperatures down to 0.35 with Reynolds number of 300. Our approach remained stable for a density ratio of up to $3.38\times {10}^4$.

In this paper we examine some foundational issues of a class of quantum engines where the system consists of a single quantum parametric oscillator, operating in an Otto cycle consisting of four stages of two alternating phases: the isentropic phase is detached from any bath (thus a closed system) where the natural frequency of the oscillator is changed from one value to another, and the isothermal phase where the system (now rendered open) is put in contact with one or two squeezed baths of different temperatures, whose nonequilibrium dynamics follows the Hu-Paz-Zhang (HPZ) master equation for quantum Brownian motion. The HPZ equation is an exact non-Markovian equation which preserves the positivity of the density operator and is valid for (1) all temperatures, (2) arbitrary spectral density of the bath, and (3) arbitrary coupling strength between the system and the bath. Taking advantage of these properties we examine some key foundational issues of theories of quantum open and squeezed systems for these two phases of the quantum Otto engines. This includes (1) the non-Markovian regimes for non-Ohmic, low-temperature baths, (2) what to expect in nonadiabatic frequency modulations, (3) strong system-bath coupling, as well as (4) the proper junction conditions between these two phases. Our aim here is not to present ways for attaining higher efficiency but to build a more solid theoretical foundation for quantum engines of continuous variables covering a broader range of parameter spaces that we hope are of use for exploring such possibilities.

Eigenstates of local many-body interacting systems that are far from spectral edges are thought to be ergodic and close to being random states. This is consistent with the eigenstate thermalization hypothesis and volume-law scaling of entanglement. We point out that systematic departures from complete randomness are generically present in midspectrum eigenstates, and focus on the departure of the entanglement entropy from the random-state prediction. We show that the departure is (partly) due to spatial correlations and due to orthogonality to the eigenstates at the spectral edge, which imposes structure on the midspectrum eigenstates.

In this paper, we study in detail the nonlinear propagation of a magnetic soliton in a ferromagnetic film. The sample is magnetized to saturation by an external field perpendicular to film plane. A generalized ($2+1$)-dimensional short-wave asymptotic model is derived. The bilinearlike forms of this equation are constructed and exact magnetic line soliton solutions are exhibited. It is observed that a series of stable lumps can be generated by an unstable magnetic soliton under Gaussian disturbance. Such magnetic lumps are highly stable and can maintain their shapes and velocities during evolution or collision. The interaction between lump and magnetic solitons, as well as the interaction between two lumps, are numerically investigated. We further discuss the nonlinear motion of lumps in ferrites with Gilbert damping and inhomogeneous exchange effects. The results show that the Gilbert-damping effects make the amplitude and velocity of the magnetic lump decay exponentially during propagation. And the shock waves are generated from a lump when quenching the strength of inhomogeneous exchange.

We predict negative temperature states in the discrete nonlinear Schödinger (DNLS) equation as exact solutions of the associated wave kinetic equation. Within the wave kinetic approach, we define an entropy that results monotonic in time and reaches a stationary state, that is consistent with classical equilibrium statistical mechanics. We also perform a detailed analysis of the fluctuations of the actions at fixed wave numbers around their mean values. We give evidence that such fluctuations relax to their equilibrium behavior on a shorter timescale than the one needed for the spectrum to reach the equilibrium state. Numerical simulations of the DNLS equation are shown to be in agreement with our theoretical results. The key ingredient for observing negative temperatures in lattices characterized by two invariants is the boundedness of the dispersion relation.

During the outbreak of a virus, perhaps the greatest concern is the future evolution of the epidemic: How many people will be infected and which regions will be affected the most? The accurate prediction of an epidemic enables targeted disease countermeasures (e.g., allocating medical staff and quarantining). But when can we trust the prediction of an epidemic to be accurate? In this work we consider susceptible-infected-susceptible (SIS) and susceptible-infected-removed (SIR) epidemics on networks with time-invariant spreading parameters. (For time-varying spreading parameters, our results correspond to an optimistic scenario for the predictability of epidemics.) Our contribution is twofold. First, accurate long-term predictions of epidemics are possible only after the peak rate of new infections. Hence, before the peak, only short-term predictions are reliable. Second, we define an exponential growth metric, which quantifies the predictability of an epidemic. In particular, even without knowing the future evolution of the epidemic, the growth metric allows us to compare the predictability of an epidemic at different points in time. Our results are an important step towards understanding when and why epidemics can be predicted reliably.