Analog systems have recently been used in several experiments in the context of convective mixing of $\mathrm{C}{\mathrm{O}}_2$. We generalize the nonmonotonic density dependence of the growth of instabilities and provide a scaling relation for the onset of instability. The results of linear stability analysis and direct numerical simulations show that these fluids do not resemble the dynamics of $\mathrm{C}{\mathrm{O}}_2$-water convective instabilities. A typical analog system, such as water–propylene glycol, is found to be less unstable than $\mathrm{C}{\mathrm{O}}_2$-water. These results provide a basis for further research and proper selection of analog systems and are essential to the interpretation of experiments.

Finite pieces of locally isostatic networks have a large number of floppy modes because of missing constraints at the surface. Here we show that by imposing suitable boundary conditions at the surface the network can be rendered effectively isostatic. We refer to these as anchored boundary conditions. An important example is formed by a two-dimensional network of corner sharing triangles, which is the focus of this paper. Another way of rendering such networks isostatic is by adding an external wire along which all unpinned vertices can slide (sliding boundary conditions). This approach also allows for the incorporation of boundaries associated with internal holes and complex sample geometries, which are illustrated with examples. The recent synthesis of bilayers of vitreous silica has provided impetus for this work. Experimental results from the imaging of finite pieces at the atomic level need such boundary conditions, if the observed structure is to be computer refined so that the interior atoms have the perception of being in an infinite isostatic environment.

The interaction dynamics of droplets on a solid surface is a fundamental problem that is important to a wide variety of industrial applications, such as inkjet printing. Most previous research has focused on a single droplet and little research has been reported on the dynamics of multiple-droplet interactions on surfaces. Recently, Zhou et al. [W. Zhou, D. Loney, A. G. Fedorov, F. L. Degertekin, and D. W. Rosen, Lattice Boltzmann simulations of multiple-droplet interaction dynamics, Phys. Rev. E 89, 033311 (2014)] reported an efficient numerical solver based on the lattice Boltzmann method (LBM) that enabled the simulation of the multiple-droplet interaction dynamics on an ideal surface (i.e., smooth and homogeneous). In order to predict the interaction dynamics in the real world, it is necessary to take into consideration the contact angle hysteresis phenomenon on a nonideal surface, which is possibly caused by the surface roughness and chemical inhomogeneity of the surface. In this paper a dynamic contact angle boundary condition is developed to take into account the contact angle hysteresis effect based on the previously reported LBM. The improved LBM is validated with experimental data from the literature. The influence of the droplet impact conditions (e.g., fluid properties and impingement velocity), droplet spacing, and surface conditions on the two-droplet interaction dynamics is investigated with the validated LBM. Interesting phenomena are observed and discussed. The interaction of a line of six droplets on a nonideal surface is simulated to demonstrate the powerful capability of the developed numerical solver in simulating the multiple-droplet interaction dynamics in the real world.

The coupling of stochastic growth and shrinkage of one-dimensional structures to random aging of the constituting subunits defines the simple association-dissociation-aging process which captures the essential features of the nonequilibrium assembly of cytoskeletal filaments. Because of correlations, previously employed mean-field methods fail to correctly describe filament growth. We study an alternative formulation of the full master equation of the stochastic process. An ansatz for the steady-state solution leads to a recursion relation which allows for the calculation of all emergent quantities with increasing accuracy and in excellent agreement with stochastic simulations.

A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems are ergodic, canonical ensemble averages can be computed as dynamical time averages over a single trajectory. Systems of this type were unknown until their recent discovery by Hoover and colleagues. The present formalism should facilitate the discovery, construction, and classification of other such systems by encompassing a wide class of them within a single unified framework. This formalism includes both canonical and generalized Hamiltonian systems in a state space of arbitrary dimensionality (either even or odd) and therefore encompasses both few- and many-particle systems. Particular attention is devoted to the physical motivation and interpretation of the formalism, which largely determine its structure. An analogy to stochastic thermostats and fluctuation-dissipation theorems is briefly discussed.

In this work, we consider a stochastic oscillator described by a discrete-state continuous-time Markov chain, in which the states are arranged in a circle, and there is a constant probability per unit time of jumping from one state to the next in a specified direction around the circle. At each of a sequence of equally spaced times, the oscillator has a specified probability of being reset to a particular state. The focus of this work is the entrainment of the oscillator by this periodic but stochastic stimulus. We consider a distinguished limit, in which (i) the number of states of the oscillator approaches infinity, as does the probability per unit time of jumping from one state to the next, so that the natural mean period of the oscillator remains constant, (ii) the resetting probability approaches zero, and (iii) the period of the resetting signal approaches a multiple, by a ratio of small integers, of the natural mean period of the oscillator. In this distinguished limit, we use analytic and numerical methods to study the extent to which entrainment occurs.

A diverse variety of processes—including recurrent disease episodes, neuron firing, and communication patterns among humans—can be described using interevent time (IET) distributions. Many such processes are ongoing, although event sequences are only available during a finite observation window. Because the observation time window is more likely to begin or end during long IETs than during short ones, the analysis of such data is susceptible to a bias induced by the finite observation period. In this paper, we illustrate how this length bias is born and how it can be corrected without assuming any particular shape for the IET distribution. To do this, we model event sequences using stationary renewal processes, and we formulate simple heuristics for determining the severity of the bias. To illustrate our results, we focus on the example of empirical communication networks, which are temporal networks that are constructed from communication events. The IET distributions of such systems guide efforts to build models of human behavior, and the variance of IETs is very important for estimating the spreading rate of information in networks of temporal interactions. We analyze several well-known data sets from the literature, and we find that the resulting bias can lead to systematic underestimates of the variance in the IET distributions and that correcting for the bias can lead to qualitatively different results for the tails of the IET distributions.

We present a systematic derivation of the Biot-Savart equation from the nonlinear Schrödinger equation, in the limit when the curvature radius of vortex lines and the intervortex distance are much greater than the vortex healing length, or core radius. We derive the Biot-Savart equations in Hamiltonian form with Hamiltonian expressed in terms of vortex lines,$$H=\frac{{\kappa }^2}{8\pi }{\int }_{|\mathbf{s}-{\mathbf{s}}^{\prime }|>{\xi }_{*}}\frac{d\mathbf{s}·d{\mathbf{s}}^{\prime }}{|\mathbf{s}-{\mathbf{s}}^{\prime }|},$$with cutoff length ${\xi }_{*}\approx 0.3416293/\sqrt{{\rho }_0},$ where ${\rho }_0$ is the background condensate density far from the vortex lines and $\kappa$ is the quantum of circulation.

Time-integrated x-ray emission spectra of laser-irradiated Au disks were recorded using transmission grating spectrometry, at laser intensities of ${10}^{13}$ to ${10}^{14}\text{W}/{\mathrm{cm}}^2$. Radiation-hydrodynamics and atomic physics calculations were used to simulate the emitted spectra. Three major plasma regions can be recognized: the heat wave, the corona, and an intermediate region connecting them. An analysis of the spectral contribution of these three plasma regions to the integrated recorded spectrum is presented. The importance of accurate atomic modeling of the intermediate plasma region, between the corona and the heat wave, is highlighted. The influence of several aspects of the atomic modeling is demonstrated, in particular multiply-excited atomic configurations and departure from local thermal equilibrium.

Linear and nonlinear ion-acoustic waves are studied in a fluid model for nonrelativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and applies equally well both to fully degenerate and classical, nondegenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long-wavelength limit, the results agree with quantum kinetic theory. Using the reductive perturbation method, the appropriate Korteweg–de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.

The effects of the helicity on the dynamics of turbulent flows are investigated. The aim is to disentangle the role of helicity in fixing the direction, the intensity, and the fluctuations of the energy transfer across the inertial range of scales. We introduce an external parameter $\alpha$ that controls the mismatch between the number of positive and negative helically polarized Fourier modes. We present direct numerical simulations of Navier-Stokes equations from the fully symmetrical case, $\alpha =0$, to the fully asymmetrical case, $\alpha =1$, when only helical modes of one sign survive. We found a singular dependency of the direction of the energy cascade on $\alpha$, measuring a positive forward flux as soon as only a few modes with different helical polarities are present. Small-scale fluctuations are also strongly sensitive to the degree of mode reduction, leading to a vanishing intermittency already for values of $\alpha \sim 0.1$. If the analysis is restricted to sets of modes with the same helicity sign, intermittency is vanishing for the modes belonging to the minority set, and it is close to that measured on the original Navier-Stokes equations for the other set.

A variability measure of the times of uniform events based on a shot-noise process is proposed and studied. The measure is inspired by the Fano factor, which we generalize by considering the time-weighted influence of the events given by a shot-noise response function. The sequence of events is assumed to be an equilibrium renewal process, and based on this assumption we present formulas describing the behavior of the variability measure. The formulas are derived for a general response function, restricted only by some natural conditions, but the main focus is given to the shot noise with exponential decrease. The proposed measure is analyzed and compared with the Fano factor.

Information thermodynamics provides a framework for studying the effect of feedback loops on entropy production. It has enabled the understanding of novel thermodynamic systems such as the information engine, which can be seen as a modern version of “Maxwell's Dæmon,” whereby a feedback controller processes information gained by measurements in order to extract work. Here, we analyze a simple model of such an engine that uses feedback control based on measurements to obtain negative entropy production. We focus on the distribution and fluctuations of the information obtained by the feedback controller. Significantly, our model allows an analytic treatment for a two-state system with exact calculation of the large deviation rate function. These results suggest an approximate technique for larger systems, which is corroborated by simulation data.

We report the observation of a surprising phenomenon consisting in a oscillating phase transition which appears in a binary mixture when this is enlightened by a strongly focused infrared laser beam. The mixture is poly-methyl-meth-acrylate (PMMA)–3-octanone, which has an upper critical solution temperature at $T_c=306.6\text{K}$ and volume fraction ${\varphi }_c=12.8\%$ [Crauste et al., arXiv:1310.6720, 2013]. We describe the dynamical properties of the oscillations, which are produced by a competition between various effects: the local accumulation of PMMA produced by the laser beam, thermophoresis, and nonlinear diffusion. We show that the main properties of this kind of oscillations can be reproduced in the Landau theory for a binary mixture in which a local driving mechanism, simulating the laser beam, is introduced.

The evolution of the surface roughness $W$ of a thin film deposited on a rough substrate is studied with a model of temperature-activated adatom diffusion, irreversible lateral aggregation, and no step energy barrier, in which the main parameter is the ratio $R$ of diffusion and deposition rates. At sufficiently low temperatures $\left(R\lesssim 10\right)$, the average number of adatom steps after adsorption is very small, thus $W$ monotonically increases with time $t$ due to an approximately uncorrelated deposition at short times. If the temperature is not very low ($R\sim {10}^3$ or larger), smoothening occurs at short times and the Villain-Lai-Das Sarma (VLDS) growth equation governs the long time roughening, which is attained after a crossover time $t_c$ that increases with the correlation length ${\xi }_i$ of the substrate. Scaling arguments predict the dependence of $t_c$ on temperature and on the substrate production time and the scaling relation for the difference between the roughness of films deposited on rough and flat substrates, in good agreement with numerical results. The effect of temperature is not a direct extension of previous results on flat substrates because the short wavelength fluctuations delay the formation of terraces. For this reason, the effective energy obtained from the dependence of $t_c$ on $R$ is $40\%$ of the energy of activated adatom diffusion. A scaling law for the initial smoothening is proposed as $W/W_i=\mathrm{\Psi }\left(t/t_{c1}\right)$, with a crossover time $t_{c1}\equiv R^{-\theta }{{\xi }_i}^z$, where $W_i$ is the substrate roughness, $\theta \approx 0.4$, and $z$ is the VLDS dynamical exponent. It provides good data collapse if $W$ is not very small and is suggested to be tested experimentally.

Anomalous spectral shift of transmission peaks is observed in a Fabry-Pérot cavity filled with a chiral anisotropic medium. The effective refractive index value resides out of the interval between the ordinary and the extraordinary refractive indices. The spectral shift is explained by contribution of a geometric phase. The problem is solved analytically using the approximate Jones matrix method, numerically using the accurate Berreman method, and geometrically using the generalized Mauguin-Poincaré rolling cone method. The $o$-mode blueshift is measured for a 4-methoxybenzylidene-$4{}^{\prime }\text{−}n$-butylaniline twisted-nematic layer inside the Fabry-Pérot cavity. The twist is electrically induced due to the homeoplanar-twisted configuration transition in an ionic-surfactant-doped liquid crystal layer. Experimental evidence confirms the validity of the theoretical model.

We study a nonlinear $q$-voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. To study the role of the multilevelness in this model we propose three methods of transferring the model from a mono- to a multiplex network. They take into account two criteria: one related to the status of independence (LOCAL vs GLOBAL) and one related to peer pressure (AND vs OR). In order to examine the influence of the presence of more than one level in the social network, we perform simulations on a particularly simple multiplex: a duplex clique, which consists of two fully overlapped complete graphs (cliques). Solving numerically the rate equation and simultaneously conducting Monte Carlo simulations, we provide evidence that even a simple rearrangement into a duplex topology may lead to significant changes in the observed behavior. However, qualitative changes in the phase transitions can be observed for only one of the considered rules: LOCAL&AND. For this rule the phase transition becomes discontinuous for $q=5$, whereas for a monoplex such behavior is observed for $q=6$. Interestingly, only this rule admits construction of realistic variants of the model, in line with recent social experiments.

In this paper, we report the synchronized dynamics of cells with activator-inhibitor pathways via an adaptive environment-mediated coupling scheme with feedbacks and control mechanisms. The adaptive character of the extracellular medium is modeled via its damping parameter as a physiological response aiming at annihilating the cellular differentiation existing between the chaotic biochemical pathways of the cells, in order to preserve homeostasis. We perform an investigation on the existence and stability of the synchronization manifold of the coupled system under the proposed coupling pattern. Both mathematical and computational tools suggest the accessibility of conducive prerequisites (conditions) for the emergence of a robust synchronous regime. The relevance of a phase-synchronized dynamics is appraised and several numerical indicators advocate for the prevalence of this fascinating phenomenon among the interacting cells in the phase space.

We conducted a molecular dynamics simulation to investigate current inversions in a nanosized water pump based on a single-walled carbon nanotube powered by mechanical vibration. It was found that the water current depended sensitively on the frequency of mechanical vibration. Especially in the resonance region, the nanoscale pump underwent reversals of the water current. This phenomenon was attributed to the dynamics competition of the water molecules in the two sections (the left and right parts) divided by the vibrating atom and the differences in phase and decay between the two mechanical waves generated by mechanical vibration and propagating in opposite directions toward the two ends of the carbon nanotube. Our findings provide an insight into water transportation through nanosized pumps and have potential in the design of high-flux nanofluidic systems and nanoscale energy converters.