Recent experimental works on one-dimensional (1D) circular Kardar-Parisi-Zhang (KPZ) systems whose radii decrease in time have reported controversial conclusions about the statistics of their interfaces. Motivated by this, here we investigate several one-dimensional KPZ models on substrates whose size changes in time as $L\left(t\right)=L_0+\omega t$, focusing on the case $\omega <0$. From extensive numerical simulations, we show that for $L_0\gg 1$ there exists a transient regime in which the statistics is consistent with that of flat KPZ systems (the $\omega =0$ case), for both $\omega <0$ and $\omega >0$. Actually, for a given model, $L_0$ and $\left|\omega \right|$, we observe that a difference between ingrowing ($\omega <0$) and outgrowing ($\omega >0$) systems arises only at long times ($t\sim t_c=L_0/\left|\omega \right|$), when the expanding surfaces cross over to the statistics of curved KPZ systems, whereas the shrinking ones become completely correlated. A generalization of the Family-Vicsek scaling for the roughness of ingrowing interfaces is presented. Our results demonstrate that a transient flat statistics is a general feature of systems starting with large initial sizes, regardless of their curvature. This is consistent with their recent observation in ingrowing turbulent liquid crystal interfaces, but it is in contrast with the apparent observation of curved statistics in colloidal deposition at the edge of evaporating drops. A possible explanation for this last result, as a consequence of the very small number of monolayers analyzed in this experiment, is given. This is illustrated in a competitive growth model presenting a few-monolayer transient and an asymptotic behavior consistent, respectively, with the curved and flat statistics.

Classical density functional theory (DFT) is a useful tool to compute the structure of the electrical double layer because it includes ion-ion correlations due to excluded-volume effects (i.e., steric correlations) and ion screening effects (i.e., electrostatic correlations beyond the electrostatic mean-field potential). This paper systematically analyzes the accuracies of three different electrostatic excess free-energy functionals, as compared to Monte Carlo (MC) simulations of the planar electrical double layer, over a large parameter space. Specifically, we tested the reference fluid density (RFD) [Gillespie et al., J. Phys.: Condens. Matter 14, 12129 (2002)], functionalized mean spherical approximation (fMSA) [Roth and Gillespie, J. Phys.: Condens. Matter 28, 244006 (2016)], and bulk fluid (BF) [Kierlik and Rosinberg, Phys. Rev. A 44, 5025 (1991); Y. Rosenfeld, J. Chem. Phys. 98, 8126 (1993)] functionals. Previous work compared these DFT methods to MC simulations only for a small set of parameters. Here, a total of twelve different cations were studied, with valences of +1, +2, and +3 and ion diameters of 0.15, 0.30, 0.60, and 0.90 nm at bulk concentrations between 1 $\mu M$ and 1 $M$. The anion always had valence −1 and diameter 0.30 nm. The structure of the double layer of these charged, hard-sphere ions was computed for surface charges ranging from 0 to $-0.50\mathrm{C}/{\mathrm{m}}^2$. All the DFTs were compared against each other for all the parameters, as well as to 378 MC simulations. Overall, RFD was the best of the three functionals, while BF was the least accurate. fMSA performed significantly better than BF, making it a reasonable choice that is less computationally expensive than RFD. For monovalent cations, all three functionals worked reasonably well, except BF was qualitatively different from MC at very low surface charges. For multivalent cations, BF underestimated charge inversion while fMSA overestimated it. All DFTs performed poorly for small multivalent ions.

Absorption refrigerators transfer thermal energy from a cold reservoir to a hot reservoir using input energy from a third, so-called work reservoir. We examine the operation of quantum absorption refrigerators when coherences between eigenstates survive in the steady state limit. In our model, the working medium comprises a discrete, four-level system. Several studies on related setups have demonstrated the performance-enhancing potential of steady-state eigenbasis quantum coherences. By contrast, in our model such coherences generally quench the cooling current in the refrigerator, while minimally affecting the coefficient of performance (cooling efficiency). We rationalize the behavior of the four-level refrigerator by studying three-level model systems for energy transport and refrigeration. Our calculations further illuminate the shortcomings of secular quantum master equations and the necessity of employing dynamical equations of motion that retain couplings between population and coherences.

We report on a modulated coherent state in a ring of nonlocally coupled oscillators. Although the identical oscillators are all synchronized under the symmetric coupling, the phase configuration has an inhomogeneous structure. This symmetry-broken coherent state exists only for a nonlocal coupling with both attracting and repulsive interactions, depending on the distance between oscillators, and emerges via a continuous bifurcation from a uniformly coherent state. We analyze the existence and stability of the modulated coherent states on the basis of Ott-Antonsen equations for the local order parameter. Our theoretical results are verified using the numerical simulations.

Experimentalists observe phenotypic variability even in isogenic bacteria populations. We explore the hypothesis that in fluctuating environments this variability is tuned to maximize a bacterium's expected log-growth rate, potentially aided by epigenetic (all inheritable nongenetic) markers that store information about past environments. Crucially, we assume a time delay between sensing and action, so that a past epigenetic marker is used to generate the present phenotypic variability. We show that, in a complex, memoryful environment, the maximal expected log-growth rate is linear in the instantaneous predictive information—the mutual information between a bacterium's epigenetic markers and future environmental states. Hence, under resource constraints, optimal epigenetic markers are causal states—the minimal sufficient statistics for prediction—or lossy approximations thereof. We propose new theoretical investigations into and new experiments on bacteria phenotypic bet-hedging in fluctuating complex environments.

Despite a vast clinical application of anesthetics, the molecular level of understanding of general anesthesia is far from our reach. Using atomistic molecular dynamics simulation, we study the effects of common anesthetics: ethanol, chloroform, and methanol in the fully hydrated symmetric multicomponent lipid bilayer membrane comprised of an unsaturated palmitoyl-oleoyl-phosphatidyl-choline (POPC), a saturated palmitoyl-sphingomyelin, and cholesterol, which exhibits phase coexistence of liquid-ordered ($l_o$)–liquid-disordered ($l_d$) phase domains. We find that the mechanical and physical properties such as the thickness and rigidity of the membrane are reduced while the lateral expansion of the membrane is exhibited in the presence of anesthetic molecules. Our simulation shows both lateral and transverse heterogeneity of the anesthetics in the composite multicomponent lipid membrane. Both ethanol and chloroform partition in the POPC-rich $l_d$ phase domain, while methanol is distributed in both $l_o\text{−}{l}_d$ phase domains. Chloroform can penetrate deep into the membrane, while methanol partitions mostly at the water layer closed to the head group and ethanol at the neck of the lipids in the membrane.

Soil-composing particles undergo wettability changes, impacting hydraulic and mechanical processes such as erosion and landslides. Such processes evolve at very small scales, typically at the particle level. Here we capture the evolution of liquid interfaces in a single particle and several particles with the lattice Boltzmann (LB) method. The paper presents a three-dimensional LB study on the droplet dynamics on a layer of uniformly packed spherical particles with varying size and intrinsic contact angle (CA) aimed at mimicking conditions comparable to those of real soils. The numerical droplet is initialized close to the granular surface and deposited by gravity. Three spreading and infiltration behaviors were identified: a droplet with a stable apparent CA, a droplet with a metastable apparent CA before infiltration, and immediate infiltration. The results showed that the formation of a droplet with a stable or metastable spherical-cap shape depends on the particle size and the intrinsic CA. Furthermore, the initial wetted zone expansion was found to be governed by inertial effects with its behavior characterized by a power law. Finally, the apparent CA, which is closely related to the intrinsic CA, was found to be influenced by the particle size due to a significant portion of the droplet being embedded into the granular surface for the larger particles and reducing the apparent CA. This paper provides a basis for future research targeting the behavior of droplet interaction with granular surfaces with variable intrinsic CAs (from wettable to superhydrophobic) such as soils and other granular materials for industrial applications. The numerical approach implemented can also be extended to model other dynamic processes for a droplet, such as evaporation, high-velocity impacting, and lateral sliding.

The granular Leidenfrost state consists of a dense granular cluster levitating above a hot granular gas. The density of particles inside the cluster can be very high and even close to the density of crystalline packing. To describe this state theoretically, one needs to know the density dependence of constitutive relations (pressure, heat losses, thermal conductivity) at these very high densities. However, the accurate expression for the coefficient of thermal conductivity is lacking. In this work, the constitutive relations were measured at high densities in molecular dynamics simulations in three different settings: a uniform freely cooling dense granulate (to measure heat losses), a uniform ensemble of elastically colliding particles (to measure pressure), and a dense granular medium between two thermal walls under gravity (to measure thermal conductivity). Next, the hydrodynamic equations with the resulting expressions were solved to describe the levitating cluster state in various parameter regimes. Separate molecular dynamics simulations were performed to test the theoretical predictions and measure the density and temperature profiles of the granular Leidenfrost state, and a good agreement with theoretical results was observed.

While studies of active nematics in two dimensions have shed light on various aspects of the flow regimes and topology of active matter, three-dimensional properties of topological defects and chaotic flows remain unexplored. By confining a film of active nematics between two parallel plates, we use continuum simulations and analytical arguments to demonstrate that the crossover from quasi-two-dimensional (quasi-2D) to three-dimensional (3D) chaotic flows is controlled by the morphology of the disclination lines. For small plate separations, the active nematic behaves as a quasi-2D material, with straight topological disclination lines spanning the height of the channel and exhibiting effectively 2D active turbulence. Upon increasing channel height, we find a crossover to 3D chaotic flows due to the contortion of disclinations above a critical activity. Above this critical activity highly contorted disclination lines and disclination loops are formed. We further show that these contortions are engendered by twist perturbations producing a sharp change in the curvature of disclinations.

Detecting critical transitions in the case of moderate or strong noise (collectively referred to as big noise) is challenging, since such noise can make a critical transition point far from the bifurcation point, leading to the failure of traditional small-noise methods. To handle this tough issue, we first transform a generic noisy system into a linear set of binomial moment equations (BMEs). Then, we can solve a closed set of BMEs obtained by truncation and use the resulting binomial moments to reconstruct a joint probability distribution of the state variables of the original system. Third, we derive a leading indicator from the closed set of BMEs. Importantly, the reconstructed distribution determines the way of critical transition (i.e., critical transition is distribution transition rather than state transition in the strong-noise case) as the system comes close to the critical transition point, whereas the derived indicator anticipates when the distribution transition occurs. Our theory has broad applications, and artificial and data examples exhibit its power.

The perturbation expansion technique is employed to solve the Boltzmann equation for the acceleration-driven steady Poiseuille flow of a dilute molecular gas flowing through a planar channel. Neglecting wall effects and focusing only on the bulk hydrodynamics and rheology, the perturbation solution is sought around the channel centerline in powers of the strength of acceleration. To make analytical progress, the collision term has been approximated by the Bhatnagar-Gross-Krook kinetic model for hard spheres, and the related problem for Maxwell molecules was analyzed previously by Tij and Santos [J. Stat. Phys. 76, 1399 (1994)]. The analytical expressions for hydrodynamic (velocity, temperature, and pressure) and rheological fields (normal stress differences, shear viscosity, and heat flux) are obtained by retaining terms up to tenth order in acceleration, with one aim of the present work being to understand the convergence properties of the underlying perturbation series solutions. In addition, various rarefaction effects (e.g., the bimodal shape of the temperature profile, nonuniform pressure profile, normal-stress differences, and tangential heat flux) are also critically analyzed in the Poiseuille flow as functions of the local Froude number. The hydrodynamic and rheological fields evaluated at the channel centerline confirmed the oscillatory nature of the present series solutions (when terms of increasing order are sequentially included), signaling the well-known pitfalls of asymptotic expansion. The Padé approximation technique is subsequently applied to check the region of convergence of each series solution. It is found that the diagonal Padé approximants for rheological fields agree qualitatively with previous simulation data on acceleration-driven rarefied Poiseuille flow.

This paper introduces a modified master-slave synchronization scheme for dynamical systems. In contrast to the standard configuration, the slave system does not receive any driving signal from the master, but rather the interaction is through a linear dynamical system. The key feature of the proposed coupling scheme is that it induces synchronization in certain systems that cannot be synchronized when using the classical static interconnection. Likewise, the dynamic coupling achieves synchronization for arbitrarily large coupling strength values in certain systems for which the classical configuration is applicable only within a narrow interval of coupling strength values. The performance of the synchronization scheme is illustrated in pairs of identical chaotic and mechanical oscillators.

We present a statistical analysis based on the height and return-time probabilities of high-amplitude wave events in both focusing and defocusing Manakov systems. We find that analytical rational or semirational solutions, associated with extreme, rogue wave (RW) structures, are the leading high-amplitude events in this system. We define the thresholds for classifying an extreme wave event as a RW. Our results indicate that there is a strong relationship between the type of RW and the mechanism which is responsible for its creation. Initially, high-amplitude events originate from modulation instability. Upon subsequent evolution, the interaction among these events prevails as the mechanism for RW creation. We suggest a strategy for confirming the basic properties of different extreme events. This involves the definition of proper statistical measures at each stage of the RW dynamics. Our results point to the need for redefining criteria for identifying RW events.

Belousov-Zhabotinsky (BZ) thin layer solution is a fruitful substrate for designing unconventional computing devices. A range of logical circuits, wet electronic devices, and neuromorphic prototypes have been constructed. Information processing in BZ computing devices is based on interaction of oxidation (excitation) wave fronts. Dynamics of the wave fronts propagation is programed by geometrical constraints and interaction of colliding wave fronts is tuned by illumination. We apply the principles of BZ computing to explore a geometry of street networks. We use two-variable Oregonator equations, the most widely accepted and verified in laboratory experiments BZ models, to study propagation of excitation wave fronts for a range of excitability parameters, with gradual transition from excitable to subexcitable to nonexcitable. We demonstrate a pruning strategy adopted by the medium with decreasing excitability when wider and ballistically appropriate streets are selected. We explain mechanics of streets selection and pruning. The results of the paper will be used in future studies of studying dynamics of cities and characterizing geometry of street networks.

We investigate numerically the yielding transition of a two-dimensional model amorphous solid under external shear. We use a scalar model in terms of values of the total local strain, derived from the full (tensorial) description of the elastic interactions in the system, in which plastic deformations are accounted for by introducing a stochastic “plastic disorder” potential. This scalar model is seen to be equivalent to a collection of Prandtl-Tomlinson particles, which are coupled through an Eshelby quadrupolar kernel. Numerical simulations of this scalar model reveal that the strain rate versus stress curve, close to the critical stress, is of the form $\dot{\gamma }\sim {(\sigma -{\sigma }_c)}^{\beta }$. Remarkably, we find that the value of $\beta$ depends on details of the microscopic plastic potential used, confirming and giving additional support to results previously obtained with the full tensorial model. To rationalize this result, we argue that the Eshelby interaction in the scalar model can be treated to a good approximation in a sort of “dynamical” mean field, which corresponds to a Prandtl-Tomlinson particle that is driven by the applied strain rate in the presence of a stochastic noise generated by all other particles. The dynamics of this Prandtl-Tomlinson particle displays different values of the $\beta$ exponent depending on the analytical properties of the microscopic potential, thus giving support to the results of the numerical simulations. Moreover, we find that other critical exponents that depend on details of the dynamics show also a dependence with the form of the disorder, while static exponents are independent of the details of the disorder. Finally, we show how our scalar model relates to other elastoplastic models and to the widely used mean-field version known as the Hébraud-Lequeux model.

Flow in porous media is known to be largely affected by pore morphology. In this work, we investigate the effects of pore geometry on the transport and spatial correlations of flow through porous media in two distinct pore structures arising from three-dimensional assemblies of overlapping and nonoverlapping spheres. Using high-resolution direct numerical simulations (DNS), we perform Eulerian and Lagrangian analysis of the flow and transport characteristics in porous media. We show that the Eulerian velocity distributions change from nearly exponential to Gaussian distributions as porosity increases. A stretched exponential distribution can be used to represent this behavior for a wide range of porosities. Evolution of Lagrangian velocities is studied for the uniform injection rule. Evaluation of tortuosity and trajectory length distributions of each porous medium shows that the model of overlapping spheres results in higher tortuosity and more skewed trajectory length distributions compared to the model of nonoverlapping spheres. Wider velocity distribution and higher tortuosity for overlapping spheres model give rise to non-Fickian transport while transport in nonoverlapping spheres model is found to be Fickian. Particularly, for overlapping spheres model our analysis of first-passage time distribution shows that the transport is very similar to those observed for sandstone. Finally, using three-dimensional (3D) velocity field obtained by DNS at the pore-scale, we quantitatively show that despite the randomness of pore-space, the spatially fluctuating velocity field and the 3D pore-space distribution are strongly correlated for a range of porous media from relatively homogeneous monodisperse sphere packs to Castlegate sandstone.

Violent relaxation is a process that occurs in systems with long-range interactions. It has the peculiar feature of dramatically amplifying small perturbations, and rather than driving the system to equilibrium, it instead leads to slowly evolving configurations known as quasistationary states that fall outside the standard paradigm of statistical mechanics. Violent relaxation was originally identified in gravity-driven stellar dynamics; here, we extend the theory into the quantum regime by developing a quantum version of the Hamiltonian mean field (HMF) model which exemplifies many of the generic properties of long-range interacting systems. The HMF model can either be viewed as describing particles interacting via a cosine potential, or equivalently as the kinetic $XY$ model with infinite-range interactions, and its quantum fluid dynamics can be obtained from a generalized Gross-Pitaevskii equation. We show that singular caustics that form during violent relaxation are regulated by interference effects in a universal way described by Thom's catastrophe theory applied to waves and this leads to emergent length scales and timescales not present in the classical problem. In the deep quantum regime we find that violent relaxation is suppressed altogether by quantum zero-point motion. Our results are relevant to laboratory studies of self-organization in cold atomic gases with long-range interactions.

We study the heat statistics of a quantum Brownian motion described by the Caldeira-Leggett model. By using the path integral approach, we introduce a concept of the quantum heat functional along every pair of Feynman paths. This approach has the advantage of improving our understanding about heat in quantum systems. First, we demonstrate the microscopic reversibility of the system by connecting the heat functional to the forward and time-reversed probabilities. Second, we analytically prove the quantum-classical correspondence of the heat functional and their statistics, which allows us to obtain better intuitions about the difference between classical and quantum heat.

This work investigates the emergence of resonance and resonance-induced localization in a weakly dissipative chain of coupled anharmonic oscillators under the influence of a harmonic force applied at one end of the chain. The dynamics of the chain is studied assuming 1:1 (fundamental) resonance, when the response of each nonlinear oscillator has a dominant harmonic component with the frequency close to the frequency of the external excitation. It is shown that weak dissipation in a strongly nonlinear chain may be a key factor preventing large-amplitude resonance. The resulting process in the dissipative system represents resonance-induced large-amplitude oscillations of a part of the chain adjacent to the actuator and escape from resonance of the distant oscillators. Conditions of the emergence of resonance and energy localization are derived. The obtained solutions indicate that the maximal concentration of energy on the excited oscillator arises together with equipartition of energy among the other resonant oscillators. An agreement between the analytical and numerical results is demonstrated.

We present an experimental study of missing-level statistics of three-dimensional chaotic microwave cavities. The investigation is reinforced by the power spectrum of level fluctuations analysis, which also takes into account the missing levels. On the basis of our data sets we demonstrate that the power spectrum of level fluctuations in combination with short- and long-range spectral fluctuations provides a powerful tool for the determination of the fraction of randomly missing levels in systems that display wave chaos such as the three-dimensional chaotic microwave cavities. The experimental results are in good agreement with the analytical expressions that explicitly take into account the fraction of observed levels $\phi$. We also show that in the case of incomplete spectra with many unresolved states the above procedures may fail. In such a case the random matrix theory calculations can be useful for the determination of missing levels.