We consider condensation in a capillary groove of width $L$ and depth $D$, formed by walls that are completely wet (contact angle $\theta =0$), which is in a contact with a gas reservoir of the chemical potential $\mu$. On a mesoscopic level, the condensation process can be described in terms of the midpoint height $\ell$ of a meniscus formed at the liquid-gas interface. For macroscopically deep grooves ($D\to \infty$), and in the presence of long-range (dispersion) forces, the condensation corresponds to a second-order phase transition, such that $\ell \sim {({\mu }_{cc}-\mu )}^{-1/4}$ as $\mu \to {\mu }_{cc}^{-}$ where ${\mu }_{cc}$ is the chemical potential pertinent to capillary condensation in a slit pore of width $L$. For finite values of $D$, the transition becomes rounded and the groove becomes filled with liquid at a chemical potential higher than ${\mu }_{cc}$ with a difference of the order of $D^{-3}$. For sufficiently deep grooves, the meniscus growth initially follows the power law $\ell \sim {({\mu }_{cc}-\mu )}^{-1/4}$, but this behavior eventually crosses over to $\ell \sim D-{(\mu -{\mu }_{cc})}^{-1/3}$ above ${\mu }_{cc}$, with a gap between the two regimes shown to be $\overline{\delta }\mu \sim D^{-3}$. Right at $\mu ={\mu }_{cc}$, when the groove is only partially filled with liquid, the height of the meniscus scales as ${\ell }^{*}\sim {\left(D^{3}L\right)}^{1/4}$. Moreover, the chemical potential (or pressure) at which the groove is half-filled with liquid exhibits a nonmonotonic dependence on $D$ with a maximum at $D\approx 3L/2$ and coincides with ${\mu }_{cc}$ when $L\approx D$. Finally, we show that condensation in finite grooves can be mapped on the condensation in capillary slits formed by two asymmetric (competing) walls a distance $D$ apart with potential strengths depending on $L$. All these predictions, based on mesoscopic arguments, are confirmed by fully microscopic Rosenfeld's density functional theory with a reasonable agreement down to surprisingly small values of both $L$ and $D$.

Several fluctuation formulas are available for calculating elastic constants from equilibrium correlation functions in computer simulations, but the ones available for simulations at constant pressure exhibit slow convergence properties and cannot be used for the determination of local elastic constants. To overcome these drawbacks, we derive a stress-stress fluctuation formula in the $\mathit{NPT}$ ensemble based on known expressions in the $\mathit{NVT}$ ensemble. We validate the formula in the $\mathit{NPT}$ ensemble by calculating elastic constants for the simple nearest-neighbor Lennard-Jones crystal and by comparing the results with those obtained in the $\mathit{NVT}$ ensemble. For both local and bulk elastic constants we find an excellent agreement between the simulated data in the two ensembles. To demonstrate the usefulness of the formula, we apply it to determine the elastic constants of a simulated lipid bilayer.

Molecular dynamics simulations are carried out to investigate the geometry effects of diatomic molecules on liquid flows in carbon nanotubes (CNTs). Oxygen molecules are considered as the fluid inside armchair ($n,n$) ($n=6–20$) CNTs. The simulated fluid temperature and bulk pressure for the liquid state are $T=133$ K and ${\rho }_b=1346{\mathrm{kg}/\mathrm{m}}^3$, respectively. In the agglomerated molecular cluster, nanoconfinement-induced structural changes are observed. As the CNT diameter decreases, it is confirmed that the flow rate significantly increases with irregular trends (discontinuity points in the profiles). From the discussion of the structure of the agglomerated fluid molecules, it is found that those trends are not simply caused by the structural changes. The main factor to induce the irregularity is confirmed to be the interlayer molecular movement affected by the combination of the molecular geometry and the arrangement of the multilayered structure.

The cascaded or central-moment-based lattice Boltzmann method (CLBM) proposed in [Phys. Rev. E 73, 066705 (2006)] possesses very good numerical stability. However, two constraints exist in three-dimensional (3D) CLBM simulations. First, the conventional implementation for 3D CLBM involves cumbersome operations and requires much higher computational cost compared to the single-relaxation-time (SRT) LBM. Second, it is a challenge to accurately incorporate a general force field into the 3D CLBM. In this paper, we present an improved method to implement CLBM in 3D. The main strategy is to adopt a simplified central moment set and carry out the central-moment-based collision operator based on a general multi-relaxation-time (GMRT) framework. Next, the recently proposed consistent forcing scheme for CLBM [Fei and Luo, Phys. Rev. E 96, 053307 (2017)] is extended to incorporate a general force field into 3D CLBM. Compared with the recently developed nonorthogonal CLBM [Rosis, Phys. Rev. E 95, 013310 (2017)], our implementation is proved to reduce the computational cost significantly. The inconsistency of adopting the discrete equilibrium distribution functions in the nonorthogonal CLBM is analyzed and validated. The 3D CLBM developed here in conjunction with the consistent forcing scheme is verified through numerical simulations of several canonical force-driven flows, highlighting very good properties in terms of accuracy, convergence, and consistency with the nonslip rule. Finally, the techniques developed here for 3D CLBM can be applied to make the implementation and execution of 3D MRT-LBM more efficient.

A quasi-one-dimensional system of repelling particles undergoes a configurational phase transition when the transverse confining potential decreases. Below a threshold, it becomes energetically favorable for the system to adopt one of two staggered raw patterns, symmetric with respect to the system axis. This transition is a subcritical pitchfork bifurcation for short range interactions. As a consequence, the homogeneous zigzag pattern is unstable in a finite zigzag amplitude range $[h_{C1},h_{C2}]$. We exhibit strong qualitative effects of the subcriticality on the thermal motions of the particles. When the zigzag amplitude is close enough to the limits $h_{C1}$ and $h_{C2}$, a transverse vibrational soft mode occurs which induces a strongly subdiffusive behavior of the transverse fluctuations, similar to single-file diffusion. On the contrary, the longitudinal fluctuations are enhanced, with a diffusion coefficient which is more than doubled. Conversely, a simple measurement of the thermal fluctuations allows a precise determination of the bifurcation thresholds.

In this paper we study the transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation (CCQGLE) under the influence of nonlinear gain, its saturation, and higher-order effects: self-steepening, third-order of dispersion, and intrapulse Raman scattering in the anomalous dispersion region. The variation method and the method of moments are applied in order to obtain the dynamic models with finite degrees of freedom for the description of stationary and pulsating solutions. Having applied the first model and its bifurcation analysis we have discovered the existence of families of subcritical Poincaré-Andronov-Hopf bifurcations due to the intrapulse Raman scattering, as well as some small nonlinear gain and the saturation of the nonlinear gain. A phenomenon of nonlinear stability has been studied and it has been shown that long living pulsating solutions with relatively small fluctuations of amplitude and frequencies exist at the bifurcation point. The numerical analysis of the second model has revealed the existence of Poincaré-Andronov-Hopf bifurcations of Raman dissipative soliton under the influence of the self-steepening effect and large nonlinear gain. All our theoretical predictions have been confirmed by the direct numerical solution of the full perturbed CCQGLE. The detailed comparison between the results obtained by both dynamic models and the direct numerical solution of the perturbed CCQGLE has proved the applicability of the proposed models in the investigation of the solutions of the perturbed CCQGLE.

Social learning is widely observed in many species. Less experienced agents copy successful behaviors exhibited by more experienced individuals. Nevertheless, the dynamical mechanisms behind this process remain largely unknown. Here we assume that a complex behavior can be decomposed into a sequence of $n$ motor motifs. Then a neural network capable of activating motor motifs in a given sequence can drive an agent. To account for $(n-1)!$ possible sequences of motifs in a neural network, we employ the winnerless competition approach. We then consider a teacher-learner situation: one agent exhibits a complex movement, while another one aims at mimicking the teacher's behavior. Despite the huge variety of possible motif sequences we show that the learner, equipped with the provided learning model, can rewire “on the fly” its synaptic couplings in no more than $(n-1)$ learning cycles and converge exponentially to the durations of the teacher's motifs. We validate the learning model on mobile robots. Experimental results show that the learner is indeed capable of copying the teacher's behavior composed of six motor motifs in a few learning cycles. The reported mechanism of learning is general and can be used for replicating different functions, including, for example, sound patterns or speech.

Phenotypic switching is one of the mechanisms by which bacteria thrive in ever changing environmental conditions around them. Earlier studies have shown that the application of steady high hydrostatic pressure leads to stochastic switching of mesophilic bacteria from a cellular phenotype having a normal cell cycle to another phenotype lacking cell division. Here, we have studied the dynamics of this phenotypic switching with fluctuating periodic pressure using a set of experiments and a theoretical model. Our results suggest that the phenotypic switching rate from high-pressure phenotype to low-pressure phenotype in the reversible regime is larger as compared to the switching rate from low-pressure phenotype to high-pressure phenotype. Furthermore, we find that even though the cell division and elongation are presumably regulated by a large number of genes the underlying physics of the dynamics of stochastic switching at high pressure is captured reasonably well by a simple two-state model.

Two-dimensional crystals on curved manifolds exhibit nontrivial defect structures. Here we consider “active crystals” on a sphere, which are composed of self-propelled colloidal particles. Our work is based on a phase-field-crystal-type model that involves a density and a polarization field on the sphere. Depending on the strength of the self-propulsion, three different types of crystals are found: a static crystal, a self-spinning “vortex-vortex” crystal containing two vortical poles of the local velocity, and a self-translating “source-sink” crystal with a source pole where crystallization occurs and a sink pole where the active crystal melts. These different crystalline states as well as their defects are studied theoretically here and can in principle be confirmed in experiments.

Nematic films are thin fluid structures, ideally two dimensional, endowed with an in-plane degenerate nematic order. In this paper we examine a generalization of the classical Plateau problem to an axisymmetric nematic film bounded by two coaxial parallel rings. At equilibrium, the shape of the nematic film results from the competition between surface tension, which favors the minimization of the area, and the nematic elasticity, which instead promotes the alignment of the molecules along a common direction. We find two classes of equilibrium solutions in which the molecules are uniformly aligned along the meridians or parallels. Depending on two dimensionless parameters, one related to the geometry of the film and the other to the constitutive moduli, the Gaussian curvature of the equilibrium shape may be everywhere negative, vanishing, or positive. The stability of these equilibrium configurations is investigated.

Collision-coalescence growth of noninertial particles in three-dimensional homogeneous isotropic turbulence is studied. Smoluchowski's coagulation equation describes the evolution of the size distribution of particles in this system. By applying a methodology based on turbulence theory, the equation is shown to have a steady-state solution, which corresponds to the Kolmogorov-type power-law spectrum. Direct numerical simulations of turbulence and Lagrangian particles are conducted. The result shows that the size distribution in a statistically steady state agrees accurately with the theoretical prediction.

Through quantum molecular dynamics (QMD), utilizing both Kohn-Sham (orbital-based) and orbital-free density functional theory, we calculate the equation of state of warm dense iron in the density range $7–30{\mathrm{g}/\mathrm{cm}}^3$ and temperatures from 1 to 100 eV. A critical examination of the iron pseudopotential is made, from which we find a significant improvement at high pressure to the previous QMD calculations of Wang et al. [Phys. Rev. E 89, 023101 (2014)]. Our results also significantly extend the ranges of density and temperature that were attempted in that prior work. We calculate the shock Hugoniot and find very good agreement with experimental results to pressures over 20 TPa. These results are then incorporated with previous studies to generate a five-phase equation of state for iron.

By controlling the vortex core energy, the three-state ferromagnetic Potts model can exhibit two types of topological paradigms, including the quasi-long-range ordered phase and the vortex lattice phase [Phys. Rev. Lett. 116, 097206 (2016)]. Here, using Monte Carlo simulations using an efficient worm algorithm, we show that by controlling the vortex core energy, the antiferromagnetic Potts model can also exhibit the two topological phases, and, more interestingly, the two topological phases can overlap with each other.

The continuous time random walk (CTRW) is often applied to the study of particle motion in disordered media. Yet most such applications do not allow for particle-particle (walker-walker) interaction. In this paper, we consider a CTRW with particle-particle interaction; however, for simplicity, we restrain the interaction to be local. The generalized Chapman-Kolmogorov equation is modified by introducing a perturbation function that fluctuates around 1, which models the effect of interaction. Subsequently, a time-fractional nonlinear advection-diffusion equation is derived from this walking system. Under the initial condition of condensed particles at the origin and the free-boundary condition, we numerically solve this equation with both attractive and repulsive particle-particle interactions. Moreover, a Monte Carlo simulation is devised to verify the results of the above numerical work. The equation and the simulation unanimously predict that this walking system converges to the conventional one in the long-time limit. However, for systems where the free-boundary condition and long-time limit are not simultaneously satisfied, this convergence does not hold.

Clique percolation has attracted much attention due to its significance in understanding topological overlap among communities and dynamical instability of structured systems. Rich critical behavior has been observed in clique percolation on Erdős-Rényi (ER) random graphs, but few works have discussed clique percolation on finite dimensional systems. In this paper, we have defined a series of characteristic events, i.e., the historically largest size jumps of the clusters, in the percolating process of adding bonds and developed a new finite-size scaling scheme based on the interval of the characteristic events. Through the finite-size scaling analysis, we have found, interestingly, that, in contrast to the clique percolation on an ER graph where the critical exponents are parameter dependent, the two-dimensional (2D) clique percolation simply shares the same critical exponents with traditional site or bond percolation, independent of the clique percolation parameters. This has been corroborated by bridging two special types of clique percolation to site percolation on 2D lattices. Mechanisms for the difference of the critical behaviors between clique percolation on ER graphs and on 2D lattices are also discussed.

We examine how stochastic time-delayed negative feedback affects the dynamical behavior of a model oscillatory reaction. We apply constant and stochastic time-delayed negative feedbacks to a point Field-Körös-Noyes photosensitive oscillator and compare their effects. Negative feedback is applied in the form of simulated inhibitory electromagnetic radiation with an intensity proportional to the concentration of oxidized light-sensitive catalyst in the oscillator. We first characterize the system under nondelayed inhibitory feedback; then we explore and compare the effects of constant (deterministic) versus stochastic time-delayed feedback. We find that the oscillatory amplitude, frequency, and waveform are essentially preserved when low-dispersion stochastic delayed feedback is used, whereas small but measurable changes appear when a large dispersion is applied.

The present paper deals with a fiber bundle model which consists of a fraction $\alpha$ of infinitely strong fibers. The inclusion of such an unbreakable fraction has been proven to affect the failure process in early studies, especially around a critical value ${\alpha }_c$. The present work has a twofold purpose: (i) a study of failure abruptness, mainly the brittle to quasibrittle transition point with varying $\alpha$ and (ii) variation of ${\alpha }_c$ as we change the strength of disorder introduced in the model. The brittle to quasibrittle transition is confirmed from the failure abruptness. On the other hand, the ${\alpha }_c$ is obtained from the knowledge of failure abruptness as well as the statistics of avalanches. It is observed that the brittle to quasibrittle transition point scales to lower values, suggesting more quasi-brittle-like continuous failure when $\alpha$ is increased. At the same time, the bundle becomes stronger as there are larger numbers of strong links to support the external stress. High $\alpha$ in a highly disordered bundle leads to an ideal situation where the bundle strength, as well as the predictability in failure process is very high. Also, the critical fraction ${\alpha }_c$, required to make the model deviate from the conventional results, increases with decreasing strength of disorder. The analytical expression for ${\alpha }_c$ shows good agreement with the numerical results. Finally, the findings in the paper are compared with previous results and real-life applications of composite materials.

We study the stable spatiotemporal patterns that arise in a three-dimensional (3D) network of neuron oscillators, whose dynamics is described by the leaky integrate-and-fire (LIF) model. More specifically, we investigate the form of the chimera states induced by a 3D coupling matrix with nonlocal topology. The observed patterns are in many cases direct generalizations of the corresponding two-dimensional (2D) patterns, e.g., spheres, layers, and cylinder grids. We also find cylindrical and “cross-layered” chimeras that do not have an equivalent in 2D systems. Quantitative measures are calculated, such as the ratio of synchronized and unsynchronized neurons as a function of the coupling range, the mean phase velocities, and the distribution of neurons in mean phase velocities. Based on these measures, the chimeras are categorized in two families. The first family of patterns is observed for weaker coupling and exhibits higher mean phase velocities for the unsynchronized areas of the network. The opposite holds for the second family, where the unsynchronized areas have lower mean phase velocities. The various measures demonstrate discontinuities, indicating criticality as the parameters cross from the first family of patterns to the second.

Kinesin is a molecular motor that transports cargo along microtubules. The results of many in vitro experiments on kinesin-1 are described by kinetic models in which one transition corresponds to the forward motion and subsequent binding of the tethered motor head. We argue that in a viscoelastic medium like the cytosol of a cell this step is not Markov and has to be described by a nonexponential waiting time distribution. We introduce a semi-Markov kinetic model for kinesin that takes this effect into account. We calculate, for arbitrary waiting time distributions, the moment generating function of the number of steps made, and determine from this the average velocity and the diffusion constant of the motor. We illustrate our results for the case of a waiting time distribution that is Weibull. We find that for realistic parameter values, viscoelasticity decreases the velocity and the diffusion constant, but increases the randomness (or Fano factor).