We investigate the effects of geometric order and fluid rheology on the dispersion of micron-sized particles in two-dimensional microfluidic porous media. Particles suspended in a mixture of glycerol and water or in solutions of partially hydrolyzed polyacrylamide (HPAM) polymers were imaged as they flowed through arrays of microscale posts. From the trajectories of the particles, we calculated the velocity distributions and thereafter obtained the longitudinal and transverse dispersion coefficients. Particles flowed in the shear-thinning HPAM solution through periodic arrays of microposts were more likely to switch between streamlines, due to elastic instabilities. As a result, the distributions of particle velocity were broader in HPAM solutions than in glycerol-water mixtures for ordered geometries. In a disordered array of microposts, however, there was little difference between the velocity distributions obtained in glycerol-water and in HPAM solutions. Correspondingly, particles flowed through ordered post arrays in HPAM solutions exhibited enhanced transverse dispersion. This result suggests that periodic geometric order amplifies the effects of the elasticity-induced velocity fluctuations, whereas geometric disorder of barriers effectively averages out the fluctuations.

A frequency-averaged quasilinear model is derived and experimentally validated for the evolution of ion acoustic turbulence (IAT) along the centerline of a 100-A class, ${\mathrm{LaB}}_6$ hollow cathode. Probe-based diagnostics and a laser induced fluorescence system are employed to measure the properties of both the turbulence and the background plasma parameters as they vary spatially in the cathode plume. It is shown that for the three discharge currents investigated, 100 A, 130 A, and 160 A, the spatial growth of the total energy density of the IAT in the near field of the cathode plume is exponential and agrees quantitatively with the predicted growth rates from the quasilinear formulation. However, in the downstream region of the cathode plume, the growth of IAT energy saturates at a level that is commensurate with the Sagdeev limit. The experimental validation of the quasilinear model for IAT growth and its limitations are discussed in the context of numerical efforts to describe self-consistently the plasma processes in the hollow cathode plume.

We describe the effect of kinetic interactions of adsorbed atoms in a mesoscale model of epitaxial growth without elasticity. Our goal is to understand how atomic correlations due to kinetics leave their signature in mechanisms governing the motion of crystal line defects (steps) at the nanoscale. We focus on the key atomistic processes related to external material deposition, desorption, and asymmetric energy barriers on a stepped surface. By starting with a kinetic, restricted solid-on-solid model in 1+1 dimensions, we derive laws that govern the motion of a single step when deposition is nearly balanced out by desorption. These mesoscale laws reveal how kinetic processes, e.g., bond breaking at the step edge, influence step motion via the correlated motion of atoms.

We propose a model-free method to detect change points between distinct phases in a single random trajectory of an intermittent stochastic process. The local convex hull (LCH) is constructed for each trajectory point, while its geometric properties (e.g., the diameter or the volume) are used as discriminators between phases. The efficiency of the LCH method is validated for six models of intermittent motion, including Brownian motion with different diffusivities or drifts, fractional Brownian motion with different Hurst exponents, and surface-mediated diffusion. We discuss potential applications of the method for detection of active and passive phases in the intracellular transport, temporal trapping or binding of diffusing molecules, alternating bulk and surface diffusion, run and tumble (or search) phases in the motion of bacteria and foraging animals, and instantaneous firing rates in neurons.

The devil's staircase structure arising from the complete mode locking of an entirely nonchaotic system, the overdamped dc+ac driven Frenkel-Kontorova model with deformable substrate potential, was observed. Even though no chaos was found, a hierarchical ordering of the Shapiro steps was made possible through the use of a previously introduced continued fraction formula. The absence of chaos, deduced here from Lyapunov exponent analyses, can be attributed to the overdamped character and the Middleton no-passing rule. A comparative analysis of a one-dimensional stack of Josephson junctions confirmed the disappearance of chaos with increasing dissipation. Other common dynamic features were also identified through this comparison. A detailed analysis of the amplitude dependence of the Shapiro steps revealed that only for the case of a purely sinusoidal substrate potential did the relative sizes of the steps follow a Farey sequence. For nonsinusoidal (deformed) potentials, the symmetry of the Stern-Brocot tree, depicting all members of particular Farey sequence, was seen to be increasingly broken, with certain steps being more prominent and their relative sizes not following the Farey rule.

We discuss the generation mechanism of fundamental rogue wave structures in $N$-component coupled systems, based on analytical solutions of the nonlinear Schrödinger equation and modulational instability analysis. Our analysis discloses that the pattern of a fundamental rogue wave is determined by the evolution energy and growth rate of the resonant perturbation that is responsible for forming the rogue wave. This finding allows one to predict the rogue wave pattern without the need to solve the $N$-component coupled nonlinear Schrödinger equation. Furthermore, our results show that $N$-component coupled nonlinear Schrödinger systems may possess $N$ different fundamental rogue wave patterns at most. These results can be extended to evaluate the type and number of fundamental rogue wave structure in other coupled nonlinear systems.

We consider a reaction-diffusion system undergoing Turing instability and augment it by an additional unilateral source term. We investigate its influence on the Turing instability and on the character of resulting patterns. The nonsmooth positively homogeneous unilateral term $\tau v^{-}$ has favorable properties, but the standard linear stability analysis cannot be performed. We illustrate the importance of the nonsmoothness by a numerical case study, which shows that the Turing instability can considerably change if we replace this term by its arbitrarily precise smooth approximation. However, the nonsmooth unilateral term and all its approximations yield qualitatively similar patterns although not necessarily developing from small disturbances of the spatially homogeneous steady state. Further, we show that the unilateral source breaks the approximate symmetry and regularity of the classical patterns and yields asymmetric and irregular patterns. Moreover, a given system with a unilateral source produces spatial patterns even for diffusion parameters with ratios closer to 1 than the same system without any unilateral term.

Some authors have recently argued that a finite-size scaling law for the text-length dependence of word-frequency distributions cannot be conceptually valid. Here we give solid quantitative evidence for the validity of this scaling law, using both careful statistical tests and analytical arguments based on the generalized central-limit theorem applied to the moments of the distribution (and obtaining a novel derivation of Heaps' law as a by-product). We also find that the picture of word-frequency distributions with power-law exponents that decrease with text length [X. Yan and P. Minnhagen, Physica A 444, 828 (2016)] does not stand with rigorous statistical analysis. Instead, we show that the distributions are perfectly described by power-law tails with stable exponents, whose values are close to 2, in agreement with the classical Zipf's law. Some misconceptions about scaling are also clarified.

Coordination shall be deemed to the result of interindividual interaction among natural gregarious animal groups. However, revealing the underlying interaction rules and decision-making strategies governing highly coordinated motion in bird flocks is still a long-standing challenge. Based on analysis of high spatial-temporal resolution GPS data of three pigeon flocks, we extract the hidden interaction principle by using a newly emerging machine learning method, namely the sparse Bayesian learning. It is observed that the interaction probability has an inflection point at pairwise distance of 3–4 m closer than the average maximum interindividual distance, after which it decays strictly with rising pairwise metric distances. Significantly, the density of spatial neighbor distribution is strongly anisotropic, with an evident lack of interactions along individual velocity. Thus, it is found that in small-sized bird flocks, individuals reciprocally cooperate with a variational number of neighbors in metric space and tend to interact with closer time-varying neighbors, rather than interacting with a fixed number of topological ones. Finally, extensive numerical investigation is conducted to verify both the revealed interaction and decision-making principle during circular flights of pigeon flocks.

Molecular dynamics simulation was used to study a model colloidal suspension with two species of slightly different sized colloidal particles in an explicit solvent. In this work we calculated the four interdiffusion coefficients for the ternary system, which were then used to calculate the decay coefficients $D_{\pm }$ of the two independent diffusive modes. We found that the slower $D_{-}$ decay mode, which is associated with the system's ability to undergo compositional changes, was responsible for the long-time decay in the intermediate scattering function. We also found that a decrease in $D_{-}$ to negligible values at a packing fraction of ${\mathrm{\Phi }}_g=0.592$ resulted in an extreme slow-down in the long-time decay of the intermediate scattering function often associated with the glass transition. Above ${\mathrm{\Phi }}_g$, the system formed a long-lived metastable state that did not relax to its equilibrium crystal state within the simulation time window. We concluded that the inhibition of crystallization was caused by the inability of the quenched fluid to undergo the compositional changes needed for the formation of the equilibrium crystal.

Simulating ice crystal growth is a major issue for meteorology and aircraft safety. Yet, very few models currently succeed in reproducing correctly the diversity of snow crystal forms, and link the model parameters to thermodynamic quantities. Here, we demonstrate that the new three-dimensional phase-field model developed in Demange et al. [npj Comput. Mater. 3, 1 (2017)] is capable of reproducing properly the morphology and growth kinetics of snowflakes in supersaturated atmosphere. Aside from that, we show that the growth dynamics of snow crystals satisfies the selection theory, consistently with previous experimental observations. Finally, we link the parameters of the phase-field model to atmospheric parameters.

We investigate fluctuations of the velocity and temperature fields in two-dimensional (2D) Rayleigh-Bénard (RB) convection by means of direct numerical simulations (DNS) over the Rayleigh number range ${10}^6\le \text{Ra}\le {10}^{10}$ and for a fixed Prandtl number $\text{Pr}=5.3$ and aspect ratio $\mathrm{\Gamma }=1$. Our results show that there exists a counter-gradient turbulent transport of energy from fluctuations to the mean flow both locally and globally, implying that the Reynolds stress is one of the driving mechanisms of the large-scale circulation in 2D turbulent RB convection besides the buoyancy of thermal plumes. We also find that the viscous boundary layer (BL) thicknesses near the horizontal conducting plates and near the vertical sidewalls, ${\delta }_u$ and ${\delta }_v$, are almost the same for a given Ra, and they scale with the Rayleigh and Reynolds numbers as $\sim {\text{Ra}}^{-0.26\pm 0.03}$ and $\sim {\text{Re}}^{-0.43\pm 0.04}$. Furthermore, the thermal BL thickness ${\delta }_{\theta }$ defined based on the root-mean-square (rms) temperature profiles is found to agree with Prandtl-Blasius predictions from the scaling point of view. In addition, the probability density functions of turbulent energy ${\varepsilon }_{u^{\prime }}$ and thermal ${\varepsilon }_{{\theta }^{\prime }}$ dissipation rates, calculated, respectively, within the viscous and thermal BLs, are found to be always non-log-normal and obey approximately a Bramwell-Holdsworth-Pinton distribution first introduced to characterize rare fluctuations in a confined turbulent flow and critical phenomena.

In this paper, we derive a fully relativistic kinetic theory for spin-1/2 particles and its coupling to Maxwell's equations, valid in the long-scale-length limit, where the fields vary on a scale much longer than the localization of the particles; we work to first order in $\hslash$. Our starting point is a Foldy-Wouthuysen (FW) transformation, applicable to this regime, of the Dirac Hamiltonian. We derive the corresponding evolution equation for the Wigner quasidistribution in an external electromagnetic field. Using a Lagrangian method we find expressions for the charge and current densities, expressed as free and bound parts. It is furthermore found that the velocity is nontrivially related to the momentum variable, with the difference depending on the spin and the external electromagnetic fields. This fact that has previously been discussed as “hidden momentum” and is due to that the FW transformation maps pointlike particles to particle clouds for which the prescription of minimal coupling is incorrect, as they have multipole moments. We express energy and momentum conservation for the system of particles and the electromagnetic field, and discuss our results in the context of the Abraham-Minkowski dilemma.

In this paper, we investigate the first exploitation of the vibrational resonance (VR) effect to detect weak signals in the presence of strong background noise. By injecting a series of sinusoidal interference signals of the same amplitude but with different frequencies into a generalized correlation detector, we show that the detection probability can be maximized at an appropriate interference amplitude. Based on a dual-Dirac probability density model, we compare the VR method with the stochastic resonance approach via adding dichotomous noise. The compared results indicate that the VR method can achieve a higher detection probability for a wider variety of noise distributions.

A model for connectedness percolation in isotropic systems of monodisperse cylinders is developed that employs a generalization of the tree-like Bethe lattice. The traditional Bethe lattice is generalized by incorporating (within a heuristic, mean-field framework) a pair of correlation parameters that describe (i) the states of occupancy of neighboring sites and (ii) the states of directly adjacent bonds, which are also allowed to be in either of two possible states. Averaging over the fluctuating states of neighboring bonds provides an operational means to modulate the dependence upon volume fraction of the average number of next-nearest-neighbor rod-rod contacts without altering the number of such nearest-neighbor interparticle contacts. The percolation threshold is shown to be a sensitive function of the average number of such next-nearest-neighbor contacts, and therefore of the quality of dispersion of the particles.

With the Lipkin-Meshkov-Glick (LMG) model as an illustration, we construct a thermodynamic cycle composed of two isothermal processes and two isomagnetic field processes, and we study the thermodynamic performance of this cycle accompanied by the quantum phase transition (QPT). We find that for a finite particle system working below the critical temperature, the efficiency of the cycle is capable of approaching the Carnot limit when the external magnetic field ${\lambda }_1$ corresponding to one of the isomagnetic processes reaches the cross point of the ground states' energy level, which can become the critical point of the QPT in the large-$N$ limit. Our analysis proves that the system's energy level crossings at low-temperature limits can lead to a significant improvement in the efficiency of the quantum heat engine. In the case of the thermodynamics limit $(N\to \infty )$, the analytical partition function is obtained to study the efficiency of the cycle at high- and low-temperature limits. At low temperatures, when the magnetic fields of the isothermal processes are located on both sides of the critical point of the QPT, the cycle reaches maximum efficiency, and the Carnot efficiency can be achieved. This observation demonstrates that the QPT of the LMG model below critical temperature is beneficial to the thermodynamic cycle's operation.

We study the collective dynamics of oscillators in a network of identical bistable time-delayed feedback systems globally coupled via the mean field. The influence of delay and inertial properties of the mean field on the collective behavior of globally coupled oscillators is investigated. A variety of oscillation regimes in the network results from the presence of bistable states with substantially different frequencies in coupled oscillators. In the physical experiment and numerical simulation we demonstrate the existence of chimeralike states, in which some of the oscillators in the network exhibit synchronous oscillations, while all other oscillators remain asynchronous.

Mechanosensitive channels are ion channels which act as cells' safety valves, opening when the osmotic pressure becomes too high and making cells avoid damage by releasing ions. They are found on the cellular membrane of a large number of organisms. They interact with each other by means of deformations they induce in the membrane. We show that collective dynamics arising from the interchannel interactions lead to first- and second-order phase transitions in the fraction of open channels in equilibrium relating to the formation of channel clusters. We show that this results in a considerable delay of the response of cells to osmotic shocks, and to an extreme cell-to-cell stochastic variations in their response times, despite the large numbers of channels present in each cell. We discuss how our results are relevant for E. coli.

Here, we studied the effect of advection on the transient ion concentration-polarization phenomenon in microchannel-membrane systems. Specifically, the temporal evolution of the depletion layer in a system that supports net flow rates with varying Péclet values was examined. Experiments complemented with simplified analytical one-dimensional semi-infinite modeling and numerical simulations demonstrated either suppression or enhancement of the depletion layer propagation against or with the direction of the net flow, respectively. Of particular interest was the third-species fluorescent dye ion concentration-polarization dynamics which was further explained using two-dimensional numerical simulations that accounted for the device complex geometry.