A horizontal flow induced by a vertical heated wall with a low Prandtl number (e.g., $\text{Pr}<1$ for air and liquid metals) is common in nature and industry. In this paper, a $\text{Pr}<1$ intrusion flow induced by a vertical heated boundary of an open sided cavity (that is, a cavity with one heated wall and open at the other end) is investigated by a scaling analysis and direct numerical simulations. The scaling analysis of the intrusion flow reveals that there are four possible flow regimes dependent on the Rayleigh and Prandtl numbers. In a typical case, the intrusion flow could travel under different dynamical and thermal processes such as unsteady (or steady) conduction-viscous, conduction-inertial, and convection-inertial dominances. Proper scaling relations have been presented to quantify these flows under different flow regimes. Furthermore, corresponding numerical simulations have verified the scaling results.

A Brownian vortex is a noise-driven machine that uses thermal fluctuations to extract a steady-state flow of work from a static force field. Its operation is characterized by loops in a probability current whose topology and direction can change with changes in temperature. We present discrete three- and four-state minimal models for Brownian vortexes that can be solved exactly with a master-equation formalism. These models elucidate conditions required for flux reversal in Brownian vortexes and provide insights into their thermodynamic efficiency through the rate of entropy production.

A comparative modeling and experimental study of the zenithal bistable liquid crystal device is presented. A dynamic Landau de Gennes theory of nematic liquid crystals is solved numerically to model the electric field induced latching of the device and the results are compared with experimental measurements and theoretical approximations. The study gives a clear insight into the latching mechanism dynamics and enables the dependence of the device latching on both material parameters and surface shape to be determined. Analytical approximation highlights a route to optimize material selection in terms of latching voltages and the numerical model, which includes an accurate surface representation, recovers the complex surface shape effects. Predictions of device performance are presented as a function of both surface anchoring strength and surface shape and grating pitch. A measurement of the homeotropic anchoring energy has been undertaken by comparing the voltage response as a function of cell gap; we find the homeotropic anchoring energies can be varied in the range 0.5 to 4 (${10}^{-4}\text{J}{\text{m}}^{-2}$).

We demonstrate that entanglement can persistently recur in an oscillating two-spin molecule that is coupled to a hot and noisy environment, in which no static entanglement can survive. The system represents a nonequilibrium quantum system which, driven through the oscillatory motion, is prevented from reaching its (separable) thermal equilibrium state. Environmental noise, together with the driven motion, plays a constructive role by periodically resetting the system, even though it will destroy entanglement as usual. As a building block, the present simple mechanism supports the perspective that entanglement can exist also in systems which are exposed to a hot environment and to high levels of decoherence, which we expect, e.g., for biological systems. Our results also suggest that entanglement plays a role in the heat exchange between molecular machines and environment. Experimental simulation of our model with trapped ions is within reach of the current state-of-the-art quantum technologies.

This paper studies an extended parallel asymmetric exclusion process, in which the anticipation effect is taken into account. The fundamental diagram of the model has been investigated via cluster mean field analysis. Different from previous mean field analysis, in which the $n$-cluster probabilities $P\left({\sigma }_i,\dots ,{\sigma }_{i+n-1}\right)$ involve the $\left(n+2\right)$-cluster probabilities $P\left({\tau }_{i-1},\dots ,{\tau }_{i+n}\right)$, our mean-field analysis is asymmetric because the three-cluster probabilities $P\left({\sigma }_i,{\sigma }_{i+1},{\sigma }_{i+2}\right)$ involve the six-cluster probabilities $P\left({\tau }_{i-1},\dots ,{\tau }_{i+4}\right)$. We find an excellent agreement between Monte Carlo simulations and cluster mean field analysis, which indicates that the mean field analysis might give the exact expression.

The stationary states of the kinetic Ising model described by the Glauber stochastic dynamics subject to a time-dependent oscillating external magnetic field was analyzed in detail on the Bethe lattice in terms of the recursion relation. The dynamic order parameter, the hysteresis loop area, and the dynamic correlation are calculated. It was found that the magnetization oscillates around nonzero values at low temperatures for the ferromagnetic phase while it only oscillates around zero values at high temperatures for the paramagnetic phase for appropriate values of the oscillating external magnetic field. The dynamic phase diagrams of the system are obtained for the given coordination numbers $q=4$ and 6. In addition to the second- and first-order phase transitions, the dynamical tricritical points are also observed.

We discuss the complex dynamics of a nonlinear random networks model as a function of the connectivity $k$ between the elements of the network. We show that this class of networks exhibits an order-chaos phase transition for a critical connectivity $k_c=2$. Also, we show that both pairwise correlation and complexity measures are maximized in dynamically critical networks. These results are in good agreement with the previously reported studies on random Boolean networks and random threshold networks, and show once again that critical networks provide an optimal coordination of diverse behavior.

This paper studies unidirectional pedestrian flow in a channel using the lattice gas model with parallel update rule. The conflict (i.e., several pedestrians intend to move to the same site) is solved by introducing probabilities as in floor field models. The fundamental diagram (FD) is investigated and it is found that when the drift strength $D\lesssim 0.5$, the FD is a concave curve. With the further increase in drift strength, a turning point appears on FD. The empirical findings show that both concave FD and FD with a turning point exist. Thus, the model might be able to reproduce both by tuning drift strength. It is also shown that in the special case $D=1$, two congested branches exist in the FD. We have carried out mean-field analysis of the FD and the mean-field results are in approximate agreement with simulations when the drift strength $D$ is small. A comparison with random sequential update rule model is also made.

Flow past a circular cylinder is investigated in the subcritical regime, below the onset of Bénard-von Kármán vortex shedding at Reynolds number ${\text{Re}}_c\simeq 47$. The transient response of infinitesimal perturbations is computed. The domain requirements for obtaining converged results is discussed at length. It is shown that energy amplification occurs as low as $\text{Re}=2.2$. Throughout much of the subcritical regime the maximum energy amplification increases approximately exponentially in the square of Re reaching 6800 at ${\text{Re}}_c$. The spatiotemporal structure of the optimal transient dynamics is shown to be transitory Bénard-von Kármán vortex streets. At $\text{Re}\simeq 42$ the long-time structure switches from exponentially increasing downstream to exponentially decaying downstream. Three-dimensional computations show that two-dimensional structures dominate the energy growth except at short times.

For parallel shear flows, transition to turbulence occurs only for perturbations of sufficiently large amplitude. It is therefore relevant to study the shape, amplitude, and dynamics of the least energetic initial disturbances leading to transition. We suggest a numerical approach to find such minimal perturbations, applied here to the case of plane Couette flow. The optimization method seeks such perturbations at initial time as a linear combination of a finite number of linear optimal modes. The energy threshold of the minimal perturbation for a Reynolds number $\text{Re}=400$ is only 2% less than for a pair of symmetric oblique waves. The associated transition scenario shows a long transient approach to a steady state solution with special symmetries. Modal analysis shows how the oblique-wave mechanism can be optimized by the addition of other oblique modes breaking the flow symmetry and whose nonlinear interaction generates spectral components of the edge state. The Re dependence of energy thresholds is revisited, with evidence for a $O\left({\text{Re}}^{-2}\right)$-scaling for both oblique waves and streamwise vortices scenarios.

The development of the Weibel instability during the expansion of a thin plasma foil heated by an intense laser pulse is investigated, using both analytical models and relativistic particle-in-cell simulations. When the plasma has initially an anisotropic electron distribution, this electromagnetic instability develops from the beginning of the expansion. Then it contributes to suppress the anisotropy and eventually saturates. After the saturation, the strength of the magnetic field decreases because of the plasma expansion until it becomes too weak to maintain the distribution isotropic. For this time, the anisotropy rises as electrons give progressively their longitudinal energy to ions, so that a new instability can develop.

In this Brief Report we investigate biomimetic fluid propulsion due to an array of periodically beating artificial cilia. A generic model system is defined in which the effects of inertial fluid forces and the spatial, temporal, and orientational asymmetries of the ciliary motion can be individually controlled. We demonstrate that the so-far unexplored orientational asymmetry plays an important role in generating flow and that the flow increases sharply with Reynolds number and eventually becomes unidirectional. We introduce the concept of configurational symmetry that unifies the spatial, temporal, and orientational symmetries. The breaking of configurational symmetry leads to fluid propulsion in microfluidic channels.

Aqueous dispersions of exfoliated, bile-salt stabilized single-wall carbon nanotubes exhibit a first order transition to a nematic liquid-crystalline phase. The nematic phase presents itself in the form of micron-sized nematic droplets also known as tactoids, freely floating in the isotropic host dispersion. The nematic droplets are spindle shaped and have an aspect ratio of about four, irrespective of their size. We attribute this to a director field that is uniform rather than bipolar, which is confirmed by polarization microscopy. It follows that the ratio of the anchoring strength and the surface tension must be about four, which is quite larger than predicted theoretically but in line with earlier observations of bipolar tactoids. From the scatter in the data we deduce that the surface tension of the coexisting isotropic and nematic phases must be extremely low, that is, of the order of nN/m.

The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles’ aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles’ extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic—scaling all ensemble components by a common deterministic scale. However, there are “random environment” settings in which the underlying scaling schemes are stochastic—scaling the ensemble components by different random scales. Examples of such settings include Holtsmark’s law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)—in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes—and present “randomized counterparts” to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.

We study the relaxation of both spontaneous and shear-induced fluctuations in suspensions of charged-stabilized colloidal particles near the glass transition by dynamic light scattering and rheology. Both observations are here understood in terms of a common structural relaxation process under a hard-sphere mode-coupling formalism. For ergodic systems, we show that the descriptions of the relaxation dynamics in time and frequency domains are governed by a common set of dynamic parameters. It is further shown that the microscopic ergodicity break-up induces the emergence of the macroscopic glass elasticity.

The field dependence of the optical transmission of tartrate-coated and polyaspartate-coated magnetite-based aqueous colloids was studied. The colloidal stock samples were diluted to prepare a series of samples containing different particle volume fractions ranging from 0.17% up to 1.52% and measured at distinct times after preparation (1, 30, 120, 240, and 1460 days). We show that the magneto-transmissivity behavior is mainly described by the rotation of linear chains, at the low-field range, whereas the analysis of the data provided the measurement of the average chain length. Results also reveal that the optical transmissivity has a minimum at a particular critical field, whose origin is related to the onset of columns of chains built from isolated particle chains, i.e., due to a columnar phase transition. We found the critical field reducing as the particle volume fraction increases and as the sample’s aging time increases. To investigate the origin of this phenomenon we used phase condensation models and Mie’s theory applied to a chain of spheres and to an infinite cylinder. Possible implications for magnetophotonic colloidal-based devices and biomedical applications were discussed.

We study the profile of a thin disk configuration as described by an axisymmetric ideal magnetohydrodynamics steady equilibrium. We consider the disk like a differentially rotating system dominated by the Keplerian term, but allowing for a nonzero radial and vertical matter flux. As a result, the steady state allows for the existence of local peaks for the vertical velocity of the plasma particles, though it prevents the radial matter accretion rate. This ideal magnetohydrodynamics scheme is therefore unable to solve the angular momentum-transport problem, but we suggest that it provides a mechanism for the generation of matter-jet seeds.

The rise and fall of a research field is the cumulative outcome of its intrinsic scientific value and social coordination among scientists. The structure of the social component is quantifiable by the social network of researchers linked via coauthorship relations, which can be tracked through digital records. Here, we use such coauthorship data in theoretical physics and study their complete evolutionary trail since inception, with a particular emphasis on the early transient stages. We find that the coauthorship networks evolve through three common major processes in time: the nucleation of small isolated components, the formation of a treelike giant component through cluster aggregation, and the entanglement of the network by large-scale loops. The giant component is constantly changing yet robust upon link degradations, forming the network’s dynamic core. The observed patterns are successfully reproducible through a network model.

This paper deals with the phenomenon of synchronization of oscillatory ensembles interacting distantly through the passive medium. Main characteristics of such a kind of synchronization are studied. The results of this work can be applied to describe the synchronization of cardiac oscillatory cells separated by the passive fibroblasts. In this work the phenomenological models (Bonhoeffer–Van der Pol) of cardiac cells as well as biologically relevant (Luo-Rudy, Sachse) models are used. We also propose equivalent model of distant synchronization and derive on its basis an analytical scaling of the frequency of synchronous oscillations.

In piecewise-smooth dynamical systems, situations can arise where the asymptotic attractors of the system in an open parameter interval are all chaotic (e.g., no periodic windows). This is the phenomenon of robust chaos. Previous works have established that robust chaos can occur through the mechanism of border-collision bifurcation, where border is the phase-space region where discontinuities in the derivatives of the dynamical equations occur. We investigate the effect of smoothing on robust chaos and find that periodic windows can arise when a small amount of smoothness is present. We introduce a parameter of smoothing and find that the measure of the periodic windows in the parameter space scales linearly with the parameter, regardless of the details of the smoothing function. Numerical support and a heuristic theory are provided to establish the scaling relation. Experimental evidence of periodic windows in a supposedly piecewise linear dynamical system, which has been implemented as an electronic circuit, is also provided.