Fluid pumping principle has been developed utilizing the interaction, on the one hand, between the electric field $\mathbf{\text{E}}$ and the gradient $\mathbf{\nabla }\widehat{\mathbf{\text{n}}}$ of the director's field, and, on the other hand, between the $\mathbf{\nabla }\widehat{\mathbf{\text{n}}}$ and the temperature $\mathbf{\nabla }T$ gradient arising in a homogeneously aligned liquid crystal (HALC) microfluidic channel. Calculations, based upon the nonlinear extension of the classical Ericksen-Leslie theory, with accounting the entropy balance equation, show that due to the coupling among the $\mathbf{\nabla }T$, $\mathbf{\nabla }\widehat{\mathbf{\text{n}},}$ and $\mathbf{\text{E}}$ in the HALC microfluidic channel the horizontal flow $\mathbf{\text{v}}=v_x\widehat{\mathbf{\text{i}}}=u\widehat{\mathbf{\text{i}}}$ may be excited. The direction and magnitude of $\mathbf{\text{v}}$ is influenced both by the heat flux $\mathbf{\text{q}}$ across the microfluidic channel and the strength of the electric field $\mathbf{\text{E}}$. The results of calculations showed that the dependence of the maximum value of the equilibrium velocity distribution $|u_{\max }(E/E_{\mathrm{th}})|$ across the LC channel versus electric field $E/E_{\mathrm{th}}$ is characterized by maximum value at $E/E_{\mathrm{th}}=2.0$. In the case when the electric field $E\gg E_{\mathrm{th}}$, the horizontal flow of the LC material completely stops and a novel mechanism of converting of the electric field in the form of the kinklike wave reorientation of the director field $\widehat{\mathbf{\text{n}}}$ can be excited in the LC channel.

The propagation of a relativistic electron-positron beam in a magnetized electron-ion plasma is studied, focusing on the polarization of the radiation generated in this case. Special emphasis is laid on investigating the polarization of the generated radiation for a range of beam-plasma parameters, transverse and longitudinal beam sizes, and the external magnetic fields. Our results not only help in understanding the high degrees of circular polarization observed in gamma-ray bursts, but they also help in distinguishing the different modes associated with the filamentation dynamics of the pair beam in laboratory astrophysics experiments.

Empirical time series of interevent or waiting times are investigated using a modified Multifractal Detrended Fluctuation Analysis operating on fluctuations of mean detrended dynamics. The core of the extended multifractal analysis is the nonmonotonic behavior of the generalized Hurst exponent $h\left(q\right)$—the fundamental exponent in the study of multifractals. The consequence of this behavior is the nonmonotonic behavior of the coarse Hölder exponent $\alpha \left(q\right)$ leading to multibranchedness of the spectrum of dimensions. The Legendre-Fenchel transform is used instead of the routinely used canonical Legendre (single-branched) contact transform. Thermodynamic consequences of the multibranched multifractality are revealed. These are directly expressed in the language of phase transitions between thermally stable, metastable, and unstable phases. These phase transitions are of the first and second orders according to Mandelbrot's modified Ehrenfest classification. The discovery of multibranchedness is tantamount in significance to extending multifractal analysis.

State-space reconstruction is essential to analyze the dynamics and internal interactions of complex systems. However, it is difficult to estimate high-dimensional conditional mutual information and select the optimal time delays in most existing nonuniform state-space reconstruction methods. Therefore, we propose a nonuniform embedding method framed in information theory for state-space reconstruction. We use a low-dimensional approximation of conditional mutual information criterion for time delay selection, which is effectively solved by the particle swarm optimization algorithm. The obtained embedded vector has relatively strong independence and low redundancy, which better characterizes multivariable complex systems and detects coupling within complex systems. In addition, the proposed nonuniform embedding method exhibits good performance in coupling detection of linear stochastic, nonlinear stochastic, chaotic systems. In the actual application, the importance of small airports that cause delay propagation has been demonstrated by constructing the delay propagation network.

Using the formalism of classical nucleation theory, we derive a kinetic equation for the size and composition distribution of an ensemble of aqueous organic droplets evolving via nucleation and concomitant chemical aging. This distribution can be drastically affected by the enthalpy of heterogeneous chemical reactions and the depletion of organic trace gases absorbed by aerosols. A partial differential equation of second order for the temporal evolution of this distribution is obtained from the discrete equation of balance via Taylor series expansions. Once reduced to the canonical form of the multidimensional Fokker-Planck equation, this kinetic equation can be solved via the method of complete separation of variables. This kinetic equation opens a new direction in the development of the kinetic theory of first-order phase transitions, while its applications to the formation and evolution atmospheric organic aerosols via concurrent nucleation and chemical aging may drastically improve the accuracy of global climate models.

Origami-inspired structures have a rich design space, offering new opportunities for the development of deployable systems that undergo large and complex yet predictable shape transformations. There has been growing interest in such structural systems that can extend uniaxially into tubes and booms. The Kresling origami pattern, which arises from the twist buckling of a thin cylinder and can exhibit multistability, offers great potential for this purpose. However, much remains to be understood regarding the characteristics of Kresling origami deployment. Prior studies have been limited to Kresling structures’ kinematics, quasistatic mechanics, or low-amplitude wave responses, while their dynamic behaviors with large shape change during deployment remain unexplored. These dynamics are critical to the system design and control processes, but are complex due to the strong nonlinearity, bistability, and potential for off-axis motions. To advance the state of the art, this research seeks to uncover the deployment dynamics of Kresling structures with various system geometries and operating strategies. A full, six-degrees-of-freedom model is developed and employed to provide insight into the axial and off-axis dynamic responses, revealing that the variation of key geometric parameters may lead to regions with qualitatively distinct mechanical responses. Results illustrate the sensitivity of dynamic deployment to changes in initial condition and small variations in geometric design. Further, analyses show how certain geometries and configurations affect the stiffness of various axial and off-axis deformation modes, offering guidance on the design of systems that deploy effectively while mitigating the effects of off-axis disturbances. Overall, the research outcomes suggest the strong potential of Kresling-based designs for deployable systems with robust and tunable performance.

We consider forced small-scale magnetic field advected by an isotropic turbulent flow. The random driving force is assumed to be distributed in a finite region with a scale smaller than the viscous scale of the flow. The two-point correlator is shown to have a stationary limit for any reasonable velocity statistics. Its spatial dependence is found to be a power law. The scaling exponent is found to be close to 3.

A chemical model is proposed for a dusty plasma consisting of electrons, ions, neutrals, and positively charged dust particles all being at thermodynamic equilibrium. An expression is derived for the Helmholtz free energy, which comprises the ideal part, taking into account the charge of dust particles, and the excess part, evaluated in the framework of the self-consistent chemical model [Phys. Rev. E 83, 016405 (2011)]. The ionization potential depression for a dust-free partially ionized hydrogen is analytically evaluated for weakly and strongly ionized states to consistently account for the presence of charged and neutral components. An ad hoc interpolation of the ionization potential depression, valid across the whole ionization region, is put forward and subsequent solution of the generalized Saha equation is found to be in a perfect agreement with exact calculations. Minimization of the Helmholtz free energy of dusty plasmas provides the number densities of free electrons, free ions, neutrals, and the dust electric charge as well. Based on consideration of weakly and strongly ionized states, a straightforward comparison is made of the ionization equilibrium in a partially ionized plasma with and without dust particles to demonstrate that at thermal equilibrium positively charged dusts are responsible for an increase in the number density of free electrons and a decrease in the number density of free ions. It is analytically proved that nonideality effects result in a growth of the number densities of free electrons and ions by obtaining the so-called electron and proton ionization potential depressions. Electric charge of dust particles is systematically studied as a full plasma component rather than considering a detailed balance of the electron and ion fluxes on the surface of a solitary dust grain.

A central problem of turbulence theory is to produce a predictive model for turbulent fluxes. These have profound implications for virtually all aspects of the turbulence dynamics. In magnetic confinement devices, drift-wave turbulence produces anomalous fluxes via cross-correlations between fluctuations. In this work, we introduce an alternative, data-driven method for parametrizing these fluxes. The method uses deep supervised learning to infer a reduced mean-field model from a set of numerical simulations. We apply the method to a simple drift-wave turbulence system and find a significant new effect which couples the particle flux to the local gradient of vorticity. Notably, here, this effect is much stronger than the oft-invoked shear suppression effect. We also recover the result via a simple calculation. The vorticity gradient effect tends to modulate the density profile. In addition, our method recovers a model for spontaneous zonal flow generation by negative viscosity, stabilized by nonlinear and hyperviscous terms. We highlight the important role of symmetry to implementation of the alternative method.

We investigate the Berezinskii-Kosterlitz-Thouless transitions for the square-lattice six-state clock model with the corner-transfer matrix renormalization group (CTMRG). Scaling analyses for effective correlation length, magnetization, and entanglement entropy with respect to the cutoff dimension $m$ at the fixed point of the CTMRG provide transition temperatures consistent with a variety of recent numerical studies. We also reveal that the fixed-point spectrum of the corner-transfer matrix in the critical intermediate phase of the six-state clock model is characterized by the scaling dimension consistent with the $c=1$ boundary conformal field theory associated with the effective $Z_6$ dual sine-Gordon model.

Via Monte Carlo simulations we study nonequilibrium dynamics in the nearest-neighbor Ising model, following quenches to points inside the ordered region of the phase diagram. With the broad objective of quantifying the nonequilibrium universality classes corresponding to spatially correlated and uncorrelated initial configurations, in this paper we present results for the decay of the order-parameter autocorrelation function for quenches from the critical point. This autocorrelation is an important probe for the aging dynamics in far-from-equilibrium systems and typically exhibits power-law scaling. From the state-of-the-art analysis of the simulation results, we quantify the corresponding exponents ($\lambda$) for both conserved and nonconserved (order-parameter) dynamics of the model in space dimension $d=3$. Via structural analysis we demonstrate that the exponents satisfy a bound. We also revisit the $d=2$ case to obtain more accurate results. It appears that irrespective of the dimension, $\lambda$ is approximately the same for both conserved and nonconserved dynamics.

The formation process and growth dynamics of the grid pattern, a cellular convective pattern in the electroconvection of nematic liquid crystals, are investigated. The grid pattern appears via a disordered state called defect turbulence with the increasing of an applied voltage. The averaged defect density increases with the applied voltage and then the defects that have been in the continuous process of creation and annihilation are frozen as grid cells forming domain structures. The area fraction of the grid domains is adopted as the order parameter. The temporal growth of the area fraction for the step voltage was also measured. By applying the Kolmogorov-Avrami model to the results, it is suggested that the growth dynamics of the grid domain is not primarily governed by domain growth, but by the local transition of the rolls to the cellular flow via preliminary grid structures that transiently appear.

Experiments on steady-state bacterial cultures have uncovered several quantitative regularities at the system level. These include, first, the exponential growth of cell size with time and the balanced growth of intracellular chemicals between cell birth and division, which are puzzling given the nonlinear and decentralized chemical dynamics in the cell. We model a cell as a set of chemical populations undergoing nonlinear mass action kinetics in a container whose volume is a linear function of the chemical populations. This turns out to be a special class of dynamical systems that generically has attractors in which all populations grow exponentially with time at the same rate. This explains exponential balanced growth of bacterial cells without invoking any regulatory mechanisms and suggests that this could be a robust property of protocells as well. Second, we consider the hypothesis that cells commit themselves to division when a certain internal chemical population reaches a threshold of $N$ molecules. We show that this hypothesis leads to a simple explanation of some of the variability observed across cells in a bacterial culture. In particular, it reproduces the adder property of cell size fluctuations observed recently in E. coli; the observed correlations among interdivision time, birth volume, and added volume in a generation; and the observed scale of the fluctuations (CV $\approx$ 10–30%) when $N$ is between 10 and 100. Third, upon including a suitable regulatory mechanism that optimizes the growth rate of the cell, the model reproduces the observed bacterial growth laws including the dependence of the growth rate and ribosomal protein fraction on the medium. Thus, the models provide a framework for unifying diverse aspects of bacterial growth physiology under one roof. They also suggest new questions for experimental and theoretical enquiry.

Grid refinement techniques are of paramount importance for computational fluid dynamics approaches relying on the use of Cartesian grids. This is especially true of solvers dedicated to aerodynamics, in which the capture of thin shear layers require the use of small cells. In this paper, a three-dimensional grid refinement technique is developed within the framework of hybrid recursive regularized lattice Boltzmann method (HRR-LBM) for compressible high-speed flows, which is an efficient collide-stream-type method on a compact D3Q19 stencil. The proposed method is successfully assessed considering several test cases, namely, an isentropic vortex propagating through transition interface, shock-vortex interaction with intersection between grid refinement interface and shock corrugation, and transonic flows over three-dimensional DLR-M6 wing with seven levels of grid refinement.

Recent advances in DNA sequencing and fluorescence imaging have made it possible to monitor the dynamics of ribosomes actively engaged in messenger RNA (mRNA) translation. Here, we model these experiments within the inhomogeneous totally asymmetric simple exclusion process (TASEP) using realistic kinetic parameters. In particular, we present analytic expressions to describe the following three cases: (a) translation of a newly transcribed mRNA, (b) translation in the steady state and, specifically, the dynamics of individual (tagged) ribosomes, and (c) runoff translation after inhibition of translation initiation. In cases (b) and (c) we develop an effective medium approximation to describe many-ribosome dynamics in terms of a single tagged ribosome in an effective medium. The predictions are in good agreement with stochastic simulations.

The relationship between velocities, tractions, and intercellular stresses in the migrating epithelial monolayer are currently unknown. Ten years ago, a method known as monolayer stress microscopy (MSM) was suggested from which intercellular stresses could be computed for a given traction field. The core assumption of MSM is that intercellular stresses within the monolayer obey a linear and passive constitutive law. Examples of these include a Hookean solid (an elastic sheet) or a Newtonian fluid (thin fluid film), which imply a specific relation between the displacements or velocities and the tractions. Due to the lack of independently measured intercellular stresses, a direct validation of the 2D stresses predicted by a linear passive MSM model is presently not possible. An alternative approach, which we give here and denote as the Stokes method, is based on simultaneous measurements of the monolayer velocity field and the cell-substrate tractions. Using the same assumptions as those underlying MSM, namely, a linear and passive constitutive law, the velocity field suffices to compute tractions, from which we can then compare with those measured by traction force microscopy. We find that the calculated tractions and measured tractions are uncorrelated. Since the classical MSM and the Stokes approach both depend on the linear and passive constitutive law, it follows that some serious modification of the underling rheology is needed. One possible modification is the inclusion of an active force. In the special case where this is additive to the linear passive rheology, we have a new relationship between the active force density and the measured velocity (or displacement) field and tractions, which by Newton's laws, must be obeyed.

The deformation of the free surface of a paramagnetic liquid subjected to a nonuniform magnetic field is studied. A transient deformation of the surface caused by the interplay of gravity, magnetic field, and surface tension is observed when a permanent magnet is moved vertically downward to the free surface of the liquid. Different concentrations of rare-earth-metal salt (${\mathrm{DyCl}}_3$) are used and different magnet velocities are studied. The deformation of the interface is followed optically by means of a microscope and recorded with a high-speed camera. The experimental results are compared and discussed with complementary numerical simulations. Detailed results are given for the static shape of the deformed surface and the temporal evolution of the surface deformation below the center of the magnet. The frequency of the surface oscillations is found to depend on the concentration of the salt and is compared with analytical findings. Finally, a potential application of the effects observed is presented.

Motivated by the recent work in skyrmions and active chiral matter systems, we examine pairs and small clusters of repulsively interacting point particles in the limit where the dynamics is dominated by the Magnus force. We find that particles with the same Magnus force can form stable pairs, triples, and higher ordered clusters or exhibit chaotic motion. For mixtures of particles with opposite Magnus force, particle pairs can combine to form translating dipoles. Under an applied drive, particles with the same Magnus force translate; however, particles with different or opposite Magnus force exhibit a drive-dependent decoupling transition. When the particles interact with a repulsive obstacle, they can form localized orbits with depinning or unwinding transitions under an applied drive. We examine the interaction of these particles with clusters or lines of obstacles and find that the particles can become trapped in orbits that encircle multiple obstacles. Under an ac drive, we observe a series of ratchet effects, including ratchet reversals, for particles interacting with a line of obstacles due to the formation of commensurate orbits. Finally, in assemblies of particles with mixed Magnus forces of the same sign, we find that the particles with the largest Magnus force become localized in the center of the cluster, while for mixtures with opposite Magnus forces, the motion is dominated by transient local pairs or clusters, where the translating pairs can be regarded as a form of active matter.

Random noise in low Reynolds number flow has rarely been used to obtain net migration of microscale objects. In this study, we numerically show that net migration of a microscale object can be extracted from random directional fluid forces in Stokes flow, by introducing deformability and inhomogeneous density into the object. We also developed a mathematical framework to describe the deformation-induced migration caused by noise. These results provide a basis for understanding the noise-induced migration of a microswimmer and are useful for harnessing energy from low Reynolds number flow.