The Bandt-Pompe permutation entropy and the Jensen-Shannon statistical complexity are used to analyze fluctuating time series of three different turbulent plasmas: the magnetohydrodynamic (MHD) turbulence in the plasma wind tunnel of the Swarthmore Spheromak Experiment (SSX), drift-wave turbulence of ion saturation current fluctuations in the edge of the Large Plasma Device (LAPD), and fully developed turbulent magnetic fluctuations of the solar wind taken from the $\mathit{Wind}$ spacecraft. The entropy and complexity values are presented as coordinates on the $\mathit{CH}$ plane for comparison among the different plasma environments and other fluctuation models. The solar wind is found to have the highest permutation entropy and lowest statistical complexity of the three data sets analyzed. Both laboratory data sets have larger values of statistical complexity, suggesting that these systems have fewer degrees of freedom in their fluctuations, with SSX magnetic fluctuations having slightly less complexity than the LAPD edge $I_{\mathrm{sat}}$. The $\mathit{CH}$ plane coordinates are compared to the shape and distribution of a spectral decomposition of the wave forms. These results suggest that fully developed turbulence (solar wind) occupies the lower-right region of the $\mathit{CH}$ plane, and that other plasma systems considered to be turbulent have less permutation entropy and more statistical complexity. This paper presents use of this statistical analysis tool on solar wind plasma, as well as on an MHD turbulent experimental plasma.

We study the classical dynamics of the Abelian-Higgs model in (1 + 1) space-time dimensions for the case of strongly broken gauge symmetry. In this limit the wells of the potential are almost harmonic and sufficiently deep, presenting a scenario far from the associated critical point. Using a multiscale perturbation expansion, the equations of motion for the fields are reduced to a system of coupled nonlinear Schrödinger equations. Exact solutions of the latter are used to obtain approximate analytical solutions for the full dynamics of both the gauge and Higgs field in the form of oscillons and oscillating kinks. Numerical simulations of the exact dynamics verify the validity of these solutions. We explore their persistence for a wide range of the model's single parameter, which is the ratio of the Higgs mass $\left(m_H\right)$ to the gauge-field mass $\left(m_A\right)$. We show that only oscillons oscillating symmetrically with respect to the “classical vacuum,” for both the gauge and the Higgs field, are long lived. Furthermore, plane waves and oscillating kinks are shown to decay into oscillon-like patterns, due to the modulation instability mechanism.

The existence and stability of optical solitons in the semi-infinite gap of parity-time (PT)-symmetric optical lattices with competing cubic and quintic nonlinearities are investigated numerically. The fundamental and dipole solitons can exist only with focusing quintic nonlinearity; however, they are always linearly unstable. With the competing effect between cubic and quintic nonlinearities, the strength of the quintic nonlinearity should be larger than a threshold for the solitons' existence when the strength of the focusing cubic nonlinearity is fixed. The stability of both fundamental and dipole solitons is studied in detail. When the strength of the focusing quintic nonlinearity is fixed, solitons can exist at the whole interval of the strength of the cubic nonlinearity, but only a small part of the fundamental solitons are stable. We also study numerically nonlinear evolution of stable and unstable PT solitons under perturbation.

We present a molecular dynamics simulation study on the controlling factors that influence the wettability of a hairy surface. By adopting the hairs with appropriate grafting density, hair length, and hair rigidity, the hairy surface shows good performance on droplet repellency. When the droplet sits on the hairy surface, the flexible hairs can spontaneously bundle with the appropriate amount of neighboring hairs to enhance the surface hydrophobicity, thus providing a new possibility to control the surface wettability. The hairy surface with tunable grafting density and hair rigidity, bridges the gap between surfaces with soft polymer brushes and surfaces that are completely hard but porous.

We study a quasi-one-dimensional system of hard disks confined between hard lines to explore the relationship between the inherent structure landscape, the thermodynamics, and the dynamics of the fluid. The transfer matrix method is used to obtain an exact description of the landscape, equation of state, and provide a mapping of configurations of the equilibrium fluid to their local jammed structures. This allows us to follow how the system samples the landscape as a function of occupied volume fraction $\varphi$. Configurations of the ideal gas map to the maximum in the distribution of inherent structures, with a jamming volume fraction ${\varphi }_J^{*}$, and sample more dense basins with increasing $\varphi$. This suggests jammed states with a density below ${\varphi }_J^{*}$ are inaccessible from the equilibrium fluid. The configurational entropy of the fluid decreases rapidly at intermediate $\varphi$ before plateauing at a low value and going to zero as the most dense packing is approached. This leads to the appearance of a maximum in both the isobaric heat capacity and the inherent structure pressure. We also show that the system exhibits a crossover from fragile to strong fluid behavior, located at the heat capacity maximum. Structural relaxation in the fragile fluid is shown to be controlled by the presence of high order saddle points caused by neighboring defects that are unstable with respect to jamming and spontaneously rearrange to form a stable local environment. In the strong fluid, the defect concentration is low so that defects do not interact and relaxation occurs through the hopping of isolated defects between stable local packing environments.

We investigate the kinetics of the ubiquitous phosphorylation-dephosphorylation cycle on biological membranes by means of kinetic Monte Carlo simulations on the triangular lattice. We establish the dependence of effective macroscopic reaction rate coefficients as well as the steady-state phosphorylated substrate fraction on the diffusion coefficient and concentrations of opposing enzymes: kinases and phosphatases. In the limits of zero and infinite diffusion, the numerical results agree with analytical predictions; these two limits give the lower and the upper bound for the macroscopic rate coefficients, respectively. In the zero-diffusion limit, which is important in the analysis of dense systems, phosphorylation and dephosphorylation reactions can convert only these substrates which remain in contact with opposing enzymes. In the most studied regime of nonzero but small diffusion, a contribution linearly proportional to the diffusion coefficient appears in the reaction rate. In this regime, the presence of opposing enzymes creates inhomogeneities in the (de)phosphorylated substrate distributions: The spatial correlation function shows that enzymes are surrounded by clouds of converted substrates. This effect becomes important at low enzyme concentrations, substantially lowering effective reaction rates. Effective reaction rates decrease with decreasing diffusion and this dependence is more pronounced for the less-abundant enzyme. Consequently, the steady-state fraction of phosphorylated substrates can increase or decrease with diffusion, depending on relative concentrations of both enzymes. Additionally, steady states are controlled by molecular crowders which, mostly by lowering the effective diffusion of reactants, favor the more abundant enzyme.

We investigate the laminar flow of two-fluid mixtures inside a simple network of interconnected tubes. The fluid system is composed of two miscible Newtonian fluids of different viscosity which do not mix and remain as nearly distinct phases. Downstream of a diverging network junction the two fluids do not necessarily split in equal fraction and thus heterogeneity is introduced into network. We find that in the simplest network, a single loop with one inlet and one outlet, under steady inlet conditions, the flow rates and distribution of the two fluids within the network loop can undergo persistent spontaneous oscillations. We develop a simple model which highlights the basic mechanism of the instability and we demonstrate that the model can predict the region of parameter space where oscillations exist. The model predictions are in good agreement with experimental observations.

A crucial part of segmented or multiple-aperture systems is control of the optical path difference between the segments or subapertures. In order to achieve optimal performance we have to phase subapertures to within a fraction of the wavelength, and this requires high accuracy of positioning for each subaperture. We present simulations and hardware realization of a simulated annealing algorithm in an active optical system with sparse segments. In order to align the optical system we applied the optimization algorithm to the image itself. The main advantage of this method over traditional correction methods is that wave-front-sensing hardware and software are no longer required, making the optical and mechanical system much simpler. The results of simulations and laboratory experiments demonstrate the ability of this optimization algorithm to correct both piston and tip-tilt errors.

Dynamics of a Brownian particle in an asymmetric microchannel that is subjected to an external oscillating force is numerically analyzed. In addition to the elastic collisions with the walls that are kind of short range interactions, the long range hydrodynamic influences of the walls have been considered in an approximate way. We demonstrate how the geometrical parameters of the channel change the rectified current of the particle. As a result of numerical calculations, we show that long range hydrodynamic interactions with walls decrease the efficiency of the Brownian ratchet.

Experiments have shown that when a horizontal cylinder rotates around the vertical axis in a granular medium, the drag force in the stationary regime becomes independent of the depth, in contradiction with the frictional picture stipulating that the drag should be proportional to the hydrostatic pressure. The goal of this study is to understand the origin of this depth independence of the granular drag. Intensive numerical simulations using the discrete element method are performed giving access to the stress distribution in the packing during the rotation of the cylinder. It is shown that the rotation induces a strong anisotropy in the stress distribution, leading to the formation of arches that screen the hydrostatic pressure in the vicinity of the cylinder and create a bubble of low pressure.

Cellular transport is achieved by the cooperative action of molecular motors which are elastically linked to a common cargo. When the motors pull on the cargo at the same time, they experience fluctuating elastic strain forces induced by the stepping of the other motors. These elastic coupling forces can influence the motors' stepping and unbinding behavior and thereby the ability to transport cargos. Based on a generic single motor description, we introduce a framework that explains the response of two identical molecular motors to a constant external force. In particular, we relate the single motor parameters, the coupling strength and the external load force to the dynamics of the motor pair. We derive four distinct transport regimes and determine how the crossover lines between the regimes depend on the load force. Our description of the overall cargo dynamics takes into account relaxational displacements of the cargo caused by the unbinding of one motor. For large forces and weak elastic coupling these back-shifts dominate the displacements. To develop an intuitive understanding about motor cooperativity during cargo transport, we introduce a time scale for load sharing. This time scale allows us to predict how the regulation of single motor parameters influences the cooperativity. As an example, we show that up-regulating the single motor processivity enhances load sharing of the motor pair.

We derive the class of population balance equations (PBE), recently applied to model the Viedma deracemization experiment, from an underlying microreversible kinetic reaction scheme. The continuum limit establishing the relationship between the micro- and macroscopic processes and the associated particle fluxes erases the microreversible nature of the molecular interactions in the population growth rate functions and limits the scope of such PBE models to strict kinetic control. The irreversible binary agglomeration processes modeled in those PBEs contribute an additional source of kinetic control. These limitations are crucial regarding the question of the origin of biological homochirality, where the interest in any model lies precisely in its ability for absolute asymmetric synthesis and the amplification of the tiny inherent statistical chiral fluctuations about the ideal racemic composition up to observable enantiometric excess levels.

We propose a framework combining detrended fluctuation analysis with standard regression methodology. The method is built on detrended variances and covariances and it is designed to estimate regression parameters at different scales and under potential nonstationarity and power-law correlations. The former feature allows for distinguishing between effects for a pair of variables from different temporal perspectives. The latter ones make the method a significant improvement over the standard least squares estimation. Theoretical claims are supported by Monte Carlo simulations. The method is then applied on selected examples from physics, finance, environmental science, and epidemiology. For most of the studied cases, the relationship between variables of interest varies strongly across scales.

We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age $\tau$ as ${\tau }^{-\alpha }$. Depending on the exponent $\alpha$, the scaling of tree depth with tree size $n$ displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition $(\alpha =1)$ tree depth grows as ${(logn)}^2$. This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus providing a theoretical support for age-dependent speciation and associating it to the occurrence of a critical point.

We study the mechanisms of frequency-synchronized cluster formation in coupled nonidentical oscillators and investigate the impact of presence of a leader on the cluster synchronization. We find that the introduction of a leader, a node having large parameter mismatch, induces a profound change in the cluster pattern as well as in the mechanism of the cluster formation. The emergence of a leader generates a transition from the driven to the mixed cluster state. The frequency mismatch turns out to be responsible for this transition. Additionally, for a chaotic evolution, the driven mechanism stands as a primary mechanism for the cluster formation, whereas for a periodic evolution the self-organization mechanism becomes equally responsible.

Propagation of traveling fronts in a three-dimensional channel with spatially varying cross section is reduced to an equivalent one-dimensional reaction-diffusion-advection equation with boundary-induced advection term. Treating the advection term as a weak perturbation, an equation of motion for the front position is derived. We analyze channels whose cross sections vary periodically with $L$ along the propagation direction of the front. Taking the Schlögl model as a representative example, we calculate analytically the nonlinear dependence of the front velocity on the ratio $L/l$ where $l$ denotes the intrinsic front width. In agreement with finite-element simulations of the three-dimensional reaction-diffusion dynamics, our theoretical results predicts boundary-induced propagation failure for a finite range of $L/l$ values. In particular, the existence of the upper bound of $L/l$ can be completely understood based on the linear eikonal equation. Last, we demonstrate that the front velocity is determined by the suppressed diffusivity of the reactants for $L\ll l$.

Upon contact between miscible solutions of reactants $A$ and $B$ along a horizontal interface in the gravity field, various buoyancy-driven instabilities can develop when an $A+B\to C$ reaction takes place and the density varies with the concentrations of the various chemicals. To classify the possible convective instability scenarios, we analyze the spatial dependence of the large time asymptotic density profiles as a function of the key parameters of the problem, which are the ratios of diffusion coefficients and of solutal expansion coefficients of species $A$, $B$, and $C$. We find that 62 different density profiles can develop in the reactive problem, whereas only 6 of them can be obtained in the nonreactive one.

We report on two-dimensional simulations of liquid bridges' dynamics inside microchannels of uniform wettability and subject to an external oscillatory flow rate. The oscillatory flow results in a zero net flow rate and its effects are compared to those of a stationary system. To handle the three phase contact lines motion, Cahn-Hilliard diffuse-interface formulation was used and the flow equations were solved using the finite element method with adaptively refined unstructured grids. The results indicate that the liquid bridge responds in three different ways depending on the substrate wettability properties and the frequency of the oscillatory flow. In particular below a critical frequency, the liquid bridge will rupture when the channel walls are philic or detach from the surface when they are phobic. However, at high frequencies, the liquid bridge shows a perpetual periodic oscillatory motion for both philic and phobic surfaces. Furthermore, an increase in the frequency of the flow velocity results in stabilization effects and a behavior approaching that of the stationary system where no rupture or detachment can be observed. This stable behavior is the direct result of less deformation of the liquid bridge due to the fast flow direction change and motion of contact lines on the solid substrate. Moreover, it was found that the flow velocity is out of phase with the footprint and throat lengths and that the latter two also show a phase difference. These differences were explained in terms of the motion of the two contact lines on the solid substrates and the deformation of the two fluid-fluid interfaces.

Previous experiments have revealed that shock waves driven through dissipative gases may become unstable, for example, in granular gases and in molecular gases undergoing strong relaxation effects. The mechanisms controlling these instabilities are not well understood. We successfully isolated and investigated this instability in the canonical problem of piston-driven shock waves propagating into a medium characterized by inelastic collision processes. We treat the standard model of granular gases, where particle collisions are taken as inelastic, with a constant coefficient of restitution. The inelasticity is activated for sufficiently strong collisions. Molecular dynamic simulations were performed for 30 000 particles. We find that all shock waves investigated become unstable, with density nonuniformities forming in the relaxation region. The wavelength of these fingers is found to be comparable to the characteristic relaxation thickness. Shock Hugoniot curves for both elastic and inelastic collisions were obtained analytically and numerically. Analysis of these curves indicates that the instability is not of the Bethe-Zeldovich-Thompson or D'yakov-Kontorovich type. Analysis of the shock relaxation rates and rates for clustering in a convected fluid element with the same thermodynamic history ruled out the clustering instability of a homogeneous granular gas. Instead, wave reconstruction of the early transient evolution indicates that the onset of instability occurs during repressurization of the gas following the initial relaxation of the medium behind the lead shock. This repressurization gives rise to internal pressure waves in the presence of strong density gradients. This indicates that the mechanism of instability is more likely of the vorticity-generating Richtmyer-Meshkov type, relying on the action of the inner pressure wave development during the transient relaxation.

Symmetry breaking is reported for continuous families of solitons in the nonlinear Schrödinger equation with a two-dimensional complex potential. This symmetry breaking is forbidden in generic complex potentials. However, for a special class of partially parity-time-symmetric potentials, it is allowed. At the bifurcation point, two branches of asymmetric solitons bifurcate out from the base branch of symmetry-unbroken solitons. Stability of these solitons near the bifurcation point are also studied, and two novel properties for the bifurcated asymmetric solitons are revealed. One is that at the bifurcation point, zero and simple imaginary linear-stability eigenvalues of asymmetric solitons can move directly into the complex plane and create oscillatory instability. The other is that the two bifurcated asymmetric solitons, even though having identical powers and being related to each other by spatial mirror reflection, can possess different types of unstable eigenvalues and thus exhibit nonreciprocal nonlinear evolutions under random-noise perturbations.