Mobility properties of spatially localized structures arising from chaotic but deterministic forcing of the bistable Swift-Hohenberg equation are studied and compared with the corresponding results when the chaotic forcing is replaced by white noise. Short structures are shown to possess greater mobility, resulting in larger root-mean-square speeds but shorter displacements than longer structures. Averaged over realizations, the displacement of the structure is ballistic at short times but diffusive at larger times. Similar results hold in two spatial dimensions. The effects of chaotic forcing on the stability of these structures is also quantified. Shorter structures are found to be more fragile than longer ones, and their stability region can be displaced outside the pinning region for constant forcing. Outside the stability region the deterministic fluctuations lead either to the destruction of the structure or to its gradual growth.

We consider two diffusively coupled populations of identical oscillators, where the oscillators in each population are coupled with a common dynamic environment. Existence and stability of a variety of stationary states are analyzed on the basis of the Ott-Antonsen reduction method, which reveals that the chimera state occurs under the diffusive coupling scheme. Furthermore, we find an exotic symmetry-breaking behavior, the so-called the heterosynchronous state, in which each population exhibits in-phase coherence, while the order parameters of two populations rotate at different phase velocities. The chimera and heterosynchronous states emerge from bistabilities of distinct states for decoupled population and occur as a unique continuation for weak diffusive couplings. The heterosynchronous state is caused by an indirect coupling scheme via dynamic environments and could occur for a finite-size system as well, even for the system that consists of one oscillator per population.

The properties of a wide range of two-dimensional network materials are investigated by developing a generalized network theory. The methods developed are shown to be applicable to a wide range of systems generated from both computation and experiment; incorporating atomistic materials, foams, fullerenes, colloidal monolayers, and geopolitical regions. The ring structure in physical networks is described in terms of the node degree distribution and the assortativity. These quantities are linked to previous empirical measures such as Lemaître's law and the Aboav-Weaire law. The effect on these network properties is explored by systematically changing the coordination environments, topologies, and underlying potential model of the physical system.

It is a longstanding debate on the absence of threshold for susceptible-infected-susceptible (SIS) model on networks with finite second order moment of degree distribution. The eigenvector localization of the adjacency matrix for a network gives rise to the inactive Griffiths phase featuring slow decay of the activity localized around highly connected nodes due to the dynamical fluctuation. We show how it dramatically changes our understanding of the SIS model, opening up new possibilities for the debate. We derive the critical condition for Griffiths to active phase transition: on average, an infected node can further infect another one in the characteristic lifespan of the star subgraph composed of the node and its nearest neighbors. The system approaches the critical point of avoiding the irreversible dynamical fluctuation and the trap of absorbing state. As a signature of the phase transition, the infection density of a node is not only proportional to its degree, but also proportional to the exponentially growing lifespan of the star. And the divergence of the average lifespan of the stars is responsible for the vanishing threshold in the thermodynamic limit. The eigenvector localization exponentially reinforces the infection of highly connected nodes, while it inversely suppresses the infection of small-degree nodes.

We study the energy landscapes of particles with short-range attractive interactions as the range of the interactions increases. Starting with the set of local minima for $6\le N\le 12$ hard spheres that are “sticky,” i.e., they interact only when their surfaces are exactly in contact, we use numerical continuation to evolve the local minima (clusters) as the range of the potential increases, using both the Lennard-Jones and Morse families of interaction potentials. As the range increases, clusters merge, until at long ranges only one or two clusters are left. We compare clusters obtained by continuation with different potentials and find that for short and medium ranges, up to about 30% of particle diameter, the continued clusters are nearly identical, both within and across families of potentials. For longer ranges, the clusters vary significantly, with more variation between families of potentials than within a family. We analyze the mechanisms behind the merge events and find that most rearrangements occur when a pair of nonbonded particles comes within the range of the potential. An exception occurs for nonharmonic clusters, i.e., those that have a zero eigenvalue in their Hessian, which undergo a more global rearrangement.

Four results associated with the diffuse-interface model (DIM) for contact lines are reported in this paper. First, a boundary condition is derived, which states that the fluid near a solid wall must have a certain density ${\rho }_0$ depending on the solid's properties. Unlike previous derivations, the one presented here is based on the same physics as the DIM itself and does not require additional assumptions. Second, asymptotic estimates are used to check a conjecture lying at the foundation of the DIM, as well as all other models of contact lines, that liquid-vapor interfaces are nearly isothermal. It turns out that, for water, they are not, although, for a more viscous fluid, they can be. The nonisothermality occurs locally, near the interface, but can still affect the contact-line dynamics. Third, the DIM coupled with a realistic equation of state for water is used to compute the dependence of the surface tension $\sigma$ on the temperature $T$, which agrees well with the empirical $\sigma \left(T\right)$. Fourth, the same framework is used to compute the static contact angle of a water-vapor interface. It is shown that, with increasing temperature, the contact angle becomes either ${180}^{\circ }$ (perfect hydrophobicity) or $0^{\circ }$ (perfect hydrophilicity), depending on whether ${\rho }_0$ matches the density of saturated vapor or liquid, respectively. Such behavior presumably occurs in all fluids, not just water, and for all sufficiently strong variations of parameters, not just that of the temperature, as corroborated by existing observations of drops under variable electric field.

We develop an adversarial-reinforcement learning scheme for microswimmers in statistically homogeneous and isotropic turbulent fluid flows, in both two and three dimensions. We show that this scheme allows microswimmers to find nontrivial paths, which enable them to reach a target on average in less time than a naïve microswimmer, which tries, at any instant of time and at a given position in space, to swim in the direction of the target. We use pseudospectral direct numerical simulations of the two- and three-dimensional (incompressible) Navier-Stokes equations to obtain the turbulent flows. We then introduce passive microswimmers that try to swim along a given direction in these flows; the microswimmers do not affect the flow, but they are advected by it. Two nondimensional control parameters play important roles in our learning scheme: (a) the ratio ${\tilde{V}}_s$ of the microswimmer's bare velocity $V_s$ and the root-mean-square (rms) velocity $u_{\text{rms}}$ of the turbulent fluid and (b) the product $\tilde{B}$ of the microswimmer-response time $B$ and the rms vorticity ${\omega }_{\text{rms}}$ of the fluid. We show that the average time required for the microswimmers to reach the target, by using our adversarial-reinforcement learning scheme, eventually reduces below the average time taken by microswimmers that follow the naïve strategy.

Relaminarization of wall-bounded turbulent flows by means of external static magnetic fields is a long-known phenomenon in the physics of electrically conducting fluids at low magnetic Reynolds numbers. Despite the large literature on the subject, it is not yet completely clear what combination of the Hartmann ($M$) and the Reynolds number has to be used to predict the laminar-turbulent transition in channel or pipe flows fed by upstream turbulent flows free of magnetic perturbations. Relying upon standard phenomenological approaches related to mixing length and structural concepts, we put forward that $M/R_{\tau }$, where $R_{\tau }$ is the friction Reynolds number, is the appropriate controlling parameter for relaminarization, a proposal which finds good support from available experimental data.

The formation and melting of a monolayered charged dust particle crystal in a DC glow discharge argon plasma is studied. The nature of the melting or formation process is established as a first-order phase transition from the variations in the Coulomb coupling parameter, the dust temperature, the structural order parameter, and from the existence of a hysteresis behavior. Our experimental results are distinctly different from existing theoretical predictions for two dimensional crystals based on the Kosterlitz-Thouless-Halperin-Nelson-Young mechanism or the grain boundary induced melting and indicate a mechanism that is akin to a fluctuation induced first-order phase transition in complex plasmas.

Ion sound waves are studied in a plasma subject to gravitational field giving rise to vertically inhomogeneous steady-state plasma conditions. Such systems are interesting by exhibiting a wave growth that is a result of energy flux conservation for pulses propagating in an inhomogeneous system. The increase of the amplitude of a pulse as it propagates along the density gradient in the direction of decreasing density gives rise to an enhanced interaction between waves and plasma particles that can be modeled by a modified Korteweg–de Vries equation. Analytical results are compared with numerical particle-in-cell simulations of the problem. Our code assumes isothermally Boltzmann distributed electrons resulting in a nonlinear Poisson equation. The ion component is treated as a collection of individual particles interacting through collective electric fields. Deviations from quasineutrality are allowed for.

In this paper, we present a finite-volume direct kinetic method, the so-called discrete unified gas kinetic scheme (DUGKS), for electrostatic plasma. One key feature of this method is the semi-implicit unsplitting treatment of particle transport and collision, and thus the time step in current DUGKS is not limited by the particle collision time. In addition, a fourth-order compact MUSCL scheme with a positivity preserving limiter is implemented in the interface reconstruction, which enables present DUGKS to preserve the favorable conservative property and positivity of distribution function. Combined with this MUSCL method, the semi-Lagrangian scheme is used for the particle transport in velocity space to remove Courant-Friedricks-Lewy restriction induced by the large electric force. As a result, the proposed DUGKS becomes an efficient and stable multiscale scheme. Several numerical experiments, including plasma sheath, linear Landau damping, collisional nonlinear Landau damping, and plasma ion acceleration, are performed to validate current DUGKS. A comparative study of current DUGKS with a general particle in cell (PIC) method which could handle particle collision in a conservative way is also presented. Theory and numerical experiments demonstrate that DUGKS is preferred for plasma flows involving small electrostatic perturbation and high collision regimes, while the PIC method is desired for the field- dominated plasma flows involving a wide range of velocities.

This work considers the usage of StyleGAN architecture for the task of microstructure synthesis. The task is the following: Given number of samples of structure we try to generate similar samples at the same time preserving its properties. Since the considered architecture is not able to produce samples of sizes larger than the training images, we propose to use image quilting to merge fixed-sized samples. One of the key features of the considered architecture is that it uses multiple image resolutions. We also investigate the necessity of such an approach.

This paper introduces improvements to the amplitude expansion of the phase-field crystal model that enable the simulation of grains within a full range of orientations. The unphysical grain boundary between grains, rotated by a crystal's symmetry rotation, is removed using a combination of the auxiliary rotation field described in our previous work and an algorithm that correctly matches the complex amplitudes according to the differences in local rotation.

A crucial step in constructing a lattice Boltzmann model is the definition of a suitable set of lattice velocities and the correct assignment of the associated weights. For high-order models, the solution of this problem requires a nontrivial effort. This paper outlines the functioning of a publicly available Python script which has been written to assist researchers in that task. The speed of sound $c_{\text{s}}$ is considered as a parameter, which can, within limits, be chosen at will. Under this premise, the Maxwell-Boltzmann constraint equations are a system of linear equations to determine the weights and hence amenable to numerical solution by standard linear algebra library routines. By suitable contractions, the tensor equations are mapped to a set of equivalent scalar equations, which simplifies the treatment significantly. For a user-supplied set of velocity shells, the software first checks if a solution for the weights exists and returns it if it also happens to be unique. In such a case, the software also calculates the range of $c_{\text{s}}$ values that yield positive weights. Standard models like D3Q19 with a well-defined special $c_{\text{s}}$ value then result as limiting cases where one of the weights vanishes. In the case of an infinite set of solutions, the user may find one particular solution by supplying a $c_{\text{s}}$ value and then minimizing one or several weights within the framework of standard linear programming. Some examples illustrate the feasibility and usefulness of the approach. A number of models that have been discussed in the literature are nicely reproduced, while the software has also been able to find some new models of even higher order.

The divergence rate method, which is used to determine the maximum Lyapunov exponent out of time series, is based on the evaluation of the time-dependent divergence exponent. For chaotic systems and in the small time regime, this exponent grows linearly in time. The asymptotic regime is instead characterized by a time-independent behavior due to the system eventually losing its memory of the starting conditions. The amplitude of this “plateau”-like divergence exponent depends both on the choice of the embedding dimension and lag and on the maximum distance of nearby starting trajectories in a way that is characteristic of the underlying dynamical system. In this paper, upon introducing the basic mathematical tools, we address the plateau evaluation for two classes of time series, those generated by a white noise source and those generated by a finite-dimensional chaotic system. The different behavior provides a novel tool to distinguish purely stochastic sources from deterministic ones, as well as to provide a precise estimate of the correlation dimension in the latter case. The method is also sensitive to correlated noise sources.

Preferential contact process limited by contact capacity remarkably affects the spreading dynamics on complex networks, but the influence of this preferential contact in social contagions has not been fully explored. To this end, we propose a behavior spreading model based on the mechanism of preferential contact. The probability in the model that an adopted individual contacts and tries to transmit the behavioral information to one of his/her neighbors depends on the neighbor's degree. Besides, a preferential exponent determines the tendency to contact with either small-degree or large-degree nodes. We use a dynamic messaging method to describe this complex contagion process and verify that the method is accurate to predict the spreading dynamics by numerical simulations on strongly heterogeneous networks. We find that the preferential contact mechanism leads to a crossover phenomenon in the growth of final adoption size. By reducing the preferential exponent, we observe a change from a continuous growth to an explosive growth and then to a continuous growth with the transmission rate of behavioral information. Moreover, we find that there is an optimal preferential exponent which maximizes the final adoption size at a fixed information transmission rate, and this optimal preferential exponent decreases with the information transmission rate. The used theory can be extended to other types of dynamics, and our findings provide useful and general insights into social contagion processes in the real world.

The effect of hydrodynamic interactions (HI) on the long-time self-diffusion in quasi-two-dimensional fluids of paramagnetic colloidal particles is investigated using a combination of experiments and Brownian dynamics (BD) simulations. In the BD simulations, the direct interactions (DI) between the particles consist of a short-ranged repulsive part and a long-ranged part that is proportional to $1/r^3$, with $r$ the interparticle distance. By studying the equation of state, the simulations allow for the identification of the regime where the properties of the fluid are fully controlled by the long-ranged interactions, and the thermodynamic state solely depends on the dimensionless interaction strength $\mathrm{\Gamma }$. In this regime, the radial distribution functions from the simulations are in quantitative agreement with those from the experiments for different fluid area fractions. This agreement confirms that the DI in the experiments and simulations are identical, which thus allows us to isolate the role of HI, as these are not taken into account in the BD simulations. Experiment and simulation fall onto a master curve with respect to the $\mathrm{\Gamma }$ dependence of $D_{\mathrm{L}}^{★}=D_{\mathrm{L}}/\left(D_0{\mathrm{\Gamma }}^{1/2}\right)$, with $D_0$ the self-diffusion coefficient at infinite dilution and $D_{\mathrm{L}}$ the long-time self-diffusion coefficient. Our results thus show that, although HI affect the short-time self-diffusion, for a quasi-two-dimensional system with $1/r^3$ long-ranged DI, the reduced quantity $D_{\mathrm{L}}^{★}$ is effectively not affected by HI. Interestingly, this is in agreement with prior work on quasi-two-dimensional colloidal hard spheres.

When a water drop impinges on a flat superhydrophobic surface, it bounces off the surface after a certain dwelling time, which is determined by the Rayleigh inertial-capillary timescale. Recent works have demonstrated that this dwelling time (i.e., contact time) is modified on curved superhydrophobic surfaces, as the drop asymmetrically spreads over the surface. However, the contact time on the curved surfaces still remains poorly understood, while no successful physical model for the contact time has been proposed. Here, we propose that the asymmetric spreading on the curved surface is driven by either the Coanda effect or inertia depending on the ratio of the drop diameter to the curvature diameter. Then, based on scaling analysis, we develop the contact time model that successfully predicts the contact time measured under a wide range of experiment conditions such as different impact velocities and curvature diameters. We believe that our results illuminate the underlying mechanism for the asymmetric spreading over the curved surface, while the proposed contact time model can be utilized for the design of superhydrophobic surfaces for various thermal applications, where the thermal exchange between the surface and the water drop occurs via a direct physical contact.

Uptake of liquid drops into capillary tubes has been experimentally studied and quantitatively analyzed. In experiments, drops of water and aqueous glycerol $(\le 50$ wt %) were drawn into cylindrical borosilicate glass and quartz tubes with an inner diameter of 0.50–0.75 mm. The meniscus height rise was measured using high-speed images captured at 4000 frames per second, and results within a conservatively defined inertial regime indicate constant uptake velocity. An increase in the inertial velocity with drop curvature was observed due to increasing Laplace pressure in the drop, as drop sizes were comparable to the width of the capillary tubes. Measured velocities were slower than predicted by a purely inertial-capillary model and best described by introducing a contact line friction, consistent with the observed variability and viscosity dependence of the results. Mean friction coefficients in borosilicate capillaries ranged from $169\pm 1$ for 50 wt % glycerol drops to $218\pm 1$ for water drops. Peaks in the instantaneous Laplace pressure caused by surface oscillations were also measured. Correlations with uptake velocity were qualitatively apparent, with a delay between peaks of similar magnitude to the inertial-capillary oscillation time.

Nonadditive Tsallis $q$-statistics has successfully been applied for a plethora of systems in natural sciences and other branches of knowledge. Nevertheless, its foundations have been severely criticized by some authors based on the standard additive Boltzmann-Gibbs approach, thereby remaining a quite controversial subject. In order to clarify some polemical concepts, the distribution function for an ideal gas with a finite number of point particles and its $q$-index are analytically determined. The two-particle correlation function is also derived. The degree of correlation diminishes continuously with the growth of the number of particles. The ideal finite gas system is usually correlated, becomes less correlated when the number of particles grows, and is finally fully uncorrelated when the molecular chaos regime is reached. It is also advocated that both approaches can be confronted through a careful kinetic spectroscopic experiment. The analytical results derived here suggest that Tsallis $q$-statistics may play a physical role more fundamental than usually discussed in the literature.