Recent studies suggest that unstable, nonchaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this article, we present a combined experimental and numerical study exploring the dynamical role of unstable equilibrium solutions and their invariant manifolds in a weakly turbulent, electromagnetically driven, shallow fluid layer. Identifying instants when turbulent evolution slows down, we compute 31 unstable equilibria of a realistic two-dimensional model of the flow. We establish the dynamical relevance of these unstable equilibria by showing that they are closely visited by the turbulent flow. We also establish the dynamical relevance of unstable manifolds by verifying that they are shadowed by turbulent trajectories departing from the neighborhoods of unstable equilibria over large distances in state space.

The effect of a soluble surfactant on the linear stability of layered two-phase Poiseuille flows through soft-gel-coated parallel walls is studied in this paper. The focus is on determining the effect of the elastohydrodynamic coupling between the fluids and the soft-gel layers on the various flow instabilities. The fluids are assumed Newtonian and incompressible, while the soft gels are modeled as linear viscoelastic solids. The effect of a soluble surfactant on the different instabilities is specifically investigated. The soft-gel-coated plates are maintained at two different solute concentrations. The dynamics of the soluble surfactant in the fluids is captured using a species transport equation. A linear stability analysis is carried out to identify different instabilities in the system. The linearized governing equations are solved numerically using a Chebyshev spectral Collocation technique. The effect of deformability of the soft gels on three distinct instability modes, (a) a liquid-liquid long-wave mode, (b) a liquid-liquid short-wave mode, and (c) a liquid-liquid Marangoni short-wave mode, is analyzed. An analytical expression for the growth rate is obtained in the long-wave length limit using an asymptotic analysis. From the long-wave analysis a stability map is obtained, in which dominant effects in different regions are identified. The Marangoni stresses can either stabilize or destabilize the interfacial instability depending on the direction of mass transfer. They have a predominantly stabilizing effect on the interfacial instability when the mass transfer is from the more viscous broader fluid to the less viscous thinner fluid. Placing a gel closer to the more viscous fluid has a stabilizing effect on this instability. The Marangoni stresses and soft-gel layers can have opposing effects on the stability of the long-wave mode. The dominant of these two opposing effects is determined by the prevailing parameters. Insights into the dominant physical causes of different instabilities are presented.

Asymmetric implosion of inertial confinement fusion capsules is known, both experimentally and computationally, to reduce thermonuclear performance. This work shows that low-mode asymmetries degrade performance as a result of a decrease in the hydrodynamic disassembly time of the hot-spot core, which scales with the minimum dimension of the hot spot. The asymmetric shape of a hot spot results in decreased temperatures and areal densities and allows more alpha particles to escape, relative to an ideal spherical implosion, thus reducing alpha-energy deposition in the hot spot. Here, we extend previous ignition theory to include the hot-spot shape and quantify the effects of implosion asymmetry on both the ignition criterion and the capsule performance. The ignition criterion becomes more stringent with increasing deformation of the hot spot. The new theoretical results are validated by comparison with existing experimental data obtained at the National Ignition Facility. The shape effects on thermonuclear performance are relatively more noticeable for capsules having self-heating and high yields. The degradation of thermonuclear burn can be as high as 45% for shots with a yield lower than $2\times {10}^{15}$ and less than 30% for shots with a higher yield.

The aim of this study is to introduce a general approach to implement curved boundaries in lattice Boltzmann simulations. The main idea is to determine boundary values by extrapolating macroscopic properties from some reference points inside the computational domain. The introduced approach is based on a unified extrapolation equation that can be employed for any macroscopic value (flow and nonflow properties) in arbitrary two- and three-dimensional geometries. In the case of nonflow simulations, the present treatment can easily apply Dirichlet and Neumann boundary conditions. By introducing a point cloud description of geometry, the new treatment can handle any complex geometry that is modeled by a CAD program. The application of the new treatment is also extended to moving boundaries, by developing a novel force calculation method. The proposed boundary treatment is tested against several well-established problems and the order of accuracy of solutions is evaluated. Numerical results show that the present treatment is of second-order accuracy with respect to the grid spacing in flow simulations, and it leads to a significant enhancement in nonflow simulations as well.

This work serves as an important extension of previous work on cavitation simulation [Sukop and Or, Phys. Rev. E 71, 046703 (2005)]. A modified Shan-Chen single-component multiphase lattice Boltzmann method is used to simulate two different heterogeneous cavitation nucleation mechanisms, the free gas bubble model and the crevice nucleation model. Improvements include the use of a real-gas equation of state, a redefined effective mass function, and the exact difference method forcing scheme. As a result, much larger density ratios, better thermodynamic consistency, and improved numerical accuracy are achieved. In addition, the crevice nucleation model is numerically investigated using the lattice Boltzmann method. The simulations show excellent qualitative and quantitative agreement with the heterogeneous nucleation theories.

Self-assembly processes are widespread in nature and lie at the heart of many biological and physical phenomena. The characteristics of self-assembly building blocks determine the structures that they form. Two crucial properties are the determinism and boundedness of the self-assembly. The former tells us whether the same set of building blocks always generates the same structure, and the latter whether it grows indefinitely. These properties are highly relevant in the context of protein structures, as the difference between deterministic protein self-assembly and nondeterministic protein aggregation is central to a number of diseases. Here we introduce a graph theoretical approach that can determine the determinism and boundedness for several geometries and dimensionalities of self-assembly more accurately and quickly than conventional methods. We apply this methodology to a previously studied lattice self-assembly model and discuss generalizations to a wide range of other self-assembling systems.

Diffusion of information in social networks has drawn extensive attention from various scientific communities, with many contagion models proposed to explain related phenomena. In this paper, we present a simple contagion mechanism, in which a node will change its state immediately if it is exposed to the diffusive information. By considering two types of nodes (smart and normal) and two kinds of information (true and false), we study analytically and numerically how smart nodes influence the spreading of information, which leads to information filtering. We find that for randomly distributed smart nodes, the spreading dynamics over random networks with Poisson degree distribution and power-law degree distribution (with relatively small cutoffs) can both be described by the same approximate mean-field equation. Increasing the heterogeneity of the network may elicit more deviations, but not much. Moreover, we demonstrate that more smart nodes make the filtering effect on a random network better. Finally, we study the efficacy of different strategies of selecting smart nodes for information filtering.

According to the evolutionary game theory principle, a strategy representing a higher payoff can spread among competitors. But there are cases when a player consistently overestimates or underestimates her own payoff, which undermines proper comparison. Interestingly, both underconfident and overconfident individuals are capable of elevating the cooperation level significantly. While former players stimulate a local coordination of strategies, the presence of overconfident individuals enhances the spatial reciprocity mechanism. In both cases the propagations of competing strategies are influenced in a biased way resulting in a cooperation supporting environment. These effects are strongly related to the nonlinear character of invasion probabilities which is a common and frequently observed feature of microscopic dynamics.

Even though viscosity is one of the fundamental properties of liquids, its microscopic origin is not fully understood. We determined the spatial and temporal correlation of molecular motions of water near room temperature and its temperature variation on a picosecond timescale and a subnanometer spatial scale, through high-resolution inelastic x-ray scattering measurement. The results, expressed in terms of the time-dependent pair correlation function called the Van Hove function, show that the timescale of the decay of the molecular correlation is directly related to the Maxwell relaxation time near room temperature, which is proportional to viscosity. This conclusion validates our earlier finding that the topological changes in atomic or molecular connectivity are the origin of viscosity in liquids.

In the present work, we have studied the liquid crystalline properties of a luminescent molecule, which presents smectic mesophases, using the emission ellipsometry technique. A methodology with photoselection of the excitation light to improve the experiment is presented. An empirical model is proposed to explain the experimental results. The Stokes parameters of the emitted light allowed the correlation of changes in the polarization degree, ellipticity angle, and rotation angle with phase transitions.

We study the effect of grain polydispersity on the bulk modulus in noncohesive two-dimensional granular solids. Molecular dynamics simulations in two dimensions are used to describe polydisperse samples that reach a stationary limit after a number of hysteresis cycles. For stationary samples, we obtain that the packing with the highest polydispersity has the lowest bulk modulus. We compute the correlation between normal and tangential forces with grain size using the concept of branch vector or contact length. Classifying the contact lengths and forces by their size compared to the average length and average force, respectively, we find that strong normal and tangential forces are carried by large contact lengths, generally composed of at least one large grain. This behavior is more dominant as polydispersity increases, making force networks more anisotropic and removing the support, from small grains, in the loading direction thus reducing the bulk modulus of the granular pack. Our results for two dimensions describe qualitatively the results of three-dimensional experiments.

Recently, singular value decomposition (SVD) was applied to standard Gaussian ensembles of random-matrix theory to determine the scale invariance in spectral fluctuations without performing any unfolding procedure. Here, SVD is applied directly to the $\beta$-Hermite ensemble and to a sparse matrix ensemble, decomposing the corresponding spectra in trend and fluctuation modes. In correspondence with known results, we obtain that fluctuation modes exhibit a crossover between soft and rigid behavior. In this way, possible artifacts introduced applying unfolding techniques are avoided. By using the trend modes, we perform data-adaptive unfolding, and we calculate traditional spectral fluctuation measures. Additionally, ensemble-averaged and individual-spectrum averaged statistics are calculated consistently within the same basis of normal modes.

Being an exemplary model of open quantum system, the spin-boson model is widely employed in theoretical and experimental studies. Beyond the weak coupling limit, the spin-boson dynamics can be described by a time-nonlocal generalized master equation with a memory kernel accounting for the dissipative effects induced by the bosonic environment. When the spin is in addition modulated by an external time-periodic electromagnetic field, the interplay between dissipation and forcing provides a spectrum of nontrivial asymptotic states, especially so in the regime of nonlinear response. Here we implement the method for evaluating the dissipative Floquet dynamics of non-Markovian systems introduced in Magazzù et al. [Phys. Rev. A 96, 042103 (2017)] to obtain these nonequilibrium asymptotic states.

The Kuramoto model is a paradigmatic tool for studying the dynamics of collective behavior in large ensembles of coupled dynamical systems. Over the past decade a great deal of progress has been made in analytical descriptions of the macroscopic dynamics of the Kuramoto model, facilitated by the discovery of Ott and Antonsen's dimensionality reduction method. However, the vast majority of these works relies on a critical assumption where the oscillators' natural frequencies are drawn from a Cauchy, or Lorentzian, distribution, which allows for a convenient closure of the evolution equations from the dimensionality reduction. In this paper we investigate the low-dimensional dynamics that emerge from a broader family of natural frequency distributions, in particular, a family of rational distribution functions. We show that, as the polynomials that characterize the frequency distribution increase in order, the low-dimensional evolution equations become more complicated, but nonetheless the system dynamics remain simple, displaying a transition from incoherence to partial synchronization at a critical coupling strength. Using the low-dimensional equations we analytically calculate the critical coupling strength corresponding to the onset of synchronization and investigate the scaling properties of the order parameter near the onset of synchronization. These results agree with calculations from Kuramoto's original self-consistency framework, but we emphasize that the low-dimensional equations approach used here allows for a true stability analysis categorizing the bifurcations.

We formulate the problem of confined Lévy flight on a comb. The comb represents a sawtoothlike potential field $V\left(x\right)$, with the asymmetric teeth favoring net transport in a preferred direction. The shape effect is modeled as a power-law dependence $V\left(x\right)\propto {\left|\mathrm{\Delta }x\right|}^n$ within the sawtooth period, followed by an abrupt drop-off to zero, after which the initial power-law dependence is reset. It is found that the Lévy flights will be confined in the sense of generalized central limit theorem if (i) the spacing between the teeth is sufficiently broad, and (ii) $n>4-\mu$, where $\mu$ is the fractal dimension of the flights. In particular, for the Cauchy flights ($\mu =1$), $n>3$. The study is motivated by recent observations of localization-delocalization of transport avalanches in banded flows in the Tore Supra tokamak and is intended to devise a theory basis to explain the observed phenomenology.

Two node variables determine the evolution of cascades in random networks: a node's degree and threshold. Correlations between both fundamentally change the robustness of a network, yet they are disregarded in standard analytic methods as local tree or heterogeneous mean field approximations, since order statistics are difficult to capture analytically because of their combinatorial nature. We show how they become tractable in the thermodynamic limit of infinite network size. This enables the analytic description of node attacks that are characterized by threshold allocations based on node degree. Using two examples, we discuss possible implications of irregular phase transitions and different speeds of cascade evolution for the control of cascades.

Bipartite (two-mode) networks are important in the analysis of social and economic systems as they explicitly show conceptual links between different types of entities. However, applications of such networks often work with a projected (one-mode) version of the original bipartite network. The topology of the projected network, and the dynamics that take place on it, are highly dependent on the degree distributions of the two different node types from the original bipartite structure. To date, the interaction between the degree distributions of bipartite networks and their one-mode projections is well understood for only a few cases, or for networks that satisfy a restrictive set of assumptions. Here we show a broader analysis in order to fill the gap left by previous studies. We use the formalism of generating functions to prove that the degree distributions of both node types in the original bipartite network affect the degree distribution in the projected version. To support our analysis, we simulate several types of synthetic bipartite networks using a configuration model where node degrees are assigned from specific probability distributions, ranging from peaked to heavy-tailed distributions. Our findings show that when projecting a bipartite network onto a particular set of nodes, the degree distribution for the resulting one-mode network follows the distribution of the nodes being projected on to, but only so long as the degree distribution for the opposite set of nodes does not have a heavier tail. Furthermore, we show that bipartite degree distributions are not the only feature driving topology formation of projected networks, in contrast to what is commonly described in the literature.

Frequency upconversion of an electromagnetic wave can occur in ionized plasma with decreasing electric permittivity and in split-ring resonator-structure metamaterials with decreasing magnetic permeability. We develop a general theory to describe the evolution of the wave frequency, amplitude, and energy density in homogeneous media with a temporally decreasing refractive index. We find that upconversion of the wave frequency is necessarily accompanied by partitioning of the wave energy into low-frequency modes, which sets an upper limit on the energy conversion efficiency. The efficiency limits are obtained for both varying permittivity and varying permeability.

We develop a theoretical approach to compute the conditioned spectral density of $N\times N$ noninvariant random matrices in the limit $N\to \infty$. This large deviation observable, defined as the eigenvalue distribution conditioned to have a fixed fraction $k$ of eigenvalues smaller than $x\in \mathbb{R}$, provides the spectrum of random matrix samples that deviate atypically from the average behavior. We apply our theory to sparse random matrices and unveil strikingly different and generic properties, namely, (i) their conditioned spectral density has compact support, (ii) it does not experience any abrupt transition for $k$ around its typical value, and (iii) its eigenvalues do not accumulate at $x$. Moreover, our work points towards other types of transitions in the conditioned spectral density for values of $k$ away from its typical value. These properties follow from the weak or absent eigenvalue repulsion in sparse ensembles and they are in sharp contrast to those displayed by classic or rotationally invariant random matrices. The exactness of our theoretical findings are confirmed through numerical diagonalization of finite random matrices.