Exactly solvable models that exhibit quantum signatures of classical chaos are both rare as well as important—more so in view of the fact that the mechanisms for ergodic behavior and thermalization in isolated quantum systems and its connections to nonintegrability are under active investigation. In this work, we study quantum systems of few qubits collectively modeled as a kicked top, a textbook example of quantum chaos. In particular, we show that the three- and four-qubit cases are exactly solvable and yet, interestingly, can display signatures of ergodicity and thermalization. Deriving analytical expressions for entanglement entropy and concurrence, we see agreement in certain parameter regimes between long-time average values and ensemble averages of random states with permutation symmetry. Comparing with results using the data of a recent transmons-based experiment realizing the three-qubit case, we find agreement for short times, including a peculiar steplike behavior in correlations of some states. In the case of four qubits we point to a precursor of dynamical tunneling between what in the classical limit would be two stable islands. Numerical results for larger number of qubits show the emergence of the classical limit including signatures of a bifurcation.

The nonideality of binary mixtures is often related to the nature of the interactions between both liquids and of the heterogeneity at the nanoscale-named microstructure. When one of the liquids is a hydrogen bonds former and the second is aprotic, the progressive diluting of the hydrogen-bonding network leads to a clustering and nanophases. By considering two mixtures, toluene-methanol and cyclohexane-methanol, the nonideality and its connection with the structure at the nanoscale and the intermolecular interactions are numerically investigated. Contrary to the toluene that is fully miscible in methanol, cyclohexane presents a high range of immiscibility which makes it a relevant system to study the nucleation (local segregation) and its propagation. In both mixtures, the deviation from the ideal behavior is observed. In the case of the toluene-methanol mixture, the initial hydrogen-bonding network corresponding to a homogenous structure is locally broken due to the favorable toluene-methanol interactions leading to the spatial heterogeneity at the origin of the nonideality. In the range of miscibility of the cyclohexane-methanol mixtures, the formation of hydrophobic nanophases of larger size is observed due to the unfavorable interactions between both components leading to a self-organizing of cyclohexane molecules. The immiscibility of cyclohexane and methanol are then correlated to the formation of nanophases and their propagation, which are also at the origin of the spatial heterogeneity. In the pure methanol, we highlight the disconnection between the clustering and the heterogeneity. We shed light on the fact that the prepeak observed in the structure factor is independent of the degree of heterogeneity, but is connected to the presence of cyclic clusters.

The mechanical behavior of athermal random fiber networks embedding particulate inclusions is studied in this work. Composites in which the filler size is comparable with the mean segment length of the network are considered. Inclusions are randomly distributed in the network at various volume fractions, and cases in which fibers are rigidly bonded to fillers and in which no such bonding is imposed are studied separately. In the presence of inclusions, the small strain modulus increases, while the ability of the network to strain stiffen decreases relative to the unfilled network case. The reinforcement induced by fillers is most pronounced in sparse networks of floppier filaments that deform in the bending-dominated mode in the unfilled state. As the unfilled network density or the bending stiffness of fibers increases, the effect of filling diminishes rapidly. Fillers lead to a transition from the soft, bending-dominated, to the stiffer, stretching-dominated, deformation mode of the network, a transition which is primarily responsible for the observed overall reinforcement. The confinement, i.e., the restriction on network kinematics imposed by fillers, causes this transition. These results provide a justification for the observed difference in reinforcement obtained in sparsely versus densely cross-linked networks at a given filling fraction and provide guidance for the further development of network-based materials.

We have advanced the energy and flux budget turbulence closure theory that takes into account a two-way coupling between internal gravity waves (IGWs) and the shear-free stably stratified turbulence. This theory is based on the budget equation for the total (kinetic plus potential) energy of IGWs, the budget equations for the kinetic and potential energies of fluid turbulence, and turbulent fluxes of potential temperature for waves and fluid flow. The waves emitted at a certain level propagate upward, and the losses of wave energy cause the production of turbulence energy. We demonstrate that due to the nonlinear effects more intensive waves produce more strong turbulence, and this, in turn, results in strong damping of IGWs. As a result, the penetration length of more intensive waves is shorter than that of less intensive IGWs. The anisotropy of the turbulence produced by less intensive IGWs is stronger than that caused by more intensive waves. The low-amplitude IGWs produce turbulence consisting up to 90% of turbulent potential energy. This resembles the properties of the observed high-altitude tropospheric strongly anisotropic (nearly two-dimensional) turbulence.

Intense short-wavelength pulses from free-electron lasers and high-harmonic-generation sources enable diffractive imaging of individual nanosized objects with a single x-ray laser shot. The enormous data sets with up to several million diffraction patterns present a severe problem for data analysis because of the high dimensionality of imaging data. Feature recognition and selection is a crucial step to reduce the dimensionality. Usually, custom-made algorithms are developed at a considerable effort to approximate the particular features connected to an individual specimen, but because they face different experimental conditions, these approaches do not generalize well. On the other hand, deep neural networks are the principal instrument for today's revolution in automated image recognition, a development that has not been adapted to its full potential for data analysis in science. We recently published [Langbehn et al., Phys. Rev. Lett. 121, 255301 (2018)] the application of a deep neural network as a feature extractor for wide-angle diffraction images of helium nanodroplets. Here we present the setup, our modifications, and the training process of the deep neural network for diffraction image classification and its systematic bench marking. We find that deep neural networks significantly outperform previous attempts for sorting and classifying complex diffraction patterns and are a significant improvement for the much-needed assistance during postprocessing of large amounts of experimental coherent diffraction imaging data.

From the phase field theory, we develop a lattice Boltzmann equation (LBE) method for $N$ ($N\ge 2$) immiscible incompressible fluids, and the Cahn-Hilliard equation, which could capture the interfaces between different phases, is also solved by LBE for an $N$-phase system. In this model, the interface force of $N$ immiscible incompressible fluids is incorporated by chemical potential form, and the fluid-fluid surface tensions could be directly calculated and independently tuned. Numerical simulations including two stationary droplets, spreading of a liquid lens with and without gravity and two immiscible liquid lenses, and phase separation are conducted to validate the present LBE, and numerical results show that the predictions by LBE agree well with the analytical solutions and other numerical results.

Oscillatory reaction-diffusion fronts are described analytically in a piecewise-linear approximation of the FitzHugh-Nagumo equations with linear cross-diffusion terms, which correspond to a pursuit-evasion situation. Fundamental dynamical regimes of front propagation into a stable and into an unstable state are studied, and the shape of the waves for both regimes is explored in detail. We find that oscillations in the wave profile may either be negligible due to rapid attenuation or noticeable if the damping is slow or vanishes. In the first case, we find fronts that display a monotonic profile of the kink type, whereas in the second case the oscillations give rise to fronts with wavy tails. Further, the oscillations may be damped with exponential decay or undamped so that a saw-shaped pattern forms. Finally, we observe an unexpected feature in the behavior of both types of the oscillatory waves: the coexistence of several fronts with different profile shapes and propagation speeds for the same parameter values of the model, i.e., a multifront regime of wave propagation.

The measurement of intracellular viscoelastic properties by Brillouin scattering is a rapidly developing field in biophysics and medicine. Here, the Brillouin spectroscopy is applied for a number of aqueous solutions of biorelevant molecules to reveal relations between the Brillouin line parameters (frequency and width) and viscosity or solute concentration. It is found that for the majority of the studied biorelevant molecules the solute concentration governs the Brillouin frequency in a universal manner. On the other hand, the relations between the macroscopic viscosity and Brillouin peak parameters are different for different solutes. We conclude that for biological fluids the viscosity evaluation from Brillouin data needs prior knowledge about the chemical composition. This result challenges the fidelity of the indirect experimental determinations of the cellular viscosity, when small molecule solutions are used for the calibration.

We describe a simple Monte Carlo simulation method to calculate the free-energy cost of localizing a single monomer of a polymer confined to a cavity. The localization position is chosen to be on the inside surface of the confining cavity. The method is applied to a freely jointed hard-sphere polymer chain confined to cavities of spherical and cubic geometries. In the latter case, we consider localization at a corner and at the center of a face of the confining cube. We consider cases of end-monomer localization both with and without tethering of the other end monomer to a point on the surface. We also examine localization of monomers at arbitrary positions along the contour of the polymer. We characterize the dependence of the free energy on the cavity size and shape, the localization position, and the polymer length. The quantitative trends can be understood using standard scaling arguments and use of a simple theoretical model. The results are relevant to those theories of polymer translocation that focus on the importance of the free-energy barrier as the translocation process requires an initial localization of a monomer to the position of a nanopore.

Directional drying of colloidal suspensions, experimentally observed to exhibit mechanical instabilities, is a nonequilibrium procedure that is susceptible to geometric confinement and the properties of colloidal particles. Here, we develop an advection-diffusion model to characterize the transport dynamics for unidirectional drying of a suspension consisting of charged particles in a confined Hele-Shaw cell. We consider the electrostatic interactions by means of the Poisson-Boltzmann cell approach with the viscous flow confined to the cell. By solving the nonequilibrium transport equations, we clarify how the multiple parameters, such as drying rate, confinement ratio, and the monovalent slat concentration, affect the transport dynamics of charged colloidal particles. We find that the drying front recedes into the cell with linear behavior, while the liquid-solid transition front recedes with power law behaviors. The faster evaporation rate creates a rapid formation of the drying front and produces a thinner transition layer. We show that confinement is equivalent to raising the effective concentration in the cell, and, accordingly, the drying front appears earlier and grows more rapidly. Under geometric confinement, a longer fully dried film is created while the total drying time is shortened. Moreover, we have theoretically illustrated that low salt loadings cause a large collective diffusivity of charged colloidal particles, which results in a colloidal network by aggregation. Thus, the drying behavior alters dramatically as salt loadings decrease, since the resulting compacted clusters of charged particles eventually convert the suspension into a gel-like material instead of a simple fluid. Our model is consistent with the current experiments and provides a simple insight for applications in directional solidification and microfluidics.

We calculate the Thomson scattering cross section in a nonrelativistic, magnetized, high-density plasma—in a regime where collective excitations can be described by magnetohydrodynamics. We show that, in addition to cyclotron resonances and an elastic peak, the cross section exhibits two pairs of peaks associated with slow and fast magnetosonic waves; by contrast, the cross section arising in pure hydrodynamics possesses just a single pair of Brillouin peaks. Both the position and the width of these magnetosonic-wave peaks depend on the ambient magnetic field and temperature, as well as transport and thermodynamic coefficients, and so can therefore serve as a diagnostic tool for plasma properties that are otherwise challenging to measure.

Near-field thermal emission can be engineered by using periodic arrays of subwavelength emitters. The array thermal emission is dependent on the shape, size, and material properties of the individual elements as well as the period of the array. Designing periodic arrays with desired properties requires models that relate the array geometry and material properties to the near-field thermal emission. In this study, a periodic method is presented for modeling two-dimensional periodic arrays of subwavelength emitters. This technique only requires discretizing one period of the array, and thus is computationally beneficial. In this method, the energy density emitted by the array is expressed in terms of the array's Green's functions. The array Green's functions are found using the discrete dipole approximation in a periodic manner by expressing a single point source as a series of periodic arrays of phase-shifted point sources. The presented method can be employed for modeling periodic arrays made of inhomogeneous and complex-shape emitters with nonuniform temperature distribution. The proposed technique is verified against the nonperiodic thermal discrete-dipole-approximation simulations, and it is demonstrated that this method can serve as a versatile and reliable tool for studying near-field thermal emission by periodic arrays.

We have constructed a fitness parameter, characterizing the intrinsic attractiveness for patents to be cited, from attributes of the associated inventions known at the time a patent is granted. This exogenously obtained fitness is shown to determine the temporal growth of the citation network in conjunction with mechanisms of preferential attachment and obsolescence-induced aging that operate without reference to characteristics of individual patents. Our study opens a window to understanding quantitatively the interplay of the rich-gets-richer and fit-gets-richer paradigms that have been suggested to govern the growth dynamics of real-world complex networks.

Spatial many-species predator-prey systems have been shown to yield very rich space-time patterns. This observation begs the question whether there exist universal mechanisms for generating this type of emerging complex patterns in nonequilibrium systems. In this work we investigate the possibility of dynamically generated hierarchies in predator-prey systems. We analyze a nine-species model with competing interactions and show that the studied situation results in the spontaneous formation of spirals within spirals. The parameter dependence of these intriguing nested spirals is elucidated. This is achieved through the numerical investigation of various quantities (correlation lengths, densities of empty sites, Fourier analysis of species densities, interface fluctuations) that allows us to gain a rather complete understanding of the spatial arrangements and the temporal evolution of the system. A possible generalization of the interaction scheme yielding dynamically generated hierarchies is discussed. As cyclic interactions occur spontaneously in systems with competing strategies, the mechanism discussed in this work should contribute to our understanding of various social and biological systems.

In this work, the short-time dynamics of simple liquid is explored both analytically and numerically with the focus on the interplay between the density fluctuations in a volume surrounding a chosen particle and its random walk motion. The particles interact via the Lennard-Jones potential with parameters corresponding to liquid argon. For large times, analytical calculations based on the fluctuation theory provides an explicit expression reproducing isothermal change of the self-diffusion coefficient in liquid argon corresponding to the experimental data. These results lead to the conclusion that such behavior is based on the reduced mobility of particles reflected in their density fluctuations that can be equivalently achieved in the cases of either low temperatures and pressures (supercooling) or moderate temperatures and high pressures (overdamping).

The Mori-Zwanzig projection operator formalism is a powerful method for the derivation of mesoscopic and macroscopic theories based on known microscopic equations of motion. It has applications in a large number of areas including fluid mechanics, solid-state theory, spin relaxation theory, and particle physics. In its present form, however, the formalism cannot be directly applied to systems with time-dependent Hamiltonians. Such systems are relevant in many scenarios such as driven soft matter or nuclear magnetic resonance. In this article we derive a generalization of the present Mori-Zwanzig formalism that is able to treat also time-dependent Hamiltonians. The extended formalism can be applied to classical and quantum systems, close to and far from thermodynamic equilibrium, and even in the case of explicitly-time-dependent observables. Moreover, we develop a variety of approximation techniques that enhance the practical applicability of our formalism. Generalizations and approximations are developed for both equations of motion and correlation functions. Our formalism is demonstrated for the important case of spin relaxation in a time-dependent external magnetic field. The Bloch equations are derived together with microscopic expressions for the relaxation times.

Complex physical systems are unavoidably subjected to external environments not accounted for in the set of differential equations that models them. The resulting perturbations are standardly represented by noise terms. If these terms are large enough, they can push the system from an initial stable equilibrium point, over a nearby saddle point, outside of the basin of attraction of the stable point. Except in some specific cases, the distance between these two points is not known analytically. Focusing on Kuramoto-like models and under simple assumptions on this distance, we derive conditions under which such noise terms perturb the dynamics strongly enough that they lead to stochastic escape from the initial basin of attraction. We numerically confirm the validity of that criterion for coupled oscillators on four very different complex networks. We find in particular that, quite counterintuitively, systems with inertia leave their initial basin faster than or at the same time as systems without inertia, except for strong white-noise perturbations.

This study investigates motion in a crowd of pedestrians walking at different speeds. Three pedestrian groups are considered (slow walkers, normal walkers, and fast walkers), and we design the experimental condition by mixing the normal walkers with either the slow or the fast walkers to create flows with different speed compositions. All the walkers in this experiment were instructed to walk along a circular course unidirectionally. Fundamental diagrams and multiple regression analysis show that the speed at which a particular pedestrian walks is determined by both the local density and the speed at which the surrounding pedestrians are walking. We also find that the spontaneous lane formation, that occurs in bidirectional flow, does not occur in flow in which the speed is heterogeneous, thereby resulting in a spatial density distribution with large variance. This corresponds to pedestrian clustering, which reduces both the mean speed and the flow rate.

We study a special variant of the noise-induced transition between spiking and bursting regimes associated with the blue sky catastrophe bifurcation in the Hindmarsh-Rose neuron model. We show that in the parameter region close to the bifurcation value, where the only attractor of the system is the limit cycle of tonic spiking type, noise can transform the spiking oscillatory regime to the bursting one. This phenomenon is studied by means of power spectral density and interspike intervals statistics. We show that noise shifts the bifurcation value, so that bursting activity can be observed for a wider parameter range. Moreover, we reveal that the stochastic spiking-bursting transitions in this system are accompanied by the change in sign of the Lyapunov exponent. We perform a detailed quantitative analysis of these phenomena with an approach that uses a concept of the stochastic sensitivity function, the confidence domains method, and Mahalanobis metrics.

Spiral waves have been observed in a variety of physical, chemical, and biological systems. They play a major role in cardiac arrhythmias, including fibrillation, where the observed irregular activation patterns are generally thought to arise from the continuous breakup of multiple unstable spiral waves. Using spatially extended simulations of different electrophysiological models of cardiac tissue, we show that a single spiral wave in the presence of heterogeneities can display chaotic tip trajectories, consistent with fibrillation. We also show that the simulated spiral tip dynamics, including chaotic trajectories, can be captured by a simple particle model which only describes the dynamics of the spiral tip. This shows that spiral wave breakup, or interactions with other waves, are not necessary to initiate chaos in spiral waves.