Structure and dynamics at soft-matter interfaces play an important role in nature and technical applications. Optical single-molecule investigations are noninvasive and capable to reveal heterogeneities at the nanoscale. In this work we develop an autocorrelation function (ACF) approach to retrieve tracer diffusion parameters obtained from fluorescence correlation spectroscopy (FCS) experiments in thin liquid films at reflecting substrates. This approach then is used to investigate structure and dynamics in 100-nm-thick 8CB liquid crystal films on silicon wafers with five different oxide thicknesses. We find a different extension of the structural reorientation of 8CB at the solid-liquid interface for thin and for thick oxide. For the thin oxides, the perylenediimide tracer diffusion dynamics in general agrees with the hydrodynamic modeling using no-slip boundary conditions with only a small deviation close to the substrate, while a considerably stronger decrease of the interfacial tracer diffusion is found for the thick oxides.

This study deals with the elastohydrodynamic coupling that occurs in the flow of a liquid layer down an inclined plane lined with a deformable solid bilayer and its consequences on the stability of the free surface of the liquid layer. The fluid is Newtonian and incompressible, while the linear elastic constitutive relation has been considered for the deformable solid bilayer, and the densities of the fluid and the two solids are kept equal. A temporal linear stability analysis is carried out for this coupled solid-fluid system. A long-wave asymptotic analysis is employed to obtain an analytical expression for the complex wavespeed in the low wave-number regime, and a numerical shooting method is used to solve the coupled set of governing differential equations in order to obtain the stability criterion for arbitrary values of the wave number. In a previous work on plane Couette flow past an elastic bilayer, Neelmegam et al. [Phys. Rev. E 90, 043004 (2014)] showed that the instability of the flow can be significantly influenced by the nature of the solid layer, which is adjacent to the liquid layer. In stark contrast, for free-surface flow past a bilayer, our long-wave asymptotic analysis demonstrates that the stability of the free-surface mode is insensitive to the nature of the solid adjacent to the liquid layer. Instead, it is the effective shear modulus of the bilayer $G_{\text{eff}}$ (given by $H/G_{\text{eff}}=H_1/G_1+H_2/G_2$, where $H=H_1+H_2$ is the total thickness of the solid bilayer, $H_1$ and $H_2$ are the thicknesses of the two solid layers, and $G_1$ and $G_2$ are the shear moduli of the two solid layers) that determines the stability of the free surface in the long-wave limit. We show that for a given Reynolds number, the free-surface instability is stabilized when $G_{\text{eff}}$ decreases below a critical value. At finite wave numbers, our numerical solution indicates that additional instabilities at the free surface and the liquid-solid interface can be induced by wall deformability and inertia in the fluid and solid. Interestingly, the onset of these additional instabilities is sensitive to the relative placements of the two solid layers comprising the bilayer. We show that it is possible to delay the onset of these additional instabilities, while still suppressing the free-surface instability, by manipulating the ratio of the shear moduli and the thicknesses of the two solid layers in the bilayer. At moderate Reynolds number and finite wave number, we demonstrate that an exchange of modes occurs between the gas-liquid and liquid-solid interfacial modes as the solid bilayer becomes more deformable. We demonstrate further that dissipative effects in the individual solid layers have an important bearing on the stability of the system, and they could also be exploited in suppressing the instability. This study thus shows that the ability to passively manipulate and control interfacial instabilities increases substantially with the use of solid bilayers.

The effects of an initial perturbation on Richtmyer-Meshkov instability are numerically studied by simulating the process of incident shock ($\mathrm{Ma}=1.27$) impacting different groups of initial multimode cosine interfaces formed by different amplitudes in initially nonuniform flows whose density is a Gaussian function. The numerical results indicate that the evolution of the interface with a large initial amplitude in a low-density nonuniform area grows fastest, while that with a small initial amplitude in a high-density nonuniform area grows slowly. Further analysis of vorticity and circulation illustrates these phenomena. The interface with a large initial amplitude in a low-density zone possesses a larger density gradient, which results in a larger amount of vorticity and circulation, leading to the fast-changing evolution of the interface. Distinctive evolution mechanisms of Richtmyer-Meshkov instability between the nonuniform flows and the uniform flows are analyzed in detail.

Plume dilution and transverse mixing can be considerably enhanced by helical flow occurring in three-dimensional heterogeneous anisotropic porous media. In this study, we perform tracer experiments in a fully three-dimensional flow-through chamber to investigate the effects of helical flow on plume spiraling and deformation, as well as on its dilution. Porous media were packed in angled stripes of materials with different grain sizes to create blocks with macroscopically anisotropic hydraulic conductivity, which caused helical flows. Steady-state transport experiments were carried out by continuously injecting dye tracers at different inlet ports. High-resolution measurements of concentration and flow rates were performed at 49 outlet ports. These measurements allowed quantifying the spreading and dilution of the solute plumes at the outlet cross section. Direct evidence of plume spiraling and visual proof of helical flow was obtained by freezing and slicing the porous media at different cross sections and observing the dye-tracer distribution. We simulated flow and transport to interpret our experimental observations and investigate the effects of helical flow on mixing-controlled reactive transport. The simulation results were evaluated using metrics of reactive mixing such as the critical dilution index and the length of continuously injected steady-state plumes. The results show considerable reaction enhancement, quantified by the remarkable decrease of reactive plume lengths (up to four times) in helical flows compared to analogous scenarios in uniform flows.

We have performed spectrally resolved x-ray scattering measurements on highly compressed polystyrene at pressures of several tens of TPa (100 Mbar) created by spherically convergent shocks at the National Ignition Facility. Scattering data of line radiation at 9.0 keV were recorded from the dense plasma shortly after shock coalescence. Accounting for spatial gradients, opacity effects, and source broadening, we demonstrate the sensitivity of the elastic scattering component to carbon $K$-shell ionization while at the same time constraining the temperature of the dense plasma. For six times compressed polystyrene, we find an average temperature of 86 eV and carbon ionization state of 4.9, indicating that widely used ionization models need revision in order to be suitable for the extreme states of matter tested in our experiment.

Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering, and life sciences. In this work, we investigate the statistical properties of $d$-dimensional isotropic Poisson geometries by resorting to Monte Carlo simulation, with special emphasis on the case $d=3$. We first analyze the behavior of the key features of these stochastic geometries as a function of the dimension $d$ and the linear size $L$ of the domain. Then, we consider the case of Poisson binary mixtures, where the polyhedra are assigned two labels with complementary probabilities. For this latter class of random geometries, we numerically characterize the percolation threshold, the strength of the percolating cluster, and the average cluster size.

The residence time of a branching Brownian process is the amount of time that the mother particle and all its descendants spend inside a domain. Using the Feynman-Kac formalism, we derive the residence-time equation as well as the equations for its moments for a branching diffusion process with an arbitrary number of descendants. This general approach is illustrated with simple examples in free space and in confined geometries where explicit formulas for the moments are obtained within the long time limit. In particular, we study in detail the influence of the branching mechanism on those moments. The present approach can also be applied to investigate other additive functionals of branching Brownian process.

Stochastic differential equations describe well many physical, biological, and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and classify complex dynamical systems is proposed within a Bayesian framework. To this end, we develop a dynamic system classifier (DSC). The DSC first abstracts training data of a system in terms of time-dependent coefficients of the descriptive stochastic differential equation. Thereby the DSC identifies unique correlation structures within the training data. For definiteness we restrict the presentation of the DSC to oscillation processes with a time-dependent frequency $\omega \left(t\right)$ and damping factor $\gamma \left(t\right)$. Although real systems might be more complex, this simple oscillator captures many characteristic features. The $\omega$ and $\gamma$ time lines represent the abstract system characterization and permit the construction of efficient signal classifiers. Numerical experiments show that such classifiers perform well even in the low signal-to-noise regime.

An aging population is bringing new challenges to the management of escape routes and facility design in many countries. This paper investigates pedestrian movement properties of crowd with different age compositions. Three pedestrian groups are considered: young student group, old people group, and mixed group. It is found that traffic jams occur more frequently in mixed group due to the great differences of mobilities and self-adaptive abilities among pedestrians. The jams propagate backward with a velocity $0.4\mathrm{m}/\mathrm{s}$ for global density ${\rho }_g\approx 1.75{\text{m}}^{-1}$ and $0.3\mathrm{m}/\mathrm{s}$ for ${\rho }_g>2.3{\text{m}}^{-1}$. The fundamental diagrams of the three groups are obviously different from each other and cannot be unified into one diagram by direct nondimensionalization. Unlike previous studies, three linear regimes in mixed group but only two regimes in young student group are observed in the headway-velocity relation, which is also verified in the fundamental diagram. Different ages and mobilities of pedestrians in a crowd cause the heterogeneity of system and influence the properties of pedestrian dynamics significantly. It indicates that the density is not the only factor leading to jams in pedestrian traffic. The composition of crowd has to be considered in understanding pedestrian dynamics and facility design.

The recently introduced concept of dynamic communicability is a valuable tool for ranking the importance of nodes in a temporal network. Two metrics, broadcast score and receive score, were introduced to measure the centrality of a node with respect to a model of contagion based on time-respecting walks. This article examines the temporal and structural factors influencing these metrics by considering a versatile stochastic temporal network model. We analytically derive formulas to accurately predict the expectation of the broadcast and receive scores when one or more columns in a temporal edge-list are shuffled. These methods are then applied to two publicly available data sets and we quantify how much the centrality of each individual depends on structural or temporal influences. From our analysis, we highlight two practical contributions: a way to control for temporal variation when computing dynamic communicability and the conclusion that the broadcast and receive scores can, under a range of circumstances, be replaced by the row and column sums of the matrix exponential of a weighted adjacency matrix given by the data.

The effect of the statistical properties of light on the value of the photoinduced reaction of the biological objects, which differ in the morphological and physiological characteristics, the optical properties, and the size of cells, was studied. The fruit of apple trees, the pollen of cherries, the microcuttings of blackberries in vitro, and the spores and the mycelium of fungi were irradiated by quasimonochromatic light fluxes with identical energy parameters but different values of coherence length and radius of correlation. In all cases, the greatest stimulation effect occurred when the cells completely fit in the volume of the coherence of the field, while both temporal and spatial coherence have a significant and mathematically certain impact on the physiological activity of cells. It was concluded that not only the spectral, but also the statistical (coherent) properties of the acting light play an important role in the photoregulation process.

We consider well-known surface disclinations by cutting, joining, and folding pieces of paper card. The resulting shapes have a discrete, folded vertex whose geometry is described easily by Gauss's mapping, in particular, we can relate the degree of angular excess, or deficit, to the size of fold line rotations by the area enclosed by the vector diagram of these rotations. This is well known for the case of a so-called “d-cone” of zero angular deficit, and we formulate the same for a general disclination. This method allows us to observe kinematic properties in a meaningful way without needing to consider equilibrium. Importantly, the simple vector nature of our analysis shows that some disclinations are primitive; and that other types, such as d-cones, are amalgamations of them.

Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term accuracy and fidelity. For long-term simulations with high efficiency, explicit symplectic algorithms are desirable. However, it is generally believed that explicit symplectic algorithms are only available for sum-separable Hamiltonians, and this restriction limits the application of explicit symplectic algorithms to charged particle dynamics. To overcome this difficulty, we combine the familiar sum-split method and a generating function method to construct second- and third-order explicit symplectic algorithms for dynamics of charged particle. The generating function method is designed to generate explicit symplectic algorithms for product-separable Hamiltonian with form of $H(\mathbf{x},\mathbf{p})={\mathbf{p}}_{i}f\left(\mathbf{x}\right)$ or $H(\mathbf{x},\mathbf{p})={\mathbf{x}}_{i}g\left(\mathbf{p}\right)$. Applied to the simulations of charged particle dynamics, the explicit symplectic algorithms based on generating functions demonstrate superiorities in conservation and efficiency.

Nematic elastomers and glasses are solids that display spontaneous distortion under external stimuli. Recent advances in the synthesis of sheets with controlled heterogeneities have enabled their actuation into nontrivial shapes with unprecedented energy density. Thus, these have emerged as powerful candidates for soft actuators. To further this potential, we introduce the key metric constraint which governs shape-changing actuation in these sheets. We then highlight the richness of shapes amenable to this constraint through two broad classes of examples which we term nonisometric origami and lifted surfaces. Finally, we comment on the derivation of the metric constraint, which arises from energy minimization in the interplay of stretching, bending, and heterogeneity in these sheets.

Group-level behavior of particles undergoing a velocity-jump process with hard-sphere interactions is investigated. We derive $N$-particle transport equations that include the possibility of collisions between particles and apply different approximation techniques to get expressions for the dependence of the collective diffusion coefficient on the number of particles and their diameter. The derived approximations are compared with numerical results obtained from individual-based simulations. The theoretical results compare well with Monte Carlo simulations providing the excluded-volume fraction is small.

We investigate the emergence of different kinds of imperfectly synchronized states and chimera states in two interacting populations of nonlocally coupled Stuart-Landau oscillators. We find that the complete synchronization in population I and existence of solitary oscillators which escape from the synchronized group in population II lead to imperfectly synchronized states for sufficiently small values of nonisochronicity parameter. Interestingly, upon increasing the strength of this parameter further there occurs an onset of mixed imperfectly synchronized states where the solitary oscillators occur from both the populations. Synchronized oscillators from both the populations are locked to a common average frequency. In both cases of imperfectly synchronized states, synchronized oscillators exhibit periodic motion while the solitary oscillators are quasiperiodic in nature. In this region, for spatially prepared initial conditions, we can observe the mixed chimera states where the coexistence of synchronized and desynchronized oscillations occur from both the populations. On the other hand, imperfectly synchronized states are not always stable, and they can drift aperiodically due to instability caused by an increase of nonisochronicity parameter. We observe that these states are robust to the introduction of frequency mismatch between the two populations.

Bistability between attracting fixed points in neuronal networks has been hypothesized to underlie persistent activity observed in several cortical areas during working memory tasks. In network models this kind of bistability arises due to strong recurrent excitation, sufficient to generate a state of high activity created in a saddle-node (SN) bifurcation. On the other hand, canonical network models of excitatory and inhibitory neurons (E-I networks) robustly produce oscillatory states via a Hopf (H) bifurcation due to the E-I loop. This mechanism for generating oscillations has been invoked to explain the emergence of brain rhythms in the $\beta$ to $\gamma$ bands. Although both bistability and oscillatory activity have been intensively studied in network models, there has not been much focus on the coincidence of the two. Here we show that when oscillations emerge in E-I networks in the bistable regime, their phenomenology can be explained to a large extent by considering coincident SN and H bifurcations, known as a codimension two Takens-Bogdanov bifurcation. In particular, we find that such oscillations are not composed of a stable limit cycle, but rather are due to noise-driven oscillatory fluctuations. Furthermore, oscillations in the bistable regime can, in principle, have arbitrarily low frequency.

The temporal evolution of a plasma channel at the trail of a self-guided femtosecond laser pulse was studied experimentally and theoretically in air, nitrogen (with an admixture of ∼3% ${\mathrm{O}}_2$), and argon in a wide range of gas pressures (from 2 to 760 Torr). Measurements by means of transverse optical interferometry and pulsed terahertz scattering techniques showed that plasma density in air and nitrogen at atmospheric pressure reduces by an order of magnitude within 3–4 ns and that the decay rate decreases with decreasing pressure. The argon plasma did not decay within several nanoseconds for pressures of 50–760 Torr. We extended our theoretical model previously applied for atmospheric pressure air plasma to explain the plasma decay in the gases under study and to show that allowance for plasma channel expansion affects plasma decay at low pressures.

We investigate the stochastic thermodynamics of a two-particle Langevin system. Each particle is in contact with a heat bath at different temperatures $T_1$ and $T_2 \left(<T_1\right)$, respectively. Particles are trapped by a harmonic potential and driven by a linear external force. The system can act as an autonomous heat engine performing work against the external driving force. Linearity of the system enables us to examine thermodynamic properties of the engine analytically. We find that the efficiency of the engine at maximum power ${\eta }_{MP}$ is given by ${\eta }_{MP}=1-\sqrt{T_2/T_1}$. This universal form has been known as a characteristic of endoreversible heat engines. Our result extends the universal behavior of ${\eta }_{MP}$ to nonendoreversible engines. We also obtain the large deviation function of the probability distribution for the stochastic efficiency in the overdamped limit. The large deviation function takes the minimum value at macroscopic efficiency $\eta =\overline{\eta }$ and increases monotonically until it reaches plateaus when $\eta \le {\eta }_L$ and $\eta \ge {\eta }_R$ with model-dependent parameters ${\eta }_R$ and ${\eta }_L$.

We use a canonical quantization procedure to set up a quantum Fokker-Planck-Kramers equation that accounts for quantum dissipation in a thermal environment. The dissipation term is chosen to ensure that the thermodynamic equilibrium is described by the Gibbs state. An expression for the quantum entropy production that properly describes quantum systems in a nonequilibrium stationary state is also provided. The time-dependent solution is given for a quantum harmonic oscillator in contact with a heat bath. We also obtain the stationary solution for a system of two coupled harmonic oscillators in contact with reservoirs at distinct temperatures, from which we obtain the entropy production and the quantum thermal conductance.