We propose a continuum model to describe the molecular alignment in thin nematic shells. By contrast with previous accounts, the two-dimensional free energy, aimed at describing the physics of thin films of nematics deposited on curved substrates, is not postulated, but it is deduced from the conventional three-dimensional theories of nematic liquid crystals. Both the director and the order-tensor theories are taken into account. The so-obtained surface energies exhibit extra terms compared to earlier models. These terms reflect the coupling of the shell extrinsic curvature with the nematic order parameters. As expected, the shape of the shell plays a key role in the equilibrium configurations of nematics coating it.

The Kelvin probe measures surface electrical potential without making physical contact with the specimen. It relies on capacitive coupling between an oscillating metal tip that is normal to a specimen's surface. Kelvin probes have been increasingly used to study surface and electrical properties of metals and semiconductors and are capable of detecting material surface potentials with submillivolt resolution at a micrometer spatial scale. Its capability for measuring electrical potential without being confounded by electrode-specimen contact makes extending its use towards biological materials particularly appealing. However, the theoretical basis for applying the Kelvin probe to dielectric or partially conductive materials such as biological tissue has not been evaluated and remains unclear. This study develops the theoretical basis underlying Kelvin probe measurements in five theoretical materials: highly conductive, conductive dielectric with rapid charge relaxation, conductive dielectric with slow charge relaxation, perfect dielectric, and tissue with a bulk serial resistance. These theoretically derived equations are then computationally analyzed using parameters from both theoretical specimens and actual biomaterials—including wet skin, dry skin, cerebrospinal fluid, and tendon. Based on these analyses, a Kelvin probe performs in two distinct ways depending on the charge relaxation rates of the sample: The specimen is treated either as a perfect dielectric or as highly conductive material. Because of their rapid relaxation rate and increased permittivity biomaterials behave similarly to highly conductive materials, such as metal, when evaluated by the Kelvin probe. These results indicate that the Kelvin probe can be readily applied to studying the surface potential of biological tissue.

Variation in cardiac pacing cycles, as seen, for example, in heart rate variability, has been observed for decades. Contemporarily, various mathematical models have been constructed to investigate the electrical activity of paced cardiac cells. Yet there has not been a study of these cardiac models when there is variation in the pacing cycles such as noise. We present a method that uses the stochasticity of pacing cycles to determine approximate models of the dynamics of cardiac cells, and use these models to detect bifurcations to alternans.

We study a continuum model of overdamped self-propelled particles with aligning interactions in two dimensions. Combining analytical theory and computations, we map out the phase diagram for the parameter space covered by the model. We find that the system self-organizes into two robust structures in different regions of parameter space: solitary waves composed of ordered swarms moving through a low density disordered background, and stationary radially symmetric asters. The self-regulating nature of the flow yields phase separation, ubiquitous in this class of systems, and controls the formation of solitary waves. Self-propulsion and the associated active convection play a crucial role in aster formation.

Cooperative interactions between ion channels are known to exist, but have so far received relatively little attention in the study of excitable membranes. Based on bifurcation analysis and stochastic simulations of an extended Morris-Lecar model, we show that cooperativity and anticooperativity can modify the range of sustained firing and cell-intrinsic noise, induce multistability, and account for a number of experimental observations, including prolongation of action-potential duration. We hypothesize that channel interactions could be an efficient mechanism to regulate the activity of neurons or cardiac muscle cells.

The field theoretic renormalization group and operator product expansion are applied to the Kazantsev-Kraichnan kinematic model for the magnetohydrodynamic turbulence. The anomalous scaling emerges as a consequence of the existence of certain composite fields (“operators”) with negative dimensions. The anomalous exponents for the correlation functions of arbitrary order are calculated in the two-loop approximation (second order of the renormalization-group expansion), including the anisotropic sectors. The anomalous scaling and the hierarchy of anisotropic contributions become stronger due to those second-order contributions.

We report an experimental study on shearing a monolayer of monodisperse bubbles floating on liquid in a narrow-gap Couette device. The bubbles in such a “bubble raft” coalesce only if the shear rate exceeds a threshold value. This is in contrast to the conventional wisdom that bubbles and drops coalesce for gentler collisions, at shear rates below a critical value. Furthermore, the threshold shear rate increases with the bubble size and the viscosity of the suspending liquid, contravening reasoning based on capillary number. Through visualization and scaling arguments, we investigate several plausible mechanisms for the anomalous coalescence. None explains all aspects of the observations. The most promising model is one based on inertial forces that compress the bubbles radially inward and accelerate film drainage.

The propagation of circularly polarized electromagnetic waves along a constant background magnetic field in an electron-positron plasma is calculated by means of both a fluid and a kinetic theory treatment. In the fluid theory, relativistic effects are included in the particle motion, the wave field, and in the thermal motion by means of a function $f$, which depends only on the plasma temperature. In this work we analyze the consistency of the fluid results with those obtained from a kinetic treatment, based on the relativistic Vlasov equation. The corresponding kinetic dispersion relation is numerically studied for various temperatures, and results are compared with the fluid treatment. Analytic expressions for the Alfvén velocity are obtained for the fluid and kinetic models, and it is shown that, in the kinetic treatment, the Alfvén branch is suppressed for large temperatures.

We address the problem of recognizing $\alpha$-stable Lévy distribution with Lévy index close to 2 from experimental data. We are interested in the case when the sample size of available data is not large, thus the power law asymptotics of the distribution is not clearly detectable, and the shape of the empirical probability density function is close to a Gaussian. We propose a testing procedure combining a simple visual test based on empirical fourth moment with the Anderson-Darling and Jarque-Bera statistical tests and we check the efficiency of the method on simulated data. Furthermore, we apply our method to the analysis of turbulent plasma density and potential fluctuations measured in the stellarator-type fusion device and demonstrate that the phenomenon of the L-H transition from low confinement, L mode, to a high confinement, H mode, which occurs in this device is accompanied by the transition from Lévy to Gaussian fluctuation statistics.

We present an x-ray microtomography study of the compaction process of cylindrical rods under tapping. The process is monitored by measuring the evolution of the orientational order parameter, local, and overall packing densities as a function of the tapping number for different tapping intensities. The slow relaxation dynamics of the orientational order parameter can be well fitted with a stretched-exponential law with stretching exponents ranging from 0.9 to 1.6. The corresponding relaxation time versus tapping intensity follows an Arrhenius behavior which is reminiscent of the slow dynamics in thermal glassy systems. We also investigated the boundary effect on the ordering process and found that boundary rods order faster than interior ones. In searching for the underlying mechanism of the slow dynamics, we estimated the initial random velocities of the rods under tapping and found that the ordering process is compatible with a diffusion mechanism. The average coordination number as a function of the tapping number at different tapping intensities has also been measured, which spans a range from 6 to 8.

The temperature and density dependence of the structure and polarization properties of bulk water were systematically investigated using the ab initio MCYna potential [Li et al., J. Chem. Phys. 127, 154509 (2007)], which includes nonadditive contributions to intermolecular interactions. Molecular dynamics simulations were conducted for isochores of 1, 0.8, and 0.6 g/cm${}^3$ and temperatures from 278 to 750 K. Special attention was paid to the structural change of water in the range from the normal boiling point to supercritical temperatures. At temperatures below the normal boiling temperature, water exhibits a tetrahedral structure along the 0.8 and 0.6 g/cm${}^3$ isochores. A significant collapse of the hydrogen bonding network was observed at temperatures of 450, 550, and 650 K. The MCYna potential was able to successfully reproduce the experimental dielectric constant. The dielectric constant and average dipole moments decrease with increasing temperature and decreasing density due to weakened polarization. A comparison is also made with SPC-based models.

Stochastic blockmodels are generative network models where the vertices are separated into discrete groups, and the probability of an edge existing between two vertices is determined solely by their group membership. In this paper, we derive expressions for the entropy of stochastic blockmodel ensembles. We consider several ensemble variants, including the traditional model as well as the newly introduced degree-corrected version [Karrer et al., Phys. Rev. E 83, 016107 (2011)], which imposes a degree sequence on the vertices, in addition to the block structure. The imposed degree sequence is implemented both as “soft” constraints, where only the expected degrees are imposed, and as “hard” constraints, where they are required to be the same on all samples of the ensemble. We also consider generalizations to multigraphs and directed graphs. We illustrate one of many applications of this measure by directly deriving a log-likelihood function from the entropy expression, and using it to infer latent block structure in observed data. Due to the general nature of the ensembles considered, the method works well for ensembles with intrinsic degree correlations (i.e., with entropic origin) as well as extrinsic degree correlations, which go beyond the block structure.

The Lyapunov exponent spectrum and covariant Lyapunov vectors are studied for a quasi-one-dimensional system of hard disks as a function of density and system size. We characterize the system using the angle distributions between covariant vectors and the localization properties of both Gram-Schmidt and covariant vectors. At low density there is a kinetic regime that has simple scaling properties for the Lyapunov exponents and the average localization for part of the spectrum. This regime shows strong localization in a proportion of the first Gram-Schmidt and covariant vectors and this can be understood as highly localized configurations dominating the vector. The distribution of angles between neighboring covariant vectors has characteristic shapes depending upon the difference in vector number, which vary over the continuous region of the spectrum. At dense gas- or liquid-like densities the behavior of the covariant vectors are quite different. The possibility of tangencies between different components of the unstable manifold and between the stable and unstable manifolds is explored but it appears that exact tangencies do not occur for a generic chaotic trajectory.

Given a complex networked system whose topology and dynamical equations are unknown, is it possible to foresee that a certain type of collective dynamics can potentially emerge in the system, provided that only time-series measurements are available? We address this question by focusing on a commonly studied type of collective dynamics, namely, synchronization in coupled dynamical networks. We demonstrate that, using the compressive-sensing paradigm, even when the coupling strength is not uniform so that the network is effectively weighted, the full topology, the coupling weights, and the nodal dynamical equations can all be uncovered accurately. The reconstruction accuracy and data requirement are systematically analyzed, in a process that includes a validation of the reconstructed eigenvalue spectrum of the underlying coupling matrix. A master stability function (MSF), the fundamental quantity determining the network synchronizability, can then be calculated based on the reconstructed dynamical system, the accuracy of which can be assessed as well. With the coupling matrix and MSF fully uncovered, the emergence of synchronous dynamics in the network can be anticipated and controlled. To forecast the collective dynamics on complex networks is an extremely challenging problem with significant applications in many disciplines, and our work represents an initial step in this important area.

This paper is devoted to fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow $d_s$ is equal to its mass fractal dimension $D$, even when the spectral dimension of the fractally porous or fissured medium is less than $D$. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.

We present an experimental study of the inverse energy cascade, spectral condensation, and turbulent particle transport in an electromagnetically driven thin layer of NaCl electrolyte. The presence of the bottom friction provides an energy sink at large scales for the turbulent flow. This energy sink crucially contributes to the balance of the forcing and dissipation which makes the inverse cascade steady. The present work provides an estimation of the linear dissipation rate on an experimental basis. We also show how the dissipation rate affects the characteristic features of the velocity spectrum and the dynamics of the spectral condensation. A quantitative study of the turbulent diffusion shows a significant decrease of the radial transport during the spectral condensation process.

Flow over a traveling wavy foil with a passively flapping flat plate has been investigated using a multiblock lattice Boltzmann equation and the immersed boundary method. The foil undergoes prescribed undulations in the lateral direction and the rigid flat plate has passive motion determined by the fluid structure interaction. This simplified model is used to study the effect of the fish caudal fin and its flexibility on the locomotion of swimming animals. The flexibility of the caudal fin is modeled by a torsion spring acting about the pivot at the conjuncture of the wavy foil and the flat plate. The study reveals that the passively oscillating flat plate contributes half of the propulsive force. The flexibility, represented by the nondimensional natural frequency $F$, plays a very important role in the movement and propulsive force generation of the whole body. When the plate is too flexible, the drag force is observed. As the flat plate becomes more rigid, the propulsive force that is generated when the undulation is confined to last part of the wavy foil becomes larger. The steady movement occurs at $F=5$. These results are consistent with the observations of some swimming animals in nature.

We develop a theory of turbulence based on the inviscid Navier-Stokes equation. We get a simple but exact stochastic solution (vortex filament model) which allows us to obtain a power law for velocity structure functions in the inertial range. Combining the model with the multifractal conjecture, we calculate the scaling exponents without using the extended self-similarity approach. The results obtained are shown to be in very good agreement with numerical simulations and experimental data. The role of more general stochastic solutions of the Navier-Stokes equation is discussed.

Through the use of Mie theory generalized to multiple spheres, the derivatives of the scattering matrix elements and ellipsometric scattering variables are found as a function of shell thickness and nonconcentricity for core-shell particles. In particular, for the case of a core-shell sphere system where the centers are not concentric, the derivatives are taken with respect to the line segment describing the distance between spherical centers. The derivatives of the scattering matrix elements can be used to calculate the changes in ellipsometric light scattering, allowing for sensitivity and precision in quantitative models of fluctuations in core-shell systems. Computed results giving model contrast for a variety of sizes and fluctuation modes are used to design and guide novel light-scattering experiments currently underway.

We examine the validity of the projected Gross-Pitaevskii simulation by taking the two-dimensional homogeneous bosonic system as an example. The long-distance behaviors of the correlation function and equilibrium temperatures show good agreement with those of the quantum Monte Carlo calculations below temperatures near the Kosterlitz-Thouless transition. We find that in the projected Gross-Pitaevskii description, one needs to estimate the optimal wave-number cutoff in temperature. In the well-described region, the projected Gross-Pitaevskii equation presents reliable predictions for the long-wave bosonic components.