Thermal vibrational convection in near-critical fluids. Part 2. Weakly non-uniform heating

The governing equations and effective boundary conditions to describe thermal vibrational convection in a near-critical fluid are derived with the help of the multiple-scale method and averaging procedure. In contrast to Part 1, this paper focuses on the effects of density non-homogeneities caused not by external heating but by vibrational and gravity stratifications due to the divergent mechanical compressibility of near-critical media. It is shown that vibrations generate non-homogeneities in the average temperature, which result in the onset of thermal convection even under isothermal boundary conditions. An agreement with the results of previous numerical and asymptotical analyses and with experiments is found.<br/

Analytical Rescaling of Polymer Dynamics from Mesoscale Simulations

We present a theoretical approach to scale the artificially fast dynamics of simulated coarse-grained polymer liquids down to its realistic value. As coarse-graining affects entropy and dissipation, two factors enter the rescaling: inclusion of intramolecular vibrational degrees of freedom, and rescaling of the friction coefficient. Because our approach is analytical, it is general and transferable. Translational and rotational diffusion of unentangled and entangled polyethylene melts, predicted from mesoscale simulations of coarse-grained polymer melts using our rescaling procedure, are in quantitative agreement with united atom simulations and with experiments.Comment: 6 pages, 2 figures, 2 table

Capture of particles of dust by convective flow

Interaction of particles of dust with vortex convective flows is under theoretical consideration. It is assumed that the volume fraction of solid phase is small, variations of density due to nonuniform distribution of particles and those caused by temperature nonisothermality of medium are comparable. Equations for the description of thermal buoyancy convection of a dusty medium are developed in the framework of the generalized Boussinesq approximation taking into account finite velocity of particle sedimentation. The capture of a cloud of dust particles by a vortex convective flow is considered, general criterion for the formation of such a cloud is obtained. The peculiarities of a steady state in the form of a dust cloud and backward influence of the solid phase on the carrier flow are studied in detail for a vertical layer heated from the sidewalls. It is shown that in the case, when this backward influence is essential, a hysteresis behavior is possible. The stability analysis of the steady state is performed. It turns out that there is a narrow range of governing parameters, in which such a steady state is stable.Comment: 14 pages, 10 figures, published in Physics of Fluid

A First Principle Approach to Rescale the Dynamics of Simulated Coarse-Grained Macromolecular Liquids

We present a detailed derivation and testing of our approach to rescale the dynamics of mesoscale simulations of coarse-grained polymer melts (I. Y. Lyubimov et al. J. Chem. Phys. \textbf{132}, 11876, 2010). Starting from the first-principle Liouville equation and applying the Mori-Zwanzig projection operator technique, we derive the Generalized Langevin Equations (GLE) for the coarse-grained representations of the liquid. The chosen slow variables in the projection operators define the length scale of coarse graining. Each polymer is represented at two levels of coarse-graining: monomeric as a bead-and-spring model and molecular as a soft-colloid. In the long-time regime where the center-of-mass follows Brownian motion and the internal dynamics is completely relaxed, the two descriptions must be equivalent. By enforcing this formal relation we derive from the GLEs the analytical rescaling factors to be applied to dynamical data in the coarse-grained representation to recover the monomeric description. Change in entropy and change in friction are the two corrections to be accounted for to compensate the effects of coarse-graining on the polymer dynamics. The solution of the memory functions in the coarse-grained representations provides the dynamical rescaling of the friction coefficient. The calculation of the internal degrees of freedom provides the correction of the change in entropy due to coarse-graining. The resulting rescaling formalism is a function of the coarse-grained model and thermodynamic parameters of the system simulated. The rescaled dynamics obtained from mesoscale simulations of polyethylene, represented as soft colloidal particles, by applying our rescaling approach shows a good agreement with data of translational diffusion measured experimentally and from simulations. The proposed method is used to predict self-diffusion coefficients of new polyethylene samples.Comment: 21 pages, 6 figures, 6 tables. Submitted to Phys. Rev.

Dark Matter Caustics

Caustics are a generic feature of the nonlinear growth of structure in the dark matter distribution. If the dark matter were absolutely cold, its mass density would diverge at caustics, and the integrated annihilation probability would also diverge for individual particles participating in them. For realistic dark matter candidates, this behaviour is regularised by small but non-zero initial thermal velocities. We present a mathematical treatment of evolution from Hot, Warm or Cold Dark Matter initial conditions which can be directly implemented in cosmological N-body codes. It allows the identification of caustics and the estimation of their annihilation radiation in fully general simulations of structure formation.Comment: 6 pages, 1 figure, Accepted for publication in MNRAS, minor edit

Analysis of vibration impact on stability of dewetting thin liquid film

Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description is reasonable and the amplitude equation holds. The linear and nonlinear analyses of the amplitude equation and the numerical computations show that such vibration stabilizes the film against dewetting and rupture.Comment: 19 pages, 11 figure

Numerical approximation of the fractional Laplacian via hp-finite elements, with an application to image denoising

The fractional Laplacian operator (−∆)s on a bounded domain Ω can be realized as a Dirichlet-to-Neumann map for a degenerate elliptic equation posed in the semi-infinite cylinder Ω × (0,∞). In fact, the Neumann trace on Ω involves a Muckenhoupt weight that, according to the fractional exponent s, either vanishes (s 1/2). On the other hand, the normal trace of the solution has the reverse behavior, thus making the Neumann trace analytically well-defined. Nevertheless, the solution develops an increasingly sharp boundary layer in the vicinity of Ω as s decreases. In this work, we extend the technology of automatic hp-adaptivity, originally developed for standard elliptic equations, to the energy setting of a Sobolev space with a Muckenhoupt weight, in order to accommodate for the problem of interest. The numerical evidence confirms that the method maintain exponential convergence. Finally, we discuss image denoising via the fractional Laplacian. In the image processing community, the standard way to apply the fractional Laplacian to a corrupted image is as a filter in Fourier space. This construction is inherently affected by the Gibbs phenomenon, which prevents the direct application to “spliced” images. Since our numerical approximation relies instead on the extension problem, it allows for processing different portions of a noisy image independently and combine them, without complications induced by the Gibbs phenomenon

Noise Can Reduce Disorder in Chaotic Dynamics

We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or natural measure) is generally highly inhomogeneous over the set, either diminishing or enhancing the contribution of these orbits into system dynamics. We show analytically and numerically a weak noise to reduce this inhomogeneity and, additionally to obvious perturbing impact, make a regularizing influence on the chaotic dynamics. This universal effect is rooted into the nature of deterministic chaos.Comment: 11 pages, 5 figure

Orbital structure of the meteor complex according to radar observations in Kazan. 1. Apparent distributions of aphelia

The results of an analysis of the orbital structure of the meteor complex accessible for radar observations at northern midlatitudes are reported. Experimentally, the study is based on the long-term monitoring of the influx of meteor matter into the Earth's atmosphere performed with the meteor radar of Kazan State University starting from 1986. The study uses a discrete quasi-tomographic method to measure the radiants and velocities of meteor showers based on goniometric data of the meteor radar and diffraction measurements of meteor velocities. The discretization of the detection environment-in particular, in terms of velocity-is shown to result in no substantial loss of measurement accuracy. The error of the measured velocity of the shower does not exceed 1.5 km/s for a standard deviation of a single velocity measurement equal to 3 km/s. Microshower representation is used with microshowers either representing the correlated part of the sporadic complex or being partial streams of major and minor showers, or fragments of the dust environment of minor bodies passing by Earth or falling onto it. The data of measurements made over the entire annual cycle are used to construct combined maps of the distribution of the observed 2263 microshowers (a total of 22 604 orbits) by their inclination, aphelion distance, and longitudes of the ascending nodes of their orbits. The observing conditions are shown to have a significant effect on the parameters of the distribution of aphelion distances for different months, and the corresponding distributions for prograde and retrograde orbits are shown to differ fundamentally. A specific feature of such distribution maps is that they allow uniform representation of both meteor showers and irregularities of the sporadic complex. © 2008 MAIK Nauka