293 research outputs found
Direct reconstruction of the two-dimensional pair distribution function in systems with angular correlations
An x-ray scattering approach to determine the two-dimensional (2D) pair
distribution function (PDF) in partially ordered 2D systems is proposed. We
derive relations between the structure factor and PDF that enable quantitative
studies of positional and bond-orientational (BO) order in real space. We apply
this approach in the x-ray study of a liquid crystal (LC) film undergoing the
smectic-hexatic phase transition, to analyze the interplay between the
positional and BO order during the temperature evolution of the LC film. We
analyze the positional correlation length in different directions in real
space.Comment: 23 pages, 8 figure
Analytic and asymptotic properties of generalized Linnik probability densities
Cataloged from PDF version of article.This paper studies the properties of the probability density function pα,ν,n(x) of the n-variate generalized Linnik distribution whose characteristic function φα,ν,n(t) is given by where {norm of matrix}t{norm of matrix} is the Euclidean norm of t ∈ ℝn. Integral representations of pα,ν,n(x) are obtained and used to derive the asymptotic expansions of pα,ν,n(x) when {norm of matrix}x{norm of matrix}→0 and {norm of matrix}x{norm of matrix}→∞ respectively. It is shown that under certain conditions which are arithmetic in nature, pα,ν,n(x) can be represented in terms of entire functions. © 2009 Birkhäuser Boston
Marangoni instability in oblate droplets suspended on a circular frame
We study theoretically internal flows in a small oblate droplet suspended on
the circular frame. Marangoni convection arises due to a vertical temperature
gradient across the drop and is driven by the surface tension variations at the
free drop interface. Using the analytical basis for the solutions of Stokes
equation in coordinates of oblate spheroid we have derived the linearly
independent stationary solutions for Marangoni convection in terms of Stokes
stream functions. The numerical simulations of the thermocapillary motion in
the drops are used to study the onset of the stationary regime. Both analytical
and numerical calculations predict the axially-symmetric circulatory convection
motion in the drop, the dynamics of which is determined by the magnitude of the
temperature gradient across the drop. The analytical solutions for the critical
temperature distribution and velocity fields are obtained for the large
temperature gradients across the oblate drop. These solutions reveal the
lateral separation of the critical and stationary motions within the drops. The
critical vortices are localized near the central part of a drop, while the
intensive stationary flow is located closer to its butt end. A crossover to the
limit of the plane film is studied within the formalism of the stream functions
by reducing the droplet ellipticity ratio to zero value. The initial stationary
regime for the strongly oblate drops becomes unstable relative to the
many-vortex perturbations in analogy with the plane fluid films with free
boundaries
Circulating Marangoni flows within droplets in smectic films
We present theoretical study and numerical simulation of Marangoni convection
within ellipsoidal isotropic droplets embedded in free standing smectic films
(FSSF). The thermocapillary flows are analyzed for both isotropic droplets
spontaneously formed in FSSF overheated above the bulk smectic-isotropic
transition, and oil lenses deposited on the surface of the smectic film. The
realistic model, for which the upper drop interface is free from the smectic
layers, while at the lower drop surface the smectic layering still persists is
considered in detail. For isotropic droplets and oil lenses this leads
effectively to a sticking of fluid motion at the border with a smectic shell.
The above mentioned asymmetric configuration is realized experimentally when
the temperature of the upper side of the film is higher than at the lower one.
The full set of stationary solutions for Stokes stream functions describing the
Marangoni convection flows within the ellipsoidal drops were derived
analytically. The temperature distribution in the ellipsoidal drop and the
surrounding air was determined in the frames of the perturbation theory. As a
result the analytical solutions for the stationary thermocapillary convection
were derived for different droplet ellipticity ratios and the heat conductivity
of the liquid crystal and air. In parallel, the numerical hydrodynamic
calculations of the thermocapillary motion in the drops were performed. Both
the analytical and numerical simulations predict the axially-symmetric
circulatory convection motion determined by the Marangoni effect at the droplet
free surface. Due to a curvature of the drop interface a temperature gradient
along its free surface always persists. Thus, the thermocapillary convection
within the ellipsoidal droplets in overheated FSSF is possible for the
arbitrarily small Marangoni numbers
Impact of the small-scale spatial distribution of dust particles on the chemical evolution of the diffuse interstellar medium
В работе проводится анализ возможного влияния газо-пылевых клампов, сформированных с помощью неустойчивости, предложенной в модели Цитовича с соавторами (2014), на химическую эволюцию диффузной межзвездной среды. Проведено моделирование диффузной среды в направлениях на объекты W49N, W31C и W51. Показано, что в модели с клампами молекулярный водород образуется на порядок быстрее и достигает максимального содержания раньше, чем в стандартной модели.In this work we perform the analysis of the effect of gas-dust clumps, possibly formed in the interstellar medium due to instability, proposed in Tsytovich et al. (2014) on the chemical evolution of the diffuse interstellar medium. We model diffuse medium along the well studied lines-of-sights in directions on W49N, W31C and W51. We found that in the model with clumps, the conversion timescale of atomic hydrogen into molecular is an order of magnitude smaller than in standard model
- …