Rheological effect on thermocapillary flow of a liquid film jet painted on a moving boundary

In the present paper, a liquid (or melt) film of relatively high temperature ejected from a vessel and painted on the moving solid film is analyzed by using the second-order fluid model of the non-Newtonian fluid. The thermocapillary flow driven by the temperature gradient on the free surface of a Newtonian liquid film was discussed before. The effect of rheological fluid on thermocapillary flow is considered in the present paper. The analysis is based on the approximations of lubrication theory and perturbation theory. The equation of liquid height and the process of thermal hydrodynamics of the non-Newtonian liquid film are obtained, and the case of weak effect of the rheological fluid is solved in detail.     

Asymptotic Expansions for the Distribution of the Maximum of Gaussian Random Fields

Some asymptotic results are proved for the distribution of the maximum of a centered Gaussian random field with unit variance on a compact subset S of ^N . They are obtained by a Rice method and the evaluation of some moments of the number of local maxima of the Gaussian field above an high level inside S and on the border S. Depending on the geometry of the border we give up to N+1 terms of the expansion sometimes with exponentially small remainder. Application to waves maximum is shown.     

An On-Line Library of Extended High-Temperature Expansions of Basic Observables for the Spin-S Ising Models on Two- and Three-Dimensional Lattices

We present an on-line library of unprecedented extension for high-temperature expansions of basic observables in the Ising models of general spin S, with nearest-neighbor interactions. We have tabulated through order ²⁵ the series for the nearest-neighbor correlation function, the susceptibility and the second correlation moment in two dimensions on the square lattice, and, in three dimensions, on the simple-cubic and the body-centered cubic lattices. The expansion of the second field derivative of the susceptibility is also tabulated through ²³ for the same lattices. We have thus added several terms (from four up to thirteen) to the series already published for spin S = 1/2, 1, 3/2, 2, 5/2, 3, 7/2, 4, 5, .     

An Equilibrium Lattice Model of Wetting on Rough Substrates

We consider a semi-infinite 3-dimensional Ising system with a rough wall to describe the effect of the roughness r of the substrate on wetting. We show that the difference of wall free energies (r)= _AW(r)– _BW(r) of the two phases behaves like (r)r(1), where r=1 characterizes a purely flat surface, confirming at low enough temperature and small roughness the validity of Wenzel's law, cos (r)r cos (1), which relates the contact angle of a sessile droplet to the roughness of the substrate     

Inverse Problem for a Class of Two-Dimensional Diffusion Equations with Piecewise Constant Coefficients

In this paper, we consider an inverse problem for a class of two-dimensional diffusion equations with piecewise constant coefficients. This problem is studied using an explicit formula for the relevant spectral measures and an asymptotic expansion of the solution of the diffusion equations. A numerical method that reduces the inverse problem to a sequence of nonlinear least-square problems is proposed and tested on synthetic data.     

Contact Transformations and Local Reducibility of ODE to the Form y‴=0

Orbits of the ODE y=0 in corresponding jet bundles are investigated. Explicit relations for the right-hand side of an arbitrary 3-order ODE necessary and sufficient for the existence of a contact transformation reducing this equation locally to the form y=0 are obtained.     

Equivalence of a -functional with the approximation behavior of some linear means for abstract Fourier series

Within the setting of abstract Cesàro-bounded Fourier series a -functional is introduced and characterized by the convergence behavior of some linear means. Applications are given within the framework of Jacobi, Laguerre and Hermite expansions. In particular, Ditzian's (1996) equivalence result in the setting of Legendre expansions is covered.

     

Numerical algorithms for uniform Airy-type asymptotic expansions

Airy-type asymptotic representations of a class of special functions are considered from a numerical point of view. It is well known that the evaluation of the coefficients of the asymptotic series near the transition point is a difficult problem. We discuss two methods for computing the asymptotic series. One method is based on expanding the coefficients of the asymptotic series in Maclaurin series. In the second method we consider auxiliary functions that can be computed more efficiently than the coefficients in the first method, and we do not need the tabulation of many coefficients. The methods are quite general, but the paper concentrates on Bessel functions, in particular on the differential equation of the Bessel functions, which has a turning point character when order and argument of the Bessel functions are equal.     

Some asymptotic expansions of moments of order statistics

Series expansions of moments of order statistics are obtained from expansions of the inverse of the distribution function. They are valid for certain types of distributions with regularly varying tails. We show that the expansions converge quickly when the sample size is moderate to large, and we obtain bounds on the rate of convergence. The special case of the Cauchy distribution is treated in more detail.     

Flow Structure of Lifted Swirling Jet Flames

Swirling combustion is widely applied in various applications such as gas turbines, utility boilersor waste incinerators. This article contributes to the ongoing research by providing experimentaldata that are gathered in the mixing zone of a lifted swirling premixed natural gas flame. Theobjective of this paper is fivefold: (1) to introduce the lifted swirling flame featuring lowNO _x emissions (2) to provide experimental data such as major species distributions, temperature and streamlines of the flow pattern, (3) to report on velocity bias in probability density function (PDF) distributions and to present PDF sequences of velocities in medium scale swirling flows, (4) to make an assessment on the local small-scale turbulence that is present in the swirling mixinglayer and (5) to provide new experimental data for model verification and development.The PDFs are corrected in order to compensate for the velocity bias phenomenon, which is typicalfor randomly sampled LDA data. Sequences of axial PDF data are presented and measurement locationsof interest are selected to look at the PDF characteristics of the internal and externalrecirculation zones, the mixing layer and the onset of the reacting flow into detail. The mixinglayer PDFs covered a wide velocity range and revealed bimodality; even the concept ofmulti-modality is suggested and explored. Analysis showed that a sum of two Gaussian distributionscan accurately envelop the experimental PDFs. The reason for this broadband turbulence behavior isto be found in combination of precessing and flapping motion of the flow structures, and also incombustion generated instabilities of the lifted flame. As a result, the flame brush is wide (largescale motion) and the mixing (small-scale turbulence) flattens any high temperatures in thecombustion process.The multi-scale turbulence concept is subsequently used to make anassessment of the local turbulence characteristics in the mixing layer.The idea is that the PDFs capture both contributions of the flow-inherent fine grain turbulence (u _l ) which is superposed on slowlarge scale fluctuating structures. It is this u _l that will be of interest in continued research on the classification of the lifted flame into acombustion regime diagram (e.g. Borghi diagram). Finally, the bimodalitycharacter in reacting flows and the prediction of large-scale structuresmay be a challenge for LES researchers.