Multiphase modelling of pouring glass over the spout lip of an industrial float in the flat glass forming process

This paper describes the numerical modelling of the three‐phase flow that is established when pouring molten glass onto a tin bath (float) under a non‐reactive atmosphere. Discharged from the furnace, the glass is spouted over a lip onto the bath, where it floats and spreads out in the form of a long ribbon, leading to the flat glass forming process. Numerically, the physical modelling must consider a multiphase problem with three immiscible phases: glass, tin and air. The simulation of this complex free‐surface flow involves the solution of the Navier–Stokes set of equations for all the phases simultaneously, using a volume‐of‐fluid formulation that introduces a marker function convected by the flow to identify each phase. The evolution of the interphases is tracked over time with the implementation of a continuous surface force algorithm. A general purpose, well‐tested commercial code, FLUENT, is employed for the computations. Firstly, a two‐dimensional model considering the symmetry plane of the float is developed to fit accurate physical and numerical parameters. The high complexity of the interphases in addition to great differences between the physical properties of the phases has required extensive tests to ensure the consistency and accuracy of the solutions. Afterwards, a complete three‐dimensional model is built to simulate the pouring process in a real geometry and predict the behaviour of the industrial facility when the operating conditions are modified. Typical flow phenomena inside the tin bath, such as tin currents, wet back flow or even the equilibrium thickness, are also obtained as a promising result of the numerical modelling. Copyright © 2008 John Wiley & Sons, Ltd.     

Analysis of the wave solution of the elastokinetic equations of a Cosserat continuum for the case of bulk plane waves

A study is made of waves in a Cosserat continuum, whose strain state is characterized by independent displacement and rotation vectors. The propagation of longitudinal and transverse bulk waves is considered. Wave solutions are sought in the form of wave trains specified by a Fourier spectrum of arbitrary shape. It is shown that if the solution is sought in the form of three components of the displacement vector and three components of the rotation vector which depend on time and the longitudinal coordinate, the initial system is split into two systems, one of which describes longitudinal waves, and the other transverse waves. For waves of both types, dispersion relations and analytical solutions in displacement are obtained. The dispersion characteristics of the solutions obtained differ from the dispersion characteristics of the corresponding classical elastic solutions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 196–203, March–April, 2008.     

Some Applications of the Ultrapower Theorem to the Theory of Compacta

The ultrapower theorem of Keisler and Shelah allows such model-theoretic notions as elementary equivalence, elementary embedding and existential embedding to be couched in the language of categories (limits, morphism diagrams). This in turn allows analogs of these (and related) notions to be transported into unusual settings, chiefly those of Banach spaces and of compacta. Our interest here is the enrichment of the theory of compacta, especially the theory of continua, brought about by the importation of model-theoretic ideas and techniques.     

A Symmetry adapted tessellation of the GEPOL surface: applications to molecular properties in solution

A procedure to partition the GEPOL molecular surface into tesserae that respects the molecular symmetry constraints is presented. Using this method it is possible to build a solvent reaction field for the Polarizable Continuum Model with the same symmetry of the nuclear potential. Several applications are reported and discussed to evaluate the performance of this new procedure. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1262–1272, 2001     

On the invariance of constitutive equations according to the kinetic theory of gases

Iterative techniques for solving the Boltzmann equation in the kinetic theory of gases yield expressions for the stress tensor and heat flux vector that are analogous to constitutive equations in continuum mechanics. However, these expressions are not generally invariant under the Euclidean group of transformations, whereas constitutive equations in continuum mechanics are usually required to be by the principle of material frame indifference. This disparity in invariance properties has led some previous investigators to argue that Euclidean invariance should be discarded as a contraint on constitutive equations. It is proven mathematically in this paper that the results of the Chapman-Enskog iterative procedure have no direct bearing on this issue. In order to settle this question, it is necessary to examine mathematically the effect of superimposed rigid body rotations on solutions of the Boltzmann equation. A preliminary investigation along these lines is presented which suggests that the kinetic theory is consistent with material frame indifference in at least a strong approximate sense provided that the disparity in the time scales of the microscopic and macroscopic motions is extremely large—a condition which is usually a prerequisite for the existence of constitutive equations.On leave from Stevens Institute of Technology, Hoboken, New Jersey 07030.     

奇特核和超核中的晕现象

讨论奇特核和超核中的各种晕现象. 根据密度相关零程对力的相对论连续谱Hartree Bogoliubov理论给出的计算结果， 预言了中子滴线附近的Ca原子核中可能存在着巨晕， 并简要介绍了O， Ni， Zr， Sn和Pb等一些质子幻数核从质子滴线到中子滴线之间的原子核基态性质. 随后给出超核内的晕现象研究， 如Ca超核内的中子晕和153ΛC内的单Λ超子晕. Halos in the relativistic continuum Hartree Bogoliubov (RCHB) theory are investigated，including giant halo in the even N Ca isotope near neutron drip line，halos in hypernuclei and the hyperon halos in 153ΛC.     

Second-order Mø øller–Plesset second derivatives for the polarizable continuum model: theoretical bases and application to solvent effects in electrophilic bromination of ethylene

An analytical theory for the energy second derivatives at second-order Mø øller–Plesset level for solvated molecules described within the polarizable continuum model is presented. The method, which is based on the differentiation of relaxed density equations for the first derivatives, is firstly presented in its formal aspects and is then applied to the study of the rate-determining step of the electrophilic bromination of ethylene in aqueous solution.Contribution to the Jacopo Tomasi Honorary Issue     

Nonuniversality and continuity of the critical covered volume fraction in continuum percolation

We establish, using mathematically rigorous methods, that the critical covered volume fraction (CVF) for a continuum percolation model with overlapping balls of random sizes is not a universal constant independent of the distribution of the size of the balls. In addition, we show that the critical CVF is a continuous function of the distribution of the radius random variable, in the sense that if a sequence of random variables converges weakly to some random variable, then the critical CVF based on these random variables converges to the critical CVF of the limiting random variable.     

时间积分透射光栅谱仪

本文简要介绍了使用中国科大首次研制成功的有聚酰亚胺衬底的透射光栅与北京电子学研究所研制的MCP(微通道板)构成的透射光栅谱仪,在功率密度～10~(14)W/cm~2的激光辐照条件下,成功地测到了平面Au、C、Al靶发射的软X射线能谱分布(相对值)和黑洞靶产生的软X射线能谱分布(相对值)。实验结果表明:用国内研制的透射光栅构成的时间积分透射光栅谱仪完全能用于激光等离子体实验。本文最后还提出了该设备的进一步改进方案。     

The atmospheric water vapor continuum below 300 GHz

Absolute attenuation rates due to water vapor and moist nitrogen have been measured in the laboratory at 138 GHz, 282 and 300 K, pressures up to 1.5 atm, and relative humidities from 80 to 100 percent. The computer-controlled measuring system is comprised of a millimeter wave resonance spectrometer (0.15 km effective path length) and a humidity simulator. Several shortcomings of earlier measurement attempts have been rectified. The data are interpreted as a water vapor continuum spectrum consisting of two terms, namely strong self-broadening (H₂O–H₂O) plus foreign-gas-broadening (H₂O–N₂) contributions. Implications of the new results for modeling atmospheric EHF window transparencies and for revising established H₂O line broadening theory are discussed.The work was supported in part by the U.S. Army Research Office under Contract AR0 101-83.