Wärmeübergang bei einphasiger freier Konvektion in der Nähe des kritischen Zustandes

Zusammenfassung Mit den Halogenkältemitteln R12 (CF₂Cl₂), R115 (C₂F₅Cl) und RC318 (C₄F_S) wurden an einem elektrisch beheizten, horizontalen Rohr (d=8 mm) Versuche zur einphasigen freien Konvektion in der Nähe des kritischen Zustandes durchgeführt. Die Messungen erstrecken sich von etwa der halben bis zur doppelten kritischen Dichte und zum 1,8-fachen kritischen Druck; dabei wurden die Fluidzustände außerhalb der beheizten Zone längs der kritischen und einer überkritischen Isotherme variiert.Je nach dem Ausgangszustand des Fluids ist die Abhängigkeit des Wärmeübergangskoeffizienten von der Heizflächenbelastung q ähnlich wie beim Filmsieden oder wie bei freier Konvektion weit unterkritischer Fluide, oder es treten Maxima im (q)-Zusammenhang auf. Die unterschiedlichen Ergebnisse können durch Analyse des Dichte- bzw. Enthalpieverlaufs in der wandnahen, beheizten Fluidzone erklärt werden.

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Free convective heat transfer near the critical state

Experiments were performed on free convective heat transfer from a horizontal, electrically heated tube (d=8 mm) to the halocarbon refrigerants R12 (CF₂Cl₂), R115 (C₂F₅Cl) and RC318 (C₄F₈) near the critical state. Density varied from approx. half to twice the critical value and pressure up to 1.8 times the critical value; the bulk fluid state was varied along the critical and one supercritical isotherm.As is partially known, at different bulk fluid states either peaks are found in the heat transfer coefficients as a function of heat flux or a behaviour similar to film boiling or to free convection at far subcritical states is observed. The different results can be explained by analyzing the density- and enthalpy-variation within the fluid near the heated wall.

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Herrn Prof. Dr.-Ing. H. Glaser, Stuttgart, zum 70. Geburtstag gewidmet.

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Die für die vorliegende Arbeit verwendete versuschanlage wurde mit Mitteln aus dem Schwepunktprogramm Siedevorgänge der Deutschen Forschungsgemeinschaft aufgebaut. Die als Versuchsstoffe benutzten Kältemittel wurden dankenswerterweise von don Farbwerken Hoechst zur Verfügung gestellt.     

High resolution study of the ν5 + ν12 band of C2H4

The combination band ν₅ + ν₁₂ of ethylene, C₂H₄, has been recorded for the first time with a high resolution Fourier transform spectrometer Bruker IFS 125HR. Assignments of transitions and preliminary rotational analysis are made. Two models (Hamiltonian of the isolated vibrational state and Hamiltonian that takes into account resonance interactions) are used. Influence of the local resonance interactions on the parameters and reproduction power of the models is discussed.     

Mathematical Programs with Vanishing Constraints: Optimality Conditions,Sensitivity, and a Relaxation Method

We consider a class of optimization problems with switch-off/switch-on constraints, which is a relatively new problem model. The specificity of this model is that it contains constraints that are being imposed (switched on) at some points of the feasible region, while being disregarded (switched off) at other points. This seems to be a potentially useful modeling paradigm, that has been shown to be helpful, for example, in optimal topology design. The fact that some constraints “vanish” from the problem at certain points, gave rise to the name of mathematical programs with vanishing constraints (MPVC). It turns out that such problems are usually degenerate at a solution, but are structurally different from the related class of mathematical programs with complementarity constraints (MPCC). In this paper, we first discuss some known first- and second-order necessary optimality conditions for MPVC, giving new very short and direct justifications. We then derive some new special second-order sufficient optimality conditions for these problems and show that, quite remarkably, these conditions are actually equivalent to the classical/standard second-order sufficient conditions in optimization. We also provide a sensitivity analysis for MPVC. Finally, a relaxation method is proposed. For this method, we analyze constraints regularity and boundedness of the Lagrange multipliers in the relaxed subproblems, derive a sufficient condition for local uniqueness of solutions of subproblems, and give convergence estimates. Research of the first author was supported by the Russian Foundation for Basic Research Grants 07-01-00270, 07-01-00416 and 07-01-90102-Mong, and by RF President’s Grant NS-9344.2006.1 for the support of leading scientific schools. The second author was supported in part by CNPq Grants 301508/2005-4, 490200/2005-2 and 550317/2005-8, by PRONEX-Optimization, and by FAPERJ.     

Scaling hot-electron generation to high-power, kilojoule-class laser-solid interactions

Thin-foil targets were irradiated with high-power (1 ≤ P(L) ≤ 210 TW), 10-ps pulses focused to intensities of I>10(18) W/cm(2) and studied with K-photon spectroscopy. Comparing the energy emitted in K photons to target-heating calculations shows a laser-energy-coupling efficiency to hot electrons of η(L-e) = 20 ± 10%. Time-resolved x-ray emission measurements suggest that laser energy is coupled to hot electrons over the entire duration of the incident laser drive. Comparison of the K-photon emission data to previous data at similar laser intensities shows that η(L-e) is independent of laser-pulse duration from 1 ≤ τ(p) ≤ 10 ps.     

Stabilized SQP revisited

The stabilized version of the sequential quadratic programming algorithm (sSQP) had been developed in order to achieve superlinear convergence in situations when the Lagrange multipliers associated to a solution are not unique. Within the framework of Fischer (Math Program 94:91–124, 2002), the key to local superlinear convergence of sSQP are the following two properties: upper Lipschitzian behavior of solutions of the Karush-Kuhn-Tucker (KKT) system under canonical perturbations and local solvability of sSQP subproblems with the associated primal-dual step being of the order of the distance from the current iterate to the solution set of the unperturbed KKT system. According to Fernández and Solodov (Math Program 125:47–73, 2010), both of these properties are ensured by the second-order sufficient optimality condition (SOSC) without any constraint qualification assumptions. In this paper, we state precise relationships between the upper Lipschitzian property of solutions of KKT systems, error bounds for KKT systems, the notion of critical Lagrange multipliers (a subclass of multipliers that violate SOSC in a very special way), the second-order necessary condition for optimality, and solvability of sSQP subproblems. Moreover, for the problem with equality constraints only, we prove superlinear convergence of sSQP under the assumption that the dual starting point is close to a noncritical multiplier. Since noncritical multipliers include all those satisfying SOSC but are not limited to them, we believe this gives the first superlinear convergence result for any Newtonian method for constrained optimization under assumptions that do not include any constraint qualifications and are weaker than SOSC. In the general case when inequality constraints are present, we show that such a relaxation of assumptions is not possible. We also consider applying sSQP to the problem where inequality constraints are reformulated into equalities using slack variables, and discuss the assumptions needed for convergence in this approach. We conclude with consequences for local regularization methods proposed in (Izmailov and Solodov SIAM J Optim 16:210–228, 2004; Wright SIAM J. Optim. 15:673–676, 2005). In particular, we show that these methods are still locally superlinearly convergent under the noncritical multiplier assumption, weaker than SOSC employed originally.     

High resolution laser spectrophotometer in the 1.06 μm region

The high resolution spectrophotometer developed on the basis of a single-mode running wave Nd-glass with line frequency continuously tuned during a generation pulse is described. The overlapping lines of water vapor near 9257.1, 9325.1 and 9343.6 cm^-1 were resolved and their strengths and positions were measured. The air broadening parameters of 9304.4 and 9305.4 cm^-1 were determined.     

A generalization of the denjoy integral

We prove that the IsekiM-integral is substantially more general than the Denjoy integral. Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 766–772, November, 1997. Translated by I. P. Zvyagin     

Pentaerythritol-based demulsifying agents and their surfactant properties

Pentaerythritol-based block copolymers of ethylene and propylene oxides were synthesized and characterized as surfactants and demulsifiers.