Analysis of dynamic process models for structural insight and model reduction .1. Structural identification measures

An important consideration in the development of mathematical models for dynamic simulation, is the identification of the appropriate mathematical structure. By building models with an efficient structure which is devoid of redundancy, it is possible to create simple, accurate and functional models. This leads not only to efficient simulation, but to a deeper understanding of the important dynamic relationships within the process. In this paper, a method is proposed for systematic model development for startup and shutdown simulation which is based on the identification of the essential process structure. The key tool in this analysis is the method of nonlinear perturbations for structural identification and model reduction. Starting from a detailed mathematical process description both singular and regular structural perturbations are detected. These techniques are then used to give insight into the system structure and where appropriate to eliminate superfluous model equations or reduce them to other forms. This process retains the ability to interpret the reduced order model in terms of the physico-chemical phenomena. Using this model reduction technique it is possible to attribute observable dynamics to particular unit operations within the process. This relationship then highlights the unit operations which must be accurately modelled in order to develop a robust plant model. The technique generates detailed insight into the dynamic structure of the models providing a basis for system re-design and dynamic analysis. The technique is illustrated on the modelling for an evaporator startup. Copyright (C) 1996 Elsevier Science Ltd

QCD thermal phase transition in the presence of a small chemical potential

We propose a new method to investigate the thermal properties of QCD with a small quark chemical potential mu. Derivatives of quark and gluonic observables with respect to mu are computed at mu=0 for two flavors of p4 improved staggered fermions with ma=0.1,0.2 on a 16(3)x4 lattice, and used to calculate the leading order Taylor expansion in mu of the location of the pseudocritical point about mu=0. This expansion should be well behaved for the small values of mu(q)/T(c)similar to0.1 relevant for BNL RHIC phenomenology, and predicts a critical curve T-c(mu) in reasonable agreement with estimates obtained using exact reweighting. In addition, we contrast the case of isoscalar and isovector chemical potentials, quantify the effect of munot equal0 on the equation of state, and comment on the complex phase of the fermion determinant in QCD with munot equal0.

Application of the Williams-Landel-Ferry model to the viscosity-temperature relationship of Australian honeys

The rheological behaviour of nine unprocessed Australian honeys was investigated for the applicability of the Williams-Landel-Ferry (WLF) model. The viscosity of the honeys was obtained over a range of shear rates (0.01-40 s(-1)) from 2degrees to 40 degreesC, and all the honeys exhibited Newtonian behaviour with viscosity reducing as the temperature was increased. The honeys with high moisture were of lower viscosity, The glass transition temperatures of the honeys, as measured with a differential scanning calorimeter (DSC), ranged from -40degrees to -46 degreesC, and four models (WLF. Arrhenius, Vogel-Tammann-Fulcher (VTF), and power-law) were investigated to describe the temperature dependence of the viscosity. The WLF was the most suitable and the correlation coefficient averaged 0.999 +/- 0.0013 as against 0.996 +/- 0.0042 for the Arrhenius model while the mean relative deviation modulus was 0-12% for the WLF model and 10-40% for the Arrhenius one. With the universal values for the WLF constants, the temperature dependence of the viscosity was badly predicted. From non-linear regression analysis, the constants of the WLF models for the honeys were obtained (C-1 = 13.7-21.1: C-2 = 55.9-118.7) and are different from the universal values. These WLF constants will be valuable for adequate modeling of the rheology of the honeys, and they can be used to assess the temperature sensitivity of the honeys. (C) 2002 Elsevier Science Ltd. All rights reserved.

N-aminopyrroledione-hydrazonoketene-pyrazolium oxide-pyrazolone rearrangements and pyrazolone tautomerism

Flash vacuum thermolysis (FVT) of 1-(dimethylamino)pyrrole-2,3-diones 5 causes extrusion of CO with formation of transient hydrazonoketenes 7. The transient ketenes 7 are observable in the form of weak bands at 2130 (7a) or 2115 cm(-1) (7b) in the Ar matrix IR spectra resulting from either FVT or photolysis of either 5 or 1,1- dimethylpyrazolium-5- oxides 8, and these absorptions are in excellent agreement with B3LYP/6-31G* frequency calculations. Under FVT conditions the ketenes 7 cyclize to pyrazolium oxides 8, which undergo 1,4-migration of a methyl group to yield 1,4-dimethyl-3-phenylpyrazole-5(4H)-one 9a and 1,4,4-trimethyl-3-phenylpyrazole-5(4H)-one 9b. All three tautomers of 9a have been characterized, viz. the CH form 9a (most stable form in the gas phase, the solid state and solvents of low polarity), the OH form 9a' (metastable solid at room temperature) and the NH form 9a (stable in aprotic dipolar solvents). The isomeric 1,4-dimethyl-5-phenylpyrazole-3(2H)-one 12 tautomerizes to the 3-hydroxypyrazole 12'. The crystal structure of the hydrochloride 14 of 9a'/9a is reported, representing the first structurally characterised example of a protonated 5-hydroxypyrazole.