Analog scaling methods

It has been common to use two fluids of different densities to simulate smoke movement from fire. One frequently used approach is to use an inverted model in a tank of fresh water with dyed or colored salt water, for visualization, in order to simulate the hot 

The initial condition is that (T — T )/T = Ys = 0 and at solid boundaries (dT/dn = dYs/dn = 0, with no heat or mass flow. Of course, radiation is ignored, but this is justified far away from the source. Note that the dimensionless source terms are Q and m where t = (1/p)12 and l is chosen according to a geometric dimension, or as Equation (12.16) for an unconfined plume depending on whether the flow is confined or unconfined. 

The saltwater, low-buoyancy system has a tendency to become laminar as the ceiling jet propagates away from the plume due to the buoyancy suppressing the turbulence. 

Heskestad, G., Modeling of enclosure fires, Proc. Comb. Inst., 1973, 14, pp. 1021-30. 

Modeling of vented enclosure fires, Part 1. Quasi-steady wood-crib source fires, FMRCJ.I.7A0R5.G0, Factory Mutual Research, Norwood, Massachusetts, July 1978. 

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The above simple large-D picture helps to establish a connection to phase transitions. However, the questions which remain to be addressed are How to carry out such an analogy to the IV-electron atoms at D = 3 and what are the physical consequences of this analogy These questions will be examined in the following sections by developing the finite size scaling method for atomic and molecular systems. 

The QWB is a generic HRQOL instrument that includes symptoms or problems plus three dimensions of functional health status (see Table 2-2). Standardized preference values for the health states represented by the QWB have been measured (via the category rating scale method, a technique related to visual analog scales) and validated on a general population sample. The QWB was available originally only as an interviewer-administered version, but a self-administered version is now available." ... 

The second, third, and fourth corrections to [MPd/b-Jl lG(d,p)] are analogous to A (- -). The zero point energy has been discussed in detail (scale factor 0.8929 see Scott and Radom, 1996), leaving only HLC, called the higher level correction, a purely empirical correction added to make up for the practical necessity of basis set and Cl truncation. In effect, thermodynamic variables are calculated by methods described immediately below and HLC is adjusted to give the best fit to a selected group of experimental results presumed to be reliable. 

The synthetic procedure described is based on that reported earlier for the synthesis on a smaller scale of anthracene, benz[a]anthracene, chrysene, dibenz[a,c]anthracene, and phenanthrene in excellent yields from the corresponding quinones. Although reduction of quinones with HI and phosphorus was described in the older literature, relatively drastic conditions were employed and mixtures of polyhydrogenated derivatives were the principal products. The relatively milder experimental procedure employed herein appears generally applicable to the reduction of both ortho- and para-quinones directly to the fully aromatic polycyclic arenes. The method is apparently inapplicable to quinones having an olefinic bond, such as o-naphthoquinone, since an analogous reaction of the latter provides a product of undetermined structure (unpublished result). As shown previously, phenols and hydro-quinones, implicated as intermediates in the reduction of quinones by HI, can also be smoothly deoxygenated to fully aromatic polycyclic arenes under conditions similar to those described herein. 

Other preparations of Nazarov s reagent and its analogs have been reported,7 but many of the procedures are labor-intensive and/or require special apparatus. The reported preparation of ethyl 3-oxo-4-pentenoate is facile (2 steps) and efficient (52% overall yield). Ail starting materials are commercially available, relatively inexpensive, and easily purified. The synthesis is also amenable to scale up and has been carried out successfully on a 1-mol scale. Other esters have also been synthesized by this method with overall yields ranging from 45-58% (see Scheme l).8 Finally, methacrolein and crotonaldehyde are also suitable reactants (see Scheme I). 

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