Group methods

Contributing group methods have been developed and published for calculating numerous other properties. However, for our purposes, it is not necessary to employ them. Moreover, there are some properties for which the method is not recommended. 

Using the principle of corresponding states for the following characteristics avoids the use of the contributing groups method ... 

Group Method The type of transformation can be deduced using group theory. For a complete exposition, see Refs. 9, 12, and 145 a shortened version is in Ref. 106. Basically, a similarity transformation should be considered when one of the independent variables has no physical scale (perhaps it goes to infinity). The boundary conditions must also simphfy (and combine) since each transformation leads to a differential equation with one fewer independent variable. 

The NEC group method for classifying flame arresters is similar to that used for electrical area classification. NFPA 497 (1997) provides the criteria for classilying gases into NEC groups for suitability for electrical area classification. 

The scaling argument provides only the exponent but not the absolute numerical value for the constant. Therefore, for quantitative results, it should be completed by some more refined technique like the afore-mentioned renormalization group method [49],... 

The methods of quantitation of anthocyanins can be divided into three major groups methods for samples with few or no interfering compounds, methods for samples with interfering compounds that absorb in the 480 to 550 nm range, and methods for quantitation of individual anthocyanin components. 

In order to be useful in practice, the effective transport coefficients have to be determined for a porous medium of given morphology. For this purpose, a broad class of methods is available (for an overview, see [191]). A very straightforward approach is to assume a periodic structure of the porous medium and to compute numerically the flow, concentration or temperature field in a unit cell [117]. Two very general and powerful methods are the effective-medium approximation (EMA) and the position-space renormalization group method. 

As a second method to determine effective transport coefficients in porous media, the position-space renormalization group method will be briefly discussed. 

Although in principle a powerful and elegant method, the position-space renormalization group method yields very complex expressions for the renormalized... 

The lattice gas model of Bell et al. [33] neither gave any detailed mechanism of the orientational ordering nor separated the contributions of the headgroup and the acyl chain. Lavis et al. [34] discussed Ref. 33 critically and concluded that the sharp kink point in the isotherm at transition was an artifact of the mean field approximation used. An improved correspondence to experimental data was claimed by the use of the real-space renormalization group method [35]. The same authors returned to the problem [35] and concluded that in addition to the orientation of the molecules, chain melting had to be included in a model which could interpret the phase transitions. 

One of the most systematic investigations into the use of organic chemical microscopy was made by Dunbar and his associates, who used a series of specific reagents to develop specific tests for various functional groups. Methods were developed for amines [24,25], carboxylic acids, anhydrides, and acid chlorides [26,27], aldehydes and ketones [28], hydroxy compounds [29], amino acids [30], and cations [31]. 

Our group has made extensive use of the RNG k-e model (Nijemeisland and Dixon, 2004), which is derived from the instantaneous Navier-Stokes equations using the Renormalization Group method (Yakhot and Orszag, 1986) as opposed to the standard k-e model, which is based on Reynolds averaging. The... 

Volumetric and morphological brain measurements are made with MRI. Modern MRI can produce detailed, high-contrast images of the entire brain in relatively short scan times with no invasive procedures or radioactivity. Thus, it is the modality of choice for detailed neuroanatomic studies in various neuropsychiatric disorders. Many groups have addressed the challenge of how to quantify subtle structural characteristics in the brain that appear to differ consistently between comparison groups. Methods such... 

Legeza, J. Roder, and B. A. Hess, Controlhng the accuracy of the density-matrix renormahzation-group method the dynamical block state selection approach. Phys. Rev. B 67, 125114... 

---