Irreducible volume

This equation indicates that the irreducible volume of the first Brillouin zone depends upon the factor-group symmetry. For Pnam-D h, there are eight operations Rj Rg as shown in Table IV. 1. Accordingly,... 

Other good news arise fiom the following observation. We notice that the fet irreducible segment volume is three times as big as that of the fee, but the number of function evaluations for each energy point of the calculation c) is never more than twice the corresponding number of the... 

If the NMR response is capable of estimating the pore size distribution, then it also has the potential to estimate the fraction of the pore space that is capable of being occupied by the hydrocarbon and the remaining fraction that will only be occupied by water. The Free Fluid Index (FFI) is an estimate of the amount of potential hydrocarbons in the rock when saturated to a given capillary pressure. It is expressed as a fraction of the rock bulk volume. The Bulk Volume Irreducible (BVI) is the fraction of the rock bulk volume that will be occupied by water at the same capillary pressure. The fraction of the rock pore volume that will only be occupied by water is called the irreducible water saturation (Siwr = BVI/cj>). The amount of water that is irreducible is a function of the driving force to displace water, i.e., the capillary pressure. Usually the specified driving force is an air-water capillary pressure of 0.69 MPa (100 psi). 

G. R. Coats, D. Marschall, D. Mardon, J. Galford 1997, A New Characterization of Bulk-Volume Irreducible Using Magnetic Resonance, paper QQ presented at the SPWLA 38 Annual Logging Symposium, Houston, TX, June 15-18, 1997. 

Procedure. Core floods were carried out in horizontally mounted Berea sandstone cores of length 61 cm and diameter 5 cm. Porosity varied from 18 to 25% and brine permeability from 100 to 800 Jim2. The cores were coated with a thin layer of epoxy and cast in stainless steel core holders using molten Cerrobend alloy (melting point 70°C). The ends of the cores were machined flush with the core holder and flanges were bolted on. Pore volume was determined by vacuum followed by imbibition of brine. Absolute permeability and porosity were determined. The cores were initially saturated with brine (2% NaCl). An oil flood was then started at a rate of lOm/day until an irreducible water saturation (26-38%) was established. 

In order to analyze the rate of the decay of chemical correlations in macromolecules of proteinlike copolymers, it is necessary to calculate the dependence on n of the irreducible correlator o>ap(n) = Yap(n) - XaXp where the reducible correlator Yap(n) is obtained by formula (Eq. 45). Correlator coap(n) is calculated as the sum of series (Eq. 45), each item of which is the product of two cofactors. The first of them is controlled just by the number of monomeric units l in a globule, as well as by their volume fraction [Pg.160]

To this list can now be added the advantages of 0(3) over U(l) electrodynamics, advantages that are described in the review by Evans in Part 2 of this three-volume set and by Evans, Jeffers, and Vigier in Part 3. In summary, by interlocking the Sachs and 0(3) theories, it becomes apparent that the advantages of 0(3) over U(l) are symptomatic of the fact that the electromagnetic field vanishes in flat spacetime (special relativity), if the irreducible representations of the Einstein group are used. 

Exercise 6.12 Suppose that G is a Lie group with a volume-one invariant integral. Suppose that (G, V, p) is a representation with character y. Show that p is irreducible if and only if /(g) dg = 1. 

The valence orbitals taken for a molecular-orbital calculation of a transition metal complex are the nd, (n + l)s, and (n + l)p metal orbitals and appropriate a and n functions of the ligands. Many of these valence orbitals are not individually basis functions for an irreducible representation in the symmetry under consideration. Symmetry basis functions transforming properly must be constructed, by methods analogous to those used throughout this volume. The results for a number of important symmetries are tabulated in this volume in various places, as follows ... 

In Part 1 of this three-volume set, Sachs [117] has demonstrated that electromagnetic energy is available from curved spacetime by using the irreducible... 

NaCl aqueous solution. About six pore volumes of the same solution was injected to stabilize the clay as well as to determine the absolute permeability and porosity (average permeability = 380 millidarcy, average porosity = 0.19). The porous medium was then flooded with Salem crude oil (viscosity at room temperature = 6 cp) to irreducible water content. Waterflood (1% NaCl) was carried out to waterbreak-through. The surfactant solution (3.16 x 10 mol/il,... 

Fig. 2. Band structure and total DOS of bulk V2O5. The energy bands are shown for characteristic paths connecting high symmetry points of the irreducible part of the orthorhombic Brillouin zone (BZ) which is included at the bottom. All energies e(k) are taken with respect to that of the highest occupied state. The DOS is given in states per unit volume and per eV.

As can be seen from Eq. (2), the observed intrinsic viscosity for each slice is proportional to the ratio of two detectors responses. It follows that detector noise, which is an irreducible component of the measurement process, introduces noise in the intrinsic viscosity that depends on this ratio. However, two detectors have different sensitivities at the tails of polymer distribution the concentration detector is less sensitive to the high-molecular-weight end and the viscometer is less sensitive to the opposite end. Thus, the noise increases dramatically on both tails of the distribution, where the ratio (2) does not produce physically meaningful values. For example, the logarithm of intrinsic viscosity computed from the slice ratios (2) sometimes does not increase monotonically with molecular weight (i.e., with decreasing elution volume V) even for the flexible coillike polymers (curves 2 in Fig. 1). 

Fig. 3 Dependence of the decimal logarithm of irreducible correlator tun = rnlw) -on distance n along polymer chain for macromolecules of equimolar composition at the values of parameters (Eq. 20) h = 70, h = 0.01. Curves are presented for macromolecules whose length is Z = 2 x lO (1) 6 x lO (2) 12 x lO (3). Thin lines represent asymptotic expressions at n n. Volume fraction of monomeric units in the globule is = 0.9...

The three components of the rotational tensor linear order. These symmetry strains are shown in fig. 4. p = corresponds to the fully symmetric volume strain. Deformations of the local environment lead to deformations of the 4f-charge cloud, microscopically one therefore has a coupling of strains to multipolar operators Op of the 4f shell. These are polynomials in J, and of degree 1 = 2, 4 and 6 which again transform as irreducible point-group representations. In the cubic case the quadrupolar (/ = 2) operators are ... 

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