It is also important that sufficiently large basis sets are used. The 6—31G(d) basis set should be considered the absolute minimum for reliable results. Some studies have used locally dense basis sets, which have a larger basis on the atom of interest and a smaller basis on the other atoms. In general, this results in only minimal improvement since the spectra are due to interaction between atoms, rather than the electron density around one atom. [Pg.252]

Thus, when p(0) and p(L) both become sufficiently Large, the right hand side of equation (10.10) should asymptote at a value which is independent of the particular substances employed or the composition of the mixture, and [Pg.92]

At the opposite limit, where all the pores are sufficiently large that bulk diffusion controls, a similar calculation can be performed. In this case the appropriate flux relations are equation (5.29) and its companion obtained by interchanging the suffixes. For the symmetric systems considered here these may be written in scalar form [Pg.131]

G is a multiplier which is zero at locations where slip condition does not apply and is a sufficiently large number at the nodes where slip may occur. It is important to note that, when the shear stress at a wall exceeds the threshold of slip and the fluid slides over the solid surface, this may reduce the shearing to below the critical value resulting in a renewed stick. Therefore imposition of wall slip introduces a form of non-linearity into the flow model which should be handled via an iterative loop. The slip coefficient (i.e. /I in the Navier s slip condition given as Equation (3.59) is defined as [Pg.158]

High explosives. Those explosives which normally burn without undue violence when ignited in an open space, but which can be detonated by a sufficiently large sudden mechanical or explosive shock. [Pg.171]

The last approximation is for finite At. When the equations of motions are solved exactly, the model provides the correct answer (cr = 0). When the time step is sufficiently large we argue below that equation (10) is still reasonable. The essential assumption is for the intermediate range of time steps for which the errors may maintain correlation. We do not consider instabilities of the numerical solution which are easy to detect, and in which the errors are clearly correlated even for large separation in time. Calculation of the correlation of the errors (as defined in equation (9)) can further test the assumption of no correlation of Q t)Q t )). [Pg.268]

In fact, the pressures will never settle completely to constant values until diffusion is complete and the composition is the same in both chambers, but by making the chambers sufficiently large this rate of drift of the pressures can be reduced below any desired level. [Pg.57]

For a particular process, this expression should be multiplied with the probability for that process as determined by projection of the END evolved state v /(t) for the system on the appropriate final state v /y described within the same basis set and at the same level of approximation as the evolved state, that is, the amplitude (< /y t /(f)) at a sufficiently large time f. [Pg.236]

While the phase rule requires tliree components for an unsymmetrical tricritical point, theory can reduce this requirement to two components with a continuous variation of the interaction parameters. Lindli et al (1984) calculated a phase diagram from the van der Waals equation for binary mixtures and found (in accord with figure A2.5.13 that a tricritical point occurred at sufficiently large values of the parameter (a measure of the difference between the two components). [Pg.659]

A special apparatus (Fig. Ill, 40,1) renders the preparation of iodides from alcohols a very simple operation. The special features of the apparatus are —(i) a wide bored (3-4 mm.) stopcock A which considerably reduces the danger of crystallisation in the bore of the tap of the iodine from the hot alcoholic solution (ii) a reservoir B for the solid iodine and possessing a capacity sufficiently large to hold all the alkyl iodide produced (iii) a wide tube C which permits the alcohol vapour fix)m the flask D to pass rapidly into the reservoir B, thus ensuring that the iodine is dissolved by alcohol which is almost at the boiling point. An improved apparatus is shown in Fig. Ill, 40, 2, a and b here a [Pg.285]

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