Intermediate range

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 )). 

The above estimates of pressure variations suggest that their magni-tude as a percentage of the absolute pressure may not be very large except near the limit of Knudsen diffusion. But in porous catalysts, as we have seen, the diffusion processes to be modeled often lie in the Intermediate range between Knudsen streaming and bulk diffusion control. It is therefore tempting to try to simplify the flux equations in such a way as to... 

Table 9.1), with the choice of buret determined by the demands of the analysis. The accuracy obtainable with a buret can be improved by calibrating it over several intermediate ranges of volumes using the same method described in Chapter 5 for calibrating pipets. In this manner, the volume of titrant delivered can be corrected for any variations in the buret s internal diameter. 

Cast-Cobalt Alloys. Cast-cobalt alloys were introduced about the same time as HSS for cutting tool appHcations. Popularly known as StelHte tools, these materials are Co-rich Cr—W—C cast alloys having properties and appHcations in the intermediate range between HSS and cemented carbides. 

There is no sharp dividing hne between pure physical absorption and absorption controlled by the rate of a chemic reaction. Most cases fall in an intermediate range in which the rate of absoration is limited both by the resistance to diffusion and by the finite velocity of the reaction. Even in these intermediate cases the equihbria between the various diffusing species involved in the reaction may affect the rate of absorption. 

Vibration beeomes eritieal in tlie intermediate ranges beeause stmetural members are relatively less massive and the speeds are high enough to mateh the resulting natural frequeneies in some eases. Thorough testing of rotors is essential, and extensive work has been done in this area. 

The most direct information obtained from LEED is the periodicity and intermediate range order within the transfer width of the surface under investigation. This can be gathered by visual inspection of the diffraction pattern and/or by relatively simple mathematical transformations of the spot profiles. 

PK. — the negative logarithm of the equilibrium constant for acids or bases. This parameter is an indicator of the strength of an acid or base. Strong acids, such as H2SO4, and HCl, have low pK s (i.e., -1.0) while strong bases such as KOH and NaOH, have pK s close to 14.0. Weak acids and weak bases fall in the intermediate range. 

Type B—Actual hood. Falls in the intermediate range between type A and type C. 

FIG. 34 (a) Log-log plot of i ads(0 ane for an adsorbed layer containing 64 chains (cf) = 0.25), where at time / = 0 the adsorption energy strength e is reduced from e = -4.0 to values between e = -1.2 and e = -0.2, as indicated in the figure. Straight lines show a power law Fads(t) oc over some intermediate range of times. The inset shows that the (effective) exponent a can be fitted to a linear decrease with e. (b) The same data but with the equilibrium part ads(l l) subtracted [23]. 

At the dissociation limit the UHF wave function is essentially an equal mixture of a singlet and a triplet state, as discussed in Section 4.4. Removal of the triplet state by projection (PUHF) lowers the energy in the intermediate range, but has no effect when the bond is completely broken, since the singlet and triplet states are degenerate here. 

The Warner function has all the desired asymptotical characteristics, i.e. a linear dependence of f(r) on r at small deformation and a finite length Nlp in the limit of infinite force (Fig. 3). In a non-deterministic flow such as a turbulent flow, it was found useful to model f(r) with an anharmonic oscillator law which permits us to account for the deviation of f(r) from linearity in the intermediate range of chain deformation [34] ... 

In Mampel s treatment [447] of nucleation and growth reactions, eqn. (7, n = 3) was found to be applicable to intermediate ranges of a, sometimes preceded by power law obedience and followed by a period of first-order behaviour. Transitions from obedience of one kinetic relation to another have been reported in the literature [409,458,459]. Equation (7, n = 3) is close to zero order in the early stages but becomes more strongly deceleratory when a > 0.5. 

The buffer layer covers the intermediate range 5 < >,+ < 30. A straight line may be drawn to connect the curve for the laminar sub-layer (equation 12.40) at y+ = 5 with the line... 

As can be seen from the above, the shape of the resolved rotational structure is well described when the parameters of the fitting law were chosen from the best fit to experiment. The values of estimated from the rotational width of the collapsed Q-branch qZE. Therefore the models giving the same high-density limits. One may hope to discriminate between them only in the intermediate range of densities where the spectrum is unresolved but has not yet collapsed. The spectral shape in this range may be calculated only numerically from Eq. (4.86) with impact operator Tj, linear in n. Of course, it implies that binary theory is still valid and that vibrational dephasing is not yet... 

Alloys of lead and thallium have a structure based upon cubic closest packing from 0 to about 87-5 atomic percent thallium. The variation of the lattice constant with composition gives strong indication that ordered structures PbTl, and PbTl, exist. In the intermediate ranges, solid solutions of the types Pb(Pb,Tl)a and Pb(Pb,Tl)TlB exist. Interpretation of interatomic distances indicates that thallium atoms present in low concentration in lead assume the same valence as lead, about 2-14, and that the valence of thallium increases with increase in the mole fraction of thallium present, having the same value, about 2-50, in PbTls and PbTl, as in pure thallium. A theory of the structure of the alloys is presented which explains the observed phase diagram,... 

Other neuronal Cl -channels are Ca " -controlled. Increases in cytosolic Ca enhances the probability of these channels being open [26,27]. These channels stabilize the membrane voltage by clamping it towards the Cl -equilibrium potential. Such channels have been found, e.g., in cultured mouse spinal neurones and in molluscan neurones. They subserve the repolarization phenomena and hence assist Ca -activated -channels. Their conductance is in the small to intermediate range. They are usually gated by depolarization. 

The practical value of supercapacitors has been proven over a certain intermediate range of currents. At lower currents ordinary batteries which have a higher... 

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