Implicit assumption

UNIQUAC is significant because it provides a means to estimate multicomponent interactions using no more than binary interaction experimental data, bond angles, and bond distances. There is an implicit assumption that the combinatorial portion of the model, ie, the size and shape effects, can be averaged over a molecule and that these can be directly related to molecular surface area and volume. This assumption can be found in many QSAR methods and probably makes a significant contribution to the generally low accuracy of many QSAR prediction techniques. 

Cullinan presented an extension of Cussler s cluster diffusion the-oiy. His method accurately accounts for composition and temperature dependence of diffusivity. It is novel in that it contains no adjustable constants, and it relates transport properties and solution thermodynamics. This equation has been tested for six very different mixtures by Rollins and Knaebel, and it was found to agree remarkably well with data for most conditions, considering the absence of adjustable parameters. In the dilute region (of either A or B), there are systematic errors probably caused by the breakdown of certain implicit assumptions (that nevertheless appear to be generally vahd at higher concentrations). 

As indicated, an implicit assumption of the JKR theory is that there are no interactions outside the contact radius. More specifically, the energy arguments used in the development of the JKR theory do not allow specific locations of the adhesion forces to be determined except that they must be associated with the contact line where the two surfaces of the particle and substrate become joined. Adhesion-induced stresses act at the surface and not a result of action-at-a-distance interatomic forces. This results in a stress singularity at the circumference of the contact radius [41]. The validity of this assumption was first questioned by Derjaguin et al. [42], who proposed an alternative model of adhesion (commonly referred to as the DMT theory ). Needless to say, the predictions of the JKR and DMT models are vastly different, as discussed by Tabor [41]. 

The sense of this procedure may be verified in Figure 4.13. An implicit assumption in this procedure is that the speed at which the sources are activated equals the speed at which the activation zone is propagated. This holds only if the flame propagates into a quiescent mixture, which does not really happen. Computational experiments with the proposed model show that this assumption is increasingly justified as a cloud s aspect ratio increases. 

Unfortunately, the circumstances of a data collection exercise are rarely adequately described and therefore, any data will be based on some explicit assumptions, some implicit assumptions, and some assumptions that are completely ignored. 

In a formal sense, isoindole can be regarde,d as a IOtt- electron system and, as such, complies vith the Hiickel (4w- -2) rule for aromatic stabilization, with the usual implicit assumption that the crossing bond (8, 9 in 1) represents a relatively small perturbation of the monocyclic, conjugated system. The question in more explicit terms is whether isoindole possesses aromatic stabilization in excess of that exhibited by pyrrole. 

Both of the current models for the central mode scattering contain the implicit assumption of cubic symmetry above Tm. Possibly because of the dramatic nature of the soft-mode behaviour and a ready understanding of the structural transformation in terms of it, there was a strong incentive to establish a link between it and the central mode scattering. A consistent difficulty with this approach is the failure to establish an intrinsic line-width for the central mode peak and the unspecified nature of the mechanism responsibly for a low-frequency resonance in the energy of the soft mode. ... 

Based on a mechanical model in a time-independent flow, de Gennes derivation tries to extrapolate it to a time-dependent chain behavior. His implicit assumptions have been criticised by Bird et al. [55]. More recent calculations extending the de Gennes dumbbell to the bead-spring situation [56] tend, nevertheless, to confirm the existence of a well-characterized CS transition results with up to 100-bead chains show a critical value of the strain rate at scs = 0.5035/iz which is just 7% higher than the value predicted by de Gennes. 

The importance of twinned crystals in demonstrating that nucleation is the relevant growth mechanism has been realized since 1949 [64, 99]6. They were first investigated extensively in polymer crystals by Blundell and Keller [82] and they have recently received increased attention as a means of establishing, or otherwise, the nucleation postulate for lamellar growth [90, 91, 95,100-102]. The diversity of opinion in the literature shows that it is very difficult to draw definite conclusions from the experimental evidence, and the calculations are often founded upon implicit assumptions which may or may not be justified. We therefore restrict our discussion to an introduction to the problem, the complicating features which make any a priori assumptions difficult, and the remaining information which may be fairly confidently deduced. 

An implicit assumption of the foregoing treatment is that A// remains independent of temperature over the range investigated. This is very nearly correct in general, and is particularly the case given that studies of reactions in solution are usually conducted over a temperature interval of only some 30-50°. In certain circumstances the temperature profiles show curvature outside the experimental error. Such cases have, or appear to have, temperature-dependent activation enthalpies. Here we explore one of the reasons for that another is given in Section 7.3. 

Note that prior applications of the proton inventory technique were to reactants in their ground states. The particular example cited, however, refers to an excited state molecule (and indeed was the first of its kind). An implicit assumption made in the... 

The determination of the AG - s depends, of course, on the choice of the reference reaction in solution. For instance, when one states that the rate enhancement by SNase is 1016, one makes the implicit assumption of the reference reaction being... 

A second approach is to compare total mining production of a metal to an estimate of its total natural flux, making the implicit assumption that all mined materials will be released to the environment in the near future (a reasonable... 

One of the sources of the fuzziness surrounding these concepts may well be the implicit assumption in structure-activity relationship (SAR) studies that molecular structure contains (i.e. encodes) the information on the biological activity of a given compound. Such an assumption cannot be incorrect, since this would imply the fallacy of SAR studies. However, the assumption becomes misleading if not properly qualified to the effect that the molecular structure of a given compound contains only part of the information on its bioactivity. Indeed, what the structure of a compound encodes is information about the molecular features accounting... 

Another commonly used approximation for which there is an analytical solution is to assume that the root acts as a zero sink for uptake. Here the solute concentration at the root surface is taken to be zero and uptake is therefore completely controlled by the diffusive flux to the root (21,40,41). The implicit assumption is that root uptake is very rapid in comparison to resupply by transport and hence the root very rapidly depletes the solute concentration at the root surface to zero and maintains it there. The validity of this assumption depends on the value of X and it is inapplicable unless X is greater than or about 10 (38). For such large X, there is a nondimensional critical time (/,.) after which it is reasonable to assume a zero sink (38,42). Approximate values of /, are... 

The transition x —> x" is determined by one-half of the external change in the total first entropy. The factor of occurs for the conditional transition probability with no specific correlation between the terminal states, as this preserves the singlet probability during the reservoir induced transition [4, 8, 80]. The implicit assumption underlying this is that the conductivity of the reservoirs is much greater than that of the subsystem. The second entropy for the stochastic transition is the same as in the linear case, Eq. (71). In the expression for the second entropy... 

When considering the processes in Figures 1.3 to 1.5, an implicit assumption was made that the processes... 

Assumptions in Risk Extrapolation. Risk extrapolation cannot be performed as a mechanical exercise, due to the need for judgment in the selection of data and application of dose-response models. In particular, there are a number of implicit assumptions inherent in risk extrapolation. They may be summarized as follows ... 

The First-Zero Method of Correlation Function Analysis. For the purpose of a practical graphical evaluation of the linear crystallinity, Eq. (8.67) can be applied to a renormalized correlation function y (x/Lapp). The method which has been proposed by Goderis et al. [162] is based on the implicit assumption that the first zero, Jto, of the real correlation function is shifted by the same factor as is the position of its first maximum, Lapp. 

Since the interaction energy /s with the finite substrate is not easy to handle due to the loss of two dimensional periodicity assumed in the derivation of Eq. 5, we simplify the substrate interaction. We considered that the substrate was a sandwich of the amorphous and the crystalline layers, and the attractive potential Uo(z) works at any point (x,y), while the translational barrier Ui(z) cos(2nx/k) only works on the crystalline substrate. The implicit assumption is that the atomic densities of the crystal and the amorphous are not so different. 

The solids particle velocity in the gas-solid two-phase jet can be calculated as shown in Eq. (27), assuming that the slip velocity between the gas and the solid particles equals the terminal velocity of a single particle. It should be noted that calculation of jet momentum flux by Eq. (26) for concentric jets and for gas-solid two-phase jets is only an approximation. It involves an implicit assumption that the momentum transfer between the concentric jets is very fast, essentially complete at the jet nozzle. This assumption seems to work out fine. No further refinement is necessary at this time. For a high velocity ratio between the concentric jets, some modification may be necessary. 

For each scenario, the statistical analysis of this type of experimental design would be a two-way analysis of variance. This is predicated on the construction of the experiment, which includes some implicit assumptions. These assumptions are... 

The coefficients produced still contain the implicit assumption that the value of AX = 1. Therefore to produce correct derivatives, it will still be necessary to divide the results from the formulas by (AX)", as above. 

Silica sol-gel glasses are porous materials, which means some kind of solid material that has holes in it. These holes are also called pores. To call a material a porous material, there is usually some kind of implicit assumption of homogenization and length scale. The holes must be smaller enough, compared to the typical size of the piece of material that is considered, so that it is reasonable to consider the material as a mixture of solid framework and pores28. 

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