Sound physics

The oldest records (a-c) and Fig. 1-2 clearly show a strong degree of temporal correlation between three biologically involved atmospheric components and climate (as indicated by temperature). Because there is a sound physical basis for the involvement of all three in climatic processes, it is necessary to study, view, and understand these variables and climate as linked components of a system. They are all dependent variables and carmot be viewed as independent with climate being imposed as an exogenous factor. 

Although the previous three chapters have been concerned with placing the CALPHAD methodology on a sound physical basis, the over-riding objective of such a method is to generate a reliable and user-fnendly output that reflects various properties of multicomponent industrial materials. The last three chapters therefore return to the more practical theme of how this can be achieved. 

Clearly CALPHAD has now come of age and is at a watershed where complex phase equilibria calculations can now be performed as a routine operation and yet have also been placed on a sound physical basis. Computer programmes exist which can perform complex calculations on a PC and which can therefore be operated at any location without extensive prior expertise. Furthermore, it is possible in many cases to predict phase equilibria in multi-component alloys to a degree which is close to that expected from experiment (see Chapter 10). It is therefore a branch of science that is mature and, indeed, has already entered the next stage of development, which emphasises the need to concentrate on extending its range of applicability. 

Despite the success of phase-diagram calculations, there is still a considerable reluctance by sections of the scientific community to accept that TC lattice stabilities represent a real physical entity as distinct from an operational convenience. This inevitably creates doubts concerning the ultimate validity of the calculations. It is therefore important to verify that TC lattice stabilities, largely derived by extrapolation, can be verified by ab initio calculations and placed on a sound physical basis. 

Fundamentally based ordering models which consider short-range ordering phenomena are rarely incorporated in CALPHAD software, and this is another area which the authors would like to see expanded. However, before this can be done in a general fashion, it is clear that ordering models need to be made more flexible, while retaining a sound physical basis, and that vibrational entropy as well as complex compositional effects must be included. 

The statistics of v may be considered stationary with sound physical basis. Therefore, we shall simply adopt ... 

The lattice approach has also been used for the systematic description of inorganic crystal structures (Wells 1975, pp. 119-55 Hyde and Andersson 1989, pp. 6-49), but the method is not just geometric and descriptive. It has a sound physical basis and can therefore be used for structure modelling. 

Barron s classification is based on sound physical principles and is a valuable contribution to our understanding of chirality phenomena. In view of the differences between the symmetry properties of the two classes, as discussed below, it is to be expected that they also differ markedly in the associated physical and chemical observables. In particular, as Barron has repeatedly emphasized, only... 

The answers to the problems outlined here lie in the further utilization of sound physical and colloidal chemical principles. Therein lies the challenge. 

Numerical calculations show that ) affects significantly the versus Vg plots. The other parameters have smaller effect on the drain current. Some of the parameters obtained with the FDTO model are different from those obtained in Ref. [157]. To obtain accurate values of the material parameters, the use of a model based on sound physics is essential. 

Owing in a large measure to the work of Wagner and co-workers, the theoretical understanding of gas-solid reactions has been put on a sound physical basis. This has greatly stimulated the development of experimental methods for the study of gas-solid reactions. In the case of gases reacting on solid surfaces no comparable theoretical development has occurred. However, the development of new experimental methods has stimulated new work in this field. 

Some quantitative assessments on how these factors determine the separation factors will be very desirable to guide systematic material development efforts for designing the next generation of inorganic membranes. Plausible theoretical models based on sound physical and chemical reasoning with justified or verified assumptions have been attempted for this purpose. 

The above model and other similar ones indicate the need to produce membranes with pore sizes significantly smaller than what have been attainable to date. Thus sound physics-based models with verified assumptions like the one presented above not only provides the quantitative information on the approximate pore size required to achieve a given separation factor for a certain gas pair such as He-CC>2 or He-N2 but also shows that one should expect, in some cases, to see a lower separation factor as the pore size decreases before a sharply increasing separation factor in the pore size approaching the size of the gas molecules. 

A regression line should be interpreted with caution. First, its vaUdity should be inferred beyond the experimentally determined values of x only when there is sound physical or theoretical justification. For example, in the above instance of regression of titration volume with pH, the quantity a does not necessarily have physical reality at pH = 0, because no experiments were run at that value. Another example is a regression plot in which the theoretically expected relation is y = fix but the least-squares straight line gives an intercept a at x = 0. The intercept may be wrongly interpreted to be a blank value of y, when in fact it may have resulted merely from there being a finite uncertainty in the value of fi for a Umited set of data. A value of y should actually be determined for x = 0. 

Based on the interpretation developed here, the assumption of constant Pt and its empirical expression by Eq. (3-32), seem to be sound physically for bubble columns. As shown in later sections, the flow properties of a fluid catalyst bed of good fluidity (e.g., cracking catalyst) are in many respects similar hence the same interpretation can be applied to the fluid catalyst bed (FCB). 

Interesting phenomena observed gave rise to some speculations which have lacked sound physical justification examples are the speculations on a massive transfer of electrons from (or to) the support to (or from) the metal, the ideas about changes of the work function of the metal by such a transfer or by the.field of the support, etc. However, these ideas have received considerable attention and unfortunately they have tended to shadow other pieces of information concerning the metal-support interaction. 

In fluid d mamics there is no specific use of the transport equation for entropy other than being a physical condition indicating whether a constitutive relation proposed has a sound physical basis or not (nevertheless, this may be a constraint of great importance in many situations). In this connexion we usually think of the second law of thermodynamics as providing an inequality, expressing the observation that irreversible phenomena lead to entropy production. 

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