Physical validation

When comparisons are to be drawn among scales derived with different criteria of physical validity, we believe this point to be especially appropriate. The SD is the explicit variable in the least-squares procedure, after all, while the correlation coefficient is a derivative providing at best a non linear acceptability scale, with good and bad correlations often crowded in the range. 9-1.0. The present work further provides strong confirmation of this conclusion. 

The linear equilibrium isotherm adsorption relationship (Eq. 11) requires a constant rate of adsorption, and is most often not physically valid because the ability of clay solid particles to absorb pollutants decreases as the adsorbed amount of pollutant increases, contrary to expectations from the liner model. If the rate of adsorption decreases rapidly as the concentration in the pore fluid increases, the simple Freundlich type model (Eqs. 8 and 9) must be extended to properly portray the adsorption relationship. Few models can faithfully portray the adsorption relationship for multicomponent COM-pollutant systems where some of the components are adsorbed and others are desorbed. It is therefore necessary to perform initial tests with the natural system to choose the adsorption model specific to the problem at hand. From leaching-column experimental data, using field materials (soil solids and COMs solutions), and model calibration, the following general function can be successfully applied [155] ... 

In the following we derive an expression for without bothering about a physically valid core-valence separation, treating E " as if it were a continuous function of rt-The acceptable discrete solutions of E " are selected afterward. 

In addition to physically realizable multiple solutions, there are also nonphysical steady states available. These solutions can be problematic, since they usually appear superficially to be valid solutions. In fact, simply by inspection, it is usually impossible to discern if a solution is physical or not. Nonphysical solutions, however, while available and computable in steady state, are unstable in their transient response. That is, a physically valid... 

As with all hydrate theory, it is important to interpret calculations at every opportunity in terms of experiments. With computer simulations, it is deceptively alluring to interpret calculations without physical validation, yet such a path can lead to false conclusions. When physical confirmation is not available, simulations should be regarded with caution. For example, at the heart of both MD and MC methods is the potential energy between individual molecules, which is itself an approximation and limits the accuracy of the simulated macroscopic properties. Such potentials should be validated in terms of their ability to predict measured properties, such as phase equilibria. 

Tunnel sterilizers must demonstrate mechanical repeatability in the same manner as batch ovens. Air velocity, air particulates, temperature consistency, and reliability of all the tunnel controls (heat zone temperatures, belt speed, and blower functions) must be proved during the physical validation studies. 

Some additional conditions must be fulfilled if the function w(k,i,j) is to generate a physically valid additive scheme. One choice relies on a sign-preserving scalar property A(i) that can be assigned to atomic orbitals. For example, appropriately scaled electronegativity can be used as such a scalar property. The choice of... 

The results surveyed in Fig. 8.3, p. 183, prove that the two-moment information model provides a robust, physically valid description of those primitive hydrophobic hydration free energies, with the additional observation that highly specific default models, particularly the hard-sphere default model, are less successful for that purpose. 

For scientific investigations the principal experimental methods are based on the measurement of physical adsorption. Results provide data on surface and pore size distribution. A recent publication showed that for a complete pore structure analysis complex calculations are necessary which demand the application of computers. Extensive software is available that includes presentation of the results as graphics that can be easily interpreted. However, it must be emphasized that all results are obtained indirectly through the use of models therefore, they can only be seen within the context of the applicable preconditions. If this is not considered, the conclusions may not be physically valid. 

The verification of the proposed model is also a two step process involving (1) mathematical validation (the process of verifying that the equations are valid algebraic descriptions of the data that is used to test the model) and (2) physical validation (the process of verifying that the mathematically validate equations also meet the ph5reical conditions imposed by the model). It is not generally realized... 

Each of the single wave simulations performed to construct a plot like in Figure 7 has physical validity regardless of the presence or lack of regions on the Hugoniot where a double shock wave can form. For this reason, it is possible to perform a physically valid single shock wave simulation without any knowledge of the existence of double shock waves. This... 

Note that this is a replacement, not an equation the sum in K-matrix theory is over ail the bound states which actually occur, whereas the trigonometric functions used to represent resonances in MQDT continue to repeat even outside the range of physical validity. They therefore include poles in an energy range below the physical resonances, whereas K-matrix theory does not. So the replacement should only be used when one is above the lowest resonances in the channel, which is anyway the range of validity of MQDT... 

The sterilizer and its associated pipework should be tested to ensure that it is adequate to maintain the positive pressures and vacuum pressures proposed in the cycle specification. The main thrust of physical validation is through tern-perature profiles. 

Suppose, however, that the interpretation of the result of a calculation is less important than its closeness to some empirical data suppose that the calculations are being performed to probe some experimentally inaccessible energies, for example. In this case the whole approach of a graduated series of models, each with its own strengths and limitations, might be inappropriate. It is more important that the numbers be right than that the physical validity of the model be correct. We might, in cases like this, simply abandon the distinction between model and numerical approximations and treat the whole calculation as an interpolation and (perhaps) extrapolation device for experimental results. 

Such difficulties with the simple Born model have stimulated attempts to develop more physically valid theoretical treatments of ion solvation, as discussed previously [121,128,131 — 134]. Relying again on the basic electrostatic approach, improved models have addressed the dielectric satura-... 

In our work, the simulations were carried out to let alkali ions diffuse at 3000 K and 2500 K, respectively, while the structural relaxation of the other ions is limited to room temperature (through velocity scaling). The diffusion coefficient and diffusion activation energy of alkali ions may thus be calculated. This approach, although computationally tricky ,is, nevertheless, physically valid. Experimental support for this approach comes from NMR studies by Stebbins et a/. [16], who found that alkali ion dynamics are effectively decoupled from the network. 

These two clear criteria have contributed to the active development of functionals. However, as a trade-off, brought about by overemphasizing these criteria for many years, we find an enormous number of functionals that attempt to enhance the physical validity with artificial additional terms or to improve the numerical accuracies with many semiempirical parameters. To solve this problem, we need the following new criteria for developing functionals ... 

The OP correlation functional (Tsuneda et al. 1999) determines the exclusion volume of the correlation hole, by assuming that it is proportional to the exclusion volume of the exchange hole coming from the combined exchange functional, in order to enhance the physical validity of the CS-type correlation functional. In this functional, only electron correlations of opposite-spin pairs are explicitly incorporated, while electron correlations of parallel-spin pairs are secondary effects from the combined exchange functional. It has only one semiempirical parameter, which is the minimum required for adapting to the exchange functional. As a result, a simple correlation functional was derived ... 

Fundamental conditions indicate the conditions that should be met by the energy components such as the kinetic, exchange, and correlation energies. As described in Sect. 5.1, fundamental conditions have been used as significant criteria for assessing the physical validities of functionals developed. Actually, in solid state physics, in which extreme electronic states are often investigated, it appears to be conventional to use functionals that meet these conditions. In this chapter, let us briefly review major fundamental conditions. 

The LR term represents the interactions caused by the Coulomb electrostatic forces, expressed by a modified Debye-Hiickel term. The physical validity of the term is limited to the very dilute region. The purpose of this term is just to provide the true limiting law at infinite dilution. 

The span depth ratio has been chosen to ensure a shear failure. Although the physical validity and accuracy is questionable, useful results can be achieved. However, attention is drawn to the following points ... 

The physical validity of the first two of these assumptions has been discussed in detail by Marshak [6], and so will not be gone into here. The... 

The authors of the present paper used viscosity of type of eqution (35) obtained by data fitting to describe satisfactorily the viscous mechanism of dynamic strength of rocks (Qi, Qian, 2003), but the physical validation of viscosity of type of eqution (35) was not given then, the study in the present paper fills this gap. 

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