Phenomenological trends

Lee CE (2002) Evolutionary genetics of invasive species. Trends Ecol Evol 17 386-391 Leonardi PI, Miravalles AB, Faugeron S, Flores V, Beltran J, Correa JA (2006) Diversity, phenomenology and epidemiology of epiphytism in farmed Gracilaria chilensis (Rhodophyta) in northern Chile. Eur J Phycol 41 247-257... 

A summary of analytic expressions obtained in this manner for all the viscoelastic functions is presented in Table 4 and 5 for the linear and cubic arrays. The well-known phenomenological analogy (8) between dynamic compliance and dielectric permittivity allows the formal use of Eqs. (T 5), (T 6), and (T 11), (T 12) for the dielectric constant, e (co), and loss, e"(co), of the linear and cubic arrays, respectively (see Table 6). The derivations of these equations are elaborated in the next section and certain molecular weight trends are discussed. 

E.J. Brandas, L.J. Dunne, J.N. Murrell, Phenomenological Description of d-Wave Condensates of High-Tc Superconducting Cuprates, in J. Maruani et al. (Eds.), New Trends in Quantum Systems in Chemistry and Physics, Kluwer Academic Publishers, Vol. 2, 2000, p. 289. 

A necessary condition for a good model is internal consistency. The phenomenological model meets this condition very well in the way it correlates the trends and features of loss factor with model parameters. This is shown in Figure 12 where the relative... 

Table HI shows the values for the kinetic and statistical parameters obtained by analyzing the data for all ternary systems according to the phenomenological model of Hall [5]. A comparison of the values of the various parameters (cf. Table II and Table III) obtained from analyses employing these two models show, generally, that larger values are obtained with the Hall model however, the trends in the derived parameters are similar. The values of the rate constants for the alcohol exchange process in the Hall model were obtained by extrapolating C —> 0 to avoid any concentration dependence of k. Using the extrapolated value of k, it was shown [5] that kj is given by...

Figure 3 illustrates how the dual site coking causes the selectivity for Q to decrease with increasing degree of site coverage at a rate which depends upon the number of sites in the cluster Clearly, the phenomenological approach cannot reveal the trends presented here ... 

Almost all physical models use simple pore geometries. Practical pore systems are, however, very complicated and contain parameters which are difficult to measure or which have a wide distribution of their characteristic parameters. The applicability of a rigorous treatment and of very refined models and physical expressions is therefore doubtful. The treatment in this chapter will make use mainly of phenomenological equations which allow description of data, data reduction and some extrapolation and which rely on experimentally determined parameter values. Gas kinetic theory and expressions based on the microscopic (atomic) level will be used only to estimate some parameter values and to predict trends. 

In summary, I have discussed a semi-phenomenological elastic theory for ion clustering in ionomers. The theory is consistent with observed trends in perfluorinated ionomers. I have also demonstrated the percolatlve nature of ion transport in these ionomers and computed quantitatively their tensile modulus. Finally, I have discussed the Influence of morphology on ion selectivity in perfluorinated ionomer blends. In particular, I have pointed out that an universally preferred morphology beneficial to all blends does not exist the ideal morphology must be individually determined based on component properties. Most of the theories and conclusions here are very general and applicable to other composite polymer systems. 

A review article by Bicerano [64] delves into the phenomenology of polymer crystallization in far greater detail including the trends for Tm and for the other crystallization parameters of homopolymers and copolymers, as well as the trends and some of the models for the kinetics of crystallization. Polypropylene, polyethylene terephthalate), and copolymers of propylene and of ethylene terephthalate, are all given detailed consideration as case studies. 

The effectiveness of the above treatment will be examined in Section 8.7, but even if it can guide us with regards to the general trend it cannot be used in a phenomenological way to estimate actual molecular properties. Perhaps for this reason, microscopic estimates [50] of the parameters in Eq. (8.19) for the reaction catalyzed by lipoxygenase were found to be very different than those obtained by fitting Eq. 

The result of a HAW LEER analysis of the CA III system is illustrated in Eig. 8.6 and the overall dependence of AAg on AG is presented in Fig. 8.7 (for more details see Ref [77]). As seen from the figures our model reproduced the observed trend. However, the origin of the trend is very different than that deduced from the two-state Marcus equation. That is, the flattening of the LEER at ApKa > 0, which would be considered in a phenomenological analysis of a two-state model as the beginning of the Marcus inverted region (where AGo = —7), is due to the behavior of the three-state system (see Ref [79]). 

Moreover, it should be noted that, taking into account the euristic and program character of this concept, in the beginning its discussion should not be limited to the consideration of a detailed picture of the interaction between the monomer and the active center. The purpose of the discussion, just as that of the entire concept, is to show the prospects and the trend of development of the future axiomatic microscopic theory of polymerization as a whole on the basis of the phenomenological analysis of particular examples. 

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