Plausibility criterion

In particular it can be shown that the dynamic flocculation model of stress softening and hysteresis fulfils a plausibility criterion, important, e.g., for finite element (FE) apphcations. Accordingly, any deformation mode can be predicted based solely on uniaxial stress-strain measurements, which can be carried out relatively easily. From the simulations of stress-strain cycles at medium and large strain it can be concluded that the model of cluster breakdown and reaggregation for prestrained samples represents a fundamental micromechanical basis for the description of nonlinear viscoelasticity of filler-reinforced rubbers. Thereby, the mechanisms of energy storage and dissipation are traced back to the elastic response of tender but fragile filler clusters [24]. 

By fitting experimental data for different deformation modes to these functions, the three network parameters of unfilled polymer networks Gc, Ge, and ne/Te can be determined. The validity of the concept can be tested if the estimated fitting parameters for the different deformation modes are compared. A plausibility criterion for the proposed model is formulated by demanding that all deformation modes can be described by a single set of network parameters. The result of this plausibility test is depicted in Fig. 44, where stress-strain data of an unfilled NR-vulcanizate are shown for the three different deformation modes considered above. Obviously, the material parameters found from the fit to the uniaxial data provide a rather good prediction for the two other modes. The observed deviations are within the range of experimental errors. 

Figure 46a shows that a reasonable adaptation of the stress contribution of the clusters can be obtained, if the distribution function Eq. (55) with mean cluster size =25 and distribution width b= 0.8 is used. Obviously, the form of the distribution function is roughly the same as the one in Fig. 45b. The simulation curve of the first uniaxial stretching cycle now fits much better to the experimental data than in Fig. 45c. Furthermore, a fair simulation is also obtained for the equi-biaxial measurement data, implying that the plausibility criterion , discussed at the end of Sect. 5.2.2, is also fulfilled for the present model of filler reinforced rubbers. Note that for the simulation of the equi-biaxial stress-strain curve, Eq. (47) is used together with Eqs. (45) and (38). The strain amplification factor X(E) is evaluated by referring to Eqs. (53) and (54) with i= 2= and 3=(l+ ) 2-l.

The four structures with three double bonds (third row) and the one with four double bonds are the most plausible Lewis structures, (b) The structure with four double bonds fits these observations best, (c) +7 the structure with all single bonds fits this criterion best, (d) Approaches (a) and (b) are consistent but approach (c) is not. This result is reasonable because oxidation numbers are assigned by assuming ionic bonding. 2.109 The alkyne group has the stiffer C—H bond because a large force constant, k, results in a higher-frequency absorption. 

The positive values obtained in practically all cases indicate that all these models may be plausible representations of the data and indeed, the correlation coefBcients, R, are greater than 0.9. Thus, statistical compliance is not a sufficient basis for model discrimination. Specifically, the thermodynamic consistency of the estimates, as proposed by Boudart et al. [3], is appropriate further scrutinizing criterion during kinetic modelling and has been gainfully employed in other reactions [4-6]. 

Obviously an exponential mapping looks also good in the sense of the first criterion. One sees easily that J r) is independent of the choice of j, such that we may as well take 7 = 1. Of course, this is only a plausiblity argument and we need a rigorous criterion for the optimum mapping. We come back to this problem in the conclusions. 

One important criterion for determining whether an association is causative is whether it is biologically plausible. Although a justification of the biological plausibility of each of our observed associations is beyond the scope of this report, it is rather common knowledge that abundant evidence from other studies confirms the plausibility of a causative link between meat use and coronary disease (22). However, this study is the first major observational study to clearly show this relationship among U.S. subjects. The associations between meat and diabetes are certainly plausible, but there is considerably less evidence from other experimental or observational studies to substantiate such a relationship. 

This point is simply a dramatization of the first defect of the theory that identifies with consciousness and S with the preconscious. If both systems have to be rational in the end, the best policy is to use rationality as the original criterion for setting them up and to hope that the line running between them will more or less coincide with the line between consciousness and the preconscious (without postulating any internal consciousness). In fact, the coincidence is far from perfect, but it is fairly good and that, no doubt, accounts for the plausibility of theories like Freud s. 

A plausible estimate of the spatial extension of a hydrogenic orbital is the radius of a spherical boundary surface within which there is a high probability of finding the electron. In order to develop this criterion on a quantitative basis, it is useful to define a cumulative probability function FW(p) which gives the probability of finding the electron at a distance less than or equal to p from the nucleus ... 

In our study of search problems we have seen that single variable systems can be optimized with ease two-variable systems, with some effort and multivariable systems, only with extreme difficulty if at all. As more variables enter a search problem, the number of experiments needed grows rapidly, and the unimodality assumption becomes less and less plausible. Thus our investigation of search problems leads directly to interaction problems, where the criterion of effectiveness depends on so many factors that it is impractical, or even impossible, to find the optimum by conventional methods. Successful techniques for solving interaction problems involve decomposing a big system into several smaller ones, as we have already done with our lines of search. 

When one thinks in terms of the many fused-ring isomers with unsatisfied valences at the edges that would naturally arise from a graphite fragmentation, this result seems impossible there is not much to choose between such isomers in terms of stability. If one tries to shift to a tetrahedral diamond structure, the entire surface of the cluster will be covered with unsatisfied valences. Thus a search was made for some other plausible structure which would satisfy all sp valences. Only a spheroidal structure appears likely to satisfy this criterion, and thus Buckminster Fuller s studies were consulted (see, for example, ref. 7). An unusually beautiful (and probably unique) choice is the truncated icosahedron depicted in Fig. 1. As mentioned above, all valences are satisfied with this structure, and the molecule appears to be aromatic. The structure has the symmetry of the icosahedral group. The inner and outer surfaces are covered with a sea of v electrons. The diameter of this C o molecule is 7 A, providing an inner cavity which appears to be capable of holding a variety of atoms. ... 

To use the D-optimality criterion to select a design it is required that the experimenter can specify a plausible model. To do so, a good portion of chemical intuition is required. As intuition is a function of experience, this can be difficult with... 

The value of P is used as a criterion to decide whether chance is a plausible explanation of the difference seen in the study data. If P is sufficiently low, chance may be thought to be an implausible explanation for the difference. The famous British statistician and geneticist Sir Ronald Fisher FRS proposed that the value 0-05 (or 5%) should be used as the criterion for judging if a value of P was sufficiently low to reject chance as the explanation of the difference - this is called the 0-05 or 5% level of statistical significance. So, the P = 0-017 would be sufficiently low to permit the conclusion that the difference was statistically significant - that is, that chance is an implausible explanation of the difference. On the other hand, P = 0-095 is not sufficiently small for chance to be thought an implausible explanation for the result put another way, the difference is not statistically significant. 

The next step of the hypothesis testing process is to identify a numeric criterion by which the plausibility of the null hypothesis is tested. This numeric criterion is called the test statistic, and we use it to decide if the value that resulted from the study contradicts the null hypothesis or not. The test statistic to be used in this case is ... 

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