Plausibility argument for

If we wish to know the number of (VpV)-collisions that actually take place in this small time interval, we need to know exactly where each particle is located and then follow the motion of all the particles from time tto time t+ bt. In fact, this is what is done in computer simulated molecular dynamics. We wish to avoid this exact specification of the particle trajectories, and instead carry out a plausible argument for the computation of r To do this, Boltzmann made the following assumption, called the Stosszahlansatz, which we encountered already in the calculation of the mean free path ... 

The center manifold approach of Mercer and Roberts (see the article Mercer and Roberts, 1990 and the subsequent article by Rosencrans, 1997) allowed to calculate approximations at any order for the original Taylor s model. Even if the error estimate was not obtained, it gives a very plausible argument for the validity of the effective model. This approach was applied to reactive flows in the article by Balakotaiah and Chang (1995). A number of effective models for different Damkohler numbers were obtained. Some generalizations to reactive flows through porous media are in Mauri (1991) and the preliminary results on their mathematical justification are in Allaire and Raphael (2007). 

PROBLEM 3.1.1. In one dimension "derive," or give a plausibility argument, for the Schrodinger equation by combining the one-dimensional classical wave equation... 

R. A. Ogg, Jr., J. Chem. Phys. 21, 2079 (1953), has shown that NO and N2O6 catalyze the exchange of labeled O2 with NO2 (no exchange without catalysis) and has presented very plausible arguments for believing the catalysis to take place via the species O—N—O—O and O2N—O—O, respectively ... 

Plausibility Argument for Surface Relaxation. As already noted above, crystal surfaces are characterized by a wide range of structural rearrangements relative to the ideal surface. One such rearrangement is surface relaxation, with the entire surface layer moving either towards or away from the subsurface layers as shown... 

The effects of pH and Cl ion concentration on the species distribution of platinum compounds have been used to fashion the following plausible argument for the chemistry of cw-DDP in vivo. With the use of thermodynamic data for the ethylenediamine (en) analogue [Pt(en)Cl2], the relative concentrations of hydrolyzed species at pH 7.4 were estimated (see Table 9.3) for blood plasma and cytoplasm (Figure 9.7). The higher chloride ion concentration in... 

Another plausibility argument for negative temperatures is to consider mixing equal amounts of two spin systems at Tg=T and Tg=-T. The resulting mixture will obviously have a temperature intermediate between the two starting spin systems and you should be able to convince yourself that its temperature will be < . 

These reactions may proceed nonenzymatically or through the action of glutathione dehydrogenase (ascorbate) (E.C. 1.8.5.1) and ascorbate-specific peroxidase (Halliwell, 1978). Despite these plausible arguments for the reduction of H2O2 by GSH, Jablonski and Anderson (1978) were unable to demonstrate a sustained reduction of either H2O2 or dehydroascorbate by chloroplasts illuminated in the presence of catalytic amounts of GSSG and NADPH. 

The existence of oscillatory behaviour for the recycled CSTR was demonstrated by Aris and Amundson." Undamped oscillations in the fonn of limit cycles occur under particular parameter values for the system and Aris and Amundson recogniied that these limit cycles should originate at the critical value when the stable steady state becomes an unstable one. Such an instance is called a bifurcation point. They developed a criterion for the direction of bifurcation and gave plausible arguments for the stability of the limit cycle. 

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