Locality argument

A local argument is going on, with one person claiming that generic labeled applesauce is poorer quality than the name brands. It is decided that a measure of the vitamin C (ascorbic acid) in each would settle the argument and because you are a chemist you have been selected to make the measurements. Vitamin C is not enough. Because dehydroascorbic acid is reduced to ascorbic acid upon standing, it is desired to determine the total amount and the amount of eaeh. 

As expected, the performance of all competing order-N methods depends on the system under investigation, the accuracy needed, the amount of experimental information available, the questions that need to be answered, and also computer-related parameters (processors, parallel architectures, etc.). All approaches have their pluses and minuses. It is also clear that the increased mathematical effort will "pay off" if at all) only beyond a critical number of atoms (around 100-1000 or so) below that, the normal route with cubic scaling is faster. Nonetheless, the same locality arguments may be used to derive linear-scaling methods for the extremely efficient calculation of electronic correlation (see Section 2.13). 

Typically, replacement refers to subsystems, rather than subterms, and so are sensitive not only to variable clashes but to the context of the surrounding system. Contextual information must be exported to support localized arguments about equivalence. 

In this extension of the localization argument from the electron- to the energy-transfer field, the differences between the quantities involved should not be overlooked. Aside from the difference between and... 

This picture suggests that the more size-symmetric ion pairs such as KCl or NaCl should exhibit stronger attraction in solution than the size-asymmetric salt LiCl. This local argument should also have a bearing on integral thermodynamic properties such as osmotic coefficients, activity coefficients, maximal solubilities or heats of solution (compare Fig. 1). Most of these properties are difficult to obtain from simulations. The osmotic coefficient (p is comparably straightforward to calculate. It is related to the osmotic pressure O via... 

However, before extrapolating the arguments from the gross patterns through the reactor for homogeneous reactions to solid-catalyzed reactions, it must be recognized that in catalytic reactions the fluid in the interior of catalyst pellets may diSer from the main body of fluid. The local inhomogeneities caused by lowered reactant concentration within the catalyst pellets result in a product distribution different from that which would otherwise be observed. 

In the next paper [160], Villain discussed the model in which the local impurities are to some extent treated in the same fashion as in the random field Ising model, and concluded, in agreement with earlier predictions for RFIM [165], that the commensurate, ordered phase is always unstable, so that the C-IC transition is destroyed by impurities as well. The argument of Villain, though presented only for the special case of 7 = 0, suggests that at finite temperatures the effects of impurities should be even stronger, due to the presence of strong statistical fluctuations in two-dimensional systems which further destabilize the commensurate phase. 

It is natural to consider the case when the surface affinity h to adsorb or desorb ions remains unchanged when charging the wall but other cases could be considered as well. In Fig. 13 the differential capacitance C is plotted as a function of a for several values of h. The curves display a maximum for non-positive values of h and a flat minimum for positive values of h. At the pzc the value of the Gouy-Chapman theory and that for h = 0 coincide and the same symmetry argument as in the previous section for the totally symmetric local interaction can be used to rationalize this result. 

While Svozil certainly does a credible job in questioning how a local fermion field theory on a tessellated space might still be made able to circumvent the species doubling problem and thereby be converted (at least formally) into a CA-like theory, one could also argue that Svozil does not take his argument as far as it could be... 

This type of argument leads us to picture a metal as an array of positive ions located at the crystal lattice sites, immersed in a sea of mobile electrons. The idea of a more or less uniform electron sea emphasizes an important difference between metallic bonding and ordinary covalent bonding. In molecular covalent bonds the electrons are localized in a way that fixes the positions of the atoms quite rigidly. We say that the bonds have directional character— the electrons tend to remain concentrated in certain regions of space. In contrast, the valence electrons in a metal are spread almost uniformly throughout the crystal, so the metallic bond does not exert the directional influence of the ordinary covalent bond. 

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