Grain model validity

One says that the above results are valid for a chain with non-interacting particles. However, the monomers in a real macromolecule interact with each another, and this ensures, above all, that parts of the molecule cannot occupy the place already occupied by other parts i.e. the probabilities of successive steps are no longer statistically independent, as was assumed in the derivation of the above probability distribution functions and mean end-to-end distance (Flory 1953). So, considering the coarse-grained model, one has to introduce lateral forces of attractive and repulsive interactions. The potential energy of lateral interactions U depends on the differences of the position vectors of all particles of the chain and, in the simplest case, can be written as a sum of pair interactions... 

Fig. 10 Integrative modelling of large macromolecular complexes. An Initial large set of experimental data is translated into spatial restraints. A coarse-grained model representing the stoichiometric composition of the protein complex is used to minimise a scoring function representative of all the restraints. Optimised structures are validated against scoring result and cluster analysis. The procedure is iterated until one single solution is found.

From the results of Section 3.3.3, it may be expected that the = 0 asymptote is valid for <0.1. In this regime the system becomes identical to the grain model presented earlier. On the other hand, when 10 the reaction of an individual grain is expected to be controlled by the intragrain diffusion. For this condition Pigford and Sliger [29] have proposed an approximate method of solution that is valid for low conversion of the solid. 

If the weak bonding model is valid for high angle grain boundaries (>20°) it follows that diffusion in amorphous preparations of a given material should also show this measure of enhanced diffusion, when compared widr die crystalline material. 

According to a theoretical analysis,262,267 the CDL model is valid for pc electrodes with very small grains (y < 5 to 10 nm) with a moderate difference of Eas0 for the different faces (A ff=0 = 0.1 to 0.15 V) and for dilute electrolyte solutions (c < 0.01 M) near the point of total zero charge. For the other cases, the IDL model should be valid. 

Eq. (5.45) agrees quite well with experimental data for grain sizes between 1 and 10 pm. Above 10 pm more complex domain walls form and the domain width is limited to about 0.8 pm. Below 1 pm the stresses are large enough to reduce the tetragonality and this simple model is no longer valid. 

Although each of these models have their own merits, it is currently not clear how much predictive power these coarse-grained potentials have. Nevertheless, coarse-graining is a valid way of studying protein folding, and in the near future might have the much sought after power to predict novel folds. 

The theory is most readily illustrated by reference to a pure explosive compound comprising uniform spherical grains of constant size. By studying systems of this character the author and associates - established beyond reasonable doubt the validity of the Eyring surface burning model. 

Based on this modeling eomputations an inversion seheme was developed whieh auto-matieally iterates the permeability and minimizes the difference between measured and modeled attenuation and velocity data in a least square sense (Courtney and Mayer 1993 Breitzke 1997). As a result S-wave veloeities and attenuation coefficients, permeabilities and elastie moduli of water-saturated sediments ean be estimated. They are strictly only valid if attenuation and veloeity dispersion can be explained by viseous losses. In coarse-grained parts deviations must be taken into account for the estimated parameters, too. Applied to the data of eore GeoB1510-2 in 170, 176 and 182 cm depth S-wave veloeities of 67, 68 and 74 m/s and permeabilities of 5-10, I-IO and 3T0 m result from this inversion seheme. 

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