Diffusion probability

The key physics of our model (see Eqs. (9) and (10)) is contained in the nonlocal diffusion kernels which occur after integrating over the atomic processes which produce step fluctuations. We have calculated these kernels for a variety of physically interesting cases (see Appendix C) and have related the parameters in those kernels to atomic energy barriers (see Appendix B). The model used here is close in spirit to the work of Pimpinelli et al. [13], who developed a scaling analysis based on diffusion ideas. The theory of Einstein and co-workers and Bales and Zangwill is based on an equihbrated gas of atoms on each terrace. The concentration of this gas of atoms obeys Laplace s equation just as our probability P does. To make complete contact between the two methods however, we would need to treat the effect of a gas of atoms on the diffusion probabilities we have studied. Actually there are two effects that could be included. (1) The effect of step roughness on P(J) - we checked this numerically and foimd it to be quite small and (2) The effect of atom interactions on the terrace - This leads to the tracer diffusion problem. It is known that in the presence of interactions, Laplace s equation still holds for the calculation of P(t), but there is a concentration... 

The K+ channel from Drosophilia consists of a single polypeptide that probably has six transmembrane a helices (fig. SI.5). The pore for K+ diffusion probably is formed from a tetramer of this polypeptide. In the a polypeptides of... 

These 3y o-Ps fraction profiles were analyzed in a manner similar to the models used for Ps diffusion in ice [31], and for Ps diffusion in low-k films [26]. In the previous models, the initial positron deposition profile is an exponential function with respect to the depth. Although an analog expression of the out diffusion probability can be given by the exponential, the deposition profile generally is not believed to be exponential. In the analysis decribed below, a Makhovian distribution was used to represent the initial positron deposition profile. Let F to be the fraction of o-Ps particles that diffuse out into the vacuum, proportional to the 3g/2g ratio presented in Figure 9. It is given by the initial positronium yield, fn, multiplied by the diffusion probability, J(E) ... 

Both fo(E) and J(E) depend on the positron incident energy, E. Based on the one-dimensional out-diffusion model, the solution for the o-Ps out-diffusion probability is... 

The factor A arises from the four possible diffusion probabilities on this surface. Depending on the surface structure and corrugation, there may exist easy and difficult pathways for diffusion with low and high activation barriers, respectively hence, on a crystallographically well defined single crystal surface, the diffu-... 

The second-phase reaction is heterogeneous and occurs at the surface of the particle. The reaction causes the reacting surface to shrink and to leave an ash layer as the particle moves through the reactor. Unlike the first-phase reaction, which is only slightly affected by temperature, the second-phase reaction is quite sensitive to variations in temperature for tests conducted in a semiflow system (10). Since a high gas flow rate was maintained in semiflow tests, gas diffusion probably does not affect the rate. At temperatures below 1700°F., the first-phase reaction rate is an order or two larger than the second-phase reaction rate, but as the temperature approaches 2000°F., the two rates become comparable. This is, of course, true only when the reaction is controlled by the chemical step. 

Simple diffusion probably accounts for the uptake of undissociated organic acids by the yeast cell. Facilitated diffusion may be involved in the transport of sugars [17], although the fact that some are taken up against a concentration gradient could indicate that active transport occurs [18]. Active transport processes are used to transport amino acids and the ions of potassium, magnesium, phosphorus and sulphate. 

The addition of Cd or Te to the capsule did not result in profiles that were significantly different to those given by the above expressions, and it was suggested that diffusion probably occurred via a defect of the form (CufCuv). Most of the... 

Here, it is interesting to see how the diffusion probability links to the light scattering autocorrelation function. Denoting Fj, q,t) the spatial Fourier transform of P(r,t), that is... 

Examination-. Examination reveals slight hyperre-fiexia diffusely (probably due to a pathologic hyperexcitability of his lower motor neurons). In resistance testing, muscle strength is normal. 

During the freezing process ordering of the molecules and heat transport take place. As mentioned by Frenkel [24] it is difficult to separate these two processes. Therefore he used the expression "structure diffusion". Probably this is the best word to describe the quantity D, which we measure in our experiment. 

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