Diffusion movement

The diffusive movement of atoms is assumed to have a range of values, and the probability that a jump of length between j and j + dj can occur is... 

Diffusion Movement of atoms, ions or molecules under an activity (or concentration) gradient. 

The history of observations of efflux associated with PTS carriers is nearly as old as PTS itself. Gachelin [82] reported that A -ethylmaleimide inactivation of a-methyl-glucoside transport and phosphorylation in E. coli was accompanied by the appearance of a facilitated diffusion movement of both a-methylglucoside and glucose in both directions, uptake and efflux. His results could not discriminate, however, between one carrier operating in two different modes, active transport for the native carrier and facilitated diffusion for the alkylated carrier, or two distinct carriers. Haguenauer and Kepes [83] went on to show that alkylation of the carrier was not even necessary to achieve efflux NaF treatment which inhibits P-enolpyruvate synthesis was sufficient but this study did not address the question of one carrier or two. 

The importance of including soil-based parameters in rhizosphere simulations has been emphasized (56). Scott et al. u.sed a time-dependent exudation boundary condition and a layer model to predict how introduced bacteria would colonize the root environment from a seed-based inoculum. They explicitly included pore size distribution and matric potential as determinants of microbial growth rate and diffusion potential. Their simulations showed that the total number of bacteria in the rhizosphere and their vertical colonization were sensitive to the matric potential of the soil. Soil structure and pore size distribution was also predicted to be a key determinant of the competitive success of a genetically modified microorganism introduced into soil (57). The Scott (56) model also demonstrated that the diffusive movement of root exudates was an important factor in determining microbial abundance. Results from models that ignore the spatial nature of the rhizosphere and treat exudate concentration as a spatially averaged parameter (14) should therefore be treated with some caution. 

Diffusion occurs when there is a concentration gradient of one kind of molecule within a fluid. In terms of random walk model, the average distance, x, after an elapsed time, t, between molecule collisions in a diffusion movement is characterized by the Einstein-Smoluchowski relation,... 

Figure 9 Schematic representation of the conversion of the diffusive movement of a species towards the electrode from radial to linear with the increase of the number of microscopic sites present at the electrode surface. Electrode of radius r...

Jouguet, (Jacques-Charles) Emile (1871 — 1943). French physicist, general inspector of mines and professor of mechanics ficole des Mine, ficole Poly technique, member French Academy of Science (1930). He was the author of Me-canique des Explosifs (1917) and conducted research on wave diffusion, movement of fluids, explosives and fundamental work on the hydro-dynamic theory of detonation. His name is associated with that of Chapman-in the famous Chapman-Jouguet condition. In their honor parameters of a steady detonation wave are usually designated by the subscript CJ... 

Although not necessary in terms of phenomenological applications, it is interesting to consider possible molecular meanings of the coefficients, Dq and D If two penetrants exist in a polymer in the two respective modes designated by "D" and "H" to indicate the "dissolved (Henry s law) and the "hole" (Langmuir) environments, then the molecules can execute diffusive movements within their respective modes or they may execute intermode jumps ... 

Barrer (1984) suggested a further refinement of the dual-mode mobility model, including diffusive movements from the Henry s law mode to the Langmuir mode and the reverse then four kinds of diffusion steps are basically possible. Barrer derived the flux expression based on the gradients of concentration for each kind of diffusion step. This leads to rather complicated equations, of which Sada (1987, 1988) proved that they describe the experimental results still better than the original dual-mode model. This, however, is not surprising, since two extra adaptable parameters are introduced. 

If it is assumed that at the moment of formation the film is not at equilibrium with the meniscus containing a dissolved surfactant, the vacancies concentration is changed, thus determining the initial nucleation rate Jq. So, the lateral diffusion movement of elementary vacancies affects the equilibrium establishment and film rupture, expressed by 7(f) [501]. 

Also note that the inequality Eq. (92) implies that there would be no Arnold diffusion for H = 0. To the contrary, Xia proved that there still exists a diffusive movement even for H = 0. He called it pseudo-Arnold diffusion [35]. 

Debye was also a much appreciated lecturer at Cornell University in the 50 s—particularly when he illustrated the random nature of diffusion movements by doing his drunkard s walk in front of the class. However, his eagerness to be an effective administrator was not so clearly manifest and after a year as Head of the Chemistry Department, he returned back to full-time research and teaching. 

M. Smoluchowski, Diffusive Movements in Liquids, Ann. Physik(Paris)25 2Q5 (1908). 

In the phenomenological treatment of the directed drift that the field brings, we take the attitude that there is a stream of cations going toward the negative electrode and anions going toward the positive one. We now neglect the random diffusive movements they do not contribute to the vectorial flow that produces an electrical current. 

We can easily imagine the case of a group of very small particles (molecules for example), which quickly change positions this produces the image describing the diffusion movement. Equation (4.34) describes the diffusion model or the model with a parabolic equation ... 

This equation shows that the conservation of a property depends on the fortuitous or natural displacement of the property produced by vector w, when that is generated through a volume (Jy/-) or/and by a surface process (vector The mentioned displacement is supplemented by a diffusion movement (Dj- in the right part of the conservation equation). This movement is characterized by steps of small dimension occurring with a significant frequency in all directions. When the diffusion movement takes place against the vector w it is often called counterdiffusion. In the case of a medium, which does not generate the property, the relation can be written as follows ... 

Science (1930). He was the author of Me-canique des Explosifs (1917) and conducted research on wave diffusion, movement of fluids, explosives and fundamental work on the hydro-dynamic theory of detonation. His name is associated with that of Chapman-in the famous... 

The three primary mechanisms responsible for mixing are convective movement of relatively large portions of the bed, shear failure that primarily reduces the scale of segregation, and diffusive movement of individual particles. 

The ensemble can be treated as a material of fixed composition. It shows the two behaviors described in Chapter 13, namely, change of shape at constant volume and change of volume at constant density by diffusive movement of material from high-compression sites to sites of lower compression. 

Considering the overall flux of material through the region affected by the inclusion, this is greater when diffusion is taken into account. On the other hand, the rate at which the inclusion changes ellipticity is slightly less. In terms of velocity fields, the strain-rate field by itself is smaller when diffusion operates than when it does not, but the sum of strain-rate field plus the velocity field for the self-diffusive movements is greater than the strain-rate field in the no-diffusion case. 

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