In the context of Figure 4, the asymptotic solution (3.24) in conjunction with (3.17) predicts that the interface, neglecting its diffusion, moves at a speed v p = ( f 1 A 1 + f 2 A 2 ) − 1 = 1.54, that is, n w ∼ 1.54 t.
Since one diffusion move involves 4 cells, D = 1.0 amounts to an expected number of 4 diffusion steps per interaction per cell.
We assume mutual physical exclusion of signaling molecules while carrying out the diffusion move.
Individual molecules are sampled randomly and two possible moves are considered—(a) diffusion move, and, (b) reaction move.
If a molecule has been selected to undergo diffusion, a random number trial with probability pdiff(i ) is used to determine whether the diffusion move will occur successfully.
The probability of successfully diffusing in a particular trial, pdiff, is multiplied by η if the direction of the diffusion move is toward the center, so that η > 1 will favor motion toward the center.
In the phosphate buffer at pH 6.8), the erosion front maintained a fairly constant position, while the diffusion front moved inward though with remarkably lower rate than the swelling front.
From the kinetic constants appearing in this equation and their temperature dependence, the diffusion coefficient and the activation energy for diffusion of moving ions in the layer were estimated and compared with those of high temperature diffusion in iron oxides.
Of the computerized and/or automated technologies, automatic take-offs have experienced the highest adoption diffusion rates, moving from 13%to40%0% aggregate adoption from 1993 to 2010, though diffusion appears to have slowed during 2005 2010.
Due to the extent of swelling, the Fickian diffusion with moving boundaries provided the most realistic reflection of the physics.
