Kink-annihilation

A similar kind of kink-annihilation exists for rules R122, R126, R146, and... 

The domain walls (or kinks, consisting of pairs of sites with value 7 = 1) that define the boundary between the two sets, however, do not evolve as they would under R90 but instead undergo pairwise annihilating random walks (see figure 3.16). Indeed, numerical analysis [grass84a] has shown that, as t —> oo, their density decreases like... 

Figure 3.31 shows sample evolutions for p = 0, 1/4 and 3/4. The space-time pattern for p = 0 rapidly settles into an ordered state consisting of checkerboard-pattern domains, separated by two-site kinks once formed, the kinks remain locked in place. As p is slowly increased, these kinks begin to undergo annihilating random walks, much like the ones we saw earlier in the evolution of (the deterministic) rule R18. Their density decreases like pkink Grassberger, et.al, observed... 

Another possibility is that two P-M reversal kinks may appear in the same polymer chain. These may translate along the chain to adjacent positions, when both kinks will be mutually annihilated. The annihilation process becomes more likely as the chain becomes longer. Eventually the possibility of backbiting and termination becomes... 

Figure 22 If a needle crystal of (TMTSF)2a04 is pressed with a force perpendicular to the needle axis, kink (K) and antikink (A) pairs are formed. The kinks can be annihilated, reproduced, and moved back and forth along the needle axis by applied stress. The reproducibility and mobility of the kinks indicate that the samples are of high crystallinity (few dislocations or defects). (From Ref. 169.)...

The standard interpretation of the KirkendaU effect micromechanism, for substitutional alloys at least, is this the partial fluxes difference causes a vacancy flux toward the more mobile component of the diffusion couple. Vacancies dismantle extra planes on this component s side, ft means dislocations cHmb and vacancy annihilation at sinks (dislocation kinks). On the slow component s side vacancies are, conversely, generated (to support the flux) bringing to extra planes building up. Thus, on the slow component s side, new lattice planes appear and, on the side of a mobile one, the old lattice planes disappear. New lattice formation is vividly displayed in Mark van Dal s and Frans van Loo s experiments, showing the KirkendaU plane bifurcation into two stable K-planes moving in the opposite directions between these two K-planes new grains appear and none of the markers remain (Chapter 6). 

The Kirkendall effect is commonly accompanied by the Frenkel effect, the void formation in the diffusion zone. In foreign literature, the Frenkel effect is often referred to as Kirkendall voiding, which is rather confusing, as Kirkendall and Frenkel effects are competitive vacancies annihilating at the dislocation kinks and causing the Kirkendall shift, cannot be used for Kirkendall voiding, and vice versa. 

If distance p is inferior to a critical value k the kink and antikink evolve towards mutual annihilation/ and the hoiiK>geneous metastable state is... 

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