Quenching by Static Traps: Initial-Value and Steady-State Problems

Simulations and effective-medium calculations were performed on the absorption of impurity particles by static sinks in three dimensions. The theory shows no qualitative effects due to two-sink clusters and agrees well with simulations. The conclusion is drawn that effective-medium theory is adequate for time-dependent impurity concentrations $C\mathrm{}\left(t\right)\mathrm{}$ above the lower bound recently demonstrated by several authors. Crossing of the concentration curves occurs at a time such that $\frac{C\mathrm{}\left(t\right)\mathrm{}}{C\mathrm{}\left(0\right)\mathrm{}}={10}^{-67\mathrm{}}$ or less.