English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we propose a solution for the time evolution of the islanddensity with irreversible aggregation and a time dependent input of particle inthe space dimensions $d=1,2$. For this purpose we use the rate equationresulting from a generalized mean field approach. A well-known technique forgrowing surfaces at the atomic scale is molecular beam epitaxy (MBE). Anotherapproach is the pulsed laser deposition method (PLD). The main differencebetween MBE and PLD is that in the case of MBE we have a continuous rate ofdeposition $F$ of adatoms on the surface whereas in the case of PLD the adatomsare deposited during a pulse of a laser which is very short in comparison tothe time span $T$ between the pulses. The generalized mean field theory is auseful model for both MBE and PLD with the most simple approximation,point-like island. We show that the parameter $T$ distinguishes the MBE regimefrom the PLD regime. We solve the rate equation for the PLD regime. We considerthe time evolution of the density of immobile islands. For large time $t\gg T$,the PLD regime dominates the MBE regime and we find that the density ofimmobile islands grows as $t^{1/2}$ whereas for MBE we find the known behaviorof the density, $t^{1/3}$ for $d=2$ and $t^{1/4}$ for $d=1$. We illustrate thisresult with Monte-Carlo simulations for $d=1,2$.

Exact solution of a mean-field approach of an irreversible aggregation with a time dependent rate deposition