4 research outputs found
Reaction Diffusion Models in One Dimension with Disorder
We study a large class of 1D reaction diffusion models with quenched disorder
using a real space renormalization group method (RSRG) which yields exact
results at large time. Particles (e.g. of several species) undergo diffusion
with random local bias (Sinai model) and react upon meeting. We obtain the
large time decay of the density of each specie, their associated universal
amplitudes, and the spatial distribution of particles. We also derive the
spectrum of exponents which characterize the convergence towards the asymptotic
states. For reactions with several asymptotic states, we analyze the dynamical
phase diagram and obtain the critical exponents at the transitions. We also
study persistence properties for single particles and for patterns. We compute
the decay exponents for the probability of no crossing of a given point by,
respectively, the single particle trajectories () or the thermally
averaged packets (). The generalized persistence exponents
associated to n crossings are also obtained. Specifying to the process or A with probabilities , we compute exactly the exponents
and characterizing the survival up to time t of a domain
without any merging or with mergings respectively, and and
characterizing the survival up to time t of a particle A without
any coalescence or with coalescences respectively.
obey hypergeometric equations and are numerically surprisingly close to pure
system exponents (though associated to a completely different diffusion
length). Additional disorder in the reaction rates, as well as some open
questions, are also discussed.Comment: 54 pages, Late
Growth of nanostructures by cluster deposition : a review
This paper presents a comprehensive analysis of simple models useful to
analyze the growth of nanostructures obtained by cluster deposition. After
detailing the potential interest of nanostructures, I extensively study the
first stages of growth (the submonolayer regime) by kinetic Monte-Carlo
simulations. These simulations are performed in a wide variety of experimental
situations : complete condensation, growth with reevaporation, nucleation on
defects, total or null cluster-cluster coalescence... The main scope of the
paper is to help experimentalists analyzing their data to deduce which of those
processes are important and to quantify them. A software including all these
simulation programs is available at no cost on request to the author. I
carefully discuss experiments of growth from cluster beams and show how the
mobility of the clusters on the surface can be measured : surprisingly high
values are found. An important issue for future technological applications of
cluster deposition is the relation between the size of the incident clusters
and the size of the islands obtained on the substrate. An approximate formula
which gives the ratio of the two sizes as a function of the melting temperature
of the material deposited is given. Finally, I study the atomic mechanisms
which can explain the diffusion of the clusters on a substrate and the result
of their mutual interaction (simple juxtaposition, partial or total
coalescence...)Comment: To be published Rev Mod Phys, Oct 99, RevTeX, 37 figure