Numeerisen analyysin ja laskennallisen
tieteen seminaari
11.4.2005 klo
14.15
U322
Marko
Rusanen, Fysiikan laboratorio
Rate equation modeling
of surface growth phenomena
Surfaces of materials have been a subject of intensive research during
past few decades. In addition to apparent technological applications
surface growth phenomena provide excellent examples of non-equilibrium
processes in statistical physics. Novel experimental methods for
measuring and imaging nanoscale surface structures have inspired also
theoretical and computational studies to explain and predict the
properties of nanostructures. These nanostructures can be manufactured
by growth of a material on top of a surface of another. By
understanding the microscopic growth mechanisms one can obtain
realiable predictions of experimental systems. One way among the others
to model surface growth is rate equations. These form a set of coupled
first order differential equations describing the time evolution of
e.g. densities of atom clusters. Solving this set can be a formidable
task due to various time scales in the problem, and sometimes
stochastic integration methods turn out to be practical. These methods
apply equally well in any other problem involving coupled differential
equations. I will describe rate equation modeling both in general and
applied in surface growth with a specific simulation method.