Math.Koll. am 25.01.06/Prof. Capasso

[Institut für Mathematik]

Mathematisches Kolloquium

EINLADUNG

zu einem

VORTRAG

von

Prof. Dr. Vincenzo Capasso
(Fakultaet fuer Mathematik, Universitaet Wien)

mit dem Thema:

''On the stochastic geometry of  birth-and-growth processes. Application to
material science, Biology and medicine''

Abstract:
Many real phenomena may be modelled as stochastic birth-and-growth
processes.  Application areas include crystallization of polymers,
crystallization  on sea shells); tumor growth; angiogenesis; etc. Because of
the strong coupling
with some  underlying field such as temperature, nutrients, etc., all this
kind of phenomena may include a space-time structured random process of
birth (nucleation), and a growth process, with stochastic rates.
A quantitative description of the evolution of the resulting random sets
can be obtained in terms of local  geometric mean densities, at various
Hausdorff dimensions  with respect to the standard Lebesgue measure.
We show how the evolution equations for mean densities can be given in terms
of the hazard function of the birth-and-growth process, thus extending, to
the non homogeneous case, known results from the literature. Once we know
the hazard function of the geometric process, it is also possible to  derive
evolution equations for  mean densities of n-facets  associated with  the
morphology of  stochastic tessellations produced by   birth-and-growth
processes.


Zeit: Mittwoch, 25. Januar 2006,  15.45 Uhr (Kaffeejause), anschlieszend
16.15 Uhr Vortrag

Ort: Fakultaet fuer Mathematik der Universitaet Wien, Nordbergstr. 15,
Seminarraum C 2.09

Harald Rindler
Karl Sigmund