Oberwolfach Reports
Full-Text PDF (765 KB) | Introduction as PDF |
Table of Contents | OWR summary
Reactive Flow and Transport Through Complex Systems
Organized by: Cornelius J. van Duijn (1), Andro Mikelic (2) and Christoph Schwab (3)
(1) Dept of Mathematics and Computer Science, TU Eindhoven, PO Box 513, 5600 MB, EINDHOVEN, NETHERLANDS(2) UFR Mathématiques, Site de Gerland, Bat.A, Université Claude Bernard Lyon 1, 50, avenue Tony Garnier, F-69367, LYON CEDEX 07, FRANCE
(3) Seminar für Angewandte Mathematik, Eidgenössische Technische Hochschule, Rämistr. 101, 8092, ZÜRICH, SWITZERLAND
The workshop \emph{Reactive Flow and Transport Through
Complex Systems}, organized by Cornelius J. van Duijn (Eindhoven),
Andro Mikeli\'c (Lyon) and Christoph Schwab (Z\"{u}rich)
was held October 30th--November 5th, 2005.
This meeting was
attended by over 46 participants with broad geographic
representation from all continents.
The theme of the conference,
\begin{center}
modeling, analysis and numerical simulation of
diffusion and transport processes in complex systems,
\end{center}
is a response to the need for more accurate, quantitative
prediction in a growing number of scientific disciplines,
particularly those related to biological applications. Here,
simple mathematical models have been found, in particular due to
the vastly increased available experimental data from these
systems, to offer only inadequate and incomplete understanding of
the observed phenomena.
This resulted in increased requirements for quantitative, verified
predictions from sophisticated mathematical as well as computational
models.
The continuous development of complex mathematical and computational models
and their verification and validation against available experimental data
is a continuous source of challenges for applied and computational mathematicians.
The complexity of the systems arises from several sources:
highly irregular geometries of membranes and interfaces (as, e.g. in
bone marrow, cell membranes, root systems of plants, membrane structures in human organs),
physical or chemical properties of the systems (e.g., models for spread
of pollution in underground medium which has uncertain material properties,
where chemical reactions take place between constituents, and where strong transport
effects on a macroscopic scale coexist with diffusion phenomena at the grain interfaces).
Quantitative mathematical and computational models of such phenomena are not
only essential for a deeper understanding of these systems but, at least
equally importantly, are a keystone in the development of new
technologies which increasingly mimic and adapt biological phenomena for
industrial purposes (e.g., root-reactor technology for the efficient production
of organic compounds, bioinspired catalysts for waste processing, to name but a few).
Accordingly, the rather wide scope of the topic of the conference and the
blend of researchers working in several areas of
applied mathematics was a necessary condition to review modelling approaches
across a number of application areas as well as across several mathematical
disciplines.
Accordingly, during the meeting, talks were presented on
homogenization, a\-nalysis and computation of multiscale problems,
models of porous media, biological flow problems, to name but a few.
In addition to the regular presentations, there were three evening
sessions organized ``on the spot'' based on the discussions which
started in the first half of the meeting. These were in each case
opened by a presentation from a person invited by the organizers,
and were devoted to the topics:
The presentations of the experts present at the meeting comprised,
naturally, a much wider scope of topics:
These talks touched on advanced mathematical methods from
dynamical systems, especially infinite dimensional ones arising
with spatially heterogeneous problems (PDEs),
asymptotic analysis, homogenization and averaging methods,
numerical multiscale methods,
methods from stochastic analysis and statistics.
Apart from advancing {\em disciplinary} mathematical methods in these
areas, in the present meeting also qualitatively new mathematical
developments emerged: for example, mathematical and computational modelling
of PDEs with stochastic data which are spatially inhomogeneous and do
{\em not} satisfy stationarity or ergodic hypotheses.
In processing experimental data (which becomes increasingly available
at lower cost and, e.g. through modern scanning techniques, also at
high volume and spatial and temporal resolution) new techniques of
image and data processing have to be developed, and the mathematical
models of complex systems have to allow for incorporation of statistical
data extracted from these experiments.
This has repercussions for the mathematical research {\em and} implies that
novel algorithms are needed to generate computational grids adapted to voxel data.
In the last five years mathematicians from analysis, stochastics and
numerics started cooperation in this interdisciplinary field of
research.
New journals specifically devoted to these issues such as the
SIAM Journal of Multiscale Analysis and Simulation, have been
successfully launched.
The previous meeting in Oberwolfach
" Multiple Scale Systems - Modeling, Analysis and Numerics "
from July 27 to August 2, 2003, gathered 42 scientists, among them
approximately 15 junior scientists, from these areas.
Since multiscale tools are crucial in many of the above themes, in
the previous meeting mainly diffusion problems were treated.
Reactive flow and transport, which were central themes in the
present meeting, emerged only recently as key issues.
The meeting was, exactly because of its wide scope, successful particularly
in cross fertilizing different areas of applied mathematics and also
raised a huge number of questions and challenges to participants documenting
that the applications of mathematics to biological, social and other
``complex systems'' which has been emerging in the past years,
is in the process of gaining momentum and, more importantly, stimulates
development of new techniques and approaches in applied and computational mathematics
at an increasing rate.
\centerline{\bf List of all talks}
\vskip10pt
}
No keywords available for this article.