Turbulent
weather!
The
growth and track of a storm, the geometrical structure of a cloud
and its role in absorbing solar and terrestrial radiation, the optimal
integration in a numerical weather forecasting model of measurements
made by different instruments operating at different locations (weather
stations, satellites, ships and planes) ... There is no doubt about
it: mathematical modelling plays a central role in all aspects of
modern meteorological science. Essential for describing and understanding
the mechanisms of weather and climate, it is used for both analysis
and prediction.
Turbulent
flows  and atmospheric movements are certainly that  can be modelled
by the NavierStokes equations. However, since meteorologists cannot
always solve these equations, they must use digital simulation using
the most powerful computers, and the most sophisticated numerical
schemes. Also of use is the mathematical theory of dynamic systems.
It
was a meteorologist, E. N. Lorenz, who in 1963 demonstrated that
even a simple dynamic system can evolve chaotically, its trajectory
highly sensitive to initial conditions. According to his wellknown
metaphor, the disturbance of the air's flow due to the flight of
a butterfly can ultimately lead to a cyclone on the other side of
the planet.
Based
on an idea of Philippe Courtier (MétéoFrance) and Claude Basdevant
(ENSEcole PolytechniqueParis).
No
damage!
The
development and testing of new cars is increasingly carried out
by virtual experiments using computer simulations. For this purpose,
engineers develop virtual vehicle models described through equations,
the solution of which requires advanced mathematical methods and
powerful computers. Virtual models also allow cars to be tested
at a lower cost.
A
virtual prototype of a car requires a global mathematical model
incorporating the vehicle characteristics as well as its interactions
with the road and the air, the description of any obstacles, etc.
This results in a system of equations which is solved on a computer
using numerical methods.
The
complexity of these models generates vast quantities of calculations
requiring the use of parallel computers.
Based
on an idea of Andreas Frommer  University of Wuppertal, Germany.
Trees
and forests
One
way to approach the effects of climate change on trees and forests
is to try to simulate their development by using models incorporating
a large number of parameters while remaining simple enough to be
used in practice. This demands close cooperation between mathematicians
and forest experts.
The main difficulties stem from the fact that there are different
levels of structural hierarchy (forest, tree, leaf, molecule, etc.)
all impacting on growth and also different time scales which coexist
(forests which may be hundreds of years old, compared to just a
few seconds for the metabolism).
Competition
for light
Recent years have brought enormous progress in modelling trees and
forests. A dynamic model, based on vital and environmental processes,
has been successfully applied to the analysis of climate change
effects, including forest management in different regions and improving
the wood quality.
New
models describe tree growth during the year and also make it possible
to predict how different trees will compete for light.
Idea
and illustrations by Marjo Lipponen. MaDaMe programme  Turku University
(Finland).
DNA:
beyond the sequence
Over
the past 20 years or so, new techniques (DNA sequencing, DNA chips,
etc.) have opened up revolutionary perspectives in biology. These
techniques generate huge amounts of extremely diverse data (sequences,
images, texts, experimental data, bibliographies). Mathematics plays
a central role in processing these data, making it possible to extract
relevant information. The subject areas most useful to this are
algorithms, probability theory, and statistics.
Proteins
are long threedimensionally folded amino acid chains. Their activity
essentially depends on the protein form after folding. A knowledge
of this threedimensional structure is necessary for many applications
(pharmacology, agriculture, etc.). The most accurate method is to
use crystallography techniques, but they are very time consuming.
This explains the many attempts to use mathematical or computer
models to 'calculate' this form.
Idea
and illustrations by Francois Rodolphe, JeanFrançois Gibrat and
Pierre Nicolas  INRA unit  Versailles 'Mathematics, Computing
& Genome'.
