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
flows - and atmospheric movements are certainly that - can be modelled
by the Navier-Stokes 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.
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 well-known
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
on an idea of Philippe Courtier (Météo-France) and Claude Basdevant
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.
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.
complexity of these models generates vast quantities of calculations
requiring the use of parallel computers.
on an idea of Andreas Frommer - University of Wuppertal, Germany.
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).
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.
models describe tree growth during the year and also make it possible
to predict how different trees will compete for light.
and illustrations by Marjo Lipponen. MaDaMe programme - Turku University
beyond the sequence
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.
are long three-dimensionally folded amino acid chains. Their activity
essentially depends on the protein form after folding. A knowledge
of this three-dimensional 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.
and illustrations by Francois Rodolphe, Jean-François Gibrat and
Pierre Nicolas - INRA unit - Versailles 'Mathematics, Computing