The 45th European Study Group Mathematics
with Industry
February 17 – 21, 2003
The aim of such a study group is to bring
together mathematicians and commercial companies to tackle industrial problems.
For the week approximately seventy participants, academic mathematicians
ranging from PhD student to professor, came to Leiden to make a start on
solving the problems presented by the five companies. The participants worked
very enthusiastic and very hard, and made nice progress towards solving the
problems. The problems were quite divers and a brief description of every
problem follows.
KLM flies to over 150 destinations with 97
aircraft. Four times a year, a new flight schedule is developed aimed
principally at maximising the number of seats which can be sold. The schedule
design takes into account operational feasibility to some extent, but
concentrates on the commercial aspects such as expected demand per destination
and the number of transfer connections at Schiphol.
Each day during operation, many adaptations
are made to this schedule to minimize delays caused by, for example, problems
with the aircraft or weather. If it is known that an aircraft will arrive at
Schiphol Airport with a delay, they try to assign its next flight to another
aircraft so that that flight can still leave on time. Usually, a couple of
other adaptations are needed to have all flights fit again. Some schedules
prove more flexible and robust than others in coping with delays. KLM wanted to
know if a simple fast method could be found to test the performance and
flexibility of a given flight schedule when incorporating the adaptations that
are made to the schedule during operation. So far they had been doing
simulations with real data and they wanted to know whether this could be
reduced or avoided.
Pacific oysters, native to Japan, were
introduced into the Eastern Scheldt Estuary in The Netherlands after the severe
winter of 1962/63 diminished the stock of European flat oysters. At that time,
it was believed that the Pacific Oyster could not breed at such latitudes.
However, during the hot summer of 1976, the first settling of larvae was
observed on dike foots and jetties after which importation of the Pacific Oyster
was immediately halted. In 1982, a second larvae outburst permanently
established the wild Pacific oysters in the waters of the Eastern Scheldt and
the population has been growing rapidly ever since.
The Pacific oyster represents a serious
environmental problem in the Eastern Scheldt due to lack of natural predators
and because they compete with other species such as cockles, mussels and
cultivated oysters for space and food. One of the tasks for the study group was
to study whether a mathematical model of the oyster population could predict
the spreading of the oyster population and even give a suggestion to how the
population growth can be brought under control.
Light-emitting polymer displays are a new,
interesting flat display principle. The active material is a very thin layer of
semi-conducting polymer. To make a full colour display red, green and blue
polymer solutions must be positioned in pixels of the order of 66 x 200 micron.
Philips is currently trying to adapt ink-jet technology to position these small
drops of polymer solution effectively.
The polymers involved in this process have a
high-molecular weight which causes the droplet formation from the ink-jet to be
highly non-Newtonian; this is unlike the behaviour of normal inks. Philips
wanted the study group to model the visco-elastic behaviour of the jetted
polymer solution to enable them to obtain information about the velocity and
droplet formation of the polymer liquid.
When a tool has been used to commit a crime
(such as using a screwdriver to open a door during a burglary) the tool leaves
certain marks which are unique to that particular tool. The question when
handling a case in court is of course whether a tool of a suspect could have
left these traces. A similar question can also be asked for shoe prints found
at a crime scene. These questions can be answered by comparing the traces to
test traces of the tool or shoe of the suspect. The position of certain lines,
curves, dents or more distinguishing marks on the tool or shoe help to match
the trace left at a crime scene. However, so far, a good subjective judgment
couldn't be made. The study group was asked to design a probability model that
gives the probability that the trace found at a scene of crime was made by the
tool or shoe of a certain suspect.
A carillon consists of around 20 to 45 bells
hung in a tower. The bells are played using a keyboard situated below and a
wire connects each bell clapper to its relevant key on the keyboard. The oldest
and simplest wire-connection system is the 'broek-system' connecting three
wires to the 'broekring': one from the clapper, one from the key and one from a
fixed point on the wall.
To construct a carillon such that all the
designing properties are satisfied, and that all the bells sound as they
should, is incredibly difficult. The carillon-builder attempts to place the
bells in a geometrically balanced way, but it is hard to prevent all the wires
from touching or to make every key and bell play equally well. The problem
posed by the museum was to come up with a method to position the bells and
wires in a tower in an optimal way.
The companies also participated very
enthusiastically in the study group which lead to great interactions and nice
results. And, they were very pleased with the work carried out during the study
group. Certainly KLM, NFI, RIVO and Philips expressed a willingness to continue
working with the academic contacts made during the study group week. Philips
has even applied for a grant to continue working on the problem. Also, KLM is
still working on the model to refine it and they will take it to the
operational departments somewhere in the beginning of 2004.
Each group has prepared a report detailing
their results and conclusions. The proceedings containing these reports are in
the final stage of preparation.
The facilities of the Lorentz Center, with
the offices situated around the pleasant common room, were very appreciated by
the participants of the study group. And, we would like to thank the staff of
the Lorentz Center for their help and support both before and during the study
group that made it into a wonderful and productive week. The workshop was also
supported by ITW (Industrial and Applied Mathematics), Technologiestichting
STW, NWO-EW, and ECMI (European Consortium for Mathematics in Industry).
D. Pik (Leiden
University, The Netherlands)
N. Ovenden (TU
Eindhoven, The Netherlands)
V. Rottschäfer
(Leiden University, The Netherlands)