The 45th European Study Group Mathematics
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)