The PHYSNUM group

One of the pillars of CRM's efforts in industrial mathematics is the PHYSNUM (Numerical Physics) group directed by Bernard Goulard. We give a short history of this group's activities.


ln September 1990, two members of the Nuclear Physics Laboratory (NPL) of the Université de Montréal, Bernard Goulard, Professor in the Physics Department for 30 years, and Jean-Marc Lina, a recent Ph.D. in theoretical physics, met Keith Scott, Ph.D. in physics and president of Fredericton-based Atlantic Nuclear Services (ANS), a consulting company involved in inspection and maintenance of nuclear reactors. For his company to remain competitive, Scott had to be at the frontier of statistical and computer technologies, which company size did not permit. Therefore he was seeking contact with a university group able to provide him with this necessary expertise. For their part Goulard and Lina had developed, through their theoretical research and the use of computers at the NPL, expertise in physical modelling, computers and mathematics. These conditions led to a collaboration which continues to the present. It began with a university-industry partnership funded by the R & D partnership program of NSERc. The first three-year project, undertaken with university collaborators, dealt with the parallelisation of a thermo-hydraulic code and has led the group to look at "wavelet transforms.' This work in this field is headed by J.-M. Lina and has brought the group international renown. The group's research interests have rapidly evolved toward the use of the Artificial Neuron Network (ANN) for reactor diagnosis, which has given birth to a second partnership project dealing with the diagnosing and monitoring at a distance of reactor problems (over 3 years). This activity which is related to a problem of signal processing , leads to deeper study of the statistics associated with ANN's and to the application of new techniques (notably results on wavelets) to medical imagery (mammography) and to teledetection. Scott is currently determining how to apply these new technologies - initially destined for application in the nuclear industry - to more diversified fields (space, environment, imagery). This work led to the creation of a subsidiary of Atlantic Nuclear, ANIQ in Montreal in 1997. It is devoted to R & D and directed by Kenneth Oxbom, Ph.D. with several members of the numerical-physics group as consultants. September 1995 was a momentous month for the numerical-physics group. It was awarded an honourable mention in the innovation partnership prize competition from NSERC and the Conference Board of Canada. ln addition, the group was invited to join the CRM by its director, Professor Luc Vinet, which has been extremely beneficial for its development.


Contact with young theoreticians, having recently obtained their doctorates, constitutes one of the fundamental roles for which the numerical-physics group was created. Taken aback by the lack of university positions and often ignored by industry because of their lack of applicable knowledge, these young researchers are generally not aware that their theoretical expertise, combined with adequate retraining, would make them extremely useful in solving important industrial problems. ln this vein, the group has offer industrial grants to young researchers holding Ph.D.'s in basic fields. It has in this manner develop experience and considerable expertise in aiding young scientists (not necessarily trained in applied science) to make the transition to an industrial setting. Indeed, until now, all members of the group have found positions in industry at the end - and often be fore the end - of their contract (for example at ANS, CAE, Lockheed Martin Electronics Systems Canada, Hydro-Québec, Caisse de Dépôts, Visual Edge). With the passage of time, the group has come to include graduate students( who are interested in the theoretical side of things but are also aware of the usefulness of practical knowledge in R & D. Currently the group is supervising four master's students and three at the doctoral level.
ln addition, Dr. Fahima Nekka, Ph.D. in Mathematics, Professor in the Faculty of Pharmacy of the Université de Montréal, and a member of the CRM, join the numerical-physics group in 1998. She brings expertise in the mathematics of fractals and experience in ophthalmology. Having collaborated with the research group at Sainte-Justine Hospital on various aspects of retinopathy in premature infants, she is able to apply her knowledge of fractals to this and other fields.
For each new university-industrial partnership, the group changes by adding one or two experts on the problem being studied (in applied mathematics, statistics or computer science). This produces a group in constant renewal, changing to match the transitory nature of its problems and creating new competence which is constantly transferred to other contexts. (ln this way, statistical methods apply to nuclear reactors 100 to new techniques in imaging.) This mobility of orientations allows the group to work in diverse fields without the constraints of departmental boundaries.