Graduate School in Nonlinear Science
Sponsored by the Danish Research Academy
MIDIT OFD CATS
Modelling, Nonlinear Dynamics Optics and Fluid Dynamics Chaos and Turbulence Studies
and Irreversible Thermodynamics Risø National Laboratory Niels Bohr Institute and
Technical University of Denmark Building 128 Department of Chemistry
Building 321 P.O. Box 49 University of Copenhagen
DK-2800 Lyngby DK-4000 Roskilde DK-2100 Copenhagen Ø
Denmark Denmark Denmark
1. SCIENTIFIC PROFILE
The Center for Modelling, Nonlinear Dynamics
and Irreversible Thermodynamics (MIDIT) at the
Technical University of
Denmark (DTU), the
Department of Optics and Fluid Dynamics (OFD) at
Risø National Laboratory (Risø), and the
Center of Chaos and
Turbulence Studies (CATS) at Copenhagen University (KU)
conduct a Graduate
School in Nonlinear Science.
In collaboration with industry,
this school provides a Danish Ph.D.
program at the highest international level with the aim of preparing
students to apply recent advances in Nonlinear Science to
outstanding problems of science and technology and
to strengthen international exchange of Ph.D. students.
Over the past three decades, science has experienced
a revolutionary shift in its fundamental paradigms.
Primarily based on linear models through the 1960s,
scientific research is now commonly motivated by
nonlinear concepts, in which the whole is more
than the sum of its parts, and the emergence of
qualitatively new phenomena is anticipated and
made welcome.
The basic theme of modern Nonlinear Science is the
interplay between chaos and coherent
structures. Formerly deemed unworthy of the
attention of a serious scientist, low order systems
of nonlinear ordinary differential equations are now
known to exhibit explosive behavior, leading to the
emergence of strange attractors upon which
phase space trajectories wander aimlessly until
the end of time. Largely ignored as being far too
difficult to solve analytically, nonlinear partial
differential equations have been found to
generate the emergence of solitary waves,
which interact as new dynamic entities at higher
levels of description.
These new paradigms lead to significant
advances in our understanding of a number of
observed phenomena in physics, chemistry, and biology. From the theory, methods
for constructive applications
in the engineering sciences have been developed, using
computer technology.
In the 1980's a number of centers for Nonlinear Science were established
at universities and research institutions in U.S.A., the European countries, and
in Japan. In Denmark, MIDIT was formed at DTU in 1985 and
CATS at KU in 1993. In close collaboration with other Danish
universities and research institutions - e.g. OFD at
RISØ - research as well as Ph.D. and Master's Degree education
were initiated at a very early stage.
Jointly, MIDIT, OFD, and CATS form the major part
of the national activity within Nonlinear Science.
The early and persistent effort has given Denmark a central placing and
recognition
within the international Nonlinear Science community.
It is in the spirit of this growing activity that
the Graduate School will operate.
Although seemingly
diverse at first reading, the facets of this
activity are, in fact, closely interrelated
components of modern research in nonlinear
dynamics including scientific computing and experimental
research.
2. ORGANIZATION AND ORGANIZATIONAL STRUCTURE
The Graduate School in Nonlinear Science was established in 1997 by The Danish
Research Academy as a collaboration between MIDIT, OFD and CATS.
MIDIT was established at DTU in 1985.
Today scientists from the DTU departments of Mathematics, Mathematical
Modelling,
Physics, Chemistry, Chemical and Energy Engineering collaborate within
the Centre.
The scientific background for MIDIT is the decisive break-throughs that have
occurred in the last three decades in nonlinear dynamics and far-from-equilibrium
statistical physics, combined with the possibilities offered by modern computer
technology for detailed modelling and simulation of complex phenomena.
The applications of the new tools from Nonlinear Science within the boundary
areas between mathematics and physics on one hand and chemistry, technological
sciences, biology and economy on the other are manifold. MIDIT stimulates
research and engineering education within Nonlinear Science and its
applications.
Chairman: Erik Mosekilde. Scientific Staff: 27
OFD at Risø
performs research and development within systems, structures and materials for
optical measurements and information processing based on diffractive optics and
nonlinear dynamics. OFD hosts close interaction between theory and experiments.
Core competences within physical optics (electromagnetic interaction with matter,
materials with special optical properties), nonlinear continuum dynamics
(self-organization, pattern formation, parametric oscillations and amplification,
soliton dynamics, collapse and turbulence in fluids and plasmas), scientific computing and
information processing.
Head of Department: Lars Lading. Scientific staff: 25
CATS was established in
1993 by the Danish Natural Science Research Council (SNF). The Center consists
of groups from the Niels Bohr Institute/Nordita (NBI), Department of Chemistry,
H. C. Ørsted Institute (HCØ), KU, and Department of
Physics, DTU.
The scientific background for CATS is the fundamental insight that the simplest
laws of nature can lead to bewildering complex dynamics, and that at the same
time such dynamics exhibit universal features largely independent of the details
of the particular underlying dynamical system.
The Center pursues theoretical and experimental research in chaos, turbulence
and related problems in physics, chemistry and biology. The Center brings
together the groups which are actively conducting research and education in
Nonlinear Science.
Head of Center: Predrag Cvitanovic'. Scientific Staff: 20
Head of the Graduate School in Nonlinear Science is professor, dr. techn.
Peter L. Christiansen, Department of Mathematical Modelling, DTU.
Christiansen holds Master of Science, Ph. D. and dr. techn. degrees from DTU.
Since 1966 he has worked at DTU and served as
Head of the Laboratory of Applied Mathematical Physics 1977-79 and 81-89.
Since its beginning in 1985 he has been coordinating secretary for the DTU
Center MIDIT.
He has been a research associate and a visiting professor at the Universities of
Michigan, New York (Courant Institute of Mathematical Sciences), Minnesota,
Arizona, and Naples and at Los Alamos National Laboratory. He is author and
co-author
of more than 130 papers in scientific journals and is presently on the editorial
board of Physica Scripta.
He has taught many courses in Applied Mathematics and Nonlinear Science and
supervised more than 30 Ph. D. students.
The Graduate School in Nonlinear Science hosts professional activity at
DTU and KU, under the auspices of the directors of Ph.D. studies, the Ph.D.
study councils, and program committees. in accordance with the University Law.
The head is in charge of the daily
running of the school, assisted by the executive committee of the steering
committee of the Graduate School. The steering committee assists the head in the
direction of the school, the planning and implementation of the activities and
the contacts with foreign scientists, institutions and Ph.D. students.
Members of the steering committee are: (Executive committee members
are indicated by *))
Morten Brøns, MIDIT
Morten Colding-Jørgensen,
Sten Bay Jørgensen, MIDIT
Alwyn C. Scott, MIDIT
Tomas Bohr, MIDIT
NOVO NORDISK
Erik Mosekilde*), MIDIT
Jens Juul Rasmussen*), OFD
Peter L. Christiansen*),
Mogens Høgh Jensen, NBI
Ole Mouritsen, MIDIT
Preben Graae Sørensen*), HCØ
MIDIT
Per Michael Johansen, OFD
Jesper Mygind, MIDIT
Jens Nørkær Sørensen, MIDIT
| | | | | | | | | | | | | | | |
3. RESEARCH EXPERTISE
36 Danish professors participate in the Graduate School in Nonlinear Science.
MIDIT, DTU
| Jørn Bindslev Hansen
Poul Scheel Larsen
Mogens Samuelsen
Tomas Bohr
Vagn Lundsgaard Hansen
Erik Mosekilde
Alwyn C. Scott
Bodil Branner
Poul Hjorth
Ole Mouritsen
Jens Nørkær Sørensen
Morten Brøns
Claus Schelde Jacobsen
Jesper Mygind
Mads Peter Sørensen
Peter L. Christiansen
Sten Bay Jørgensen
Niels Falsig Pedersen
Hans True
| | |
| OFD, RISØ
| Poul Michael Petersen
CATS, NBI and HCØ
| Finn Hynne
Per Michael Johansen
P. S. Ramanujam
Preben Alstrøm
Mogens Høgh Jensen
Jens-Peter Lynov
Jens Juul Rasmussen
Predrag Cvitanovic
Mogens T. Levinsen
Poul Michelsen
Mark Saffman
Clive Ellegaard
Preben Graae Sørensen
Anders H. Nielsen
Jørgen Schou
Axel Hunding
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
CATS, MIDIT and OFD collaborate within Framework Programs sponsored by SNF
and participate in EU-, NATO-, and ESF-sponsored international
programs and networks.
The Graduate School in Nonlinear Science has collaboration agreements with
important research institutions and universities which send their leading scientists
and Ph.D. students to attend the school.
MIDIT, CATS, and OFD collaborate with industrial companies in co-sponsored
Ph.D.projects.
4. CALENDAR OF ACTIVITIES 1998
PhD Courses and Workshops
- Nonlinear Science Festival
,
Thematic Workshop
at the Niels Bohr Institute, December 7-12,
coordinators: P. Cvitanovic and P. L. Christiansen.
Number of participants: 120
- Stochastic Processes and Applications
,
Ph.D. Course by Andrey L. Pankratov at MIDIT,
October-January 1999. Number of participants: 8
- Workshop on Coherent Structures,
Turbulence, Anomalous Transport in Plasmas and Fluids
at OFD, Risø, October 21-23, organizers: Jens Juul Rasmussen and
Volker Naulin. Number of participants: 24
- Burst on
Parametric Processes in Nonlinear Optical Materials
at OFD, Risø, October 19-20,
organizer: Per Michael Johansen. Number of participants: 10
-
Summerschool on Dynamical Systems' Aspects of Transport and Diffusion in
the Atmosphere and the Ocean at Bornö, Sweden, July 26
- August 2, organizer: Mogens Høgh Jensen. Number of participants: 30
- Mini Course
on Spatial Optics
at OFD, Risø,
27-28 May, organizers: M. Saffman and J. Juul Rasmussen.
Number of participants: 23
- Workshop on
Chaotic Synchronization and Two-Dimensional Maps
at Department of Physics, DTU, May 18-21, organizers: Erik Mosekilde
and Carsten Knudsen. Number of participants: 35
-
Miniworkshop on
Oscillations and Spatial Structures in Chemical Systems
at Department of Chemistry, H. C. Ørsted Institute, May 7, organizer:
Preben Graae Sørensen. Number of participants: 25
-
Mini Burst on
Nonlinear Transport in Superconductive and Mesoscopic Systems
at MIDIT, February 26-27, organizer: G. M. Fischer. Number of
participants: 28
Core Courses for the Graduate School in Nonlinear Science
- Nonlinear Waves, Coherent Structures, and Stochastic Dynamics
at MIDIT, DTU, organizers: Mads Peter Sørensen and Peter L. Christiansen,
MIDIT, and Jens Juul Rasmussen, OFD
(1998: replaced by DTU course 04421)
- Diffusion,
Transport, and Non-equilibrium Statistical Mechanics
at NBI, KU, organizer: Predrag Cvitanovic, NBI
- Existing Ph.D. Courses in Nonlinear Science at DTU and KU
Guest Professors
- M. Salerno, University of Salerno, Italy: Lecture series,
December
- J. Tuszynski, University of Alberta, Canada: Lecture series,
December
- J. C. Eilbeck, Mathematics Department, Heriot-Watt University,
Scotland: Nonlinear Science Festival, invited speaker
- K. Ø. Rasmussen,
Center for Nonlinear Studies, Los
Alamos, USA: Ph.D. supervision November-December and
Nonlinear Science Festival, invited speaker
- Magnus Johansson, Linköping University, Sweden: Nonlinear Science Festival, invited
speaker
- Martin Bees, University of Surrey, UK: Nonlinear Science Festival, invited
speaker
- V. Pudkaradze, University of Chicago, USA: Nonlinear Science Festival, invited
speaker
- D. Postnov, Saratov State University, Russia: Nonlinear Science Festival, invited
speaker
- M. Golubitsky, University of Houston, Texas, USA: Nonlinear Science Festival, invited
speaker
- H. W. Broer, University of Groningen, Netherlands: Nonlinear Science Festival, invited
speaker
- M. Markosova, Slovak Academy of Sciences, Bratislava, Slovakia:
Nonlinear Science Festival, invited speaker
- H. Nishimori, Osaka Prefecture University, Japan:
Nonlinear Science Festival, invited speaker
- G. Vattay,Eötvös University, Budapest, Hungary:
Nonlinear Science Festival, invited speaker
- D. Biswas, Bhabha Atomic Research Centre, Mumbai, India:
Nonlinear Science Festival, invited speaker
- B. Georgeot, Université Paul Sabbatier, Toulouse, France:
Nonlinear Science Festival, invited speaker
- H. H. Rugh, University of Warwick, UK:
Nonlinear Science Festival, invited speaker
- R. Artuso, Como University, Italy:
Nonlinear Science Festival, invited speaker
- T. Schreiber, University of Wupperthal, Germany:
Nonlinear Science Festival, invited speaker
- Christian Reick, University of Hamburg, Germany:
Nonlinear Science Festival, invited speaker
- S. Watanaba, Ibaraki University, Mito, Japan:
Nonlinear Science Festival, invited speaker
- S. Creagh, University of Nottingham, UK:
Nonlinear Science Festival, invited speaker
- Elisabeth Schröder, Chalmers University, Gothenburg, Sweden:
Nonlinear Science Festival, invited speaker
- M. Oxborrow, National Physical Laboratory, Teddington, UK:
Nonlinear Science Festival, invited speaker
- Stephanie Reimann, University of Jyväskylä, Finland:
Nonlinear Science Festival, invited speaker
- N. Pavloff, Paris, France:
Nonlinear Science Festival, invited speaker
- G. Baier, University of Tübingen, Germany:
Nonlinear Science Festival, invited speaker
- G. Huber, University of Arizona, Tucson, USA:
Nonlinear Science Festival, invited speaker
- W. van de Water, University of Eindhoven, Netherlands:
Nonlinear Science Festival, invited speaker
- G. Tanner, University of Nottingham, UK:
Nonlinear Science Festival, invited speaker
- A. Wirzba, Institute for Nuclear Physics, Darmstadt, Germany:
Nonlinear Science Festival, invited speaker
- R. Grauer, University of Düsseldorf, Germany:
Nonlinear Science Festival, invited speaker
- B. Mottelsen, NBI, Copenhagen:
Nonlinear Science Festival, invited speaker
- Roberto Livi, Dipartimento di Fisica, Universita' di Firenze,
Italy: Lecture December 3
- A. Spohn, ENS de Mécanique et d'Aerotechnique, Poitiers,
France: Lecture, December 2
- G. Careri, Department of Physics, Rome, Italy: Lecture series,
November
- G. Dewel, Free University, Brussels, Belgium: Lecture series,
November
- P. M. Luschnikov, Landau Institute, Moscow, Russia: Ph.D. supervision
November-December and lecture November 26
- J. L. Bona, Department of Mathematics, University of Texas, Austin,
USA: Lecture November 20
- Jerzy Piotrowski, Faculty of Automobiles and Heavy Machines
Engineering, Warsaw University of Technology, Poland: Lecture November 5
- H. Clercx, Eindhoven, Netherlands: Workshop on Coherent
Structures, invited speaker
- Y.B. Gaididei, Academy of Sciences of Ukraine, Ukraine: Ph.D.
supervision, October
- T. Klinger, University of Kiel, Germany: Workshop on Coherent
Structures, invited speaker
- V. Mezentsev, Institute of Automation and Electrometry,
Novosibirsk, Russia: Ph.D. supervision and lecture series
October-December
- D. Montgomery, Dartmouth, USA: Workshop on Coherent Structures,
invited speaker
- V. Muto, Department of Applied Mathematics, University of
Pais Vasco, Bilbao, Spain: Ph.D. supervision October
- Andrey L. Pankratov, Institute for Physics of Microstructures of RAS,
Nizhny Novgorod, Russia: Ph.D. course October-January 1999
- H. L. Pécseli, Oslo University, Norway: Workshop on Coherent
Structures, invited speaker
- K. Rypdal, University of Tromsø, Norway: Workshop on Coherent
Structures, invited speaker
- S. Sakai, Electrotechnical Laboratory, Uzmezano, Japan: Ph. D. supervision
and lecture October 13
- B. I. Sturman, Institute of Automation, Novosibirsk, Russia: Ph.D.
supervision October and Burst on Parametric Processes in Nonlinear
Optical Materials, invited speaker
- V. I. Karpman, Racah Institute of Physics, University of
Jerusalem, Israel: Lecture series September
- Yuri Kivshar, Optical Sciences Centre, Australian National University,
Canberra, Australia: Planning of Ph.D. supervision and lecture September 25
- J. Levitan, University of Bar Ilan, Israel: Ph.D. supervision
September and lecture September 10
- Ling Miao, McGill University, Montreal, Canada: Ph.D. supervision
and lecture series August-November
- E. V. Podivilov, Institute of Automation, Novosibirsk, Russia: Ph.D.
supervision September-October and Burst on Parametric Processes in Nonlinear
Optical Materials, invited speaker
- O. Bang, Australian National University, Canberra, Australia: Ph.D.
supervision August and December and Nonlinear Science Festival, invited
speaker
- H. Haken, University of Stuttgart, Germany: Ph.D. supervision
and lecture series August
- N. Kukthtarev, Alabama A&M University, Huntsville,
U.S.A: Ph.D. supervision and lecture August 12
- M. Laradji, Department of Physics, University of
Prince Edwards Island, Canada: Lecture series August
- W.Zhai, Train & Track Research Institute, The Southwest Jiaotong
University, Chengdu, China: Ph.D. supervision and lecture series
July-September
- J.-G. Caputo, INSA de Rouen, France: Ph.D. supervision and lecture
series July-August and November
- A. Vulpiani, Department of Physics, Rome University, Italy:
Summerschool on Dynamical Systems' Aspects, invited speaker
- U. Frisch, Nice, France: Summerschool on Dynamical Systems'
Aspects, invited speaker
- E. Aurell, Stockholm, Sweden: Summerschool on Dynamical Systems'
Aspects, invited speaker
- V. Artale, ENEA, Rome, Italy: Summerschool on Dynamical Systems'
Aspects, invited speaker
- G. Boffetta, Torino, Italy: Summerschool on Dynamical Systems'
Aspects, invited speaker
- T. Tel, Budapest, Hungary: Summerschool on Dynamical Systems'
Aspects, invited speaker
- E. Zambianchi, Naples, Italy: Summerschool on Dynamical Systems'
Aspects, invited speaker
- J. Moloney, Mathematics Department, University of Arizona, USA:
Lecture series June-July
- Y. Zhang, Conductus Inc., Sunnyvale, California, USA: Ph.D.
supervision June-July and lecture June 18
- Alexandre Zenchuk, Landau Institute, Moscow, Russia:
Lecture series June
- L. Bergé, CEA, Bruyères-le-Châtel, France:
Mini Course on Spatial Optics and Nonlinear Science festival, invited
speaker
- A. V. Mamaev, Institute of Mechanical Problems, Moscow, Russia:
Ph.D. supervision May and Mini Course on Spatial Optics, invited speaker
- W. E. Torruellas, Washington State University, USA: Mini Course
on Spatial Optics, invited speaker
- A. Zozulya, Worcester Polytechnic Institute, Mass., USA:
Mini Course on Spatial Optics, invited speaker
- Gian-Italo Bischi, Urbino, Italy: Workshop on Chaotic
Synchronization, invited speaker
- Laura Gardini, Parma and Urbino, Italy: Workshop on Chaotic
Synchronization, invited speaker
- Peter Grassberger, Jülich, Germany: Workshop
on Chaotic Synchronization, invited speaker
- Carsten Knudsen, Department of Applied Mathematics, University
of Leeds, UK: Workshop on Chaotic Synchronization,
invited speaker
- Y. Majstrenko, Department of Mathematics, Kiev, Ukraine:
Ph.D. supervision May-June, Workshop on Chaotic Synchronization and
Nonlinear Science Festival,
invited speaker
- C. Mira, Toulouse, France: Workshop on Chaotic Synchronization,
invited speaker
- Arkady Pikovsky, Potsdam, Germany: Workshop on Chaotic Synchronization,
invited speaker
- Michael Rosenblum, Potsdam, Germany: Workshop on Chaotic Synchronization,
invited speaker
- I. Schreiber, Prague, Czech Republic: Workshop on Chaotic
Synchronization and Miniworkshop on
Oscillations and Spatial Structures, invited speaker
- Stephen Scott, University of Leeds, UK: Miniworkshop on
Oscillations and Spatial Structures, invited speaker
- Kenneth Showalter, Department of Chemistry, University of West
Virginia, USA: Ph.D. supervision March-May, lecture April 15, and
Miniworkshop on Oscillations and Spatial Structures, invited speaker
- Mads Kærn, University of Toronto, Canada: Miniworkshop on Oscillations and Spatial
Structures and Nonlinear Science Festival, invited speaker
- Lars Folke Olsen, University of Odense: Miniworkshop on Oscillations and Spatial
Structures, invited speaker
- Javid Atai,
Department of Electrical Engineering, University of Sydney,
Australia: Lecture April 23
- Reinhold Kleiner, Physics Institute,
University of Erlangen-Nürnberg, Germany:
Lecture March 12
- G. M. Fischer, Department of Physics, DTU: Mini Burst on Nonlinear
Transport in Superconductive and Mesoscopic Systems Department of Physics,
organizer
- E. A. Kuznetsov,
Landau Institute for Theoretical Physics,
Moscow, Russia: Lecture series January and Nonlinear Science Festival,
invited speaker
5. ENTRANCE REQUIREMENTS
To enter the Graduate School in Nonlinear Science the candidate must have passed
courses in nonlinear dynamics at Master's degree level.
At DTU and KU such courses are given under the Mathematics, Informatics,
Physics, and Chemistry programs.
Applicants for a full Ph.D. study at the school will be evaluated by program committees.
At DTU the admission of Ph.D. students is essentially based on the
average of grades obtained in the Master's degree courses.
At Risø the applicants are interviewed in addition.
At KU, the Master's thesis is particularly emphasized.
Co-sponsored grants will be advertised internationally. In connection with the selection
of Ph.D. students for these grants
we plan to interview as many as possible of the applicants.
6. PH.D. STUDENTS AND POST DOCs
Danish Ph.D. students
MIDIT, DTU: Total
17 Danish Ph.D.s
5 Ph.D.'s co-sponsored with:
Danish Research Academy,
Research Centre Bygholm,
Danish Fundamental Metrology Institute,
Force Institute,
Topsil,
Danish Technical Research Council,
Academy of Technical Sciences, and
European Union
(1993-97 MIDIT, DTU: Total: 22 Danish Ph.D.s)
OFD, RISØ: Total 10 Danish Ph.D.s
9 Ph.D.'s co-sponsored with:
Danish Research Academy,
Danish Natural Science Research Council,
and UNIC-C,
(1993-97 OFD, RISØ: Total 8 Danish Ph.D.s)
CATS, KU: Total 9 Danish Ph.D.s
4 Ph.D.'s co-sponsored with:
Danish Research Academy,
Danish Natural Science Research Council,
UNIC-C,
DTU,
Risø,
European Union, and
FOFT
(1993-97 CATS, KU: Total 16 Ph.D.s)
Total 35 Danish Ph.D.s
About 10 Danish Ph.D. students are expected to enter the school each year.
Thus the total enrolment over a five year period amounts to about 50 Danish Ph.D.
students.
Foreign Ph.D. students
MIDIT, OFD, CATS: Total 29 Foreign Ph.D.'s
Many of the foreign Ph.D. students come from the home institutions of our Guest
Professors (who recommend the students) or from other institutions in contact with
our school. The students typically spend a couple of months here,
participating in the activities of the school and working on their Ph.D. thesis.
Their stay constitutes an important part of their Ph.D. training. We issue a diploma
recognizing their achievements here.
Post Docs
15 Post Docs, sponsored by various sources, are working in connection with the
Graduate School (MIDIT: 3, OFD: 3, and CATS: 9).