Directors:
P. Cvitanovi\'c, Professor, Physics & Astronomy (CAS)
S.H. Davis, Professor, Engineering Sciences &
Applied Math. (MEAS)
Executive Committee:
H. Riecke, Associate Professor, Engineering Sciences & Applied
Math. (MEAS)
M. Silber, Assistant Professor,
Engineering Sciences & Applied Math. (MEAS)
S.A. Solla, Professor, Physiology (NUMS) and Physics and Astronomy (CAS)
Key Participants:
K. Burns, Professor, Mathematics (CAS)
J. Franks, Professor, Mathematics (CAS)
J.C. Houk, Professor and Chair, Physiology (NUMS)
W.L. Kath, Professor, Engineering Sciences & Applied Math. (MEAS)
P. Kumar, Professor, Electrical & Computer Engineering (MEAS)
S. Lichter, Professor, Mechanical Engineering (MEAS)
B.J. Matkowsky, Professor and Chair, Eng. Sciences & Applied Math. (MEAS)
F. Mussa-Ivaldi, Associate Professor, Physiology (NUMS)
J.M. Ottino, Professor and Chair, Chemical Engineering (MEAS)
M. Swartz, Assistant Professor, Biomedical Engineering (MEAS)
P. Umbanhowar, Assistant Professor, Physics & Astronomy (CAS)
P.W. Voorhees, Professor, Materials Science and Engineering (MEAS)
The key to the school and
departmental abbreviations used throughout the proposal:
CAS ¯ Weinberg College of Arts and Sciences
MEAS McCormick School of Engineering and Applied Science
NUMS Northwestern University Medical School
BME Department of Biomedical Engineering
ChE Department of Chemical Engineering
ECE Department of Electrical & Computer Engineering
ESAM Department of Engineering Sciences & Applied Mathematics
MSE Department of Materials Science and Engineering
Math Department of Mathematics
ME Department of Mechanical Engineering
PaA Department of Physics & Astronomy
Phys Department of Physiology
Goal: to establish a first class training program in nonlinear science that bridges across disciplines to equip students for the rapidly changing needs of industry and academia.
Traditional Ph.D. training involves a departmental core curriculum followed by specialization in a single focused area of research; within this framework, a broad and interactive scientific experience is postponed until the graduates become post-doctoral fellows or industrial employees. The aim of the proposed IGERT traineeships is to produce a different type of Ph.D.: flexible, broadly trained, and better prepared for the rapidly changing needs of industry and academia. Nonlinear science is by nature a cross-disciplinary field that cuts across the basic sciences and traditional engineering. We intend to create a training environment that emphasizes the unity of fundamental concepts underlying a variety of physical and biological phenomena, provides the mathematical and computational framework for their analysis, and reveals their wide ranging scientific, engineering, and medical applications.
We propose to join faculty forces across the many disciplines where nonlinear science plays or has the potential to play a pivotal role, in a unifying educational effort that spans several departments. Our aim is to provide graduate students with tools that will enable them to venture into novel areas of application as the need and opportunity arise in their future careers. Our strategy for success is to use the funding provided by the IGERT program to create a novel interdisciplinary environment built upon the strengths of individual research programs. Northwestern University has the infrastructure and the right mix of strong faculty to offer integrated Ph.D. training in nonlinear science. IGERT support will bring together faculty from the Weinberg College of Arts and Sciences, the McCormick School of Engineering and Applied Science, and the Northwestern University Medical School, each of them an expert in specific and complementary areas of nonlinear science.
We propose to establish a high quality cross-disciplinary graduate training program that emphasizes acquisition of the conceptual, mathematical, and computational tools needed for current and future scientific and engineering applications of nonlinear science. The backbone of our program is a year-long training course in which general lectures taught by faculty with diverse scientific backgrounds will be followed by specific projects carried out by small teams of students supervised by pairs of faculty members with complementary expertise and perspective. This course will provide a common background and lead to Ph.D. research with a strong preference for dual-advisor projects. These activities will be complemented by a regular nonlinear sciences research seminar, a student seminar, a visitor program, an internship program, and a yearly regional conference.
Nonlinear science provides a common conceptual framework as well as mathematical and computational tools applicable to a broad spectrum of important problems in science and engineering.
In the last two decades, investigations of nonlinear phenomena have developed into a very active research field with a significant impact on fundamental research in the natural and biomedical sciences, mathematics, and engineering. A glance at the current contents of leading professional publications reveals a vigorous activity which reflects a common foundation for otherwise disparate disciplines. For example, pattern formation research at Northwestern University, based on generic concepts of symmetry and stability, provides unifying explanations to such diverse phenomena as waves in vibrated layers of granular materials, convection in fluids, and patterns in the transverse sections of wide-area lasers.
The goal of the proposed program is to provide training and research opportunities that emphasize nonlinear methods and their relevance to a broad range of applications and research fields. The strategy is to build upon the interplay between conceptual frameworks, which provide tools for the analysis and characterization of complex dynamical behavior, and novel applications, which act as a trigger for further theoretical development.
Northwestern University scientists pursue a comprehensive range of research within the unifying theme of nonlinear, complex dynamics. We highlight here some of these research efforts and indicate connections that would gain strength and coherence under the IGERT program.
The richness of pattern formation phenomena has stimulated very active research on spatially extended dynamical systems. Classic examples occur in fluid convection driven by temperature gradients, water waves excited in liquid layers, combustion-flame fronts in gases and solids, and coarsening in elastically stressed solids. Pattern formation issues arise in the study of Turing patterns in chemical and biological systems, in the analysis of information processing, storage, and retrieval in the brain, and in the characterization of convective transport in poroelastic, stressed media such as lung tissue. Applications to materials science arise in modeling the dynamics of thin films and interfaces.
Powerful theoretical tools developed for the characterization of localized structures and spatio-temporal chaos are complemented by a theoretical description of maps and flows, of relevance to experiments on the mixing of highly viscous fluids as well as transport in granular materials and complex fluids. Recently discovered oscillons, localized waves in vibrated granular media, are conceptually related to solitons, whose importance as long-distance information carriers has been exploited in applications of nonlinear optics to telecommunications and optical processing.
Mathematical research in nonlinear dynamics at Northwestern University focuses on ergodic theory as well as classical and quantum chaos; it includes work on knots that occur as closed orbits of flows and periodic orbits of low dimensional dynamical systems, as well as geometrical and dynamical aspects of geodesics on general manifolds. The periodic orbit theory applies these mathematical results to physical problems such as far-from-equilibrium transport, conductance of mesoscopic devices, and the semiclassical quantization of classically chaotic systems.
Applications to computational neuroscience range from research on synchronized oscillations and chaos in recurrent neural networks to the design of computationally efficient nonlinear controllers for limb motion.
The proposed graduate training will immerse students in a highly cooperative, interdisciplinary research community built on existing strengths that will be unified into a program based on the acquisition of conceptual tools and exposure to relevant applications.
The need for a strong foundation in the analysis of nonlinear dynamical systems is common to many graduate programs in science, engineering, and mathematics. At Northwestern University, courses on nonlinear dynamics are currently taught in the applied mathematics, electrical engineering, mathematics, and physics departments, each from a different perspective, and draw students from biomedical, civil and mechanical engineering, materials science, and chemistry, as well as from the departments offering the courses. (For a listing of courses, seminar series, workshops and other activities offered by Northwestern University consult the Nonlinear Science Program homepage www.phys.nwu.edu/ ~ canis/).
While students would clearly benefit from a program based on a broad, coherent, and unified view of nonlinear science, departmental and school boundaries need to be superseded by an integrated structure that provides a framework for scientific cooperation otherwise based on isolated collaborations between individual faculty members. The program to be built around the IGERT initiative will generate a new level of integration in graduate education: it will involve faculty in different departments in an effort to unify the nonlinear science curriculum across the three participating schools. It is important to note that in this endeavor we have the enthusiastic support of the chairs of all of the participating departments.
The graduate education in the proposed IGERT program differs from the conventional model in a number of significant ways, as emphasized in the following description of the components of this integrated effort.
The students will enroll in the Ph.D. program of a participating department (applied mathematics, mathematics, physics, neurobiology and physiology (CAS), physiology (NUMS), and a number of engineering departments), and obtain a minor in Nonlinear Science through the Nonlinear Science Program. The IGERT program would allow us to attract the top recruits by offering additional years of support at the outset, beyond the initial nine-month fellowships currently offered by the participating departments.
The core of the cross-disciplinary training program will be a:
1. Nonlinear Science Course, a
year-long course on the mathematical and computational
techniques of nonlinear science, and their application
to the analysis of nonlinear processes in diverse systems.
This course is intended for second-year graduate students;
the format will
be two quarters of lectures taught by one or two
faculty members and supplemented by review sessions
led by senior graduate students in the program,
followed by one or two quarters
of research on specific projects
carried out by small teams of students supervised by
pairs of faculty members with complementary expertise and perspectives.
Examples of possible projects are listed
below.
The course will gather
all nonlinear science students in an activity that
stresses commonalities among various fields, and it will
provide a sense of intellectual community fundamental
to the success of the program.
The course work will require
coordinated collaboration with
peers and teachers
from different backgrounds, thus stimulating
communication skills that
will prove invaluable in future careers
in industry or academia.
The following activities will be an integral part of the graduate
program:
2. Welcoming workshop/retreat before the start of each
fall quarter, to introduce the incoming
students to the faculty and existing students.
New students
will identify a suitable Nonlinear Science Advisor
from outside their
own department, who will oversee
the student's progress during the first two years
in tandem
with the departmental advisor.
3. Interdisciplinary nonlinear science seminar. This seminar
series, initiated in January 1997, has drawn a wide attendance from
the participating departments.
The scope of the seminar will be broadened to include
engineering and biological applications; industrial researchers
will be invited to discuss nonlinear problems that arise in
their environment.
4. Graduate student seminar. This new series organized for and by
the students will focus on student research projects; it will
also provide a forum for
directed discussion seminars on ethics and
conflict of interest in research.
5. Internships at other institutions. During their second summer
the students will be able to work in an external academic or
government lab, to master an
experimental technique or theoretical approach not readily
available internally. Formal commitments from
about ten internship hosts at research centers in
US and Europe have already been secured.
6. Co-advised, cross-disciplinary thesis projects.
Thesis research becomes the student's primary
activity by the third year. Competitive fellowships will be
awarded to students who are engaged in cross-disciplinary research
co-advised by a pair of faculty members.
7. Visitor program. An active visitor program will help
promote and maintain national, international and
industrial collaborations. Priority
will be given to visitors whose research relates to that of
participating Northwestern University faculty, and who demonstrate potential as external
mentors to our graduate students.
8. Regional Nonlinear Science Workshop. A yearly interdisciplinary meeting
will be organized jointly with other Midwestern universities,
to expose students to the forefront of
research, and to give them an opportunity to
present their own work in poster sessions.
Three small-scale workshops, organized with U. of Chicago,
have already taken place.
A sample list of topics for the projects part of the Nonlinear Science Course:
1. Neurocontrol of Biomorphic Systems: The project combines concepts and tools of theoretical neurocomputing and nonlinear adaptive control in nonlinear limb dynamics, and applies them to the control of a biomimetic robotic system.
2. Solitons and Solitary Waves: The project focuses on optical solitons and/or coherent structures in other media. For example, students will set up experiments and observe the propagation of solitons in optical fibers, and compare with theory by simulating the experiments numerically within the framework of analytical models of nonlinear pulse propagation.
3. Pattern Formation: Students will investigate pattern formation phenomena in a physical, chemical or biological system. For example, some students might investigate spiral waves in excitable media (heart, neurons, EEG-activity), while others might concentrate on patterns in forced systems (e.g. surface waves on liquids or granular media).
4. From Low- to High-Dimensional Chaos: Each project will require mastery of the same basic set of techniques of the theory of low-dimensional chaotic systems, including intensive computation and graphical visualization. An experimental physicist might use the theory to compute conductance fluctuations in a microdot, while a physiology student might analyze chaotic data from a neurophysiology experiment.
Program summary: First year students will take core courses required by their respective departments, as well as individually selected electives in a preparatory Nonlinear Science sequence. All students will gain exposure to current research through the Interdisciplinary Nonlinear Science Seminar and the Graduate Student Seminar. During their first summer the students will work on a small-scale research project. Departmental course work will continue during the second year, in parallel with the intensive Nonlinear Science Course (the core of the proposed program made possible by the IGERT grant), as well as advanced courses based on group study of research topics. Thesis research becomes the students' primary activity by the third year. Lectures within the visitor program will provide further exposure to current research. Senior students will have responsibility for the Graduate Student Seminar series. Care will be taken to keep the average time-to-degree within ~ 5 years.
IGERT funding will also enable us to implement a series of measures to aid recruitment and retention of students from under-represented groups: Summer Internships for Minority and Women Undergraduates for the summer between their junior and senior year, Rosalind Franklin Graduate Fellowships to attract promising women and minority students, and a Women in Science Seminar series to bring women graduate students and faculty together on a regular basis, providing a natural forum for mentoring. The participating faculty has a well established record of mentoring students from under-represented groups, in activities of the Association for Women in Mathematics, and within the AT&T Bell Laboratories Graduate Research Program for Women.
The proposed directors of the IGERT program are P. Cvitanovi\'c (PaA) and S.H. Davis (ESAM). Prior to moving to Northwestern University, Cvitanovi\'c built up and directed the Center for Chaos and Turbulence Studies at the Niels Bohr Institute, Copenhagen. Davis, a former director of the Multiphase Flow Center at Northwestern University, has a long record of directing interdisciplinary research and graduate studies.
The day-to-day training, research, and other activities of the program will be supervised by the Executive Committee (EC), who will ensure that fellowships, internships and visitor invitations are awarded in accordance to the goals of the program. The directors will appoint an external panel of prominent scientists to advise the EC during regular visits to the Institute. The evaluation of the program will rely on detailed feedback from students, internship hosts, participating faculty, external advisory board, long-term visitors, and thesis advisors. Annual assessments will concentrate on the performance of the Nonlinear Science Course, Women in Science Seminar, Nonlinear Science Seminar, Visitor Program, and Regional Conference. After two years it will be possible to also assess the internships, recruitment, retention, Rosalind Franklin Fellowships, PhD theses time-to-degree, and publications.
Northwestern University already has a strong faculty in nonlinear sciences. Its commitment to strengthening the research effort in this field is demonstrated by recent senior faculty appointments in physics (Cvitanovi\'c), physiology (Solla), as well as the junior appointment in experimental nonlinear physics (Umbanhowar).
Northwestern University encourages cross-departmental and interdisciplinary research. The Nonlinear Science Institute at Northwestern University, which will begin operation in Winter 2000, pending support through the IGERT grant, aims at furthering such an environment. The Institute would span the Weinberg College of Arts and Sciences, the McCormick School of Engineering and Applied Science, and the Northwestern University Medical School.
The IGERT Nonlinear Science Program office and the common meeting room will be housed in the same building as the participating engineering, applied mathematics, and physics departments. The building already has student computer laboratories and offers video-teleconferencing capabilities. Except for the laboratories in the Northwestern University Medical School (Chicago campus), the participating faculty laboratories are all housed in the same building. An effort will be made to provide shared office space and computer facilities for the Nonlinear Science Program graduate students.
The Deans of the three participating Schools and the University, at the level of the University's Vice President for Research, strongly support the initiative, and will fund the Institute for an initial three-year period, during which time the Nonlinear Science Institute is expected to secure additional University and external support. The three participating Schools and the University have committed $50K/year seed funding ($150K over 3 years in all) which will provide for
In addition, as the tuition allowance of the IGERT program does not cover the full tuition of the students on fellowships ($21,280), the Graduate School will contribute $246,240 towards tuition.