Over the past two decades, investigations of nonlinear systems have revealed that the simplest laws of nature can lead to bewilderingly complex dynamics, and yet that such dynamics exhibit universal features which are largely independent of many details of the underlying system. Thus, phenomena as disparate as neuronal dynamics and mixing of granular materials can be studied with the same mathematical tools. Common themes that arise in the study of nonlinear systems include their qualitative dynamics, structural stability, long-term behavior, chaos, bifurcations, and the impact of symmetries on the dynamics. By stressing the unity of the underlying concepts and using the accumulated experience of scientists from diverse backgrounds, investigators of nonlinear phenomena are transforming important problems once considered intractable, or even ill-posed, into promising new fields. Methods developed in the study of nonlinear systems are now being applied to such areas as pattern formation, quantum theory, bimotor control, computational neuroscience, nonlinear optics, crystal growth, granular flows, biological fluids, mixing, nonequilibrium transport, and combustion. These problems cut across many fields, and traditionally have been studied only by researchers in their individual fields, e.g., chemical, mechanical, or electrical engineering, physics, applied and pure mathematics, or the biological and health sciences. The aim of the program, Dynamics of Complex Systems in Science and Engineering, is to provide unique training to graduate students at Northwestern who work on problems involving nonlinear phenomena. A systematic study of nonlinear systems should be an important part of the education of all Ph.D. students who will be dealing with complex systems later in their careers. The most remarkable single aspect of nonlinear systems is the commonality of the mathematics that describe them, despite the wildly varying contexts. It is clear that a strongly cross-disciplinary program of study for nonlinear systems will be far superior to any based in a single department or discipline. Student Timeline Components Overview of the various components. 1. Welcoming workshop retreat: The incoming graduate students will be introduced to the faculty and more senior students during a weekend retreat to take place in the early fall, before the first week of classes. On this occasion the new students will meet the faculty and graduate students associated with the program. The main purpose of this meeting is to bring the incoming students into the community and give them an overall view of the scientific activities of the program. Presentations will be given by the senior graduate students, who may report on the results from their work during the second-year project course, from their internship, or from their thesis research. In addition, the retreat will provide an informal setting for the discussion of general topics of concern and interest to scientists. It is also a natural setting for establishing student-mentor relationships, as well as identifying a suitable Advisor for each student. 2. Advisor: This faculty member, typically outside the student’s own department, oversees the student’s progress through the (missing word). Initially, the Advisor helps the departmental advisor direct the student’s course of study, with special attention to the background courses needed for the intensive second year course. As the student progresses through the program, the Advisor’s role shifts from that of an advisor on courses to one of a mentor who takes an interest in the student’s development as a scientist. 3. Summer Project: During the summer between the first and second year, students will work on small-scale research projects with members of the faculty. Since the students will be on the Fellowship and will not require support by a goal-oriented grant of a specific faculty member, this project can be exploratory for both the student and the faculty members, and will allow the student to get a better feeling for an area of research before he/she decides to start a thesis in it. The summer research projects will also involve 2-3 advanced undergraduates from underrepresented groups to aid in identifying and recruiting talented students to our training program. 4. Nonlinear Sciences Course: The centerpiece of the proposed graduate training will be the cross-disciplinary nonlinear science course based on teaching across departments and schools and on student research projects. This year-long intensive course, intended for students in their second year of graduate study, will constitute one of the students’ elective courses in their respective Ph.D. programs. It will be taught by faculty from the , the , and the (missing words) . The participating graduate students will be recruited primarily from departments of Applied Mathematics, Mathematics and physics, the Institute for Neuroscience, and a number of engineering departments (Biomedical, Chemical, Electrical and Mechanical Engineering, and Material Science). The course will provide the students with an in-depth, integrated treatment of different aspects of nonlinear science, while also introducing concrete examples of important nonlinear processes in diverse systems. It will equip the students with the necessary tools for investigating nonlinear systems in their specific fields of interest. The course will start with lectures on the qualitative behavior of dynamical systems described by ordinary differential equations and maps, including fundamental elements of bifurcation theory, low-dimensional chaotic dynamics, and an introduction to dynamical systems with many degrees of freedom. In the Winter and Spring quarters the students will split into 2-3 project-focussed teams comprised of approximately 5 students each and supervised by 2 faculty members with complementary expertise and perspectives. The students in a given team will focus on one theme, with each student pursuing his or her own project as part of the larger group effort; this ensures that each student learns all aspects of a specific area, while still gaining valuable team-work experience. Progress in nonlinear science rests on the close interplay among theory, experiment, and computation. This will be reflected in the course by including a strong computational component in each student’s experimental and/or theoretical project. 5. Internship Program: To complement their thesis research, students will be encouraged to participate in an internship program. The goal of this program is to provide the students with supplementary training that will significantly broaden and strengthen their education. For example, students working on theoretical projects might intern in experimental labs, while students working on experimental theses might collaborate on theoretical or computational projects. In other cases the internship could allow the student to master a specific experimental technique or theoretical approach not readily available at Northwestern, but important for the student’s thesis research. Students, together with their advisors, will make the initial contact with the internship host. A brief proposal will then be written that clearly states the goals of the internship. We expect that internships will last 3-6 months. The experience of the hosts chosen for the internship program shows that this length of time is usually sufficient to achieve meaningful results and sometimes even form the basis for a publication. After the first three months the host in agreement with the thesis advisors decide whether the project is successful and whether the internship will be extended to the full six months. Upon returning to Northwestern the student will present his/her results in the form of a written report and a brief presentation in the Graduate Seminar Series. The internships will be make use of the extensive connections the Northwestern faculty have with other institutions and labs. Close contact between the thesis advisors and the student’s host will contribute substantially to the success of the internships. At the same time, the internships will provide opportunities for these contacts to grow into full-fledged collaborations. Frequently Asked Questions for IGERT Students General Information IGERT Student Responsibilities IGERT Seminars Internships and Travel Choosing an Advisor Other IGERT Programs General Information What does IGERT stand for? IGERT stands for the Integrative Graduate Education and Research Traineeship Program. Where is the IGERT Commons Room? Tech L550 (Yes, there actually is a fifth floor in the Tech building!). Find directions to the room by linking through Contacts on the IGERT website. What kind of information can I find at the IGERT website? The IGERT website (http://www.complex-systems.northwestern.edu) has a description of the program, a schedule of seminars and other IGERT events, a list of important contacts, as well as a listing of the IGERT program requirements and courses offered. In short, the website is the best place to begin any search for IGERT information. Where should I go to address IGERT financial matters? For payroll concerns, see Edla d'Herckens. For reimbursements, see Judy Piehl. Both are located in the ESAM office, Tech M426. IGERT Student Responsibilities What are my responsibilities as a 1st year graduate student in the IGERT program? Are there course requirements? There are no course requirements for first year graduate students in the IGERT program, but regular attendance to meetings and seminars is expected. What are my responsibilities as a 2nd year graduate student in the IGERT program? Course requirements? 2nd year graduate students are required to take Interdisciplinary Nonlinear Dynamics (438-1), which is offered each fall quarter. IGERT students should also take at least one of the IGERT project courses (438-2, 3) offered in the winter and spring quarters. Again, regular attendance to meetings and seminars is expected. Do Senior IGERT students have any additional responsibilities? Students that have more than one year experience are expected to give or host a Student Seminar in addition to the regular IGERT responsibilities. Do I need to acknowledge IGERT in journal publications? How? Yes. The proper way to acknowledge IGERT in research publications is: "This research has been supported in part by the NSF-IGERT program 'Dynamics of Complex Systems in Science and Engineering' (DGE-9987577)." IGERT Seminars What are the seminars that IGERT offers? Nonlinear Seminar- The Nonlinear Seminar generally takes place on Fridays from 2-3pm in the ESAM conference room (M416). The seminar features lectures on a wide range of topics in Nonlinear Dynamics. Graduate Student Seminar - The Graduate Student Seminar features talks from IGERT graduate students, and usually takes place in the ESAM conference room (M416) at times and dates announced at the beginning of each quarter. Besides being a chance for IGERT students to gain experience giving scientific talks, the seminar is also an opportunity to learn more about peer research. Generally, faculty attendance is discouraged, with the exception of special Student Seminar topics on ethics and career development, which are given by selected faculty members. Refreshments (usually pizza and soda) are served after each seminar. Brown Bag Lunch - The Brown Bag lunch is an informal meeting for IGERT students that usually takes place in the IGERT Room, Tech L550. About half of the Brown Bag Lunches involve an informal talk given by a faculty member or student, and the other half are simply opportunities to eat lunch and socialize with the other IGERT students. The schedule for Brown Bag Lunches is usually posted at the beginning of each quarter. Seminar for Women in Science and Engineering - The Seminar for Women in Science and Engineering features talks and discussions on topics that are of interest to women in science and engineering. There are usually about 3 meetings per quarter, with dates and times posted on the IGERT website. All are welcome to attend. What is the Nonlinear Seminar Focus Topic? Can I suggest a Focus Topic?What are the seminars that IGERT offers? The Nonlinear Seminar includes special Focus Topics, which consist of a series of speakers who specialize in a specific area of research that may be of interest to IGERT participants. Any IGERT participant may propose a Focus Topic for the Nonlinear Seminar. For graduate students interested in a specific topic, it is suggested that they work with their advisor to develop a list of potential Focus Topic speakers, and contact the Nonlinear Seminar Director (see website) for more information. What is "Take-the-Speaker-to-Lunch"? Every Friday before the Nonlinear Seminar, a group of IGERT students takes the Seminar Speaker to lunch (lunch paid for by the IGERT program). Generally, an e-mail is sent out by the Take-the-Speaker-to-Lunch coordinator (see website) earlier on during the week. If you are interested in attending the lunch, simply respond to the e-mail. Do I have to give a Student Seminar? Graduate students with over one year of experience in the IGERT program are expected to either give or host one Student Seminar per year. Internships and Travel When should I do my internship? The time period for interning may vary from student to student. Some students may wish to do an internship early, before beginning dissertation work, and others may prefer to do an internship much later. It is largely up to the student and his or her advisor. How long does the internship last? IGERT students generally intern for at least a three month period, but longer internships (~ 6 months) are also encouraged. Does IGERT pay me during my internship? IGERT can provide funds to help with travel and expenses during the internship. How do I set up the internship? Much of the responsibility for arranging the internship rests on the student. A good place to begin is the IGERT website, which has a description of the internship program, a listing of potential hosts and examples of previous internships. Students can also contact the IGERT internship coordinator (see website) for advice. Does IGERT give money to go to conferences? When should I do my internship? Yes, see the website for information and contacts regarding IGERT travel grants. Can I request a travel grant if I don't have research to present? Yes. In fact, first year students with either no advisor or no research to present are encouraged to apply for travel grants to attend conferences of particular interest. Choosing an Advisor Do I have to choose an advisor who is currently affiliated with the IGERT program? No. By being IGERT-fellows students are not restricted in their choice of advisors in any way. Students new to Northwestern, who are offered a two-year IGERT fellowship are completely free in their choice of research topic and advisor. For more senior students the requirement to be funded by IGERT is that their thesis work fit into the framework of the program which is broadly defined as interdisciplinary nonlinear science. In this context it is worth mentioning that in the past a number of IGERT students have chosen faculty advisors who were not IGERT members at the time but who subsequently became members of the program. Other IGERT Programs What is the IGERT Mentoring Program? How does it work? The IGERT Mentoring Program matches incoming IGERT students with more senior students in order to ease the transition into IGERT and/or graduate school at Northwestern, in general. Students are grouped loosely according to disciplines, and are encouraged to get together in informal settings. Information about the Mentoring program can be found on the IGERT website. What should I know about inter-university IGERT workshops? The Northwestern IGERT program for dynamics of complex systems works with other IGERT programs in related research fields to offer joint workshops. These workshops provide a good opportunity for students to give and listen to informal talks.