(1) the NSF coversheet (NSF Form 1207) showing the name of the proposed PFC director (principal investigator or PI) and the pre-proposal title.
Predrag Cvitanovic, PI
Leonid Bunimovich, CoPI
Kurt Wiesenfeld, CoPI
Michael Schatz, CoPI
Stephen P. DeWeerth, CoPI
Physics Frontier Center in Nonlinear Science
Summary
We propose to establish a Physics Frontier Center in Nonlinear Science at Georgia Tech to bring together, in a cross-disciplinary program, faculty, researchers and students in basic sciences, engineering, medicine, and other disciplines where fundamental concepts in nonlinear dynamics play a central role. The understanding of complex systems, including turbulence, was identified by the MRC as one of the six grand challenges for physics in a new era. Control of a variety of nonequilibrium processes, such as turbulence and adhesion, was also cited as one of the directions that will critically impact another grand challenge, that of creating new materials. Georgia Tech's CNS stands to respond to these challenges by concentrating on the following 3 components: (1) Complex dynamics and chaos in classical and quantum systems, (2) Dynamics of spatially extended systems, and (3) Nonlinear dynamics in biology. These MRC's are based on the broad interdepartmental expertise of Georgia Tech faculty in nonlinear phenomena and address physics and life sciences problems including far-from-equilibrium transport and mixing in classical and quantum regimes, dynamics and control of fluids and electrical circuits, power generation, communication systems, and dynamics in optical, electronic and biological settings. The Center will take advantage of Georgia Tech's role as the leading technological university in the Southeast by sponsoring an active outreach program that includes hosting visiting researchers from academic and industrial settings as well as lecturing by Center members at a wide range of scientific, educational, and technical sites throughout the Southeast. In this way, the Center will be serving as a regional, national and international focal point for extending methods of nonlinear science to an even wider range of applications and research fields. Coupled with the interdisciplinary nature of the proposed research, these initiatives fit well with the recommendation of the NRC report to physics departments ``to review and revise their curricula to ensure that they are engaging and effective for a wide range of students and that they make connections to other important areas of science and technology''.
(3) Limit the narrative section as a whole to no more than thirteen pages total, including tables, and illustrations, regardless of the number of major research activities.
In the narrative provide the following:
· a brief overview of the PFC as a whole, including a concise rationale for establishing the PFC, and an outline of the existing and planned capabilities of the participating institutions in physics research and education (Limit: 1 page);
Nonlinear science cuts across many disciplines in the natural sciences, engineering and medicine. In the last two decades, investigations of nonlinear phenomena have developed into a very active research field. A glance at the current contents of leading professional publications reveals that nonlinear science has had a significant impact on a broad spectrum of natural sciences, mathematics and engineering.
Nonlinear science teaches the students to formulate problems in a systematic manner and provides common methods to solving diverse problems, wherever they might arise: science, engineering, medicine, or finance. In equipping the students with skills that are cross-discipline, method based, rather than discipline specific, nonlinear science offers the students a broad, diverse education, and prepares them for today's rapidly evolving professional environment.
Young researchers will be equipped with the tools and intuition needed to tackle complex nonlinear problems arising in many guises and various technical fields. Cross-disciplinary research and communication skills will be developed through intensive project based courses, in which small teams investigate a topic guided by faculty members with complementary perspectives. This training will give young researchers a deep learning experience outside their Ph.D. thesis research. Internships at other academic or individual research centers will provide young researchers with additional cross-disciplinary perspectives. Cross-departmental research seminars and student-run seminars, regional workshops, yearly retreats, and an active visitor program will contribute to generating a highly cooperative, diverse, cross-disciplinary research environment.
The goal of the proposed Physics Frontier Center in Nonlinear Science (PFCNS) program is to provide research and advanced training that emphasizes nonlinear methods and their impact on a diverse range of applications and research fields.
The Physics Frontier Center in Nonlinear Science (PFCNS) graduate training and research program will bring together Georgia Tech faculty and graduate students in pure sciences and engineering, as well as establishing bridges to other research institutions in the Southeast. The cross-disciplinary program emphasizes the unity of fundamental concepts underlying a broad range of scientific research areas: pattern formation, biophysics, classical and quantum chaos; and engineering problems involving liquids, interface motion and pattern control.
GT is the leading science and technology research
and training institution in the Southeast,
with strong state and industrial support.
It is a first rate engineering school, in process of rapid growth. PFCNS
would in particular profit from the planned expansion
and building up of the Georgia Tech/Emory Biomedical Engineering
Department.
GT's location in Midtown of the fast growing Atlanta,
with quick access to one of the world's best airports,
makes it ideal for visitors and workshops, and it
traditionally serves as a meeting place for researchers from
universities in the South, as
well as a site for major international conferences.
PFCNS will provide infrastructure to bring together students, post-docs,
visitors from different disciplines.
· a description of pertinent achievements under prior NSF support, where applicable; (Limit: 2 pages);
Predrag Cvitanovic, PI (until moving to Georgia Tech) - IGERT #9987577: Northwestern University Dynamics of Complex Systems in Science and Engineering (2000-2004)
L. Bunimovich CoPI and Director - GIG #9632032: Southeast Applied Analysis Center (1996-2001 at $100K/year) has been very successful in establishing regional educational initiatives which Nonlinear Science PFC intends to extend and build upon.
L. Bunimovich - DMS #997215: Dynamics and Kinetics (1999-2001)
M. Schatz - CTS #9876590: Experiments on Dynamics and Control of Spatiotemporal Chaos in Thermal Convection (1999-2001)
S.P. DeWeerth - BES #9872759:
A VLSI Model of Muscular Mechanics, Architecture, and Control.
Under this grant (and a previous grant, IBN-9511721), we developed integrated
circuits that modeled nonlinear biological systems including bursting neurons
and central pattern-generating circuits, the intersegmental control of
axial locomotion, and the mechanical structures that underlie force
generation in muscles. Of particular relevance to this proposal, we
also analyzed those system using non-linear dynamical techniques, and
developed some new hypotheses for how their biological counterparts may
operate. Our most recent accomplishment have been to develop
hybrid nonlinear oscillators consisting of interconnects living and silicon
neurons. These two grants funded the Ph.D. education of six Ph.D.
students, three of whom have graduated, and numerous M.S. and undergraduate
students.
R.F. Fox - MP #9819646: Stochastic and Nonlinear Phenomena in Physics and Biology (1999 - 2002)
R. Hernandez - CHE #9703372: Reaction Dynamics of Polymerization and a Computer-Enhanced Dialectic in the Physical Chemistry Curriculum (1997 - 2002)
T. Uzer - PHY #0099372:
Rydberg Electron Dynamics in External Fields (2001 - 2004)
· a description of each major research component (MRC), including
names of faculty-level participants and numbers of undergraduate and graduate
students and postdoctoral associates in each group (Limit: 2 pages for
each major research component description, some preface which
highlights past impact of this area on significant technical
problems);
Cross-disciplinary research theme and Major Research Components
We highlight here the Major Research Components (MRCs) of the Center, and the ways in which they are interconnected. The initials bracketed by [...] refer to faculty participants.(1) Chaos in classical and quantum systems
1) Chaos in classical and quantum systemsGT is considered as one of the world centers in the studies of classical and quantum chaos. We plan to build on our existing strength by research in the following areas:
Ergodic theory and statistics of dynamical systems : [LB,PC,RWG] GT has some world-renowned researchers in the area of ergodic theory, statistics and transport in dynamical systems. Their research ranges form proofs of existence and non-degeneracy of transport coefficients in classical models of statistical mechanics to the development of new models which capture some essential features of real physical systems. One of the central problems is the rate of convergence to an equilibrium. This research deals both with conservative and dissipative systems. The pure mathematics research topics at Georgia Tech concerns braids that occur as closed orbits of flows and periodic orbits of low dimensional systems [RWG], geometrical and dynamical problems connected with geodesics of generalized billiards [LB,RWG].
The periodic orbit theory ~[PC] applies these deep mathematical results to physical problems such as far-from-equilibrium transport, conductance of mesoscopic devices, and the semi-classical quantization of classically chaotic systems such as helium. GT has pioneers in application of dynamical systems theory to problems in operations research and logistics, which proved to be very efficient on a factory floor.
Classical and quantum chaos : [PC,RF,TU] GT has been at the forefront of quantum chaos research since the very inception of the field, pioneered, (among others), by J. Ford. The research is concentrated on the basic mechanisms of chaos in Hamiltonian systems and chaos-order transitions in finite and infinite-dimensional systems. Such transitions are usually due to bifurcations. The almost nonexistent area of bifurcations in spatially extended systems is one of the main research areas in the mathematical study of dynamical systems in GT [LB]. Recent efforts have been particularly fruitful on so-called ``Rydberg'' atoms in which an electron is promoted to such a high energy state that it almost becomes a classical object. Rydberg atoms and molecules represent an extreme form of matter: They can be as large as a fine grain of sand, can outlive excited states of ordinary atoms by many orders of magnitude, and at the same time are extremely sensitive to certain perturbations. In a recent example, the first construction of the generalized coherent states of the Rydberg problems has shed new light on the quantum-classical correspondence [RF] because the associated Husimi-Wigner states have a direct interpretation in the corresponding classical phase space. By this means it is seen that the classical Lyapunov exponent is a quantum signature of classical chaos.
In the next few years, using the interdisciplinary facilities provided by PFCNS, we plan to attack a number of problems in quantum chaos, all of which have been inspired by recent experiments and where traditional reduced-dimensionality models fail due to unconserved angular momenta. These are, specifically, ionization of Rydberg states in rotating microwave fields, the chaotic scattering of Rydberg electrons, and phase-space transition state theory.
LEFT ROOM FOR PC HERE.
All these require three or more degrees of freedom (`3dof') .
Most early knowledge about quantum chaos in atomic systems can be traced back to two fundamental experiments, both of which were performed on Rydberg atoms: Quasi-Landau oscillations in Rydberg atoms placed in strong magnetic fields, and the ionization of Rydberg atoms in linearly polarized strong microwave fields. The interpretation of the Quasi-Landau oscillations in terms of a particular periodic orbit of the Hamiltonian -- an elementary example of Gutzwiller's trace formula -- ushered in the application of classical mechanics to a wide variety of quantum problems -- a very fruitful approach from which we are still benefitting. The interpretation of the microwave ionization problem remained a puzzle to atomic theory until its stochastic, diffusional nature was uncovered through the then-new theory of chaos. The theory of systems with two or fewer degrees of freedom sufficed to interpret both experiments in quantum chaos. However, the latest generation of experiments have broken new ground in the dynamics of multidimensional chaotic systems. Conceiving the theory for these experiments is essential because classical dynamics of multidimensional systems undergoes a fundamental change when the number of degrees of freedom exceeds two: Beyond that threshold, we are faced with a wealth of new physics. Yet the forays into this vast area are comparatively rare because beyond this divide we lack both diagnostic tools, and new computational methods. Wavelet methods in time-frequency domain shows great potential as a diagnostic of chaos in higher dimensions [TU] as well as being a promising new tool for numerical analysis [JG].
Chaotic ionization of electrons in microwave fields: The new generation of stochastic ionization experiments break all continuous symmetries of the Coulomb problem by using eliptically polarized microwaves, and therefore require dynamical treatment beyond two degrees of freedom. Their ionization yield curves interpolate between the linear and and circular polarization cases in an uneven way, and their rich features depend very sensitively on the polarization. We have recently shown how to account for most of these features using semiclassical strong-field atomic physics [TU]. However, a satisfactory classical-mechanical treatment of this problem is still needed, and we will take on this challenging problem.
Phase-space transition states and chaotic ionization of electrons . We [TU] have recently found that chaotic ionization of hydrogen in crossed electric and magnetic fields, a 3dof problem, is governed by a phase-space Transition State (TS)-- a key concept from the theory of chemical reactions, untouched since the days of Wigner for lack of theoretical understanding and inadequate computing power. We have found the long-sought classical structures that act as transition states in phase space beyond 2dof, the needed breakthrough the Normally Hyperbolic Invariant Manifolds (NHIM). In the next few years we will be applying these ideas to a wide variety of physical systems, since the transition state is not confined to chemical reaction dynamics and the ionization of atoms, but describes all dynamical systems which evolve from "reactants" to "products", e.g., the rearrangements of atomic nanoclusters, conductance due to ballistic electron transport through microjunctions, diffusion jumps in solids, to the capture of comets and asteroids.
Nonstationary stochastic dynamics : [RH,RF] The dynamics of reduced-dimension coordinates describing an effective solute in a physical process as diverse as protein folding or polymerization can involve nonlinear responses in the effective solvent. These responses across space and time can be characterized as nonstationary. In one limit, spatial heterogeneity in solvents has given rise models using the generalized Langevin equations with space-dependent friction. In another limit, when the solute is sufficiently concentrated, the collective solute dynamics can give rise to a time-dependent self-constistent friction. Using multiplicative stochastic processes [RF], quantum fluctuations can be described through the density matrix. The fluctuations create both energy eigenvalue shifts and relaxation.
Hybrid systems : [LB] Physically most important systems are neither purely deterministic nor purely random but rather share both of these features. Such models appear in the theory of disordered systems, in chemical kinetics, in theoretical computer science (Turing machines with many heads and/or many tapes). Time evolution of such systems is often quite counter-intuitive. GT researchers are among pioneers developing a theory of such systems which is of great interest for the collision-based computing, a new and rapidly developing area of computer science.
(2) Dynamics of spatially extended systems
Nonlinear dynamics of spatially extended systems seek deeper understanding of phenomena as diverse as turbulence, neural dynamics, pattern formation and dynamics of excitable media from a unified viewpoint. At GT the following sub-topics are actively pursued: [KW,MS,RG,PC,LB,RF]
Nonlinear oscillatory systems: [KW]
The lion's share of progress in nonlinear physics has been for the
low dimensional systems, i.e. situations where the asymptotic behavior can
be described in terms of a small number of variables. One of the most
fundamental questions facing the field today is whether these impressive
advances can be extended to dynamical systems with many degrees of
freedom. An important class of such "complex systems" is coupled
oscillator arrays, wherein many simple (low-dimensional) elements are
connected to form a composite system. Such arrays have been intensively
studied over the past decade, resulting in substantial progress in
fundamental understanding. Attention has now shifted from the behavior of
arrays under idealized circumstances to more realistic situations.
Our present work on coupled oscillator arrays has two parts, each motivated
by a current topic in applied physics:
Antenna arrays: So-called smart antenna arrays have novel applications in radar, imaging, and communications technologies. There is a need for arrays which operate at ever higher frequencies, a pressure which stresses present device technology, which seeks to keep the individual elements isolated and non-interacting. A new set of ideas has been put forward which exploits interactions to achieve desired behavior spontaneously, i.e. without direct manipulation of each individual elements. In a collaboration with experimentalists at UC Santa Barbara, we are exploring these ideas for generating rapid beam scanning and/or spatial beam shaping. The goal is to determine the appropriate coupling architecture which will yield the desired attractor for the array dynamics.
VLSI Oscillator Arrays: [SPD, WLD] We have developed arrays of nonlinear oscillators using very large-scale integrated (VLSI) circuits. These analog circuits are implemented using "vanilla CMOS" processes that are used typically for standard digital circuit designs, thus producing very cost-effective implementations. Our initial efforts have been focused on developing and testing van der Pol oscillators and on implementing nearest-neighbor coupling in these arrays. Our focus for future development is to develop a larger variety of oscillator types as well as more diverse connectivity schemes (e.g. small-world networks). The application of this work is two-fold: First, we can use these arrays to test general theories about coupled-oscillator arrays in a real physical system that has substantial flexibility (e.g. in connectivity). Second, we can use these circuits as modeling tools for other systems, such as the antenna arrays mentioned above, which are much more costly to implement than are our circuits. Although our VLSI circuits are not fast enough for radar or other high-frequency applications, we are exploring the possibility of applying them to lower-frequency applications such as sonar.
High frequency tunable electromagnetic generators: Superconducting arrays are capable of converting direct current into extraordinarily high frequency voltage waveforms. Arrays of thousands of elements, oscillating synchronously, are necessary to achieve useful power levels. Present understanding of the dynamics of these arrays are predicated on coupled ordinary differential equations; however, as the technological pressure continues to push the need for larger arrays operating at ever higher frequencies, issues associated with distributed electrodynamical effects become increasingly important. This represents a significant new frontier for coupled oscillator theories.
Magnetic Avalanches: [KW]
This work is directly motivated by previous studies of self-organized
criticality, which has excited great interest but remains a largely
theoretical and/or mathematical phenomenon. It has proven difficult to
connect these ideas with real physical systems which are well characterized.
We have an excellent candidate system: granular superconductors subject to
a slowly varying magnetic field. The resulting chain-reaction dynamics is
a phenomenon call "flux creep". Experiments indicate that the sudden
rearrangements induced in the superconducting current distribution diplays
complex dynamics, with avalanche sizes over very many scales. The physics
is very well understood, and accurately described by coupled ordinary
differential equations, and also apparently by an associated cellular
automaton model.
The main goals of the project are (1) to explore the origin
of the complex dynamics displayed by this system, (2) to characterize it,
and (3) to understand the conditions under which the cellular automaton
will stably follow the differential equations.
Spatiotemporal chaos: [LB,PC] The aim of research in this area is to generalize the theory of temporal chaos to systems with spatial extent and correspondingly large (even infinite) number of degrees of freedom. These systems display dynamics which is chaotic in time and space. The general theory of mappings and flows is used to understand and describe the mechanisms of mixing and transport in fluid systems. The tools of geometric and statistical analysis are used to study the role of coherent structures and their relationship to the chaotic attractors of extended systems.
Characterization of extended systems: [PC,RG] The spatiotemporally chaotic dynamics is so complex that exact analytic description is typically impossible. However, due to natural dissipation only a relatively small number of degrees of freedom are active. These active degrees of freedom can be used to provide an approximate, but rather accurate description of the dynamics. Such a description can be obtained, for instance, by projecting the dynamics onto an approximate invariant manifold constructed using the proper orthogonal decomposition of the state, or singular value decomposition of the Jacobian of the system. The goal of the periodic orbit theory [PC] is to predict the long time averages of dynamical observables.
Pattern formation: [MS,RG] Classic examples occur in fluid convection, parametrically-excited surface waves, Turing patterns in chemical and biological systems. Later studies discovered that this phenomenon occurs in systems that extend from microscopic (pattern formation and self-assembly in colloidal monolayers and binary alloy solidification) to cosmic scales (Saturn rings and spiral galaxies). Current research on pattern formation is concentrated on defect dynamics and controlled pattern selection in fluid systems and pattern formation in the brain and cardiac tissue. Experimental methods have been developed by MS to characterize and quantify spatiotemporal chaos, in particular the disorder due to defect instabilities such as the spiral defect chaos. The first quantitative measurements of penta-hepta defect dynamics in the Benard convection have been recently carried out. Dynamics methods have been applied to controlled patterning of crystal surface growth at atomic scales.
Control of extended systems: [MS,RG]
Dynamics of thin films and interfaces, solid and liquid: [MS,RG,KW,E. Conrad (physics)] overlaps with pattern formation, control and fluid dynamics. GT research on the growth of solid films, contributing to our understanding of morphological instabilities of interfaces in crystal growth [?], and the closely related problems of the dynamics of ? [?], is a prime example of a successful cross-departmental collaboration based on co-advising of graduate students.
Dynamics of complex fluids: [GPN,MS] is technologically important, involving processes with rich chaotic dynamics. The application of the general theory of mappings and flows to experiments on mixing of highly viscous fluids has been notably successful [?]. Current theoretical and experimental investigations aim at the understanding of transport in complex fluids [?]. Much of naturally occurring and industrial mixing takes place in shear flows of fluids of slight viscosity, in which transport is mediated by localized structures [?].
Dynamics of thin films and interfaces: [GPN,MS] GT research on the growth of solid films, contributing to our understanding of morphological instabilities of interfaces in crystal growth [?], and the closely related problems of the dynamics of ? [?], is a prime example of a successful cross-departmental collaboration based on co-advising of graduate students.
(3) Nonlinear Dynamics in Biology
The interdisciplinary nature of the Center offers excellent opportunities in selected areas of biology and biophysics. Our combined effort in this area brings together researchers from several Georgia Tech units (biology, physics, mathematics, and biomedical engineering departments) as well as Emory Universitys School of Medicine. Ongoing work spans the range from the subcellular level to single cell, inter-neuronal, and whole-brain levels. The research projects share a common theme, that the phenomena involve complex, often chaotic and/or stochastic, dynamics. In all areas described below, we have both experimental and theoretical components.
(3a) Interplay of Nonlinearity and Noise.
The combination of
stochasticity and nonlinear dynamics can lead to important physical and
biological effects. One such effect we are studying is rectified Brownian
motion and its significance for molecular motors [RF], for example in
kinesin motion along microtubules. A larger issue is that rectified
Brownian motion potentially provides a unified mechanism for a great many
basic cellular processes, whereby metabolic Gibbs free energy can be
converted into mechanical work. [RF]
Another fundamental noise driven effect is stochastic resonance, in which
detection of weak signals is enhanced by the presence of noise. In
collaboration with experiments at Carleton College, we are testing the
hypothesis that stochastic resonance plays a functional role in hearing at
level of single hair cells. In vitro experiments show that SR occurs at
noise levels comparable to the inherent Brownian motion of hair bundles in
vivo. If confirmed, the hypothesis would resolve a longstanding mystery
of why many animals (including humans) have two different types of hair
cells, in terms of their different responses to noise. [KW]
Noise also plays a critical role in neocortical interactions.
Neocortical data obtained from experiments on rats serve as the basis for
a biologically relevant mesoscopic neural network model. Exact results
can be obtained for noise driven binary interactions; the robustness of
certain dynamical properties allow us to extrapolate to more complex types
of interactions. This approach fills a gap between detailed biophysical
simulations which cannot make rigorous global predictions and a
generalized models which allow exact statements but on a level of
description remote from biology. [LB]
(3b) Bioinformatics, Biomedical engineering (WD, Borodovsky), Biology
(Dusenbery, Wartel), Biophysics (RF):
Analysis of bioinformatics data,
i.e. sequences derived from the structure of proteins and DNA molecules,
reveals that these data are "chaotic" in the sense that along a molecule
the spatial variation is analogous to the temporal variation in chaotic
systems. These experimental findings motivate application of methods of
analysis of chaotic systems to this new domain. One goal is to develop
new computationally treatable models that combine observable and hidden
variables such as Hidden Markov models. Such models can be trained and
tested on available data to produce new verifiable predictions. The
overall aim of these efforts is to generate new insights into the complex
mechanisms governing genetic information transfer. [LB, MB] NOTE:
earlier draft listed WD, Dusenbery, Wartel, and RF.
Kurt: I don't know whether the next paragraph describes any of their work at all.
(3c) Neurocomputation and Neuromorphic Engineering
Neuromorphic Systems / Motor Control: [SPD, Rob Butera] We are using very large-scale integrated (VLSI) circuits to model a number of biological systems. For example, we have developed such neuromorphic models of numerous motor-control systems that produce rhythmic oscillations (see Results from Prior Research section). The future work focuses on the development of systems that incorporate mechanical actuation (i.e. in robots) and sensory feedback to "close the loop" around the oscillators. This feedback modulates the behaviors of these nonlinear systems; the analysis of the resulting behaviors represents an excellent opportunity to learn more about the dynamical properties of the control of movement in biological systems.
Hybrid Neural Oscillators: [SPD, Ron Calabrese, Rob Butera, Gennady Cymbalyuk] Many biological system exhibit complex, nonlinear oscillations. It is difficult to study these oscillations in the system, however, because of the lack of control/variability of the underlying neural parameters. We are developing the technology to create hybrid neural oscillators that combine, via electrical interfaces, biological elements that underlie these oscillations with artificial models of these elements implemented using VLSI circuits and/or real-time computer models. The resulting hybrid systems represent an excellent merger of biological realism with the controllability that is only present in the artificial systems, resulting in a testbed that facilities the in-depth study of the biophysics and dynamics of the biological circuits.
Hybrid Neural Microsystems and the Control of Behavior: [Steve Potter, SPD, WLD] The nonlinear, dynamical behaviors of populations of neurons are robust, adaptive, and rich in their set of computational primitives. Harnessing the power of this tissue would facilitate the ability to develop engineered systems that emulate the complex computational power found in nervous systems. However, it is difficult to interface to these systems in an effective manner. We have the ability to interface to large populations of neurons in a dish, and have utilized this to use neural tissue to control the external world in a closed-loop configuration, in which the neurons to adapt to their external environment. The use of nonlinear dynamical analysis techniques with advances that we are making in this hybrid technology will lead to the utility of neural tissue for a variety of tasks, from the control of machines (e.g. robots) to the creation of biological computers capable of perform difficult operations such as spatiotemporal pattern recognition significantly faster than any digital computer.
note: WLD should have also added a paragraph on Ditto's control of chaos in cardiac/neural systems
(3d) Spatiotemporal Activity in the Human Brain
In a new collaborative
effort, we are studying the relationship between brain activity and
cognition. Experiments performed at Emory University monitor a subject's
brain activity while they perform simple motor or cognitive tasks.
Activity is measured using continuous magnetic resonance imaging,
resulting in time- and space-resolved images. Despite ample evidence for
the nonlinearity of neural activity, conventional neuroimaging studies
take a linear, subtractive approach to experimental design and analysis.
In contrast, our approach is grounded in notions from nonlinear dynamics.
When a continuous variation of the cognitive task results in a sudden
qualitative change in behavior, we view this as a bifurcation of the
neural system. In addition to direct analysis of the spatiotemporal data
by modern time series methods, we are also pursuing a model-based approach
to investigate how unavoidable physiological factors such as slow
hemodynamic response affect intrinsically interesting complex dynamics.
[GB, KW]
· a description of proposed activities in education and human resource
development, including the promotion of diversity and outreach; proposed
collaborations with industry and/or other sectors; shared experimental facilities;
international collaboration (Limit: 2 pages);
Education and training program
The proposed graduate and post-doctoral training will immerse young researchers 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 research efforts programs in science, engineering, and mathematics. At GT, courses on nonlinear dynamics are currently taught in the mathematics and physics departments, each from a different perspective, and draw students from biomedical, civil, aerospace, electrical, and mechanical engineering, materials science, and chemistry, as well as from the departments offering the courses. (For a current listing of courses, seminar series, workshops and other activities consult the CNS homepage www.cns.gatech.edu/research).
While students would clearly benefit from a program based on a broad, coherent, and unified view of nonlinear science, college 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 PFCNS initiative will generate a new level of integration in graduate and post-graduate education: it will involve faculty in different departments in an effort to unify the nonlinear science curriculum across the participating schools.
The graduate education and post-graduate training in the proposed PFCNS 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, and take nonlinear science courses coordinated by PFCNS.
The core of the cross-disciplinary training program will be:
1. Nonlinear Science Course, a 2-semester sequence 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 a semester of lectures supplemented by review sessions led by senior graduate students in the program, followed by a semester of research on specific projects carried out by small teams supervised by faculty members with complementary expertise and perspectives. 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 activities of the training program will be:
2. Welcoming workshop/retreat before the start of each fall semester, to introduce the incoming young researchers to the PFCNS. 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 2001, has drawn a wide attendance from the participating departments. PFCNS would enable us to broaden the scope of the seminar to engineering and biological applications.
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, government, or industrial lab to master an experimental technique or theoretical approach not readily available at GT.
6. 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 GT faculty, and who demonstrate potential as external mentors to our graduate students and junior researchers.
7. Regional Nonlinear Science Workshop. A yearly interdisciplinary meeting will be organized jointly with other Southeastern universities, to expose students from regional universities to the forefront of research, and to give them an opportunity to present their own work in poster sessions.
8. Joe Ford Fellowships, so named to honor late Joseph Ford (B.S. Physics, Georgia Tech 1952, professor Georgia Tech 1961-1995), one of the pioneers of nonlinear dynamics, both through founding Physica D, the first journal devoted to nonlinear dynamics, and through his many contributions to the theory of classical and quantum chaos.
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. 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).
3. 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.
Graduate training 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 PFCNS 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. Efforts will be made to keep the average time-to-degree within approx. 5 years.
PFCNS funding will also enable us to implement a series of measures to aid recruitment and retention of students from under-represented groups, by offering Summer Internships for Minority Undergraduates and engaging PFCNS faculty in education outreach activities.
Internship Program
To complement their research students and post-doctoral fellows will be encouraged to participate in an internship program. The goal of this program is to provide the trainees with supplementary training that will significantly broaden and strengthen their education. For example, a trainee working on theoretical projects might intern in experimental labs, while trainee working on experimental theses might collaborate on theoretical or computational projects. In other cases the internship could allow a specific experimental technique or theoretical approach not readily available at GT, but important for the trainee's thesis research.Trainee, aided by the advisor, 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 will decide whether the project is successful and whether the internship will be extended to the full six months. Upon returning to GT the trainee will present his/her results in the form of a written report and a brief presentation in the Graduate Seminar Series.
Regional, national and international connections
The internships and other training initiatives
will make use of the extensive connections the
GT 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.
Several examples of such cross
fertilization are already in place:
MS and GPN collaborate on microfluidics. MS and RG
combine their experimental and theoretical skills in control of
spatiotemporal chaos to problems of aerospace and nuclear engineering,
coating problems, KW and GSB.
GT provides rich intellectual environment in which PFCNS
would function. In that context,
within science schools, as well within the region,
following preeminent scientists should be mentioned:
E. Carlen, M. Loss, L. Erdos and E. Harrell
(mathematical physics group, School of Mathematics),
W. Gangbo
(School of Mathematics / CDSNS),
M. Borodovsky
(Biomathematics),
D. Dusenbery and R. Wartel
(Biology),
G. Hentchel and F. Family
(Physics, Emory University),
and
N. Chernov and N. Simanyi
(Mathematics, U. of Alabama in Birmingham).
The PFCNS fluid dynamics Physics & Mech. Eng. program interacts with GT
Institute of Paper Sciences & Technology [C. Aidun] where the fundamental
problem of pattern formation is relevant to increased efficiency in coating
wallpaper.
As a member of the External Advisory Board, Space Medicine and Life
Sciences Research Center, Morehouse School of Medicine,
GPN
provides guidance regarding fluid mechanics issues
associated with tissue growth.
GT is a first rate engineering school, in process of rapid growth. PFCNS would in particular profit from and contribute to the planned expansion and building up of the Georgia Tech/Emory Biomedical Engineering Department.
Nationally there are about 10 nonlinear science centers that GT group collaborates with, in particular the NSF IGERT programs at Northwestern, Cornell and U. of Arizona. Internationally, there are about 15 "Sister Nonlinear Science Centers" interested in collaborating with PFCNS in organizing workshops, exchanging researchers, hosting interns, located in Mexico, Germany, Denmark, United Kingdom, Italy, Israel, Argentina, Hungary, Chile and Austria. A complete list is available on cns.physics.gatech.edu/centers/sisters.html
Educational outreach
Following the successful NSF Southeast Applied Analysis Center (GIG
#9632032)
outreach program, PFCNS would send the members of the Center
to deliver lectures on various topics of modern physics, biology and
mathematics as "Center ambassadors"
in the Southwest area nonresearch educational institutions
and historically black colleges and universities.
PFCNS would offer a teaching reduction to the members who
perform exceptionally as lecturers.
· and an outline of the proposed arrangements for administration and management of the PFC (Limit: 2 pages);
Administration and Assessment
The proposed PFCNS director is P. Cvitanovic (Physics). Prior to moving to GT, Cvitanovic co-founded and directed (1993-1998) the Center for Chaos and Turbulence Studies at the Niels Bohr Institute, Copenhagen, one of Europe's leading centers for nonlinear science. In the period 1997-2000 Cvitanovic led the initiative to create a Center for Complex Systems at the Northwestern University, and was the PI on the NSF IGERT Complex Systems in Science and Engineering program, awarded to Northwestern in 2000.The day-to-day training, research, and other activities of the program will be supervised by the Executive Committee (EC), which will ensure that fellowships, internships and visitor invitations are awarded in accordance to the goals of the program. The evaluation of the program will rely on detailed feedback from students, internship hosts, participating faculty, long-term visitors, and thesis advisors. Annual assessments will concentrate on the performance of the PFCNS J. Ford Fellows, student internships, Nonlinear Science Course, Nonlinear Science Seminar, Visitor Program, and Regional Conference. After two years it will be possible to also assess the recruitment, retention, PhD theses time-to-degree measures, and publications.
PFCNS faculty:
- Gregory S. Berns, Assistant Professor, Psychiatry, Emory University
- Leonid A. Bunimovich, Regents' Professor, Mathematics (COS)
- Predrag Cvitanovic', G. Robinson Chair, Professor, Physics (COS)
- Stephen P. DeWeerth, Associate Professor, Georgia Tech/Emory Biomedical Engineering Department
- William L. Ditto, Professor, Georgia Tech/Emory Biomedical Engineering Department
- Ronald F. Fox, Regents' Professor, Chair of School of Physics (COS)
- Jeff Geronimo, Professor, Mathematics (COS)
- Robert W. Ghrist, Assistant Professor, Mathematics (COS)
- Roman Grigoriev, Assistant Professor, Physics (COS)
- Rigoberto Hernandez, Assistant Professor, Chemistry (COS)
- G. Paul Neitzel, Professor, Mechanical Engineering (CE)
- Michael Schatz, Assistant Professor, Physics (COS)
- Andrey Shilnikov, Assistant Professor, Mathematics and Statistics, Georgia State University
- Turgay Uzer, Professor, Physics (COS)
- Eric R. Weeks, Assistant Professor, Physics, Emory University
- Kurt Wiesenfeld, Professor, Physics (COS)
Institutional Resource Commitments
Georgia Tech already has a strong faculty in nonlinear sciences, ranked 5th nationally in the 1999 U.S. News survey. Its commitment to strengthening the research effort in this field is demonstrated by recent chaired faculty appointment in physics (Cvitanovic), and continued recruiting efforts in mathematics and physics (junior experimental nonlinear physics faculty search in 2001, senior experimental nonlinear physics faculty search for 2002), planned expansion in biosciences (including chair appointments) coupled to the planned expansion of both Schools, as well as a .................Georgia Tech actively encourages cross-departmental and inter-disciplinary research. The GT Center for Nonlinear Science (CNS) which began operation July 2001 already aims at furthering such an environment, and acts as a seed program for the proposed PFCNS which would span GT COS, GT COE, and Emory Medical School.
The PFCNS office and the common meeting room will be housed in the physics building. The building already has student computer laboratories. Except for the laboratories in the Emory Medical School, the participating faculty laboratories are situated at GT. An effort will be made to provide shared office space and computer facilities for the PFCNS junior researchers and graduate students.
The GT CNS will require substantial computing resources to implement the MRC's, through single- and parallel processor computing of nonlinear models and algorithms. Fortunately GT already has a CCMST providing a 72-processor IBM SP2, and its codirector is a member of CNS, R. Hernandez. Up to 1/3 of this resource will be available to the CNS with the part-time funding of a research scientist and a commitment ($500,000) to CNS to upgrade part of the facility at year 3 via a costsharing agreement with GT.
The Deans of the participating Colleges and the Institute, at the level of the University's Vice-Provost for Research, strongly support the initiative, and will fund CNS for an initial three-year period, during which time the CNS is expected to secure additional external support. GT has committed $147K/year seed funding for period 2001-2004, which will provide for
- funding for 2-3 postdoctoral research associates
- distinguished lecturer series
- visitors
- workshops
- budget for the Nonlinear Science seminars and operational expenses.
- full-time secretarial support
- part-time computer systems manager
- part-time webpages manager/author
Cost sharing at a level of 15%
percent of the requested total amount of NSF funds is required for all
proposals submitted in response to this solicitation.
REMEMBER THAT COMMITTEMENT OF GATECH FOR SOME MATCHING FUNDS IS BASICALLY A NECESSARY CONDITION FOR NSF TO FUND SUCH PROPOSALS.
Five-year awards are expected to range in size between $0.5 million/year and $4 million/year, with an average award size of approximately $2M/year. The budget for the full proposal may not be larger than the pre-proposal budget.
Complete budget pages for each year of support (1-5) and a five-year summary budget justification. A five-year budget summary will be automatically generated by FastLane. Provide separate budget pages for the PFC as a whole and for each participating institution.
Also, in tabular form as follows, summarize the overall
support levels planned for each of the major activities of the PFC as a
whole. (Note: The Table below should be entered in the "Project Description"
FastLane form.)
| Summary Table of Requested NSF Support | ||
|---|---|---|
| Activity | Year One | Five Year Total |
| MRC 1: Chaos in classical and quantum systems | ???,000 | ???,000 |
| MRC 2: Dynamics of spatially extended systems | ???,000 | ???,000 |
| MRC 3: Nonlinear dynamics and biology | ???,000 | ???,000 |
| Shared Facilities | ???,000 | 1,???,000 |
| Seed Funding and Emerging Areas | 0 | 0 |
| Education and Human Resources | 0 | 0 |
| Outreach | ?,000,000 | ?,000,000 |
| Administration | ???,000 | ???,000 |
| Total | ?,???,000 | ??,???,000 |
For each entry in the Table, include indirect costs. Column totals must equal the total budget requested from NSF for the period shown. Include major capital equipment under shared facilities. Support for graduate students should normally be included under research, not under education and human resources.
Concurrently with submission of the pre-proposal, please submit by e-mail to pfc@nsf.gov the following: (2) a list of individuals (and their affiliations) outside the participating institutions whose participation in the review of the pre-proposal might constitute a conflict-of-interest through, e.g., association with the participants or their institutions; and (3) a list of individuals who might be suitable to serve as impartial reviewers.
(2) Individuals with potential conflict-of-interest (collaborators of the senior staff of the proposed PFCNS):
- Andreas Andreou, Johns Hopkins University
- Ron Calabrese, Emory University
- Avis Cohen, University of Maryland
- Mike Cross, California Institute of Technology (G Romanov PhD adviser)
- Gennady Cymbalyuk, Emory University
- Reid Harrison, University of Utah
- Phil Holmes, Princeton
- Tim Horiuchi, University of Maryland
- Robert Jernigan, NCI, NIH
- Christof Koch, California Institute of Technology
- Brain Meadows, Navy Research Laboratories
- Bill Miller, University of California
- Brad Minch, Cornell University
- Joe Neff, Navy Research Laboratories
- Steve Potter, California Institute of Technology
- T. Richard Nichols, Emory University School of Medicine
- Heinz Schuster, Universitat Kiel, Germany
- Harry Swinney, U of Texas (M. Shatz PhD adviser)
- Sara A Solla, Northwestern University School of Medicine (PI's spouse)
(3) Individuals suitable as impartial reviewers
- Robert Behringer, Duke
- David Campbell, Boston University
- Giulio Casati, Centro dei Sistemi Dinamici, U. dell'Insubria, Como
- E.G.D. Cohen, Rockefeller University
- Robert E. Ecke, Los Alamos National Laboratory
- Theo Geisel, Max-Planck-Institut Stromnungsforschung, Gottingen
- John Guckenheimer, Cornell
- Martin Gutzwiller, IBM and Yale
- Eric Heller, Harvard
- Leo P. Kadanoff. U. of Chicago
- Holger Kantz, Max-Planck-Institut Physik komplexer Systeme, Dresden
- Jon Keating, BRIMS, Hewlett-Packard Labs, Bristol, UK
- Sidney Nagel, U. of Chicago
- Edward Ott, U. of Maryland
- Hermann Riecke, Northwestern U.
- Thomas Seligman, Centro Intern. de Ciencias, Cuernavaca, Mexico
- Mary Silber, Northwestern U.U.
- Uzi Smilansky, Complex Systems, Weizmann Institute, Israel
- Steve Strogatz, Cornell
Proposals must be submitted by the following date(s):
Preliminary Proposals (required): August 20, 2001
Full Proposals by 5:00 PM local time: January 25, 2002
Pre-proposals MUST be submitted electronically by 5:00 PM, local time, August 20, 2001. Principal Investigators will be notified of the results of pre-proposal review on or about October 30, 2001.