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Overview
Thematic Basis for the Group Effort
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 on the 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.
Major Research Efforts
Northwestern University scientists pursue a comprehensive range of research within
the unifying theme of nonlinear dynamics. We highlight here a selection of these research efforts. A more complete
listing is available through the web sites of the individual participants.
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 tissues. Applications to
materials science arise in modeling the dynamics of thin films,
interfaces, and dendritic growth.
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.
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.
Topics
Pattern Formation
• Hermann Riecke Applied Math
• Mary Silber Applied Math
• Bernie Matkowsky Applied Math
• Paul Umbanhowar Physics and Astronomy
Spatiotemporal patterns appear spontaneously in a wide range of physical,
chemical, and biological systems when they are driven sufficiently far
from thermodynamic equilibrium. The classic example is Rayleigh-Bènard
convection in a fluid layer heated from below. For sufficiently strong
heating fluid motion sets in, typically in the form of convection rolls.
As the driving parameter is increased, regular patterns are supplanted by patterns
that are more and more irregular in space and time, resulting in states that are intermediate
between ordered patterns and turbulence. Some snapshots of patterns from two
different fluid experiments are presented in Fig. 1. Examples can, for instance, also
be found on the web pages of H. Riecke and P. Umbanhowar.
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Figure 1: a) Super-lattice structure in parametrically excited surface waves [1]. b) Oblique waves
('zigs' and 'zags') and traveling rectangle patterns observed experimentally in electro-convection of
nematic liquid crystals [2]. |
Early pattern-formation research focused on relatively simple spatially periodic structures,
e.g. convection rolls or hexagonal structures. The open questions addressed by current
research concern structures with more complexity. These can be spatially periodic complex
patterns (see Fig. 1a), spatially localized structures (see Fig. 2), or structures that are chaotic in
time as well as space ("spatio-temporal chaos"). Applied pattern formation research is
motivated by the goal of utilizing the spatial structures, or, in the event
that they are undesirable, of suppressing their formation. In either case the origin
and nature of spatial structures must be well understood. Fundamental theoretical
challenges arise because pattern-forming systems represent nonlinear dynamical systems with
many degrees of freedom. A vivid illustration can be found in electroconvection of nematic
liquid crystals (see Fig. 1b) where patterns consist of ever-changing patches of
traveling convection rolls of different orientation. Research challenges include giving precise
characterizations of such states, identifying the relevant mechanisms for their creation,
and being able to control their evolution.
Figure 2: Localized standing wave (`oscillon') in vertically vibrated layer of granular
medium.
Pattern formation is not limited to fluid systems. In materials science the spatial structures arising at
the liquid-solid interface of a growing crystal are known to greatly affect the properties of the resulting
crystal, and therefore have a profound technological impact. Similar structures are observed in flame fronts where
they affect the combustion process. Both topics are discussed in Interface Dynamics.
In laser beams with large cross-sections, transverse spatial structures in the form of
waves can develop. They are undesirable in many applications and have led to active
and promising research in pattern control. For other examples of pattern formation in
nonlinear optics, see Nonlinear Optics.
Fundamental to pattern formation research is the observation that they are determined by cooperative interactions on large scales
and hence many aspects of the phenomena can be understood on a "macroscopic level."
Only certain aspects of the detailed microscopic physics of the fluid or laser, say,
contribute to the overall behavior, allowing a unified approach to phenomena in diverse physical, chemical, and
biological systems. This approach, which accentuates certain key concepts, applies
when an underlying state with certain symmetries loses stability with the change
of a parameter. Nonlinearity is essential for the saturation of the instability. Moreover,
symmetries of the system typically result in the simultaneous presence of many destabilizing
modes; for a linear system, the resulting state would be an arbitrary superposition of these
exponentially-growing modes. In pattern-forming systems nonlinearity leads not only to
saturation of instabilities, but also to selection of certain modes which then dominate
the system (so-called "pattern selection").
Central features that enter the unified description of patterns include the symmetries of the
problem and the character of the instability. Remarkably, this information is often
sufficient to make qualitative and semi-quantitative predictions for the patterns that
arise. For example, it was possible for Riecke and collaborators to predict the outcome of
a periodic forcing of the traveling waves observed in electroconvection well before the
microscopic equations describing the traveling waves were known.
We investigate spatio-temporal chaos in various types of systems and show a transition between
an ordered, stripe-like state of spatio-temporal chaos to a disordered one involving the
unbinding of defects/vortices. This raises questions regarding connections to phase
transitions in equilibrium. Do the chaotic dynamics play a role similar to thermal noise in
equilibrium? What are the differences? These studies are therefore closely connected
to the theory of phase transitions. In electroconvection (see Fig. 1b) spatio-temporal
chaos occurs immediately above threshold and is therefore one of the few cases that hold promise for
quantitative analysis within Ginzburg-Landau equations.
Parametrically excited patterns arise, for example, when a fluid (or granular medium) is
subjected to a periodic vibration. For example, "superlattice programs" observed only
recently in experiments on parametrically excited surface waves (see Fig. 1a) were
predicted to exist on the basis of symmetry and bifurcation theory arguments. We have investigated
superlattice Turing patterns in chemical reaction-diffusion systems. We have 22
partial synchronization, pattern formation, and chaos in spatially discrete arrays
of Josephson junctions. In this system, parametric instability is responsible for a lack
of total synchronization of the array. Their investigation focuses on the effect of
spatio-temporal pattern formation on the current-voltage characteristics of this high-frequency electronic
device. Umbanhowar has developed a sophisticated vibration control method and
is perfecting a novel visualization technique which will enable a more quantitave
comparison of experiment and theory in this area.
In recent experiments various localized structures confined to only a small part of
the homogeneous system have been observed as localized circular excitations (See Fig. 2) of
the surface "dipoles" and chains. What keeps these structures from
spreading over the whole system? We have investigated localization mechanisms
theoretically. This provides feed-back for the experiments and identifies connections to
localized structures in electroconvection ("worms") as well as in optics and combustion.
Pattern formation has great potential for cross-disciplinary investigations arising,
e.g., in interfaces, nonlinear optics, as well as in granular media.
Here we sketch additional examples that connect pattern formation research in various participating departments.
We have initiated a research project on controlling pattern formation in a model of
a coherently pumped three-level laser. Here the goal is to design a feedback control
scheme, based on the symmetries of a targeted space and time periodic patterned state, that
will lead to a stable regular pattern in place of the spatio-temporally chaotic
state that occurs in the absence of the control. This project benefits from collaboration
with the IGERT nonlinear optics group as well as ideas developed by Chen
and collaborators on identifying unstable periodic orbits in dynamical systems.
We have investigated the dynamics of coupled discrete nonlinear elements such as Josephson junctions
or lasers. Building on the insight on synchronization gained in these studies,
we proposed to address the binding problem in neural networks.
If a neural network is presented with a number of objects with a number
of different properties (e.g. a brown, low chair and a yellow, tall lamp) then
all the items and properties (brown, low, yellow, tall, chair, lamp) are excited in the network
but
it is not clear how the binding of "brown" and "low" with "chair" is performed
in the brain. Conjectures based on binding through coherent oscillations in neural
activity have received recent experimental support; questions on the
conditions under which such synchronous firing can arise and be sustained do
now required analytic and numerical investigation.
For more details about research in this area, see also the web pages of
Riecke,
Silber,
Matkowsky,
Umbanhowar.
Mixing
• Julio M. Ottino Chemical Engineering
Mixing of viscous
fluids is important in the context of materials processing, reactive
and non-reactive polymer processing, food processing and
stabilization of hazardous wastes. Transitional mixing is of
relevant in bioreactors, and turbulent reactive mixing is critical in
the understanding of atmospheric chemistry and pollution control.
Liquid-solid mixing plays a critical role in pharmaceutical
manufacturing and the paper and rubber industries. Solid-solid mixing
is important in catalyst preparation, blending and processing of
ceramics precursors, and the pharmaceutical industry. In all of its
guises, the potential impact on engineering practices quite
significant. Fundamental developments in mixing research for fluid
and granular solids applications have over the past decade largely
been spurred by developments in the theory of nonlinear dynamics.
Patients on
chemotherapy experience reduced or eliminated platelet and neutrophil
counts, and consequently suffer from bleeding and infection traumas.
Ex vivo production of hematopietic cells can reduce patient risk
by supplying the necessary cells until transplanted. The ultimate
goal is to characterize and modify the flow around hematopoietic
cells so as to provide adequate nutrient and chemical balances
without damaging or unintentionally harvesting the cells. The
geometry initially studied consists of a series of parallel grooves,
perfused by fluid flowing transverse to the grooves. The simplest
steady flow in this geometry produces closed, 2D streamlines with
only diffusive transport between the fluid in the groove, where the
hematopoietic cells would reside and the free stream above. To
produce chaotic transport, the free stream flow is periodically
modulated. Fig. 1 shows experimental quasi-2D mixing of a dye into
such a groove after 1 and 30 oscillations respectively.
Figure 1: (left) Steady 2d streamlines in cross section of groove, produced
by boundary integral equation method simulation. No mixing occurs between
fluid in the groove and the stream outside. (middle) and (right) tracer-
experiment after 1 and 30 periodic oscillations of the free stream flow.
Dye stream along top of groove is now entrained into grooved cavity.
A set of problems
complementary to fluid mixing arises in chaotic granular
advection. Remarkably, despite the considerable differences
between fluids and grains (grains can arch, segregate, avalanche, and
must dilate in order to flow), one can apply some of the same
nonlinear dynamics tools to granular systems. For example, consider
a thin, quasi-2D tumbler consisting of two parallel plates separated
by a small distance. If the plates enclose a half-filled cylinder of
grains, mixing in the tumbling regime is fairly slow and mainly
diffusive. If, however, the plates enclose a square container, again
half filled, then the flow is periodic. Consequently, chaotic
advection is produced, very much as periodically driving 2D fluid
systems can produce chaotic advection.
Nevertheless, the
understanding of the fundamentals of granular segregation and mixing
remains incomplete. Often, granular systems evolve quickly through
complex dynamics into a state of self-organization. For example, in
a short tumbled cylinder this may lead to radial segregation; and in
long cylinders to axial. banding. More mixing action does not
guarantee a better-mixed final system; in fact, the very same forcing
used to mix may unmix. Thus, self-organization results from two
competing effects: chaotic advection or chaotic mixing, as in the
case of fluids, and flow-induced segregation, a phenomenon without
parallel in fluids.
An example is shown
in Fig. 2, where the pattern arises from the suppression of mixing
by the segregation. The rich array of behaviors is ideally suited to
nonlinear dynamics based investigations, with the experiments
interfacing directly with the theory.
Figure 2: Competition between mixing and segregation in granular material
in circular, elliptic, and square tumblers.
Future research
under the auspices of the IGERT grant is planned to develop a measure
of mixing.
For more details about research in this area, see also the web pages of
Ottino.
Nonlinear Optics
• Prem Kumar Computer Engineering
• William L. Kath Applied Math
As the transmission rate of optical communication systems has
steadily increased in response to the growing demand for signal
capacity, optical pulses have grown shorter in duration and increased
in amplitude to the point where neither dispersion (the tendency for
different frequencies of light to propagate at different speeds) nor
the intrinsic nonlinear dependence of the index of refraction upon
signal intensity can be neglected. In such a situation the basic
model for the evolution of optical pulses is the nonlinear
Schrödinger equation .
From a practical
standpoint, the nonlinear dependence greatly increases the difficulty
of understanding system behavior, in that standard linear
communications theory is no longer applicable. On the other hand,
new techniques have become available, since the nonlinear Schrödinger
(NLS) equation possesses a rich mathematical structure. In
particular, it is completely integrable via the increase scattering
transform, and can be thought of as an infinite dimensional
Hamiltonian system. Perturbed NLS equations are therefore
interesting from a dynamical systems point of view, particularly
since perturbations generically can produce interactions between
large numbers of modes and possibly quite complicated or even chaotic
behavior. In the case when only a few modes are excited by the
perturbing terms, inverse scattering provides a tool, namely soliton
perturbation theory, with which to understand the dynamics of pulses
when additional perturbing effects are present. Other perturbation
methods, such as averaging, are also extremely useful.
As described above,
a number of recent experimental results have been obtained. In
particular, fiber-optic parametric oscillators have been developed
and the all-optical storage of data packets has been accomplished. In
addition, work is currently in progress on optical-fiber based clock
recovery and regeneration. Both theoretical models and numerical
simulations will be developed to explain the observed behavior of
already constructed devices and to suggest ways to improve their
performance. We shall investigate the possibility of devising new
methods which can be used to obtain improved predictions of systems
behavior. One of the is to attempt to break the pulse evolution up
into two parts: the pointwise evolution inside the storage loop, and
the stroboscopic evolution from one period to the next. Note that
such a result, if successful, would be a PDE version of a Poincarè
map. Such techniques are certainly useful for investigating the
chaotic behavior of periodically forced ODEs.
The basic equation
describing pulses in a recirculating loop with amplification and
filtering is the Ginzburg-Laundau equation. Because at high bit
rates, pulses are closely spaced together, it is necessary to have
many pulses recirculating at any one time, and the dynamics of the
pattern of pulses play an important role. We shall expand the ongoing
interdisciplinary interactions to now take advantage of existing
expertise in pattern formation at Northwestern. The pattern
selection behavior occurring in optical systems appears to be similar
in spirit to that observed in fluid and other systems, but there are
a number of differences. Nevertheless, there are sufficient
similarities that indicate that such a collaborative effort will be
very productive.
It has been known
for some time that it is possible to excite Kerr solitons in
Erbium-doped fiber that simultaneously are self-induced transparency
(SIT) solitons for the doped 2-state atoms. In addition, work has
been performed which attempts to generalize the SIT soliton concept
to 3-state lambda-type systems. The idea is to associate an SIT
soliton with each leg of the lambda transition, which then couple
through the excited state. Classical effects like soliton dragging,
which can be exploited for developing ultra-high speed soliton-based
packet-switched communication networks operating at 100’s of
Gb/s rates, have been shown to occur efficiently in model 3-state
systems. Therefore, it is natural to ask if the two SIT solitons can
simultaneously be made to be the Kerr solitons of the host fiber that
is doped with such 3-state atoms. Such pulses would allow for new
types of pulse interactions in nonlinear, optical fibers and could
lead to new types of optical switches and memory devices.
For more details about research in this area, see also the web pages of
Kumar and
Kath.
Neuroscience
• Ferdinando A. Mussa-Ivaldi Physiology
• Sara A. Solla Physiology/Physics & Astronomy
• Nelson Spruston Neurobiology & Physiology
Nonlinearity is a common domain is of
operation for the brain. The central nervous system of any living
creature must be capable of carrying out two major classes of
operations that may be characterized as ill-posed inverse mappings;
one is the class of transformation of sensory signals into meaningful
perceptions; the other is the class of transformations of action
goals into motor commands. An example of the former is the inverse
optical problem that is routinely solved by our visual system when
the two-dimensional distorted images on the retina are transformed
into three-dimensional representations of the corresponding objects.
In carrying out this transformation, the brain is capable of
extracting stable features, such as the color and the shape of an
object, out of a constantly changing pattern of physical signals. An
example of the second class of mappings – from action goals to
motor commands – is the inverse transformation that must be
carried out to move a hand towards a target in space. This is called
an “inverse problem” because the goal is to generate a
nonlinear differential equation of motion for which the desired
trajectory is a solution of the controlled system. Unlike its direct
counterpart –the problem of determining the trajectory that
results from a given equation of motion – the inverse problem
admits in general multiple solutions.
Besides routinely dealing with
nonlinear problems, the brain itself is made out of a large number of
highly interconnected nonlinear constituents. Individual neurons
receive multiple stimulations that interact in a nonlinear manner to
control the membrane potential. Neurons respond to stimulation
beyond a preset threshold through the firing of action potentials
that are transmitted down the axons; increasing stimulation results
in an increased firing rate until saturation is reached at a maximal
firing rate associated with an unavoidable refractory period between
the firing of subsequent action potentials. Such built-in nonlinear
response has dramatic consequences for the functional properties of
neuronal networks, from the possibility of synchronized oscillations
and chaotic behavior in recurrent networks to the enhanced
computational capabilities of layered networks designed for the
implementation of sensory maps.
The functionality of neuronal
assemblies is largely determined by their connectivity, as specified
by the strength of the synaptic contacts. The plasticity of synaptic
strengths allows for changes that occur on two different time scales:
long term changes associated mostly with postsynaptic cells lead to
learning, while short term changes associated mostly with presynaptic
cells lead to depression of facilitation of postsynaptic activity.
Efforts at understanding the dynamics of synaptic adaptation and
their impact on neuronal activity incorporate crucial nonlinear
effects that arise because the synaptic changes are themselves
activity controlled.
A central issue in the generation of
complex sensorimotor behavior is the representation of time and
temporal sequences. Recent theoretical studies have demonstrated
that complex patterns of coordination may be encoded by motor
commands with little temporal structure, provided that the force
fields generated by these commands have a sufficiently nonlinear
structure. Some of our current studies are aimed at understanding
how this approach may describe the operation of pattern generators
within the central nervous system. A related topic involves the
encoding of serial events into spatial patterns of neural activity
and the decoding of such spatial patterns into sequential motor
commands. The goal is to develop a theoretical framework for the
representation of temporal sequences; the model needs to include a
mechanism for competitive pattern recognition, a positive feedback
for the enhancement of activity associated with working memory, and
an overall recursive dynamical structure. The role of learning in
the stabilization of this complex dynamical system remains to be
elucidated.
A new area is based on the results of
recent patch-clamp experiments. Action potentials actively invade
and back-propagate along the dendrites of CA1 pyramidal neurons in a
frequency-dependent manner; a prolonged form of sodium channel
inactivation in dendrites weakens the back-propagation during high
frequency action potential firing. To understand the dynamics of
this process, involved in memory functions through its impact on
synaptic integration and plasticity, new models of sodium channels
need to be developed and incorporated into current cellular models of
dendritic trees.
For more details about research in this area, see also the web pages of
Mussa-Ivaldi,
Solla and
Spruston.
Interface Dynamics
• Stephen H. Davis Applied Math
• P.W. Voorhees Materials Science & Engineering
• Bernie Matkowsky Applied Math
Interfaces separating two material phases occur in numerous areas of
application. In fluid dynamics there are interfaces separating two
fluid phases, as in thin liquid films, droplets, spreading, nucleate
boiling, and the fronts separating nematic and isotropic liquid
crystals. Interfaces between solids and fluids are important in
crystal growth and deformable porous media. Interfaces between two
solid phases are important in phase transformations in alloys and in
the dewetting of polymer and crystalline films on solid substrates.
In combustion, flame fronts separate the unburned reactants from the
burned products of combustion. In solid-fuel combustion, in which
solid melts prior to burning, there re two interfaces, the melting
front and the reaction front. In addition, interfaces may separate
multiphase media as when a bubbly or particle-laden fluid abuts a
second fluid, in combustion involving mixtures, or in porous media.
The last occurs in combustion synthesis of materials, in waste
incinerators, in underground oil recovery, and in living tissue.
Interfacial dynamics is the controlling factor in a whole spectrum of
high-technology industrial-product manufacture and simultaneously the
inspiration for fundamental scientific investigation.
In all the cases
mentioned above the phase interface is a moving free boundary whose
shape, position, and dynamics are to be determined. Each of these
represent nonlinear problems involving instability and bifurcation
phenomena, wave-length selection, and chaotic behavior. The above
examples exhibit the whole gamut of dynamical phenomena including
coalescence and rupture, melting, freezing, sedimentation,
agglomeration, chemical reactions, moving contact lines, cellular,
pulsatile, dendritic and spiral patterns, chaotic behavior, and all
the particular idiosyncracies of suspensions, colloids, foams, and
granular or porous materials.
The dynamics of
thin liquid films are controlled by capillarity,
thermocapillarity, viscous and long-range molecular forces and have
broad influence on heat-transfer phenomena and devices. We have
studied thin viscous films on substrates and the effects of surface
tension and van der Waals attractions on the rupture of the films and
the creation and dynamics of contact lines.
The dynamics of
thin solid films are controlled by nonlinear diffusion,
surface energy, and elasticity and have application to the integrity
of microelectronic devices and interconnects. A pinhole in an
otherwise continuous film can open and destroy the entire film
coverage. We have studied the development of islands of crystalline
film on substrates by linear and nonlinear stability methods and have
studied solid-film dewetting of crystalline films on substrates
including the effects of surface energy, surface diffusion, and
elastic strains on island, and hole shapes, their contact lines, and
their modes of instability. Further, we have examined the nonlinear
evolution of whiskers and tubules, and Ostwald ripening in the
presence of elastic stresses, a process that controls the particular
size in solid-solid composites.
The interface
between solid and liquid is the site of phase transformation
in crystal growth, a process that for binary alloys involves a
nonlinear-diffusion problem applicable to combustion synthesis of
materials. We are currently investigating the interaction of counter
propagating temperature pulses (hot spots) that occur in solid fuel
combustion. When the pulses meet, their interaction can, at one
extreme, lead to their complete annihilation, and at the other
extreme, they can pass through each other essentially unaffected, as
is the case for solitons. The goal is to describe the transition
between the two extremes.
A new area of
interest will be the merging and coalescence of positive and negative
phospholipid bilayer vesicles. To treat the membranes as thin films
new physical/electrical properties and certain non-continuum features
have to be taken into account.
We shall begin on
the interaction of flames and flame-grown diamond films. This effort
will bring together recent studies on kinetically controlled phase
transformation and combustion for the design of diamonds with
predictable microstructures.
Another direction
for cross-disciplinary research will be the investigation of front
polymerization, a new technological process in which monomers are
continuously fed into a reactor and converted into the desired
polymers in an interface separating monomer from polymer. The
frontal polymerization process offers advantages over conventional
technologies.
For more details about research in this area, see also the web pages of
Davis,
Voorhees, and
Matkowsky.
Faculty Projects
Students Projects
Publications by IGERT students
This research has been supported in part by the
NSF-IGERT program "Dynamics of Complex Systems in Science and Engineering"
(DGE-9987577).
| INTERFACES AND COMBUSTION |
|
| Title: |
Simple representation of contact-line dynamics in a level-set model of an immiscible fluid interface |
| Authors: |
K.A. Smith, J.M. Ottino, and P. B. Warren |
| Title: |
Encapsulated drop breakup in shear flow |
| Authors: |
K.A. Smith, J. M. Ottino and M. Olvera de la
Cruz |
| Journal: |
Physical Review Letters,93 (20): Art. No. 204501, 2004 |
| Title: |
Mathematical modeling
of the eukaryotic heat shock response: Dynamics of the hsp70 promoter. |
| Authors: |
T. R. Rieger, R. I. Morimoto, and V. Hatzimanikatis |
| Journal: |
Biophysical Journal, Accepted, 2004. |
| Title: |
Dopamine Modulation in a Basal Ganglio-Cortical Network Implements Saliency-Based Gating of Working Memory |
| Authors: |
Gruber, A.J., P. Dayan, B.S. Gutkin, and S.A. Solla |
| Title: |
Prediction of EMG from Multiple Electrode Recordings
in Primary Motor Cortex |
| Authors: |
E.A. Pohlmeyer, L.E. Miller, F.A. Mussa-Ivaldi, E.J. Perreault, S.A. Solla, and D.T. Westwick |
| Title: |
A weakly nonlinear analysis of
impulsively-forced Faraday waves. |
| Authors: |
A. Catlla , J. Porter, M. Silber |
| Journal: |
Physical Review E, Submitted, 2004 |
| Title: |
Electro-Absorption-Modulator Based
Self-Starting Opto-Electronic Oscillator for Generating Ultralow-Jitter Ultrahigh-Rate Short Optical Pulses and
Ultralow Phase-Noise RF Signals for Applications in Optical Processing |
| Authors: |
J. Lasri, P. Devgan, and P. Kumar. Provisional Patent NU23006. |
| Title: |
Techniques for Generating Ultralow-Jitter and
Ultrahigh-Rate Short Optical Pulses Synchronized Simultaneously at Multiple Wavelengths in Multiple Fiber-Optic Telecom Bands |
| Authors: |
J. Lasri, P. Devgan, and P. Kumar. Provisional Patent NU23059. |
| Title: |
A 10-GHz Rate
Microstructure-Fiber Based Widely-Tunable Optical Parametric Oscillator in the Telecom Band |
| Authors: |
J. Lasri, P. Devgan, R. Tang,
J.E. Sharping and P. Kumar |
| Title: |
Microstructure-Fiber Based Optical Parametric
Amplifier in the 1550nm Telecom Band |
| Authors: |
Renyong Tang, Preetpaul Devgan, Jay
E. Sharping, Paul Voss, Jacob Lasri, and Prem Kumar |
| Title: |
Self-assembling Fluidic Machines |
| Authors: |
B.A. Grzybowski, M. Radkowski, C. Campbell, J.N. Lee & G.M. Whitesides |
| Journal: |
Applied Physics Letters, 84 (10): 1798-1800, 2004 |
| Title: |
Feedback Control of Traveling Wave
Solutions to the Complex Ginzburg Landau Equation |
| Authors: |
K.A. Montgomery, and M. Silber |
| Journal: |
Nonlinearity, 17 (6): 2225-2248, 2004 |
| Title: |
Destabilization and Localization of Traveling Waves by an Advected Field |
| Authors: |
A. Roxin, and H. Riecke |
| Journal: |
Physica D, 156 (1-2): 19-38, 2001 |
| Title: |
Two-Frequency Forced Faraday Waves: Weakly Damped Modes and Pattern Selection |
| Authors: |
Mary Silber, and Chad M.Topaz |
| Journal: |
Physica D, 143 (1-4): 205-225, 2000 |
Presentations by IGERT students
Y. Katz
"Characterization of DNA Flexibility using Quantitative Atomic Force
Microscopy". Poster with Mark E. Greene, Jon B. Preall, Jon Widom and
Mark C. Hersam. Materials Research Society Fall Meeting, Boston, MA, 2004
Y. Katz
"Computational modeling of scaled synaptic inputs on CA1 dendritic
shafts and spines". Poster with Rachel E. Trana, William L. Kath, Nelson
Spruston. Society for Neuroscience Meeting, San Diego, CA, Oct. 2004.
Y. Katz
"Powerful dendritic attenuation of distally generated EPSPs suggests an
important role for dendritic spike initiation in the distal dendrites
of CA1 pyramidal neurons." Poster with Timothy Jarksy, Alex Roxin,
William L. Kath, Nelson Spruston. Society for Neuroscience Meeting, San Diego, CA, Oct. 2004.
C.J. Campbell (2004) "Wet Stamping (WETS) for Nanopatterning of
Structures via Reaction-Diffusion". 2004 AIChE Chicago Chapter Student Poster
Competition. (Best Graduate Student Poster)
K. Kandere-Grzybowska, C.J. Campbell, Y. Komarova, B.A. Grzybowski,
G.G. Borisy (2004). "Dynamics of microtubule cytoskeleton and focal adhesions
in micropatterned cells". American Society for Cell Biology, Washington, D.C.
C.J. Campbell "Micro- and Nanofabrication through
Reaction-Diffusion". NSF-IGERT Dynamics of Complex Systems Graduate Student
Seminar, Northwestern University.
J.A. Pedersen. "Cell/Extracellular
Matrix Coupling in 3D Hydrogels." Presentation, Meeting of the Midwest Microscopy and Microanalysis Society, Evanston, IL, March 2004.
D. Weir, "Switch Characterization and the Haptic Profile", IEEE 12th International
Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems (HAPTICS 2004), Chicago, IL, Accepted Mar. 2004.
K. Montgomery, "Nonlinear Analysis of a Coupled Mechanism for Enhancing Amplification in
Auditory Hair Cells", Joint Mathematics Meetings, Phoenix, AZ, Jan. 2004.
K. Montgomery, "A Nonlinear Analysis of the Amplification Properties of Auditory Hair
Cells", Dynamics Days, Chapel Hill, NC, Jan.
2004.
C.J. Campbell, B.A. Grzybowski (2003). "Micro- and Nanopatterning via
Reaction-Diffusion". 2003 Department of Chemical and Biological Engineering
Annual Retreat, Northwestern University.
K. Montgomery, "Nonlinear Processing in the Auditory System", Oberlin College Seminar,
Oberlin, OH,
Dec. 2003.
A. Cattlá, "Comparison of Faraday Wave with Impulsive, Sinusoidal, and Multi-Frequency
Forcing", American Physical Society Division of Fluid Dynamics, East Rutherford, NJ, Nov. 2003.
A. Cattlá, "Impulsively Forced Faraday Waves", Fields Institute Workshop on Patterns in
Physics, Toronto, Ontario, Canada, Nov. 2003.
D. Stouffer, "Characterization of Food Web Data with Experimental Bias", AIChE 2003 Annual
Meeting, San Francisco, CA, Nov. 2003.
A. Cattlá, "Impulsively Forced Faraday Waves", CAM Graduate Students Physics Meeting,
Merida, Quintana Roo, Mexico, Oct. 2003.
P. Devgan, J. Lasri, R. Tang, P. Kumar, "Ultralow-Jitter Multiwavelength Synchronized
Optical Pulse Source for C-, L- and U-Bands", IEEE Lasers and Eletro-Optics Society (LEOS) Annual Meeting, Tucson, AZ, Oct. 2003.
D. Weir, "Switch Haptics: Pushing and Measuring Buttons", Ford Research Collaboration Presentation,
Ford Motor Company Scientific
Research Laboratory, June 2003.
J. Pedersen, "Cytoskeletal Response to Mechanical Forces in a 3D Environment", ASME Bioengineering
Division Summer Meeting, Key
Biscayne, FL, June 2003.
D. Weir, "Switch Haptics: Pushing and Measuring Buttons", Masters Thesis Defense,
Northwestern University, May 2003.
K. Montgomery, "Bifurcation Analysis of Amplification and Tuning Mechanisms of Auditory Hair Cells",
SIAM Dynamical Systems Conference, Snowbird, UT, May 2003.
A. Cattlá, "Impulsively Forced Faraday Waves", SIAM Dynamical Systems Conference, Snowbird, UT, May
2003.
P. Devgan, "Unique Application to Optical Signal Processing Due to Nonlinearities in Optical
Fibers and Optoelectronic Devices", IGERT Graduate Student Seminar, Northwestern University, May 2003.
D. Weir, "Switch Haptics: Pushing and Measuring Buttons", IGERT Graduate Student Seminar, Northwestern
University, Apr. 2003.
M. Melhus, "A New Creature in the Pattern Zoo", IGERT Graduate Student Seminar, Northwestern
University, Mar. 2003.
T. R. Rieger, R. I. Morimoto, and V. Hatzimanikatis, "Mathematical Modeling of the Eukaryotic Heat
Shock
Response", IGERT Graduate
Student Seminar, Northwestern University, Mar. 2003.
K. Montgomery, "Exploring Neural Computation: My Experiences at Woods Hole", IGERT Graduate Student
Seminar, Northwestern
University, Feb. 2003.
T. R. Rieger, R. I. Morimoto, and V. Hatzimanikatis, "Mathematical Modeling of the Human Heat Shock
Response", AICHE 2002,
Indianapolis, IN, Nov. 2002.
A. Cattlá, "Impulsively Forced Faraday Waves", American Physical Society, Division of Fluid Dynamics,
Dallas, TX, Nov. 2002.
K. Montgomery, "Amplification and Tuning Mechanisms of Auditory Hair Cells", Joint IGERT Workshop, Oak
Brook, IL, Oct. 2002.
A.J. Gruber, "Dopamine Induced Bistability in Medium Spiny Neurons Enhances the Detection of
Temporally Correlated Input Signals", Joint IGERT Workshop, Oak Brook, IL, Oct. 2002.
A. Cattlá, "Impulsively Forced Faraday Wave Patterns", SIAM 50th Anniversary Conference, Philadelphia,
PA, July 2002.
K. Montgomery, "Stabilization of Traveling Wave Solutions to the CGLE via Feedback
Control", SIAM 50th Anniversary Conference, Philadelphia, PA, July 2002.
D. Weir, "Switch Haptics", IGERT Graduate Student Seminar, Northwestern University, Mar. 2002.
A.J. Gruber, "Neuromodulatory Effects of Dopamine on Striatal Spiny Neurons", RIKEN summer program,
Wako-Shi, Japan, July 2000.
Graduated Students:
A. Roxin, "Slip at a Solid-Liquid Interface", SIAM Dynamical Systems Conference, Snowbird, UT, Nov.
2003.
A. Roxin, "A smallworld network of excitable integrate-and-fire neurons", SIAM Dynamical Systems
Conference, Snowbird, UT, Nov.
2003.
A. Roxin, "A Complex Model of a Single Cell and A Simple Model of Many Cells", IGERT Graduate Student
Seminar, Northwestern
University, Oct. 2002.
A. Roxin, "Self-sustained Activity in a Network of Excitable Neurons with Local and Global Coupling",
Joint IGERT Workshop, Oak
Brook, IL, Oct. 2002.
C. M. Topaz, "Dynamics and Pattern Formation for the Non-Specialist", Harvey Mudd College, Department
of Mathematics, Feb. 2002.
C. M. Topaz, "Dynamics and Pattern Formation for the Non-Specialist", Olin College of Science and
Engineering, Jan. 2002.
C. M. Topaz, "Superlattice Pattern Selection in Faraday Waves", MIT, Department of Mathematics, Dec.
2001.
A. Roxin, "Rotating Convection in an Anisotropic System", American Physical Society, Division of Fluid
Dynamics, San Diego, CA,
Nov. 2001.
C. M. Topaz, "Pattern Selection of Weakly Damped Faraday Waves Forced with Two Frequencies", SIAM
Dynamical Systems Conference,
Snowbird, UT, May 2001.
A. Roxin, "Destabilization of Traveling Waves by an Advected Field", SIAM Dynamical Systems
Conference, Snowbird, UT, May 2001.
C. M. Topaz, "Pattern Selection of Two-Frequency Forced Faraday Waves", American Physical Society,
Division of Fluid Dynamics,
Washington, DC, Nov. 2000.
A. Roxin, "Destabilization of Traveling Waves by an Advected Field", American Physical Society,
Division of Fluid Dynamics,
Washington, DC, Nov. 2000.
C. M. Topaz, "Pattern Selection of Two-Frequency Forced Faraday Waves", International Congress of
Theoretical and Applied
Mechanics, Chicago, IL, Sept. 2000.
C. M. Topaz, "Faraday Wave Pattern Selection in the Presence of Competing
Instabilities", American Physical Society, Division of Fluid Dynamics, New Orleans,
LA, Nov. 1999.
C. M. Topaz, "Parametrically Excited Surface Waves: Normal Form Symmetries and Pattern Selection",
SIAM Dynamical Systems
Conference, Snowbird, UT, May 1999.
Posters by IGERT students
T. R. Rieger, R. I. Morimoto, and V. Hatzimanikatis, "Regulation of the Eukaryotic Heat Shock
Response", Midwest Stress and
Chaperone Meeting, Evanston, IL, Jan. 2004.
A.J. Gruber, P. Dayan, B.S. Gutkin, and S.A. Solla, "Dopamine Modulation in a Basal Ganglio-Cortical
Network Implements Saliency-Based Gating of Working Memory", Neural Information Processing Systems Annual Meeting, Vancouver, Canada, Dec. 2003.
A.J. Gruber, P. Dayan, B.S. Gutkin, and S.A. Solla, "Dopaminergic Enhancement of Spatial Working
Memory through Single Unit
Modulation in a Basal Ganglio-Cortical Network Model", Society for Neuroscience Annual Meeting, New Orleans, LA, Nov. 2003.
T. R. Rieger, R. I. Morimoto, and V. Hatzimanikatis, "Regulation of the Eukaryotic Heat Shock
Response", Michigan State Symposium
of Biological Networks, East Lansing, MI,
Oct. 2003.
J. Pedersen, "Measurements of Cytoskeletal Dynamics in a 3D Environment." BMES 2003 Annual Fall
Meeting, Nashville, TN, Oct. 2003.
E. A. Pohlmeyer, "Prediction of EMG from Multiple Electrode Recordings in Primary Motor Cortex",
International Conference of the
IEEE Engineering in Medicine and Biology Society, 25th Annual Meeting, Cancun, Mexico, Sept. 2003.
T. R. Rieger, R. I. Morimoto, and V. Hatzimanikatis, "Regulation of the Eukaryotic Heat Shock
Response" Biochemical Engineering
XIII, Boulder, CO, July 2003.
J. Lasri, P. Devgan, R. Tang, J.E. Sharping and P. Kumar, "A 10-GHz Rate
Microstructure-Fiber Based Widely-Tunable Optical Parametric Oscillator in the Telecom Band", Conference on Lasers and Electro-Optics (CLEO), Baltimore, MD, June 2003.
P. Devgan, R. Tang, J. Lasri, and P. Kumar, "On the Road to 40Gb/s - Technologies for Packet Switched
Optical Networks", ECE Graduate Poster Session, Northwestern University, May 2003.
E. A. Pohlmeyer, "Prediction of EMG from Multiple Electrode Recordings in M1", Neural Control of
Movement Thirteenth Annual Meeting, Santa Barbara, CA, Apr. 2003.
T. R. Rieger, R. I. Morimoto, and V. Hatzimanikatis, "Modeling of the Eukaryotic Heat Shock Response",
Midwest Stress and Chaperone Meeting, Evanston, IL, Jan. 2003.
A.J. Gruber, S.A. Solla, and J.C. Houk, "Dopamine Induced Bistability Enhances Signal Processing in
Spiny Neurons", Neural
Information Processing Systems Annual Meeting, Vancouver, Canada, Dec. 2002.
K. Montgomery, "Comparing the Effectiveness of Two Feedback Control Methods in Stabilizing Traveling
Wave Solutions to the Complex
Ginzburg Landau Equation", Dynamics Days, Baltimore, MD, Jan. 2002.
A.J. Gruber, D.J. Surmeier, and J.C. Houk, "Bistability Induced by Dopamine Neuromodulation: a
Cellular Mechanism for Explaining
Why Striatal Neuron Responses Can Be Enhanced or Depressed by Reward Expectation", The Society for Neural Control of Movement
Annual Meeting, Seville, Spain, Mar. 2001.
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