Igor Mezic - US grants

DMS 9803555

Mathematical Methods for Chaotic Advection in Three-dimensional Fluid
Flows

PI: Igor Mezic

The goal of the proposed research is to extend the existing theory of
chaotic advection and mixing in two-dimensional, time-dependent flows.
In particular, we wish to study three-dimensional incompressible steady
and unsteady and two- and three-dimensional compressible flows using
the methods of geometric theory of dynamical systems. We will also
study effects of reaction and diffusion on the motion of particles in
these flows, properties of chaotic advection in general, and particular
models of great relevance in engineering applications: flows between
concentric and eccentric rotating cylinders. These problems will be
addressed starting from our recent developments in geometric theory of
three-dimensional divergence-free vector fields. The issues of
cantori, resonances and lobe dynamics in volume-preserving maps and
flows will be addressed through theoretical analysis and computer
simulation. Connection with experiments on mixing in three-dimensional
flows will be made. Effects of inertia and viscosity on chaotic mixing
will be studied via asymptotic, large Reynolds number analysis in
conjunction with the transport theory of dynamical systems. This will
allow for discussion of the change of mixing properties of laminar,
incompressible, viscous flows with the change of the Reynolds number.
Further, we will study the effects of molecular diffusion on chaotic
advection based on the perturbative multiple-scales method combined
with ergodic theory, and through numerical simulations. We will
investigate a general relationship between the pure advection problem
(possibly with chaotic mixing) and the full advection-diffusion
problem. We will study reaction-diffusion-advection equations through
the combination of tools mentioned before. We shall pursue nonlinear
stability analysis in search of effects of chaotic advection on
stability. The particular examples we will be studying are flows
between concentric rotating cylinders. Compressible flows received
virtually no attention in chaotic advection studies. We propose to
remedy this situation by pursuing a basic study of this problem.
Simple model flows will be identified starting with a compressible
vortex flow in a cylindrical container. Comparison with the behavior of
incompressible flows will be pursued.

The above study is useful in a variety of technological contexts. There
is a recent surge of interest in micro- and nano-scale technology that
poses a number of mathematical challenges. For example, flows in
devices such as large mixers and combustion chambers are designed to
mix well by moving the flow in a turbulent regime and thus causing
enhanced mixing by rapid random movements of fluid in the flow. This is
not possible in microscopic devices. The process of mixing needs to be
understood much better in order to design microscopic mixers,
combustion chambers etc. necessary as the building block of
microscopic processing devices and microengines. The mixing process in
such devices is typically three-dimensional. Thus, the design of
microscopic mixing devices will benefit from the fundamental study of
three-dimensional mixing processes outlined above. In addition, the
performance of macroscopic devices is challenged by new requirements
on the levels of environmental chemical pollution (NO_x) and sound
pollution. The improvement in the design of these devices will be based
on a better understanding of the underlying mixing processes. The above
study will provide some of the crucial concepts for such design by
unraveling the fundamentals of mixing in three-dimensional flows and
using these concepts to study the effect of mixing on combustion and
noise production.

Proposal Number: CTS 9977605

Principal Investigator: R. Smith

This Major Research Instrumentation (MRI) award supports the acquisition of a Particle Image Velocimetry (PIV) and a spectrometer for use in MOCVD reactors. The PIV will be used to in the design of flow in microchannels and reaction chambers. The micron resolution measurements of the PIV system will be combined with the nano-resolution of an Atomic Force Microscope to study microscale transport associated with complicated surfaces. The PIV will also the measurement of velocity fields immediately above the surface with simultaneous AFM measurements will allow the examination of the evolution of the surface. The instruments will be used of study mixing and transport processes associated with biological fluid mechanics, such as tissue engineering and endothelial tissue evolution.

Spatial mixing issues in MOCVD reactors will also be investigated. The use of the spectrometer and CCD arrays will give estimates of multiple gas concentrations at multiple points within the reactor. Fiber optic lines will be used to pipe the light from various points within the reaction chamber. This will give the capability of developing and experimentally verifying models of gas flow and mixing dynamics. These models will be used to design high performance feedback controllers.


hot wire anemometry and data acquisition system to support the Multidisciplinary Undergraduate Research in Turbulence project at Valparaiso University. The project will investigate atmospheric and engineering scale turbulent transport. The project's main focus is on the education and training of students in both Colleges of Engineering and of Arts and Sciences in the specific areas of atmospheric turbulence, environmental pollution in turbulent air and water flows, and generalized modeling of the turbulent transport of mass and thermal energy. In addition, it will be used in developing an educational seminar for faculty from nearby institutions.

PI's Name, Institution: Igor Mezic, University of California at Santa Barbara Proposal Number: 9875933 Proposal Title: "Nonlinear Dynamics and Control from Microscale to Macroscale to Classroom" Project Abstract:
We propose to develop mathematical methods to study problems related to engineering of devices at the microscale, such as microscale mixers, and dynamics and control of macroscale devices such as compression systems. The new methods that we will develop are built on an interdisciplinary mix of ideas from dynamical systems and ergodic theory, control theory and microscale physics.
We will study mixing of fluids in geometries of the scale of 1 micron. The work proposed here includes the study of active control of mixing as well as treatment of new physical effects such as rarefaction and electric double layer, introduced by the small scale of the devices. We will provide a fundamental theory for control of mixing in this context using methods of robust control theory and ergodic theory. This study will provide theoretical backbone for the rapidly evolving field of control in microfluid systems.
We also propose to study the dynamics and control of macroscopic and microscopic compression systems. We have recently developed a mathematical model for axial compression system dynamics by averaging and scaling of the Navier-Stokes equations. A rigorous study of the solutions will be pursued and the relevant applied mathematics methods developed. Possibilities of active control of boundary layer instabilities using the so-called microflaps will be studied. Microcompressors for the use in micro jet engines are currently being developed. Modelling and control issues in microcompressors will be studied.
We will familiarize students with the current developments on the interface between applied mathematics and engineering. We propose to teach a Nonlinear Phenomena class that uses examples from the research described above as the background motivation and problem generator. The students in our research group will be exposed to a truly interdisciplinary set of topics from dynamical systems, control theory, mathematics, microscale physics and engineering.

The applications of microfluidic devices (which involve liquids moving in spaces measured in micrometers, i.e. millionths of a meter) are growing explosively. As a specific example, consider the development of microsystems for blood testing and screening. For consumers, one could envision devices available in drugstores that could perform genetic screening for conditions of concern to individuals. At a larger scale, use of such devices in blood banks could significantly reduce the time and blood lost in screening the 14 million pints of blood donated per year. Sample preparation is a critical bottleneck in the development of integrated miniature analytical systems, and it remains largely unaddressed. It is currently done outside the microsystem by mixing, shaking, and pipetting, because there are no effective integrated design method. Improved computational methods promise to allow integration and interconnection of microfluidics. This will have an effect analogous to automated methods for VLSI design on microelectronics; it will revolutionize the field.

This project will develop a computational infrastructure for simulation and design of microfluidic systems involving non-Newtonian, micrometer/nanometer-scale flows dominated by surface-related phenomena. Computational tools and analytical tools will be developed and used to compare with theoretical and experimental results. The project emphasizes methods to deliver complex molecules to flow surfaces, to create surface reaction sites and to provide the components for molecular-scale mixing and dispensing. It will design, fabricate, and characterize both stationary and oscillating MEMS fluidic channels and surfaces to evaluate molecular-scale mixing, flow, delivery, and dispensing of complex biological fluids. The focus will be on surface dominated flow and reaction phenomena that can be scaled for delivery of single molecules to programmed reaction sites. Such surface-related phenomena should find broad application in making MEMS-based, "chip-scale" analytical instruments and "biochips". The computational tools required to analyze and design such devices are currently nonexistent. This project brings together a team of computer scientists, numerical analysts, fluid dynamicists, experimentalists, and microscale process theoreticians who will collaborate closely on creating those tools and using them.

9910001
Nicolaenko

This three-year award for U.S.-France collaboration in applied mathematics involves Basil Nicolaenko, Harindra Fernando, Alex Mahalov and a graduate student from Arizona State University, and Igor Mezic of the University of California at Santa Barbara. The French team is led by Marie Farge at the Ecole Normale Superieure in Paris, France and includes French researchers from Grenoble, Cachan, and Lyon. The objective of the collaboration is the study of geophysical flows in fully developed turbulent regime by means of numerical simulations using adaptive pseudo-spectral and adaptive wavelet methods. Several numerical codes for different models in two to three spatial dimensions, with and without rotation, stratification and transport of passive and reactive scalars will be developed.

This award represents the U.S. side of a joint proposal to the NSF and the French National Center for Scientific Research (CNRS). NSF will cover travel funds and living expenses of the U.S. investigators and graduate student. The CNRS will support the French researchers' visits to the United States. The collaboration is interdisciplinary. U.S. and French teams represent expertise in applied mathematics, fluid mechanics, meteorology and chemistry. The project will advance understanding of code development for environmental flows that have applications in air pollution, ozone depletion (in Antarctic, for example), and have a role in inertio-gravity waves in the stratosphere.

PROPOSAL NO.: CTS-0404444
PRINCIPAL INVESTIGATOR: CARL MEINHART
INSTITUTION: UNIVERSITY OF CALIFORNIA- SANTA BARBARA


NIRT: TITANIUM-BASED BIOMOLECULAR MANIPULATION TOOLS

This proposal was received in response to Nanoscale Science and Engineering initiative, NSF 03-043, category NIRT. Novel micro/nanofluidic chips will be develop and optimized for separating, mixing, concentrating and positioning biomolecules and cells. Pioneering work in titanium micro/nanofabrication technology with alternating current electrokinetics & microfluidics will be developed to provide unique tools for the biotechnology industry. Titanium is a relatively new platform for fabrication of nanostructures. It allows complicated 3-D electrode structures to be fabricated, and is biologically compatible. Theoretical and experimental analysis of electrokinetic phenomena will be conducted to investigate details of the underlying physics. The titanium fabrication technology has the potential to revolutionize micro/nanoscale devices, especially in the areas of biotechnology, drug delivery, and in vivo sensing & probing, where durability and bio-compatibility are critical. The advanced electrokinetics and nanoscale electrode structures can be used to concentrate small (~50 nm) proteins and viral particles, which has not been achievable previously using dielectrophoresis. This research project will provide an opportunity to educate graduate students in the areas of micro/nano fabrication, nanofluidics, electrokinetics, and cell culturing in micro/nanodevices. The PIs teach a newly-developed three course sequence at the senior/graduate level on MEMS/NEMS design & fabrication, micro/nanofluidics & electrokinetics. These courses give students broad exposure to fundamental issues and the current state of the art in MEMS/NEMS and train students for careers and research opportunities in nanotechnology. The research program will also be used to advance underrepresented groups in science and engineering. In addition, the PIs will continue their outreach activities at local high schools, educating students and teachers about how science and technology impacts society, and encouraging students to pursue careers in nanotechnology & science.

We will study nonlinear dynamics of bioparticles at nanoscale for the purpose of design of enhanced sensitivity biosensors. The physical processes that we can improve by pursuing such a study include 1) molecular focusing for purposes of detection and reaction and 2) separation methods for molecular sorting. The essential idea of the proposal is that a combination of hydrodynamic and electromagnetic forces, designed using dynamical systems theory, can enable trapping and separation methods for submicron scale bioparticles. We will focus our study on applications in dielectrophoretic biomolecule manipulation where forces on particles are generated by spatially nonhomogeneous alternating current electric fields and induced fluid flows. However, the dynamical systems aspects of the theory are projected to have broader impact to enabling technologies for manipulation of particles with electromagnetic fields and fluid flows.

In particular, major medical technology breakthroughs and advances in security against bioterror will be enabled by the use of electromagnetic fields and fluid flows for manipulation and detection of materials and processes at the nanometer scale. However, the accuracy, speed and sensitivity of the currently available devices is not at the level that allows for such breakthroughs. The lack of quality is in part due to the lack of understanding of nonlinear dynamics of processes and motions at micro- and nanoscale. In our work we will provide such an understanding that will ultimately enable development of fast, miniaturized devices for detection of biotoxins. Our results will also impact developments in the area of point-of-care diagnostics, where medical doctors will be able to perform a simple check based on the "cheek swab" that can tell them whether to administer an antibiotic (and which one, at that) or not in the matter of minutes. The broader impact of the proposed project includes interdisciplinary education of the members of the group. We are planning several educational activities where some of the biotechnology issues that we study will be popularized for K-8 and high-school level students in the region.

DESCRIPTION (provided by applicant): There are effective behavioral interventions to treat alcohol use disorders, but over time, treatment gains are often lost when clients find themselves unable to resist drinking because of negative emotions and appetitive cues. The power of internal and environmental triggers to elicit relapse, even among clients with conscious abstinence goals and extended abstinence, is compelling and well-documented. Thus, bolstering clients' ability to withstand drinking triggers and craving in real time could have tremendous public health impact. This application proposes translational research that focuses on the a priori defined and malleable baroreflex (BAR) mechanism. The BAR is a dynamic mechanism that helps to regulate automatic-visceral reactivity to triggers of alcohol and other drug use by regulating bidirectional communication between the heart and brain. A key feature of the BAR mechanism is that it can be consciously manipulated using a simple behavioral breathing technique called resonance breathing. This manipulation can occur in the moment and outside of the treatment context as triggers are anticipated or encountered. This application proposes a randomized clinical trial of a BAR-based intervention (added to behavioral treatment as usual) in conjunction with laboratory assessments (pre-post intervention design), and computational modeling to validate the operation of the BAR as a biobehavioral change mechanism. The sample comprises women with young children from an empirically supported, intensive outpatient behavioral treatment program (IOP). The intervention involves daily use of iPhone applications (apps) during IOP treatment weeks 4-12. Those randomized to the active intervention will be trained to use an existing resonance breathing app to activate the BAR mechanism as they anticipate or confront emotions or cues that can trigger relapse. Participants in the placebo group will use an app that does not affect the BAR. Aim 1 will address whether activating the BAR mechanism accelerates and stabilizes positive behavior change, specifically change in alcohol and drug use, anxiety, craving, depression during and after treatment. Aim 2 will compare natural versus manipulated changes in BAR functioning pre- to post- intervention using physiological, and, for a subset of women, fMRI data to correlate biological and behavioral change. Aim 3 will characterize how and for whom the BAR mechanism supports behavior change using computational modeling to capture change across multiple interacting biological systems within a person. The novelty of this study comes from focusing on a well-specified automatic-physiological mechanism, capturing change in the dynamic space of real life replete with triggers and affective changes, characterizing the BAR mechanism across biobehavioral levels using variable-and person-centered quantitative strategies, and focusing on an understudied population whose positive behavior change can have important immediate and long-term health implications. If successful, the proposed research will set the stage for a new generation of mechanism-based intervention approaches and personalized prognostic models.

This project will advance the control of continuum soft robots in complementary areas of representation and implementation. First, it will explore the use of data-driven modeling techniques that are especially well-suited to high-dimensional nonlinear systems. Continuum systems are high dimensional because they may be formed into many distinct, independent shapes, while soft structures frequently exhibit nonlinear dynamics due to their characteristically large deformations. Second, it will explore sensing and actuation using materials that change their mechanical properties in response to light. Light may be steered to various parts of the robot through waveguides made from compliant materials in a variety of geometries, chosen to naturally match the compliance and geometry of the robot. Multiple commands or measurements may be combined on a single waveguide by using different colors of light for different signals. This helps address the large number of sensors and actuators needed to fully monitor and control these high-dimensional systems. The results of this work will be a new class of optically controllable, continuum, compliant, and configurable robots, or C4 optorobots for short. The capabilities of C4 optorobots will be valuable in numerous applications, including inspection of hard-to-reach areas and minimally invasive surgery. This project will include validation experiments, such as a representative engine inspection task, simulated tissue ablation in the heart, and simulated blood clot removal in the brain. Outreach activities of this project will focus on training of graduate and undergraduate students from underrepresented groups, including community college students, in emerging areas of soft robotics.

This project will combine two key innovations - Koopman Operator Theory (KOT) and light-modulated materials design. KOT uses a data-driven approach to identify the eigenmodes of a complex, nonlinear system, thus enabling optimization of control inputs for greatest impact. KOT can produce a linear dynamical model that matches the system behavior, suitable for use in a model-based control. Light combined with photoresponsive materials can provide such control inputs because wavelength, intensity, pulse duration, and spatial distribution can be precisely and nearly instantaneously controlled. Accordingly, this project will accomplish the following goals: 1) Use KOT to extract and formulate linear, dynamic models of C3 robotic sub-systems and implement model-based control schemes using finite control inputs; 2) Develop transduction mechanisms, through engineered light delivery, novel chemical synthesis, and integration into light-responsive materials, to actuate C3 robotic sub-systems; 3) Integrate light-activated robotic sub-systems and model-based linear control schemes to realize controllable, continuum, compliant, and configurable robots -- C4 optorobots.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

With support from the Chemical Theory, Models and Computational Methods (CTMC) program in the Division of Chemistry and the Office of Multidisciplinary Activities (OMA), Jason R. Green of the University of Massachusetts Boston and Igor Mezic of the University of California-Santa Barbara will work to advance the fundamental understanding of how to regulate transformations of energy in chemically-active materials. To benefit applications across the energy, biomedical, and healthcare industries, it is necessary to design materials that execute functional behaviors on chosen time scales. Predicting these dynamical processes requires new theoretical methods to simultaneously navigate their large design space, control the timing of dynamical functions, and regulate the dissipation of energy. This project aims to address this need by combining machine learning and physical theory to create new methods for the design and optimization of functional materials with tailored optical, mechanical, or photonic properties on finely tuned time scales. Coupled to these scientific aims, the project will collaboratively create an active learning curriculum to teach chemists the statistical techniques of data science and contribute to the training of a diverse AI(artificial intelligence)-aware workforce.<br/><br/>Materials chemistry now aims to create dissipative materials that function dynamically, forming patterns and generating work on finite time scales. Recent experiments have taken the first steps to identify chemical systems that drive transient formation of materials structures. However, further progress requires navigating their large design space and regulating flows of energy from the nanoscale up. Machine learning has potential to guide experiments and accelerate this process but is not yet able to optimize the energy efficiency and timed delivery of structure. The proposed project will address this challenge by strategically incorporating recent advances in statistical mechanics into predictive models from machine learning. The specific objectives will be to (i) construct the data-driven dynamics of active hydrogels with techniques from AI, (ii) show that thermodynamic speed limits can be cast as optimally predictive models in machine learning, and (iii) implement these speed limits as design principles for maximizing yield and minimizing dissipation. The project includes dedicated activities to develop strength in STEM (science, technology, engineering and mathematics) at the intersection of data science and theoretical chemistry and to broaden participation in STEM through targeted outreach.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.