CURRICULUM VITAE
M. Gregory Forest

Present Positions:

Professor of Mathematics

Co-Director, Institute for Advanced Materials, NanoScience & Technology

Associate Chair of Applied Mathematics

Member of Curriculum in Applied and Materials Sciences

The University of North Carolina at Chapel Hill

Chapel Hill, NC 27599-3250

Major Fields:

Mathematics & Modeling of Complex Fluids & Soft Matter Materials, Transport Phenomena, Nonlinear Waves & Soliton Theory

Educational History:

B.S., Mathematics, University of New Orleans, May, 1972

M.S., Mathematics, University of New Orleans, December, 1973

Ph.D., Mathematics, University of Arizona, August, 1979, Adviser D. W. McLaughlin

Tenure-Track Faculty Positions:

University of North Carolina, 1996-present

Ohio State University, 1979-1996

Visiting Academic Positions:

Department of Mathematics, University of California-Berkeley: March-May, 1983

Center for Nonlinear Studies, Los Alamos National Laboratory: January, 1985; January-March, 1986;

January-May, 1987; January-March, 1989, 1990; February, 1991-1993

Department of Mathematics, Princeton University: September-December, 1986

Mathematical Sciences Research Institute, Berkeley: January, 1991, March, 1993, March, 1994

Program in Applied Mathematics, University of Colorado-Boulder: August, 1990

Department of Mathematics, University of Utah: January-June, 1995

Administrative Positions Held:

Associate Chair of Applied Mathematics, UNC-CH: 1996-1998, 2000-present

Senior Associate Dean for the Sciences, College of Arts and Sciences, UNC-Chapel Hill: 1998-2000

Consulting Experience:

Los Alamos National Laboratory; Hoechst-Celanese Corporation, Charlotte, NC; Corning, Inc., Corning,

A. Publications

Multiphase averaging and the inverse spectral solution of KdV(with H. Flaschka and D. W. McLaughlin), Comm. Pure Appl. Math. 33, 739-784 (1980).
Spectral theory for the periodic sine-Gordon equation: a concrete viewpoint (with D. W. McLaughlin), J. Math Phys., 23(7), 1248-1277 (1982).
Modulations of sinh-Gordon and sine-Gordon wavetrains (with D. W. McLaughlin), Studies in Appl. Math. 68, 11-59 (1983).
On the modulational stability of two-phase sine-Gordon wavetrains (with N. Ercolani and D. W. McLaughlin), Studies in Applied Math. 71 (2), 91-101 (1985).
Modulations of perturbed KdV wavetrains (with D. W. McLaughlin), SIAM Journal of Applied Math. 44(2), 287-300 (1984).
The geometry of real sine-Gordon wavetrains (with N. Ercolani), Comm. Math. Phys. 99, 1-49 (1985).
Modulational instabilities of periodic sine-Gordon waves: a geometric analysis (with N. Ercolani and D. W. McLaughlin), Lectures in Appl. Math. 23,149-166 (1985).
Oscillations and instabilities in near integrable PDE's (with N. Ercolani and D. W. McLaughlin), Lectures in Appl. Math. 23, 3-46 (1985).
The origin and saturation of modulational instabilities, (with N. Ercolani and D. W. McLaughlin), Physica D 18, 472-474 (1986).
Geometry and modulation theory for the periodic nonlinear Schrödinger equation (with J. E. Lee), IMA Volumes in Mathematics and Its Applications, Volume 2, 35-70, Springer-Verlag (1986).
A one-dimensional theory for viscoelastic fluid jets, with application to extrudate swell and draw-down under gravity (with S. Bechtel and D. Bogy), Journal of Non-Newtonian Fluid Mechanics 21, 273-308 (1986).
A quasi-periodic route to chaos in a near-integrable PDE (with A. Bishop, D. W. McLaughlin and E. Overman), Physica D 23D, 293-328 (1986).
Hamiltonian structure for the modulation equations of a sine-Gordon wavetrain (with N. Ercolani, D. W. McLaughlin, and R. Montgomery), Duke Mathematical Journal 55(4), 949-983 (1987).
Effective stress rates of viscoelastic free jets (with S. Bechtel and K. Lin), J. Non-Newtonian Fluid Mechanics 26, 1-41 (1987).
On the behavior of viscoelastic free jets with elliptical cross-section (with S. Bechtel and K. Lin), J. Non-Newtonian Fluid Mechanics 27, 87-126 (1988).
Correlations between chaos in the perturbed sine-Gordon equation and finite modal equations, Proceedings of Fourth International Conference on Nonlinear Evol. Eq. and Dyn. Syst., Montpellier, France, June 1987, edited by J. Leon, World Scientific (1988). An extended abstract of this paper also appears in Proceedings of the Cornell MSI Workshop, May, 1987.
Geometry of the modulational instability III. Homoclinic orbits (with N. Ercolani and D. W. McLaughlin) Physica D 43, 349-384 (1990).
1-D closure models for 3-D incompressible viscoelastic free jets: von Kármán flow geometry and elliptical cross-section (with S. Bechtel, D. Holm, and K. Lin), J. Fluid Mech. 196, 241-262 (1988).
A quasiperiodic route to chaos in near-integrable PDE: homoclinic crossings (with A. R. Bishop, D. W. McLaughlin, and E. A. Overman), Physics Letters A 127, 335-340 (1988).
Geometry of the modulational instability, Part I: Local analysis (with N. Ercolani and D. W. McLaughlin), Memoirs of the A.M.S., to appear.
Geometry of the modulational instability, Part II: Global analysis (with N. Ercolani and D. W. McLaughlin), Memoirs of the A.M.S., to appear.
Modal representations of chaotic attractors for the driven, damped pendulum chain (with A. R. Bishop, D. W. McLaughlin, and E. A. Overman), Phys. Lett. A 144 17-25 (1990).
Numerical evidence for global bifurcations leading to switching phenomena in long Josephson junctions (with S. Pagano, R. Parmentier, et. al.) Journal of Wave Motion 22, 213-226 (1990).
Correlations between chaos in a perturbed sine-Gordon equation and a truncated model system, (with A. R. Bishop, R. Flesch, D. R. McLaughlin, and E. A. Overman), SIAM Journal of Math. Analysis 21 (6), 1-26 (1990).
Change-of-type behavior in viscoelastic slender jet modules (with Q. Wang), Theoretical and Computational Fluid Dynamics 2, 1-25 (1990).
Numerical inverse spectral transform for the periodic sine-Gordon equation: theta function solutions and their linearized stability, (with R. Flesch and A. Sinha), Physica D 48, 169-231 (1991).
Modeling fiber-spinning processes with a comprehensive perturbation theory, (with S. E. Bechtel and J. Cao), FED - Vol. 124, refereed proceedings of symposium on Recent Developments in Non-Newtonian Flows and Industrial Applications, ASME Press, 1991.
Frequency and phase locking of spatially periodic perturbed sine-Gordon breather trains, (with S. P. Sheu and A. Sinha), SIAM Journal of Applied Mathematics 52 (3), 746-761 (1992).
Enhancement of optical bistability by periodic layering, (with R. Camassa and R. Knapp), Journal of Nonlinearity 5, 721-742 (1992).
Practical applications of a higher order perturbation theory for slender viscoelastic jets and fibers, (with S. Bechtel and J. Cao), Journal of Non-Newtonian Fluid Mechanics 41, 201-273 (1992).
Closure to all orders in 1-D models for slender viscoelastic free jets, I. An integrated theory for axisymmetric torsionless flows, (with S. Bechtel and K. Lin), Journal of Stability and Applied Analysis of Continuous Media 2, 1-43 (1992).
Instability-driven energy transport in nearly integrable, many degree-of-freedom Hamiltonian systems, (with C. Goedde and A. Sinha), Physical Review Letters 68 (18), 2722-2725 (1992).
Non-isothermal modelling of fiber spinning, (with S. Bechtel and Q. Wang), refereed proceedings of Symposium on Recent Advances in Non-Newtonian Fluid Flows, 1992 Winter Annual Meeting, ASME, edited by D. A. Siginer, Vol. 153, 37-48, ASME Press, New York (1992).
Illustration of an optimization procedure for fiber-spinning operating conditions: Maximum draw ratio under a Maxwell thin-filament model, (with S. Bechtel, J. Cao), Journal of Rheology 37 (2), 237-287 (1993).
Fully nonlinear modal equations for nearly integrable p.d.e., (with N. Ercolani, D. McLaughlin and A. Sinha), Journal of Nonlinear Science 3, 393-426 (1993).
Chaotic transport and integrable instabilities in a nearly integrable, Hamiltonian, discrete sine-Gordon lattice, (with C. Goedde and A. Sinha), Physica D 67, 347-386 (1993).
Dynamics of slender viscoelastic free jets, ( with Q. Wang), SIAM J. Appl. Math. 54 (4), 996-1032 (1994).
A numerical study of nearly integrable modulation equations, (with A. Sinha), Singular Limits of Dispersive Wave Equations, edited by N. Ercolani, I. Gabitov, D. Levermore and D. Serre, Plenum Publishing, 1994.
Computation and stability of fluxons in a singularly perturbed sine-Gordon model of the Josephson junction, (with D. Brown, B. Miller and N. A. Petersson), SIAM J. Appl. Math. 54(4), 1048-1066 (1994).
Numerical simulations of nonisothermal fiber spinning processes, (with Qi Wang), Recent Advances in Non-Newtonian Flows, ASME Press, New York, refereed proceedings of ASME Summer Meeting, Lake Tahoe, June, 1994, edited by G. Vradis and D.A. Siginer (1994).
1-D models for thin filaments of polymeric liquid crystals, (with Q. Wang and S.E. Bechtel), Developments in Non-Newtonian Flows, ASME Press, New York, refereed proceedings of ASME International Congress and Exposition, Chicago, IL, November, 1994, edited by S.E. Bechtel and D. Siginer (1994).
Modeling failure in polymeric liquid filaments, with Q. Wang and S.E. Bechtel, Developments in Non-Newtonian Flows, ASME Press, New York, refereed proceedings of ASME International Congress and Exposition, Chicago, IL, November, 1994, edited by S.E. Bechtel and D. Siginer (1994).
Symmetry-breaking instabilities and chaotic transport in Hamiltonian sine-Gordon discrete lattices, (with C. Goedde and A. Sinha), Mathematics and Computers in Simulation 37, 323-339 (1994).
Torsional effects in high-order viscoelastic thin-filament models, (with S. Bechtel, K. Bolinger and J. Cao), SIAM J. Appl. Math. 55(1),58-99 (1995).
A new model to determine dynamic surface tension and elongational viscosity using oscillating jet measurements, (with S. E. Bechtel, J. A. Cooper, N. A. Petersson, D. L. Reichard, A. Saleh, and V. Venkataramanan), Journal of Fluid Mechanics 293, 379-403 (1995).
Recovery of the Rayleigh capillary instability from slender 1-D inviscid and viscous models, (with S. E. Bechtel and C. D. Carlson), Physics of Fluids 7(12), 2956-2971 (1995).
Modeling and computation of the onset of failure in polymeric liquid filaments, (with S. E. Bechtel and Q. Wang), Journal of Non-Newtonian Fluid Mechanics 58, 97-129 (1995).
Thermomechanical equations governing a material with prescribed temperature-dependent density, with application to nonisothermal plane Poiseuille flow, (with D. Cao and S. E. Bechtel), Journal of Applied Mechanics 63(4), 1011-1018 (1996).
1-D models for thin filaments of liquid crystalline polymers: coupling of orientation and flow in the stability of simple solutions, (with Q. Wang and S. E. Bechtel), Physica D 99(4), 527-554 (1997).
This paper is available in PostScript

Exploiting accurate spinline measurements for elongational material characterization, (with V. Ramanan, V. Gauri, K. Koelling, S. Bechtel), J. Rheology 41(2), 1-24 (1997).

One-dimensional isothermal spinning models for liquid crystalline polymer fibers, (with Q. Wang, S. Bechtel), J. Rheology 41(4), 821-850 (1997).
This paper is available in PostScript

Onset of oscillations in nonsoliton pulses in nonlinear dispersive fibers, (with Kenneth T-R McLaughlin), J. Nonlinear Science 7, 1-20 (1997).
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The effect of dynamic surface tension on the oscillation of slender elliptical Newtonian jets, (with S. E. Bechtel, N. Youssef, H. Zhou), J. Applied Mechanics 65 (3), 694-704 (1998).
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Viscoelastic free surface jets and filaments, (with S. E. Bechtel and J. Cao), invited contribution for Proceedings for the Symposium on Rheology and Fluid Mechanics of Nonlinear Materials, ASME International Mechanical Engineering Congress and Exposition, Dallas, TX (1998).
This paper is available in PostScript

A thin-filament melt spinning model with radial resolution of temperature and stress, (with G. Henson, D. Cao, and S. Bechtel), J. Rheology 42(2), 329-360 (1999).

The Role of Microstructure in Taming the Rayleigh Capillary Instability of Cylindrical Jets, (With Qi Wang), Physica D (special issue on Nonlinear Waves and Solitons in Physical Systems), 123, 161-182 (1998) .
This paper is available in PostScript

Anisotropic Microstructure-Induced Reduction of the Rayleigh Instability for Liquid Crystalline Polymers, (With Qi Wang), Physics Letters A 245, 518-526 (1998).

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Free Surface Viscoelastic and Liquid Crystalline Polymer Fibers and Jets, (With S.E. Bechtel, Q. Wang, H. Zhou) invited book chapter in Advances in Non-Newtonian Flows and Rheology, edited by D. Siginer, D. DeKee, R Chhabra, Elsevier Science Publishers (1998).

This paper is available in PostScript

Dynamics of Free Surface and Pure Elongational Flows of Liquid Crystalline Polymers, (With Q. Wang, H. Zhou), Rheology and Fluid Mechanics of Nonlinear Materials, edited by D. Siginer, D. DeKee, FED-Vol. 246, MD-Vol. 81, ASME, New York, 1998, 101-114.

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The Figures are available in PostScript

An Isothermal Model for High-Speed Spinning of Liquid Crystalline Polymer Fibers - Coupling of Flow, Orientation, and Crystallization, (With T. Ueda), Journal of Non-Newtonian Fluid Mechanics 84, 109-121 (1999).

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Near-Equilibrium Dynamics of Doi Models for Liquid Crystal Polymer Flows: Catastrophic and Regularized Behavior, (With Q. Wang), Journal of Non-Newtonian Fluid Mechanics 83, 131-150 (1999).

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An Anelastic, Scale-Separated Model for Mixing, With Application to Atmospheric Transport Phenomena, (With R. McLaughlin), Physics of Fluids 11(4), 1-13, (1999).

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On the Exact Solution of the Geometric Optics Approximation of the Defocusing Nonlinear Schrodinger Equation, (With O. Wright, K. T-R McLaughlin), Physics Letters A 257, 170-174 (1999).

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A Model Study of the Spinning of Thermotropic Liquid Crystalline Polymers: Fiber Performance Predictions and Bounds on Throughput, (With Q. Wang, H. Zhou), Advances in Polymer Technology 18(4), 314-335 (1999).

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Non-soliton Pulse Evolution in Normally Dispersive Optical Fibers, (With N. Kutz, K. T-R McLaughlin), J. Optical Society of America B 16(11), 1856-1862 (1999).

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Nonhomogeneous Patterns with Core Defects in Elongational Flows of Liquid Crystal Polymers, (With Q. Wang, H. Zhou), Journal of Rheology, 43(6), 1573-1582, 1999.

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Thermotropic liquid crystalline polymer fibers, (with Hong Zhou and Qi Wang), SIAM J. Appl. Math. 60(4), 1177-1204 (2000).

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Non-focusing Instabilities in Coupled, Integrable Nonlinear Schrodinger PDEs (With O. Wright, D. W. McLaughlin, D. Muraki), Journal of Nonlinear Science, 10, 291-331, (2000).

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Exact banded patterns from Doi-Marrucci-Greco model of nematic liquid crystal polymers, (with Q. Wang and H. Zhou), Physical Review E 61 (6), 6665-6672, (2000).

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Homogeneous pattern selection and director instabilities of nematic liquid crystal polymers induced by elongational flows, (with Q. Wang and H. Zhou), Physics of Fluids 12(3), 490-498 (2000).

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On the construction of orbits homoclinic to plane waves in integrable coupled nonlinear Schrodinger systems, (with S. Sheu and O. Wright), Physica Letters A 266, 24-33 (2000).

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On the Backlund-Gauge transformation and homoclinic orbits of a coupled nonlinear Schrodinger system, (with O. Wright), Physica D: Nonlinear Phenomena, 141, 104-116 (2000).

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Some Riemann-Green functions for the geometric optics approximation of the defocusing nonlinear Schrodinger equation, (with O. Wright and K. T-R McLaughlin), refereed proceedings of the 16th IMACS World Congress, (2000).

Methods for the exact construction of mesoscale patterns in rod-like nematic liquid crystal polymers, (with Q. Wang and H. Zhou), Physica D-Nonlinear Phenomena 152, 288-309(2001).

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A model for a spreading and melting droplet on a heated substrate, (with D. M. Anderson and R. Superfine), SIAM J. Appl. Math. 61(5), 1502-1525, (2001).

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On the flow-phase diagram for discotic liquid crystals in uniaxial extension and compression, (with Q. Wang and H. Zhou), Liquid Crystals, 28(5), 717-720(2001).

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Non-Newtonian viscous oscillating free surface jets, and a new strain-rate dependent viscosity form for flows experiencing low strain rates, (with S. Bechtel, K. Koelling, N. Youseff, and H. Zhou), Rheologica Acta 40, 373-383(2001).

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Transient behavior of thermal optical glass fiber drawing processes, (with H. Zhou), European J. Appl. Math. 12, 479-496 (2001).
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Symmetries of the Doi kinetic theory for nematic polymers of arbitrary aspect ratio: at rest and in linear flows, (with Q. Wang and R. Zhou), Physical Review E, Vol. 66 (3), 031712 (2002).
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A hydrodynamic theory for solutions of nonhomogeneous nematic liquid crystalline polymers with density variations, (with Q. Wang and R. Zhou), refereed proceedings of ASME International Mechanical Engineering Congress, N.O., La., IMECE2002-32189 (2002).
This paper is available in PDF

Explicit flow-aligned orientational distribution functions for dilute nematic polymers in weak shear, (with Q. Wang and R. Zhou), refereed proceedings of ASME International Mechanical Engineering Congress, N.O., La., IMECE2002-32185 (2002).
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Full-tensor alignment criteria for sheared nematic polymers (with R. Zhou, Q. Wang), J. Rheology 47(1), 105-128 (2003).
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Monodomain response of finite-aspect-ratio macromolecules in shear and related linear flows, (with Q. Wang), Rheologica Acta 42, 20-46 (2003).
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An integrable model for stable:unstable wave coupling phenomena, (with O. Wright), Physica D 178, 173-189 (2003).
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Computational observation of a weakly compressible mixing barrier in idealized anelastic fluid equations, (with R. McLaughlin and H. Zhou), Physics of Fluids, 15 (10), 2872-2885, 2003.
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Thermal expansion models of viscous fluids based on limits of free energy, (with S. Bechtel, F. Rooney, and Q. Wang), Physics of Fluids, to appear (2003).
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A kinetic theory for solutions of nonhomogeneous nematic liquid crystalline polymers with density variations, (With Q. Wang, R. Zhou), J. Fluid Engineering, Vol. 126(2), 180-188, 2004.
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The weak shear kinetic phase diagram for nematic polymers, (with Q. Wang and R. Zhou), Rheol. Acta, Vol. 43(1), 17-37, 2004.
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Structure scaling properties of confined nematic polymers in plane Couette cells: the weak flow limit, (with Q. Wang, H. Zhou, and R. Zhou), J. Rheology 48(1), 175-192, 2004.
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Scaling behavior of kinetic orientational distributions for dilute nematic polymers in weak shear, (with Q. Wang, R. Zhou), JNNFM, Vol. 116 (2-3), 183-204, 2004.
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Modomain response of arbitrary aspect ratio nematic polymers in general linear planar flows, (with Q. Wang, R. Zhou, and E. Choate), JNNFM, Vol. 118(1), 17-31, 2004.
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The flow-phase diagram of Doi-Hess theory for sheared nematic polymers II: finite shear rates, (With Q. Wang, R. Zhou), Rheol. Acta, accepted, appeared online, 2004
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Likelihood & Expected-time Statistica of Monodomain Attractors in Sheared Discotic and Rod-like Nematic Polymers, (With X.Y. Zheng, Q. Wang, R. Zhou), Rheol. Acta, accepted, appeared online, 2004.
This paper is available in HTML

Exact scaling laws for electrical conductivity properties of nematic polymer nano-composite monodomains , (With X.Y. Zheng, R. Lipton, Q. Wang, R. Zhou), Adv. Func. Mat., accepted, 2004.
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Chaotic boundaries of nematic polymers in mixed shear and extensional flows , (With Q. Wang, R. Zhou), Phys. Rev. Lett., Vol.93 (8), 088301, 2004.
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Kinetic structure simulations of nematic polymers in plane Couette cells, I: The algorithm and benchmarks, (With Q. Wang, R. Zhou), SIAM Mutilscale Modeling and Simulation, accepted, 2004.
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B. Submitted refereed research articles

Structure evolution in tumbling and kayaking nematic liquid crystalline polymers between shearing plates, (with Q. Wang and H. Zhou), UNC-CH Program in Applied Mathematics Preprint PAMPS2002-2, to be submitted to J. Non-Newtonian Fluid Mech.

Connections between stability, convexity of internal energy, and the second law for compressible Newtonian fluids, (with S.E. Bechtel, F. Rooney, and Q. Wang), J. Appl. Mechanics, revision in review.

C. Non-research scholarly articles

Mathematical challenges in nanoscience and nanotechnology: an essay on nanotechnology implications, Proceedings of a Workshop

Nano-Materials: Can we do the Math?, solicited essay by the American Association for the Advancement of Science, for posting on the EurekAlert! website for international journalists (2002).

D. Research Grants

Principal Investigator, National Science Foundation (N.S.F.) Grant No. MCS-8002969, effective July 1, 1980 - December 31, 1983, entitled "Inverse Spectral Theory and Concrete Aspects of Periodic Solitons".
Co-Principal Investigator, N.S.F. Grant No. MCS-8202288 (with N. Ercolani), effective July 1, 1982 - December 31, 1984, entitled "Applications of Algebraic Geometry to Quasi-Periodic Soliton Theory".
Co-Principal Investigator, N.S.F. Grant No. DMS-8411002 (with N. Ercolani), effective October 1, 1984 - April 30, 1988, entitled "Applications of Algebraic Geometry to Quasi-Periodic Soliton Theory".
Co-Principal Investigator, Air Force Office of Scientific Research (A.F.O.S.R.) Grant 88-064, Officer A. Nachman (with S. Bechtel), effective April 1, 1988 - April 1, 1990, entitled "Modeling of Free Viscoelastic Jets and Instability Mechanisms".
Principal Investigator, N.S.F. Grant No. DMS-8803465, effective June 1, 1988 - September 30, 1991, entitled "Development and Applications of Periodic Soliton Theory for Nearly Integrable P.D.E.".
Co-Principal Investigator, A.F.O.S.R. Grant 90-0253, Officer A. Nachman (with S. Bechtel), effective April 1, 1990 - March 31, 1993, entitled "On the Behavior of Non-Newtonian Fluids: Analysis, Computation and Experiment".
Principal Investigator, N.S.F. Grant No. DMS-9104806, effective April 1, 1991 - Match 31, 1994, entitled "Nearly Integrable Nonlinear Wave Phenomena: Theory and Applications"
Co-Principal Investigator, A.F.O.S.R. Grant 93-NM001, Officer A. Nachman (with S. Bechtel), effective July 1, 1993 - September 30, 1996, entitled "Toward Technological Application of Non-Newtonian Fluids and Complex Materials".
Co-Principal Investigator, A.F.O.S.R. Grant 93-NM229, (with S. Bechtel), AASERT Program, "Modeling of Viscoelastic Jets and Fibers: Inverse Problems for Material Characterization", effective July 1, 1993 - June 30, 1996.
Co-Principal Investigator, N.S.F. Grant No. CTS-9319128, (with S. E. Bechtel), effective May 15, 1994 - April 30, 1997, "measuring material properties in manufacturing and agricultural processes".
Co-Principal Investigator, N.S.F. Grant No. DMS-9403596, (with E. Overman), effective June 1, 1994 - May 31, 1997, "Nearly Integrable Nonlinear Wave Phenomena: Theory and Applications".
Principal Investigator, A.F.O.S.R. Grant F49620-97-1-0001, effective October 1, 1996 - November 30, 1999, "Fiber Flows and Technological Applications".
Principal Investigator, N.S.F. Grant No. DMS-9704549, effective July 1, 1997 0- June 30, 2000, "Nearly Integrable PDE's: Open Mathematical Problems and Their Technological Applications".
Principal Investigator, Department of Defense "DURIP" grant for research equipment, October 1, 1998- September 30, 1999, "Full resolution of melt to solid phases of liquid crystalline polymers and glasses in fiber processing".
Co-Principal Investigator, N.S.F. Grant No. CTS-9711109, (with S.E. Bechtel), effective July 1, 1997- June 30, 2000, "Material characterization of agricultural and industrial solutions and melts in extensional processes".
Principal Investigator, N.S.F. Grant No. DMS-9977409, (with applied math group at UNC-CH), SCREMS Program, September 1, 1999- August 31, 2002, for equipment and systems support.
Principal Investigator, A.F.O.S.R. Grant No. 99-NM-008, effective October 1, 1999 through September 30, 2002, "High-Performance Macromolecular Materials".
Principal Investigator, N.S.F. Grant No. DMS-0072553, effective August 1, 2000 through September 30, 2002, "Mathematical Descriptions of Anisotropic Fluids and Optical Pulse Propagation".
Co-PI, N.S.F. INT-0096938, June, 2000-August, 2002, support for Otis Wright to visit from Middle East to UNC-CH.
Co-PI, N.S.F. CTS (with K. Koelling, S. Bechtel, Ohio State U.), August, 2001-September, 2004, "Shear and extensional rheology of nanoclays and nanotubes in polymer melts and solutions".
Co-PI, N.S.F. Major Research Instrumentation Program (with applied math group and computational scientists at UNC-CH), A Distributed Computing Environment, August, 2001-July, 2004.
Co-PI, NASA URETI multi-university grant on Biologically Inspired Materials, with E.T. Samulski et al., 2002-2007.
PI, A.F.O.S.R., "High-Performance Macromolecular Materials", December, 2002-November, 2005.
PI, N.S.F., "Mathematical Aspects of Flow-Processed Nano-Materials", June, 2003-May, 2006.

E. Teaching Recognition:

Meritorious Teaching Award, Liberal Arts College, University of Arizona, 1979

F. Ph.D. Students Advised

Jong-Eao Lee, "Geometry and Modulation Theory for the Periodic Nonlinear Schrödinger Equation", 1986. now tenured at National Chiao Tung University, Hsinchu, Taiwan.
Karen Bolinger, "Pointwise Closure Models for Slender, non-Newtonian Free Jets", 1990, now Assistant Professor at Arkansas State University.
Qi Wang, "Dynamics of Slender Viscoelastic Free Jets", 1991, now Professor at Florida State University.
Jian-Zhong Cao, "Higher Order Perturbation Theory for Slender Viscoelastic Jets and Fibers with Torsion", June, 1992.
S. P. Sheu, "Homoclinic Orbits for a Systems of Coupled Nonlinear Schrödinger Equations", August, 1992, now Assistant Professor in Taiwan.
C. D. Carlson, "An analysis of the Rayleigh capillary instability in slender jets", March, 1996, now employed by the Hoechst Celanese Corporation, Charlotte, NC.

G. Current Ph.D. Students

Eric Choate
Joohee Lee
Lingxing Yao
Xiaoyu Zheng

H. M.S. Students at UNC-CH, advised or co-advised

Greg Robbins, graduated August, 2002
Alison Hall
John Bakken

H. Postdoctoral Students Supervised

B. Maulik, Battelle Postdoctoral Fellowship, 1988-1990.

D. Muraki, AFOSR funding, 1990.

O. Wright, AFOSR funding, 1991-1993.

B. Umarov, funded by Uzbek Academy of Science, 1990.

C. Goedde, Battelle Postdoctoral Fellowship, 1990-1992, NSF funding, 1992-1994.

J. Cao, AFOSR funding, 1992-1995.

Hong Zhou, University of North Carolina and AFOSR funding, 1996-1999.

Tetsuji Ueda, University of North Carolina and AFOSR funding, 1996-1997.

Daniel Anderson, University of North Carolina and AFOSR funding, 1996-1999.

Ruhai Zhou, UNC and AFOSR funding, 2001-2004

I. Presentations (since 1996)

1996, "Slender filament flows and technological applications", Department of Mathematics, Indiana University, January 19
1996, "The interplay between basic science and precision technological tools for fiber manufacture", Corning, Inc., Wilmington, NC, April 2
1996, "Some scientific issues relevant to fiber spinning processes", Hoechst Celanese Corporation/University of North Carolina Polymer Workshop, Friday Center, UNC, Chapel Hill, NC, November 7
1996, "Isothermal hydrodynamics of liquid crystalline polymer fibers", Applied Mathematics Workshop for Materials Studies and Industrial Applications, Penn State University, October 25
1996, "The coupling of orientation, birefringence, and crystallinity in fiber spinning models", Hoechst Celanese Corporation, Charlotte, NC, October 18
1997, "Mathematical models for fiber spinning processes: how mathematics and materials science fit together", talk to Materials Science Program graduate students, UNC, Chapel Hill, February 3
1997, "Orientation coupling to flow in liquid crystalline fibers", Society of Rheology Annual Meeting, Galveston, TX, February 16
1997, "Orientation and crystallization in fiber flows", SIAM Materials Science Meeting, Philadelphia, PA, May 12
1997, "Liquid crystalline polymer filaments: Taming of the Rayleigh instability", 17th Annual International Conference on Nonlinear Waves and Solitons in Physical Systems, Center for Nonlinear Studies, Los Alamos National Laboratory, May 16
1997, "Liquid crystalline polymer fibers", Hoechst Celanese Corporation, Summit, NJ, June 3
1997, "Demonstration of the new spin model to calculate fiber birefringence from first principles", Hoechst Celanese Corporation, Charlotte, NC, July 17
1997, "Interactions between microstructure and hydrodynamics", Applied Math Seminar, Department of Mathematics, Duke University, Durham, NC, October 6
1997, "Suppression of the Rayleigh capillary instability by rigid-rod microstructure", Society of Rheology 69th Annual Meeting, Symposium on Liquid Crystals: Structure and Rheology, October 23
1998, "Modeling of Liquid Crystal Polymer Fiber Processes", Workshop on Industrial Mathematics, Utah State University, June 11
1998, "Interactions between microstructure and flow", Applied Mathematics Seminar, UNC-CH, September 4
1998, "Elongation-induced biaxial patterns and instabilities", Society of Rheology 70th Annual Meeting, Monterey, CA, Session on Coupling Flow and Order in Fluids, October 7.
1998, "Microstructural influence on capillary instability of cylindrical jets", Applied and Interdisciplinary Mathematics Seminar, University of Michigan, September 21.
1998, "Interactions between microstructure and flow", Mathematics Department Colloquium, University of Michigan, September 22
1998, "Interactions between microstructure and flow", Applied Mathematics Colloquium, University of Arizona, October 9
1998, "Interactions between microstructure and flow (of polymers and liquid crystalline polymers)", Courant Institute of Mathematical Sciences, NYU, Applied Math Colloquium, November 20
1999, "A framework for defects and textures in flows of liquid crystal polymers", University of Pennsylvania, Workshop on Multicomponent and Multiphase Fluid Dynamics, March 13
1999, "Interactions between microstructure and flow of liquid crystal polymers", Mathematical Sciences Research Institute Workshop on Self-Assembling Geometric Structures in Material Science, Berkeley, CA, April 12
1999, "Interactions between microstructure and flow of liquid crystal polymers", IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena, plenary address, University of Georgia, April 15
1999, "Dynamics of Microstructure/Flow Interactions", SIAM Workshop on Dynamical Systems, plenary address, Snowbird, Utah, May 24
1999, "Exact and modulated patterns in liquid crystal polymers", Society of Rheology Annual Meeting, Madison, WI, October 9
1999, "Exact descriptions of coherent structures in anisotropic fluids," Workshop on Integration of Integrability into Science and Mathematics, in honor of V. Zakharov, Tucson, AZ, October 30
2000, "Flows of liquid crystalline polymers", University of California-Irvine Colloquium, Irvine, CA, March 13, 2000
2000, "Flows of liquid crystal polymers, Southeastern Regional Meeting of the American Mathematical Society, Lafayette, LA, April 15
2000, "Mesoscale patterns from a Doi-Marrucci-Greco model for liquid crystalline polymers", Materials Research Society Spring Meeting, Symposium on Multiscale Modeling of Organic Materials, San Francisco, CA, April 25
2000, "Phase and conformation transitions in liquid crystalline polymers", SIAM Materials Science Meeting, Philadelphia, PA, May 24
2000, "Liquid crystalline polymers and other macromolecular fluids", Center for Advanced Scientific Computation, Lawrence Livermore National Laboratory, June 27
2000, "High performance macromolecular materials", Air Force Office of Scientific Research Grantees' and Contractors Meeting, Stanford University, June 29
2000, "Discotic liquid crystals in extension and compression", Wright-Patterson Air Force Base, Richard Vaia host scientist, Dayton, OH, July 20
2000, "Modeling of mesoscale structures in flows of liquid crystalline polymers", Liquid Crystal Institute, Kent State University, October 11
2000, "Modeling of mesoscale structures in flows of liquid crystalline polymers", North Carolina State University, Mathematics Department, November 1; UNC-Chapel Hill, November 17
2001, "Dynamics of structures in macromolecular fluids", Dynamics Days 2001, hosted by Duke University, Durham, NC, January 4
2001, "Flow phenomena of rodlike and discotic LCPs", Clemson University, joint Mathematics and Center for Advanced Engineering Fibers and Films colloquium, Clemson, SC, January 29
2001, "Mesostructure evolution in tumbling nematic LCPs between shearing plates", 72nd Annual Meeting of Society of Rheology, Hilton Head, SC, February 15
2001, "Mesostructure evolution in tumbling nematic LCPs between shearing plates", 3rd Pacific Rim Rheology Conference, Vancouver, BC, July 9
2001, "Shear-induced monodomains of nematic polymers: finite aspect ratio effects", 3rd Pacific Rim Rheology Conference, Vancouver, BC, July 9
2001, "Dynamic precursors to structure formation in sheared macromolecular fluids", A.F.O.S.R. Contractor and Grantee Annual Meeting, Stanford, CA, July 24
2001, "Dynamics of shear-induced monodomains for finite-aspect-ratio macromolecules", Society of Rheology Meeting, Bethesda, MD, October 21
2001, "Dynamic precursors to structure formation in sheared macromolecular fluids", AICHE Annual Meeting, Reno, Nevada, November 4-9
2001, "Mathematical aspects of simple flows containing simple molecules", Applied Mathematics Seminar, UNC-CH, November 16
2001, "Monodomain presursors and mesostructure evolution in linear and nearly linear flows of rigid, ellipsoidal macromolecules", Materials Research Society Fall Meeting, Boston, MA, November 28
2002, "The dynamics of nematic liquids in shear and related linear flows", Utah State Workshop on Mathematics in Industry, Logan, UT, March 1-2
2002, "The dynamics of nematic liquids: molecular theory and averaged descriptions", University of New Mexico Symposium of the Center for Advanced Studies, Albuquerque, NM, April 18-19
2002, "The orientational degeneracy of nematic liquids and its role in the dynamical response to shear flow", Fourth International Conference on Dynamical Systems and Differential Equations, Wilmington, NC, May 24-27
2002, "The dynamics of nematic liquids: molecular theory and averaged descriptions", Joint meeting of Italy and U.S. Mathematics Societies, Symposium on Mathematical Problems in Soft Matter Modeling, Pisa, Italy, June 12-16
2002, "Free energy characterizations of mechanical incompressibility in thermal viscous flow", Fourteenth U.S. National Congress of Theoretical and Applied Mechanics, Symposium for Dan Joseph, Blacksburg, VA, June 23-28
2002, "Dynamic Precursors and Structure Formation in Flowing Nematic Polymers", SIAM Fiftieth Anniversary Meeting, Symposium on Materials Science, Philadelphia, PA, July 10

2002, "Microscopic and mesoscopic predictions of nematic polymers in shear-dominated flows", Marrucci Symposium, National Meeting of the Society of Rheology, Minneapolis, MN, Oct. 15

2002, "Passing between molecular and mesoscopic descriptions of high-performance macromolecular materials", International Mechanical Engineering Congress and Exposition, New Orleans, LA Nov. 19

2002, "Laminar flows of nematic polymers: molecular theory and averaged descriptions", Northwestern University, Applied Mathematics Colloquium, Evanston, IL, Dec. 5

2003, "Laminar flows of nematic polymers: issues critical to high-performance materials", University of Colorado-Boulder, Applied Mathematics Colloquium, Boulder, CO, Jan. 18

2003, "Mathematics of high-performance materials", AMS Special Session on the Mathematics of Materials, Rob Lipton, Organizer, Baton Rouge, LA, March 14

2003, "Laminar flows of nematic polymers: passing between kinetic and mesoscopic scale models", Workshop on Multiscale Theory and Computation in Nano Materials, Wright-Patterson AFB, Dayton, OH, March 29

2003, "What�s math got to do with nano-materials?", UNC-Chapel Hill Mathematics Graduate Visions Seminar, April 14

2003, "Laminar flows of nematic polymers: high-performance materials in the making", Carnegie Mellon University, Mathematics Department and Center for Nonlinear Analysis, Pittsburgh, PA, May 1

2003, "The dynamics of nematic polymers in laminar flows: a zoo of bifurcations associated with bulk molecular phase transitions", SIAM Dynamical Systems Annual Meeting, Snowbird, UT, May 28

J. Professional Activities and Service

Editor for SIAM J. Appl. Mathematics

Referee for Physica D, Mathematical Reviews, SIAM J. Appl. Math., the National Science Foundation (Theoretical Physics, Applied Mathematics, and Classical Analysis), Transactions of the A.M.S., Physical Review B, AFOSR, SIAM J. Math. Analysis, Physical Review Letters, Physics Letters A, Journal of Mathematical Physics, the Department of Energy, Chaos Journal, Journal of Nonlinear Science, Journal of Dynamics and Differential Equations, Physics of Fluids A, Nonlinearity, Physical Review E.
Co-organizer, with James Turner of a mentoring/research enhancement program, Summer, 1991-1994 for students from historically black colleges, at Ohio State University

Co-organizer, with Y. Kodama and E. Overman, of a Workshop on Nearly Integrable Nonlinear Wave Phenomena in Nonlinear Optics, December, 1990, at Ohio State University
Member of Forum Steering Committee, Society of Industrial and Applied Mathematics, May, 1992-1996
Organizer of SIAM Forum meeting, June 4,5, 1993, Indianapolis, IN
Member of SIAM Advisory Committee for ``Mathematics in Industry'' Initiative, 1993-1996
Member of organizing committee, with E.Wayne and W.Craig, for MSRI Workshop on Dynamical Systems Methods for Partial Differential Equations, Berkeley, CA, March 14-18, 1994
Member of organizing committee, Math Tower Conference to dedicate the new Math Building at Ohio State University, March 18,19, 1994
Member of organizing committee, Penn State Workshop on Applied Mathematics for Materials Studies and Industrial Applications, State College, PA, October 24-26, 1996
Member of Advisory Committee, Curriculum in Applied and Materials Sciences, University of North Carolina, 1997-present
Member of SIAM Committee on Science Policy, 1998-present
Member of Director's Review Committee for Computing Sciences, Lawrence Berkeley Laboratory, May 27,28, 1998
Member of External Panel to Review UC-Berkeley Physical Sciences Organized Research Units, February 27,28, 2000
Panel Member of Workshop on "Societal Implications of Nanoscience and Nanotechnology", Hosted by the U.S. Interagency Working Group on Nanoscience and Nanotechnology, Washington, DC, September 28-29, 2000
Panel Member for 2000 Mathematics Chairs' Colloquium at the National Academy of Sciences in Washington, DC, November 10-11, 2000
Member, NSF Mathematical Sciences Postdoctoral Research Fellowships Panel, 2000-2003
Member, Program Committee for a Workshop of the University of North Carolina System on ``Computational Modeling in Higher Education'', March 25,26, 2002, at the North Carolina Supercomputing Center, Research Triangle Park, NC.
Member, Local Development Committee for the Statistical and Applied Mathematical Sciences Institute (SAMSI), an NSF-DMS Institute in the Research Triangle Park, NC.

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