Department of Mathematics

Applied Mathematics Group


Educational Background

Previous Positions

Research Interests

Collaborators

Publications

Vita

Weekly Schedule


M. Gregory Forest
Grant Dahlstrom Distinguished Professor, Department of Mathematics




Office: 316A Phillips Hall
Phone: (919) 962-9606
Email: forest @ amath.unc.edu

Educational Background
    B.S., Mathematics, Louisiana State University in New Orleans, May, 1972
    M.S., Mathematics, Louisiana State University in New Orleans, December, 1973
    Ph.D., Mathematics, University of Arizona, August, 1979; Advisor: David W. McLaughlin
 Current Position
    Grant Dahlstrom Distinguished Professor, Department of Mathematics
    Co-Director, Institute for Advanced Materials, NanoScience and Technology, UNC-CH
    Member, Curriculum in Applied and Materials Sciences
Previous Positions
    Assistant Professor, Ohio State University, September, 1979 thru August, 1984
    Associate Professor, Ohio State University, September, 1984 thru August, 1989
    Professor, Ohio State University, September, 1989 thru July, 1996
    Senior Associate Dean, College of Arts and Sciences, University of North Carolina at Chapel Hill, July 1, 1998 thru June 30, 2000
 Research Interests
Collaborators
 Publications
  1. Multiphase averaging and the inverse spectral solution of KdV(with H. Flaschka and D. W. McLaughlin), Comm. Pure Appl. Math. 33, 739-784 (1980).

  2. Spectral theory for the periodic sine-Gordon equation: a concrete viewpoint (with D. W. McLaughlin), J. Math Phys., 23(7), 1248-1277 (1982).

  3. Modulations of sinh-Gordon and sine-Gordon wavetrains (with D. W. McLaughlin), Studies in Appl. Math. 68, 11-59 (1983).

  4. 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).

  5. Modulations of perturbed KdV wavetrains (with D. W. McLaughlin), SIAM Journal of Applied Math. 44(2), 287-300 (1984).

  6. The geometry of real sine-Gordon wavetrains (with N. Ercolani), Comm. Math. Phys. 99, 1-49 (1985).

  7. 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).

  8. Oscillations and instabilities in near integrable PDE's (with N. Ercolani and D. W. McLaughlin), Lectures in Appl. Math. 23, 3-46 (1985).

  9. The origin and saturation of modulational instabilities, (with N. Ercolani and D. W. McLaughlin), Physica D 18, 472-474 (1986).

  10. 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).

  11. 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).

  12. 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).

  13. 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).

  14. Effective stress rates of viscoelastic free jets (with S. Bechtel and K. Lin), J. Non-Newtonian Fluid Mechanics 26, 1-41 (1987).

  15. 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).

  16. 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.

  17. Geometry of the modulational instability III. Homoclinic orbits (with N. Ercolani and D. W. McLaughlin) Physica D 43, 349-384 (1990).

  18. 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).

  19. 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).

  20. Geometry of the modulational instability, Part I: Local analysis (with N. Ercolani and D. W. McLaughlin), Memoirs of the A.M.S., to appear.

  21. Geometry of the modulational instability, Part II: Global analysis (with N. Ercolani and D. W. McLaughlin), Memoirs of the A.M.S., to appear.

  22. 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).

  23. 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).

  24. 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).

  25. Change-of-type behavior in viscoelastic slender jet modules (with Q. Wang), Theoretical and Computational Fluid Dynamics 2, 1-25 (1990).

  26. 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).

  27. 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.

  28. 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).

  29. Enhancement of optical bistability by periodic layering, (with R. Camassa and R. Knapp), Journal of Nonlinearity 5, 721-742 (1992).

  30. 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).

  31. 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).

  32. 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).

  33. 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).

  34. 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).

  35. 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).

  36. 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).

  37. 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.

  38. 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).

  39. 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).

  40. 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).

  41. 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).

  42. 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).

  43. 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).

  44. 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).

  45. 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).

  46. 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).

  47. 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).

  48. 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

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

  50. 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

  51. Onset of oscillations in nonsoliton pulses in nonlinear dispersive fibers, (with Kenneth T-R McLaughlin), J. Nonlinear Science 7, 1-20 (1997).
    This paper is available in PostScript

  52. 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).
    This paper is available in PostScript

  53. 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

  54. 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).

  55. 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

  56. Anisotropic Microstructure-Induced Reduction of the Rayleigh Instability for Liquid Crystalline Polymers, (With Qi Wang), Physics Letters A 245, 518-526 (1998).
    This paper is available in PostScript

  57. 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

  58. 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.
    This paper is available in PostScript
    The Figures are available in PostScript

  59. 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).
    This paper is available in PostScript

  60. 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).
    This paper is available in PostScript

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

  62. 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).
    This paper is available in PDF

  63. 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).
    This paper is available in PostScript

  64. 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).
    This paper is available in PostScript

  65. 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.
    This paper is available in PDF

  66. Thermotropic liquid crystalline polymer fibers, (with Hong Zhou and Qi Wang), SIAM J. Appl. Math. 60(4), 1177-1204 (2000).
    This paper is available in PDF

  67. 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).
    This paper is available in PostScript

  68. 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).
    This paper is available in PDF

  69. 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).
    This paper is available in PDF

  70. 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).
    This paper is available in PDF

  71. 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).
    This paper is available in PDF

  72. 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).

  73. 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).
    This paper is available in PDF

  74. 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).
    This paper is available in PDF

  75. 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).
    This paper is available in PDF

  76. 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).
    This paper is available in PDF

  77. Transient behavior of thermal optical glass fiber drawing processes, (with H. Zhou), European J. Appl. Math. 12, 479-496 (2001).
    This paper is available in PDF

  78. 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).
    This paper is available in PDF

  79. 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

  80. 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).
    This paper is available in PDF

  81. Full-tensor alignment criteria for sheared nematic polymers (with R. Zhou, Q. Wang), J. Rheology 47(1), 105-128 (2003).
    This paper is available in PDF

  82. Monodomain response of finite-aspect-ratio macromolecules in shear and related linear flows, (with Q. Wang), Rheologica Acta 42, 20-46 (2003).
    This paper is available in PDF

  83. An integrable model for stable:unstable wave coupling phenomena, (with O. Wright), Physica D 178, 173-189 (2003).
    This paper is available in PDF

  84. 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.
    This paper is available in PDF

  85. 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).
    This paper is available in PDF

  86. 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.
    This paper is available in PDF

  87. The weak shear kinetic phase diagram for nematic polymers, (with Q. Wang and R. Zhou), Rheol. Acta, Vol. 43(1), 17-37, 2004.
    This paper is available in PDF

  88. 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.
    This paper is available in PDF

  89. 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.
    This paper is available in PDF

  90. 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.
    This paper is available in PDF

  91. The flow-phase diagram of Doi-Hess theory for sheared nematic polymers II: finite shear rates, (With Q. Wang, R. Zhou), Rheol. Acta, 44(1), 80-93, 2004
    This paper is available in PDF

  92. Extension-enhanced conductivity of liquid crystalline polymer nano-composites , (With H. Zhou, X. Zheng, Q. Wang, R. Lipton), Macromolecular Symposia, 28, 81-89, 2005
    This paper is available in PDF

  93. 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, 44(3), 219-234, 2005.
    This paper is available in PDF

  94. 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., 15(4), 627-638, 2005.
    This paper is available in PDF

  95. Chaotic boundaries of nematic polymers in mixed shear and extensional flows , (With Q. Wang, R. Zhou), Phys. Rev. Lett., Vol.93 (8), 088301, 2004.
    This paper is available in PDF

  96. 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, 3(4), 853-870, 2005.
    This paper is available in PDF

  97. Anisotropy and heterogeneity of nematic polymer nano-composite film properties, (With X. Zheng, R. Zhou, Q. Wang, R. Lipton) IMA Volume 141, Modeling of Soft Matter, 85-98, 2005.
    This paper is available in PDF

  98. Kinetic structure simulations of nematic polymers in plane Couette cells, II: In-plane structure transitions, , (With R. Zhou, Q. Wang), SIAM Mutilscale Modeling and Simulation, Vol. 4, 1280-1304, 2005.
    This paper is available in PDF

  99. Anisotropy and dynamic ranges in effective properties of sheared nematic polymer nano-composites, (With X. Zheng, R. Zhou, Q. Wang, R. Lipton) Adv. Func. Mat., Vol. 15, 2029-2035, 2005.
    This paper is available in PDF
    The journal cover related to this paper is also available in PDF

  100. Alignment and rheo-oscillator criteria for sheared nematic polymer films in the monolayer limit, (With J. Lee, R. Zhou), Discrete Contin. Dyn. Syst., Vol. 6, 339-356, 2005.
    This paper is available in PDF

  • 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.

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