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03/07/97
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Baldwin, P. and Kiehn, R. M., 1991, "Cartan's
Topological
Structure", This was first presented at the Santa Barbara conference in
Topology in Fluid
Dynamics. A much amplified version has been submitted for publication. Also
see Kiehn 1992a
Bamberg, P. and Sternberg, S., 1990, A Course in Mathematics
for Students of Physics. Vol I and II, (Cambridge University
Press, Cambridge)
Berge, B., Pomeau, Y. and Vidal, C., 1984, Order within Chaos,
(Wiley, NY) p. 161.
Bishop, R. L. and Goldberg, S. I., 1968, Tensor Analysis on
Manifolds, (Dover, N. Y.) p. 199.
Cartan, E., 1899, "Sur certaine expressions differentielles
et le systeme de Pfaff" Ann Ec. Norm. 16, p. 329.
Cartan, E., 1937, La Theorie des Spaces a Connexion Projective,
Hermann, Paris, (1937)
Cartan, E., 1945, "Systems Differentials Exterieurs et leurs
Applications Geometriques", Actualites sci. et industrielles
, p .944.
Cartan, E., Lecons sur les invariants integrauxs, Hermann,
Paris (1958).
Chern, S. S., 1944, "A Simple intrinsic proof of the Gauss
-Bonnet formula for Closed Riemannian Manifolds", Annals
of Math. 45, p. 747- 752.
Chern, S.S. ,1988, "Historical Remarks on Gauss-Bonnet",
MSRI 04808-88, Berkeley, CA.
Croquette, V. and Williams, H., 1989, "Nonlinear of oscillatory
instability on finite convective rolls", in Advances in
Fluid Turbulence, edited by G. Doolen, R, Ecke, D. Holm and
V. Steinberg, (North Holland, Amsterdam ) p. 300.
von Dantzig, D., 1934, "Electromagnetism Independent of metrical
geometry", Proc. Kon. Ned. Akad. v. Wet. 37, pp. 521-531,
644-652, 825-836 .
Flanders, H., 1963, Differential Forms, (Academic Press,
New York (1963), p. 92 .
Forsyth, A. R. (1959), Theory of Differential Equations (Dover,
N.Y.) p.96
Frisch, U., 1991, "From global (Kolmogorov 1941) scaling
to local (multifractal) scaling in fully developed turbulence"
to appear in the Proc. Roy. Soc. A
Gellert, W., 1977, et.al. Editors, The VNR Concise Encyclopedia
of Mathematics (Van Nostrand, New York ), p.686.
Greub, W., Halperin, S. and Vanstone, R., 1973, Connections,
Curvature and Cohomology, (Academic Press, New York).
Hermann, R., 1968, Differential Geometry and the Calculus of
Variations, (Academic Press, New York ), p. 254.
Hocking, J. G.,1961, Topology , (Addison Wesley, N.Y.),
p.2.
Kida, S.,Yamada, M., and Ohkitani, K., 1989, " A route to
chaos and turbulence" in Advances in Fluid Turbulence,
edited by G. Doolen, R, Ecke, D. Holm and V. Steinberg, (North
Holland, Amsterdam ) p. 116.
R. M. Kiehn and J. F. Pierce, (1969) "An Intrinsic Transport Theorem"
, Phys Fluids 12 1971
Kiehn, R. M., (1974), "Modifications of
Hamilton's Principle
to include Dissipation", J. Math Phys
R. M. Kiehn, (1975), "Conformal Invariance and Hamilton Jacobi theory for
dissipative systems"
J. Math Phys. 16, 1032
Kiehn, R. M., 1975, "Submersive equivalence classes for metric
fields", Lett. al Nuovo Cimento 14, p. 308.
Kiehn, R. M., (1975a), "A Geometric model for supersymmetry",
Lett. al Nuovo Cimento 12, p. 300.
Kiehn, R. M. , (1975b), "Intrinsic
hydrodynamics with applications
to space-time fluids", Int. J. of Eng. Sci. 13, p.
941.
Kiehn, R. M., (1976), "Retrodictive
Determinism", Int.
J. of Eng. Sci. 14, p. 749
V. E. Sanders and R. M. Kiehn, (1977), "Dual Polarized Ring Lasers",
IEEE J Quant Elec QE-13 739
R. M. Kiehn, (1977b) "Periods on manifolds,
Quantization, and Gauge",J. Math Phys.18, 614
A. K. Schultz, R. M. Kiehn, E. J. Post and J. B. Roberds,(1979),
" Lifting of the Four-fold EM Degeneracy and PT Symmetry" Physics
Letters, 74A 384
Kiehn, R. M., (1986), "Falaco
Solitons";, The recognition of Falaco solitons
was made in 1986 while in the swimming pool of a life long friend in Rio de
Janeiro.
The concepts were first presented as a talk at the winter (1987) meeting of
Dynamics Days in Austin,
and later at an APS meeting. Also see Kiehn 1991c and Kiehn 1992a.
Nov 1987. "Why are these disks dark?" with Sterling et.al. Phys Fluids 30 11
Kiehn (1988). APS meeting in Baltimore: with C. Daggs "Topological Torsion and
the ABC flow"
Mar (1989). APS meeting at Houston.
" Talk with abstract:"Topological Torsion, Frenet Torsion, and Helicity
Density"
Kiehn (1989) Invited panelist Unanswered questions in Fluid Mechanics
SAF meeting of the ASME.
"Irreversible Topological Evolution in Fluid Mechanics" ASME
89-WA/FE-5 1989.
Kiehn, R. M., (1990a) "Topological Torsion,
Pfaff Dimension
and Coherent Structures";, in: H. K. Moffatt and T. S. Tsinober
eds, Topological Fluid Mechanics, (Cambridge University
Press), 449-458 .
Kiehn, R. M., (1990b), "Irreversible Topological Evolution
in Fluid Mechanics" in Some Unanswered Questions in Fluid
Mechanics ASME- Vol. 89-WA/FE-5, Trefethen, L. M. and Panton,
R. L. Eds.
Kiehn, R.M., Kiehn, G. P., and Roberds, R. B., (1991)
Kiehn R. M., (1991d), "Are there three kinds
of superconductivity", Int. J. of Mod. Phys. 10,1779
Klein, F., 1955,Geometry from an elementary viewpoint, Dover.
Klein, J., 1962, Ann. Inst. AIFUB Fourier, Grenoble 12, p. 1 .
Kolmogorov, A. V. ,1941, Dolkl. Akad. Nauk SSSR, 31, p. 99 .
Lamb, H., 1937, Hydrodynamics, (Cambridge University Press)
p. 617-619.
Landau, L. and Lifshitz, M, (1959) , Fluid Mechanics, (Pergamon
Press, London ) p.106.
Lipschutz, S.1965, General Topology, (Schaum, New York)
p.88.
Lovelock, D. and Rund, H., 1989, Tensors, Differential Forms
and Variational Principles, (Dover, New York).
Meserve, B. E., 1983, Projective Geometry, (Dover, New
York).
Nash, C. and Sen, S., 1989, Topology and Geometry for Physicists,
(Academic Press, San Diego).
Schouten, J. A. and Van der Kulk, W.,1949, Pfaff's Problem
and its Generalizations, (Oxford Clarendon Press)
Schultz, A., Kiehn, R. M., Post, E. J., and Roberds, R. B., 1979,
"Lifting of the four fold EM degeneracy and PT asymmetry",
Phys Lett 74A, p.384.
Schuster, H. G.,1984, Deterministic Chaos, Physics Verlag
(1984)
Slebodzinsky, W., 1970, Exterior Forms and their Applications,
(PWN Warsaw).
Stewart, I., 1988, The Problems of Mathematics, (Oxford,
NY) p 177.
Zimin, V., 1991, "Hierarchical Models of Turbulence"
in: Non-linear Dynamics of Structures, edited by R.Z. Sagdeev,
U. Frisch, F. Hussain, S. S. Moiseev and N. S. Erokhin, (World
Scientific Press, Singapore ) p.273-288.
and Time-reversal symmetry Breaking, Singular Solutions and Fresnel
Surfaces";, Phys Rev A, 43 , p. 5665
Kiehn, R. M. , (1991a), "Continuous
Topological Evolution"
This article was first written in 1991, and presented at an APS meeting. Pieces
were used in some of the
articles listed below. An updated version has been submittted for publication.
Kiehn, R. M.,(1991b) "Topological Parity and the turbulent
state of a Navier Stokes Fluid", This article was presented as a poster at
Dynamics Days. A
complete version has been submitted to Fluid DynamicsResearch
Kiehn, R. M., (1991c), "Compact Dissipative
Flow Structures
with Topological Coherence Embedded in Eulerian Environments",
in: Non-linear Dynamics of Structures, edited by R.Z. Sagdeev,
U. Frisch, F. Hussain, S. S. Moiseev and N. S. Erokhin, (World
Scientific Press, Singapore ) p.139-164.
Kiehn, R. M.,(1992a) "Topological Defects,
Coherent Structures
and Turbulence in Terms of Cartan's Theory of Differential Topology"
in "Developments in Theoretical and Applied Mathematics"
Proceedings of the SECTAM XVI conference, B. N. Antar, R. Engels,
A.A. Prinaris and T. H. Moulden, Editors, The University of Tennessee
Space Institute, Tullahoma, TN 37388 USA.
Kiehn, R. M., (1992b) "Instability Patterns,
Wakes and Topological
Limit Sets"; Poitier IUTAM conference 1992. .
Kiehn, R. M., (1992c0
"Hydrodynamic Wakes and Minimal Surfaces
with Fractal Boundaries"; Barcelona ERCOFTAC meeting.
Kiehn, R. M., (1994) "Topology and
Turbulence"; 1994 APS abstract. Submitted.