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J.D. Crawford and E. Knobloch. On degenerate Hopf bifurcation with broken O(2) symmetry, Nonlinearity 1 (1988) 617-652.

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J.D. Crawford, M. Golubitsky, and W. Langford. Modulated rotating waves in O(2) mode interaction, Dynamics and Stability of Systems 3 (1988) 159-175.

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J.D. Crawford, E. Knobloch, and H. Riecke. Competing parametric instabilities with circular symmetry, Phys. Lett. A 135 (1989) 20-24.

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J.D. Crawford, E. Knobloch, and H. Riecke. Mode interactions and symmetry, in Proc. of the International Conference on Singular Behavior and Nonlinear Dynamics, vol. 1, S. Pnevmatikos et al. (eds), Samos, Greece, World Scientific, 1989, pp. 277-297.

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J.D. Crawford, E. Knobloch, and H. Riecke. Period-doubling mode interactions with circular symmetry, Physica D 44 (1990) 340-396.

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H. Riecke, J.D. Crawford and E. Knobloch. Temporal modulation of a subcritical bifurcation to travelling waves, in New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena: The Geometry of Nonequilibrium, P. Coullet and P. Huerre (eds), NATO ASI Series B 237, Plenum Press, 1991, pp. 61-64.

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J.D. Crawford, M. Golubitsky, M.G.M. Gomes, E. Knobloch. and I. Stewart, Boundary conditions as symmetry constraints, in Singularity Theory and its Applications, Warwick 1989 Part 2, R.M. Roberts and I.N. Stewart (eds), Lecture Notes in Mathematics, Springer-Verlag, 1991, pp. 63-79.

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J.D. Crawford. Amplitude equations on unstable manifolds: singular behavior from neutral modes, in Modern Mathematical Methods in Transport Theory (Operator Theory: Advances and Applications, vol. 51), W. Greenberg and J. Polewczak (eds), Birkhauser Verlag, 1991, pp. 97-108.

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J.D. Crawford and E. Knobloch. Symmetry and symmetry-breaking bifurcations in fluid dynamics, Annu. Rev. Fluid Mech. 23 (1991) 341-387.

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J.D. Crawford. Surface waves in non-square containers with square symmetry, Phys. Rev. Lett. 67 (1991) 441-444.

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J.D. Crawford. Normal forms for driven surface waves: boundary conditions, symmetry, and genericity, Physica D 52 (1991) 429-457.

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J.D. Crawford. Introduction to bifurcation theory, Rev. Mod. Phys. 63 (1991) 991-1037.

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J.D. Crawford, J.P. Gollub, and David Lane. Hidden symmetries of parametrically forced waves, Nonlinearity 6 (1993) 119-164.

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J.D. Crawford. ${D_4\dot{+} T^2}$ Mode interactions and hidden rotational symmetry, Nonlinearity 7 (1994) 697-739.

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J.D. Crawford. Amplitude expansions for instabilities in populations of globally-coupled oscillators, J. Stat. Phys. 74 (1994) 1047-1084.

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J.D. Crawford. Universal trapping scaling on the unstable manifold of a collisionless electrostatic mode, Phys. Rev. Lett. 73 (1994) 656-659.

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J.D. Crawford. Amplitude equations for electrostatic waves: universal singular behavior in the limit of weak instability, Phys. Plasmas 2 (1995) 97-128.

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J.D. Crawford. Scaling and singularities in the entrainment of globally-coupled oscillators, Phys. Rev. Lett. 74 (1995) 4341-4344.

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J.D. Crawford. D₄-symmetric maps with hidden Euclidean symmetry, in Pattern Formation: Symmetry Methods and Applications, J. Chadam et al. (eds) Amer. Math. Soc., 1995, 93-124.

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J.D. Crawford and A. Jayaraman. Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling, Phys. Rev. Lett. 77 (1996) 3549-3552.

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J.D. Crawford and E. Knobloch. Amplitude equations for coupled electrostatic waves in the limit of weak instability, J. Plasma Physics 60 (1998) 159-180.

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J.D. Crawford and A. Jayaraman. Amplitude equations for unstable electrostatic waves: multiple species. J. Math. Phys., 39 (1998) 4546.

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J.D. Crawford and K.T.R. Davies. Phase dynamical models of globally coupled oscillators: singularities and scaling with arbitrary coupling. To appear in Physica D (1999), (preprint, patt-sol/9701006 at LANL archives).

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J.D. Crawford and A. Jayaraman. First principles justification of the ``Single Wave Model''. Phys. Plasmas. 6 (1999) 666-673.

WIDTH="79" HEIGHT="34" ALIGN="MIDDLE" BORDER="0" SRC="img7.gif" ALT="$(K-K_c)^{1\over2}$"> for the Kuramoto model but scales like K-K_c for more general couplings than assumed by Kuramoto. These results resolve analytically several long-standing issues in both theoretical and numerical studies of this important model.

John David wrote two influential review articles, one on basic bifurcation theory [15] and one with Edgar Knobloch on the use of equivariant bifurcation theory for studies of pattern formation in fluid dynamics [12]. A bibliography of John David's contributions to pattern formation and bifurcation theory is included below.

John David was a consummate scholar, devoted to deep understanding of important and challenging problems. His solutions to these problems were always innovative offering a fresh perspective. At home both in physics and mathematics John David was an invaluable colleague, generous with his time and ideas, and a rare knack for explaining scientific principles to friends, colleagues and students. His lectures were a model of clarity and he was a much sought-after speaker. At the workshop his delight in being back in the milieu he so loved was almost palpable. He will be greatly missed by all of us.

 

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