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Title
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Summary
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Reference
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Dwnld
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[17]
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Complex singularities and the Lorenz
attractor.
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We suggest that the mathematical analysis of the Lorenz system
could be a problem in analytic function theory. A complete and
consistent formal development of singular solutions
of the Lorenz system is given.
Convergence is proved using a technique that is simpler, more
transparent and more powerful than that of Hille.
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DV and S. Şahutoğlu, submitted.
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pdf
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[16]
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Stable manifolds and the transition to turbulence in pipe flow
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A numerical method is devised for disturbing the laminar
motion in such a way that it hits a given traveling wave while
transitioning to turbulence. The connection of exact
solutions of the Navier-Stokes equation to experiment is
discussed.
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DV and P. Cvitanović, J. Fluid Mech., vol. 627
(2009), p. 215-233.
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pdf
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[15]
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Heteroclinic connections in plane Couette flow
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A numerical method for locating heteroclinic connections,
illustrations of the change in streak patterns along some
connections, and phase space portraits.
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J. Halcrow, J.F. Gibson, P. Cvitanović and DV,
J. Fluid Mech., vol. 611 (2009), p. 365-376.
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pdf
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[14]
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The critical layer in pipe flow at high Reynolds number
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Computations up to Re=75000. Details of
numerical method for locating traveling
waves and relative periodic orbits.
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DV, Phil. Trans. Roy. Soc., vol. 367 (2009), p. 561-576.
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pdf
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[13]
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The dynamics of transition to turbulence in plane Couette flow
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Possible role of lower branch solutions in transition to turbulence.
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[in]
Mathematics and computation: a contemporary view.
The Abel Symosium 2006. Springer-Verlag. Berlin. 2008.
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pdf
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[12]
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Recurrent motions within plane Couette turbulence.
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Relative periodic orbits that correspond to coherent motions
in the near-wall region of turbulent boundary layers.
Importance of spanwise drift. Outline of numerical method for
finding relative periodic or traveling wave or equilibrium
solutions of the Navier-Stokes equation.
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DV, J. Fluid Mech., 580 (2007), 339-358.
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pdf
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[11]
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Shuffling cards for blackjack, bridge, and other card games
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The number of shuffles to mix a deck depends upon the way the
cards are dealt (in bridge). Determining the total variation
distance is NP complete. Excellent estimates are computed and
partially justified in a variety of situations.
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Under revision
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pdf
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[10]
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Stable manifolds and homoclinic points near resonances in the
restricted three-body problem
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Proof of existence of homoclinic points near resonances
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DV, Celestial Mechanics and Dynamical Astronomy,
94 (2006), 213-235.
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pdf
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[9]
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Normal approximations for descents and inversions of permutations
of multisets
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In a long list of numbers, each instance where a larger number
precedes (immediately) a smaller number is an inversion
(descent). Central limit theorems for descents and
inversions. Application to DNA sequences.
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M. Conger and DV, J. Theor. Probab., 20 (2007), 309-325.
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pdf
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[8]
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Linear stability analysis of resonant periodic motions in the
restricted three-body problem
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Resonant periodic motions are alternately stable and unstable.
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DV, J. Dynamics and Differential Equations, 17 (2005),
271-292.
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pdf
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[7]
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Riffle shuffles of decks with repeated cards
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Descent polynomials for decks with repeated cards.
Combinatorics and algorithms for descent polynomials.
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M. Conger and DV, Annals of Probability, 34 (2006),
804-819.
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pdf
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[6]
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The fractal property of the Lorenz attractor
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Detailed computations of the fractal structure of the Lorenz
attractor. Numerical method for extended precision computation
of periodic orbits in which most of the arithmetic uses
double precision.
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DV, Physica D, 190 (2004), 115-128.
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pdf
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[5]
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Symbolic dynamics and periodic orbits of the Lorenz attractor
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Computation of orbits with special symbol sequences. Numerical
demonstration of the density of periodic orbits in a strange
attractor. First computation of the fractal structure of the Lorenz
attractor deduced by Lorenz in 1963. Appendix describes an
essential extension to the numerical method of [3].
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DV, Nonlinearity, 16 (2003), 1035-1056.
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pdf
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[4]
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How many timesteps for a cycle? Analysis of the Wisdom-Holman
algorithm?
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DV, BIT, 42 (2002), 194-205.
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[3]
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The Lindstedt-Poincaré technique as an algorithm for
computing periodic orbits
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Computation of periodic orbits reduces to a two point
boundary value problem (BVP). The method described has two
novelties: the nonlinear BVP is linearized before
it is discretized and the Lindstedt-Poincaré device
is used to find the period. The method is especially
accurate (as illustrated further in [5]).
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DV, SIAM Review, 43 (2001), 479-495.
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pdf
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[2]
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Global errors of numerical ODE solvers and Lyapunov's theory
of stability
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Linear upper bounds for global error of trajectories that
converge to stable structures such as fixed points, periodic
orbits, and invariant torii.
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DV, IMA J. Numer. Anal., 21 (2001), 387-406.
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pdf
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[1]
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Random Fibonacci sequences and the number 1.13198824...
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Asymptotic growth rate of random Fibonacci sequences.
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DV, Math. Comp., 69 (2000), 1131-1155.
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pdf
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[0]
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Condition numbers of random triangular matrices
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Random triangular matrices are exponentially
ill-conditioned. Asymptotically exact formulas
for the condition number are determined in
several situations.
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DV and L.N. Trefethen, SIAM J. Matrix. Anal. Appl., 19 (1998),
564-581.
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pdf
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