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  • 1
    Electronic Resource
    Electronic Resource
    Direct simulation of antiparallel vortex stretching and helicity
    Amsterdam : Elsevier
    Nuclear Physics B (Proceedings Supplements) 2 (1987), S. 605 
    Details
    ISSN: 0920-5632
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1016/0920-5632(87)90074-0
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  • 2
    Electronic Resource
    Electronic Resource
    Development of singular solutions to the axisymmetric Euler equations (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 1472-1491 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A variety of initially smooth axisymmetric flows with swirl are simulated with a variable mesh, finite-difference code with particular attention paid to the production of large (divergent) vorticity. Away from the symmetry axis, the evolution is entirely consistent with expectations based on the isomorphism with two-dimensional convection. Vortex sheets form on the leading face of "plumes'' and their trailing edges roll up. When a "plume'' begins to fission, a cusp develops at the cleavage point via a Rayleigh–Taylor-like instability and the maximum (three-dimensional) vorticity diverges, approximately, as inverse time squared. For technical reasons, the Boussinesq approximation was employed for this part of the simulation which observed, overall, a 106 increase in vorticity. The diverging strain was generated progressively more locally, justifying the approximation. Analytic estimates are provided which significantly constrain the singular solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858422
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  • 3
    Electronic Resource
    Electronic Resource
    Effect of an externally applied electric field on excitation propagation in the cardiac muscle (1994)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 4 (1994), S. 547-555 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Classical theory of potential distribution in cardiac muscle (cable theory) postulates that all effects of electric field (internally or externally applied) should decay exponentially with a space constant of the order of the tissue space constant (∼1 mm). Classical theory does not take into account the cellular structure of the heart. Here, we formulate a mathematical model of excitation propagation taking into account cellular gap junctions. Investigation of the model has shown that the classical description is correct on the macroscopic scale only. At microscopic scale, electric field is modulated with a spatial period equal to the cell size (Plonsey and Barr), with the zero average. A very important new feature found here is that this effect of electric field does not decay at arbitrary big distances from the electrode. It opens the new way to control the excitation propagation in the cardiac muscle. In particular, we show that electric field can modify the velocity of propagation of an impulse in cardiac tissue at arbitrary big distances from electrode. In 2-dimensions, it can make rotating waves drift. To test these predictions, experiments with cardiac preparations are proposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166046
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  • 4
    Electronic Resource
    Electronic Resource
    Spiral wave drift induced by stimulating wave trains (2001)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 11 (2001), S. 487-494 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We investigate the drift of a spiral wave core in a homogeneous excitable medium under the influence of a periodic stimulation by wave trains close to the core. Two important results were found. First, as opposed to existing theories of spiral wave drift, we observe drift induced by wave trains with periods larger than the period of the freely rotating spiral wave. Second, when investigating the drift of meandering spirals we found that the property of meandering of spirals is not robust against periodic stimulations. Simple phenomenological arguments are provided to explain these observations. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1395624
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  • 5
    Electronic Resource
    Electronic Resource
    Models of defibrillation of cardiac tissue (1998)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 8 (1998), S. 188-203 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Heterogeneities, such as gap junctions, defects in periodical cellular lattices, intercellular clefts and fiber curvature allow one to understand the effect of an electric field in cardiac tissue. They induce membrane potential variations even in the bulk of the myocardium, with a characteristic sawtooth shape. The sawtooth potential, induced by heterogeneities at large scales (tissue strands) can be more easily observed, and lead to stronger effects than the one induced at the cellular level. In the generic model of propagation in cardiac tissue (FitzHugh), 4 mechanisms of defibrillation were found, two mechanisms based on excitation (EA,EM), and two—on de-excitation (DA,DM). The lowest electric field is required by an EM mechanism. In the Beeler–Reuter ionic model, mechanism DM is impossible. We critically review the experimental basis of the theory and propose new experiments. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166297
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  • 6
    Electronic Resource
    Electronic Resource
    Anomalous diffusion of tracer in convection rolls (1989)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 462-469 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The dispersion of a passive tracer in a two-dimensional, spatially periodic stationary flow, such as convection rolls, is studied in the large Peclet number limit. In the case where injection, at time t=0, is localized in one roll, two regimes exist. First, there is an anomalous diffusion regime in which the number of invaded rolls grows like t1/3. This regime is due to the presence of separatrices between rolls that induce trapping of tracer within each roll. At a later time, when t(very-much-greater-than)Td (the diffusion time within a roll), the usual diffusion regime is recovered, yet with an effective diffusive coefficient κeff that is greater than the molecular diffusivity κ by a factor proportional to the square root of the Peclet number.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857415
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  • 7
    Electronic Resource
    Electronic Resource
    Small-scale properties of scalar and velocity differences in three-dimensional turbulence (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 3974-3984 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Turbulent flows are known to concentrate strong vorticity in vortex tubes, giving rise to large velocity jumps across the tubes. When a passive scalar is advected by the flow, very steep scalar fronts separate well-mixed regions, and result in large scalar differences. The properties of these large jumps are investigated by studying the probability distribution functions of velocity, scalar differences as a function of the separation between the points, of the Reynolds and of the Prandtl number. Over the range of parameters covered by the direct numerical simulations reported here (20≤Rλ≤90 and 1/32≤Pr≤1), it is found that the widths of the velocity (respectively, the scalar) jumps scale like the Kolmogorov length (respectively, like the Batchelor length). For both the scalar and the velocity, the large differences over small distance become rarer as the Reynolds number increases. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868387
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  • 8
    Electronic Resource
    Electronic Resource
    A numerical study of the mixing of a passive scalar in three dimensions in the presence of a mean gradient (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 2118-2132 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The mixing of a passive scalar in the presence of a mean gradient is studied in three dimensions by direct numerical simulations. The driving velocity field is either a solution of the three-dimensional (3-D) Navier–Stokes equations, at a microscale Reynolds number in between 20 and 70, and with a Prandtl number varying between 1/8 and 1, or a solution of the Euler equation restricted to a shell of wave numbers, which formally corresponds to an infinite Prandtl number. The probability distribution function (PDF) of the scalar gradients parallel and perpendicular to the direction of the mean gradient are studied. The gradients parallel to the mean gradient have a skewness of order 1 in the range of Péclet number considered. The PDFs are sharply peaked and their maxima correspond to a perfect mixing of the scalar. The PDF of the scalar gradient perpendicular to the mean gradient are reasonably well fit by stretched exponentials. Similar properties are observed for the restricted Euler model. In physical space, the scalar is well mixed in large domains, separated by narrow regions, where very large gradients concentrate. These "cliffs'' are found to sit in regions where the flow is hyperbolic, whereas the scalar gradients are much weaker where the flow is elliptic. The present results are generally in agreement with the conclusions reached in a comparable study in two dimensions by Holzer and Siggia (to appear in Phys. Fluids). The stretching acting on the scalar is studied by computing various correlations between scalar gradient and velocity derivatives, as well as the correlations between vorticity and scalar gradient.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868216
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  • 9
    Electronic Resource
    Electronic Resource
    Collapsing solutions to the 3-D Euler equations (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 220-241 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A three-dimensional adaptive mesh code is used to search for singularities in the incompressible Euler equations. For the initial conditions examined, the maximum vorticity eventually grows only exponentially. The small scales are quasi-two-dimensional and the vorticity has a pronounced tendency to develop sharp jumps in magnitude. The vorticity is very nearly parallel to the eigenvector of the rate-of-strain matrix whose eigenvalue is the smallest in magnitude. This eigenvalue is positive and much smaller than the others.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857824
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  • 10
    Electronic Resource
    Electronic Resource
    Vortex dynamics and the existence of solutions to the Navier–Stokes equations (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 1606-1626 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The Biot–Savart model for a vortex filament predicts a finite time singularity in which the maximum velocity diverges as (t*−t)−1/2 for the time t tending to t*. The filament pairs with itself, yet remains locally smooth even though the characteristic length scales as (t*−t)1/2. A multiscale perturbative treatment of the Euler equations is developed for solutions that are locally a two-dimensional vortex dipole centered on a slowly varying three-dimensional space curve. For short periods of time the Euler and Biot–Savart solutions agree. Provided this correspondence persists, a sufficiently small viscosity ν will not control the divergence in the maximum velocity until it is of order exp(cst/ν), where cst is a constant of order the filament circulation. Singularities in the Navier–Stokes equations cannot be easily dismissed. The most questionable step in the arguments presented occurs for ν=0, namely whether the Euler vortex dipole solutions break down when they self-stretch.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866226
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