Biomedical subjects

D del-Castillo-Negrete

Publications and source records attributed to D del-Castillo-Negrete.

4 recordsLinked to original sources

PubMed2005

Nondiffusive transport in plasma turbulence: a fractional diffusion approach.

Numerical evidence of nondiffusive transport in three-dimensional, resistive pressure-gradient-driven plasma turbulence is presented. It is shown that the probability density function (pdf) of tracer particles' radial displacements is strongly non-Gaussian and exhibits algebraic decaying tails. To model these results we propose a macroscopic transport model for the pdf based on the use of fractional derivatives in space and time that incorporate in a unified way space-time nonlocality (non-Fickian transport), non-Gaussianity, and nondiffusive scaling. The fractional diffusion model reproduces the shape and space-time scaling of the non-Gaussian pdf of turbulent transport calculations. The model also reproduces the observed superdiffusive scaling.

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PubMed2003

Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach.

The use of reaction-diffusion models rests on the key assumption that the diffusive process is Gaussian. However, a growing number of studies have pointed out the presence of anomalous diffusion, and there is a need to understand reactive systems in the presence of this type of non-Gaussian diffusion. Here we study front dynamics in reaction-diffusion systems where anomalous diffusion is due to asymmetric Levy flights. Our approach consists of replacing the Laplacian diffusion operator by a fractional diffusion operator of order alpha, whose fundamental solutions are Levy alpha-stable distributions that exhibit power law decay, x(-(1+alpha)). Numerical simulations of the fractional Fisher-Kolmogorov equation and analytical arguments show that anomalous diffusion leads to the exponential acceleration of the front and a universal power law decay, x(-alpha), of the front's tail.

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PubMed2000

Chaotic scattering and self-organization in spheromak sustainment

Flux core spheromak sustainment by electrostatic helicity injection is studied in resistive MHD. The geometry has magnetized electrodes at the ends held at a potential difference V. For V>V(c) the central current column is kink unstable. The nonlinear state with V just above V(c) has a large volume of flux surfaces, with rotational transform provided by the helical kinking of the column. As V increases the kink becomes stronger, the tori are destroyed, and the field lines exhibit chaotic scattering. The distribution of field line lengths L, related to confinement and parallel current density, is studied. At larger V or larger Lundquist number S, a limit cycle appears.

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PubMed2000

Destabilization of the m = 1 diocotron mode in non-neutral plasmas

The theory for a Penning-Malmberg trap predicts m = 1 diocotron stability. However, experiments with hollow profiles show robust exponential growth. We propose a new mechanism of destabilization of this mode, involving parallel compression due to end curvature. The results are in good agreement with the experiments. The resulting modified drift-Poisson equations are analogous to the geophysical shallow water equations, and conservation of line integrated density corresponds to that of potential vorticity. This analogy predicts Rossby waves in non-neutral plasmas and an m = 1 instability in fluids.

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