Long-time properties of MHD turbulence and the role of symmetries

We investigate long-time properties of three-dimensional MHD turbulence in the absence of forcing and examine in particular the role played by the quadratic invariants of the system and by the symmetries of the initial configurations. We observe that, when sufficient accuracy is used, initial conditions with a high degree of symmetries, as in the absence of helicity, do not travel through parameter space over time whereas by perturbing these solutions either explicitly or implicitly using for example single precision for long times, the flows depart from their original behavior and can become either strongly helical, or have a strong alignment between the velocity and the magnetic field. When the symmetries are broken, the flows evolve towards different end states, as predicted by statistical arguments for non-dissipative systems with the addition of an energy minimization principle, as already analyzed in \cite{stribling_90} for random initial conditions using a moderate number of Fourier modes. Furthermore, the alignment properties of these flows, between velocity, vorticity, magnetic potential, induction and current, correspond to the dominance of two main regimes, one helically dominated and one in quasi-equipartition of kinetic and magnetic energy. We also contrast the scaling of the ratio of magnetic energy to kinetic energy as a function of wavenumber to the ratio of eddy turn-over time to Alfv\'en time as a function of wavenumber. We find that the former ratio is constant with an approximate equipartition for scales smaller than the largest scale of the flow whereas the ratio of time scales increases with increasing wavenumber.Comment: 14 pages, 6 figure

A paradigmatic flow for small-scale magnetohydrodynamics: properties of the ideal case and the collision of current sheets

We propose two sets of initial conditions for magnetohydrodynamics (MHD) in which both the velocity and the magnetic fields have spatial symmetries that are preserved by the dynamical equations as the system evolves. When implemented numerically they allow for substantial savings in CPU time and memory storage requirements for a given resolved scale separation. Basic properties of these Taylor-Green flows generalized to MHD are given, and the ideal non-dissipative case is studied up to the equivalent of 2048^3 grid points for one of these flows. The temporal evolution of the logarithmic decrements, delta, of the energy spectrum remains exponential at the highest spatial resolution considered, for which an acceleration is observed briefly before the grid resolution is reached. Up to the end of the exponential decay of delta, the behavior is consistent with a regular flow with no appearance of a singularity. The subsequent short acceleration in the formation of small magnetic scales can be associated with a near collision of two current sheets driven together by magnetic pressure. It leads to strong gradients with a fast rotation of the direction of the magnetic field, a feature also observed in the solar wind.Comment: 8 pages, 4 figure

A New Family of Planets ? "Ocean Planets"

A new family of planets is considered which is between rochy terrestrial planets and gaseous giant ones: "Ocean-Planets". We present the possible formation, composition and internal models of these putative planets, including that of their ocean, as well as their possible Exobiology interest. These planets should be detectable by planet detection missions such as Eddington and Kepler, and possibly COROT (lauch scheduled in 2006). They would be ideal targets for spectroscopic missions such as Darwin/TPF.Comment: 15 pages, 3 figures submitted to Icarus notes (10 july 2003

The imprint of large-scale flows on turbulence

We investigate the locality of interactions in hydrodynamic turbulence using data from a direct numerical simulation on a grid of 1024^3 points; the flow is forced with the Taylor-Green vortex. An inertial range for the energy is obtained in which the flux is constant and the spectrum follows an approximate Kolmogorov law. Nonlinear triadic interactions are dominated by their non-local components, involving widely separated scales. The resulting nonlinear transfer itself is local at each scale but the step in the energy cascade is independent of that scale and directly related to the integral scale of the flow. Interactions with large scales represent 20% of the total energy flux. Possible explanations for the deviation from self-similar models, the link between these findings and intermittency, and their consequences for modeling of turbulent flows are briefly discussed

Ideal evolution of MHD turbulence when imposing Taylor-Green symmetries

We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the four-fold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a re-gridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of $6144^3$ points, and three different configurations on grids of $4096^3$ points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out, and the singularity time could be somewhere between $t=2.33$ and $t=2.70.$ More robust conclusions will require higher resolution runs and grid-point interpolation measurements of maximum current and vorticity.Comment: 18 pages, 13 figures, 2 tables; submitted to Physical Review

Should pancreaticoduodenectomy be performed in the elderly?

BACKGROUND/AIMS: Pancreaticoduodenectomy (PD) is indicated in benign or malignant pancreatic head diseases. It is a difficult operation with high morbidity especially in elderly patients. The aim of our study was to determine whether pancreaticoduodenectomy is associated with higher morbidity and mortality in patients ≥ 70 years old. METHODOLOGY: During 17 years, 173 patients were operated by Whipple intervention, whatever the disease. From a prospective database, patients were divided in 2 groups (Group A ≥ 70 years old, Group B <70). RESULTS: Postoperative mortality was not significantly higher in elderly (12% vs. 4.1%; p=0.06). However, re-intervention and morbidity were more important in univariate analysis (p=0.03 and p=0.002 respectively). In multivariate analysis, age ≥ 70 years old was not an independent prognostic factor of mortality (p=0.27) and re-intervention (p=0.07). Whereas age (p=0.04) and preoperative morbidity (p=0.02) were independent prognostic factors of morbidity. CONCLUSIONS: PD requires careful patient selection. However, age should not be a limiting factor