Conformal invariance in three-dimensional rotating turbulence

We examine three--dimensional turbulent flows in the presence of solid-body rotation and helical forcing in the framework of stochastic Schramm-L\"owner evolution curves (SLE). The data stems from a run on a grid of $1536^3$ points, with Reynolds and Rossby numbers of respectively 5100 and 0.06. We average the parallel component of the vorticity in the direction parallel to that of rotation, and examine the resulting $_\textrm{z}$ field for scaling properties of its zero-value contours. We find for the first time for three-dimensional fluid turbulence evidence of nodal curves being conformal invariant, belonging to a SLE class with associated Brownian diffusivity $\kappa=3.6\pm 0.1$. SLE behavior is related to the self-similarity of the direct cascade of energy to small scales in this flow, and to the partial bi-dimensionalization of the flow because of rotation. We recover the value of $\kappa$ with a heuristic argument and show that this value is consistent with several non-trivial SLE predictions.Comment: 4 pages, 3 figures, submitted to PR

A comparison of spectral element and finite difference methods using statically refined nonconforming grids for the MHD island coalescence instability problem

A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)] is applied to simulate the problem of MHD island coalescence instability (MICI) in two dimensions. MICI is a fundamental MHD process that can produce sharp current layers and subsequent reconnection and heating in a high-Lundquist number plasma such as the solar corona [Ng and Bhattacharjee, Phys. Plasmas, 5, 4028 (1998)]. Due to the formation of thin current layers, it is highly desirable to use adaptively or statically refined grids to resolve them, and to maintain accuracy at the same time. The output of the spectral-element static adaptive refinement simulations are compared with simulations using a finite difference method on the same refinement grids, and both methods are compared to pseudo-spectral simulations with uniform grids as baselines. It is shown that with the statically refined grids roughly scaling linearly with effective resolution, spectral element runs can maintain accuracy significantly higher than that of the finite difference runs, in some cases achieving close to full spectral accuracy.Comment: 19 pages, 17 figures, submitted to Astrophys. J. Supp

Research on processes for utilization of lunar resources quarterly report, 16 jul. - 15 oct. 1964

Lunar resource utilization - silicate reduction unit and carbon monoxide reduction reacto

Ignition system for space shuttle auxiliary propulsion system Quarterly technical progress narrative, 29 Jun. - 27 Sep. 1970

Design of spark and plasma pulse igniters for space shuttle propulsion syste

Surgery and the Spectrum of the Dirac Operator

We show that for generic Riemannian metrics on a simply-connected closed spin manifold of dimension at least 5 the dimension of the space of harmonic spinors is no larger than it must be by the index theorem. The same result holds for periodic fundamental groups of odd order. The proof is based on a surgery theorem for the Dirac spectrum which says that if one performs surgery of codimension at least 3 on a closed Riemannian spin manifold, then the Dirac spectrum changes arbitrarily little provided the metric on the manifold after surgery is chosen properly.Comment: 23 pages, 4 figures, to appear in J. Reine Angew. Mat

Space - Single Precision Cowell Trajectory Program

Single Precision Cowell Trajectory program - digital computer program for trajectory computatio

SFPRO - Single Precision Cowell Trajectory Processor

Digital computer program for IBM 7094 computer to generate spacecraft tracking station calculation

Beyond fingerprinting: Choosing predictive connectomes over reliable connectomes

Recent years have seen a surge of research on variability in functional brain connectivity within and between individuals, with encouraging progress toward understanding the consequences of this variability for cognition and behavior. At the same time, well-founded concerns over rigor and reproducibility in psychology and neuroscience have led many to question whether functional connectivity is sufficiently reliable, and call for methods to improve its reliability. The thesis of this opinion piece is that when studying variability in functional connectivity—both across individuals and within individuals over time—we should use behavior prediction as our benchmark rather than optimize reliability for its own sake. We discuss theoretical and empirical evidence to compel this perspective, both when the goal is to study stable, trait-level differences between people, as well as when the goal is to study state-related changes within individuals. We hope that this piece will be useful to the neuroimaging community as we continue efforts to characterize inter- and intra-subject variability in brain function and build predictive models with an eye toward eventual real-world applications