Predictions for the First Parker Solar Probe Encounter

We examine Alfv\'en Wave Solar atmosphere Model (AWSoM) predictions of the first Parker Solar Probe (PSP) encounter. We focus on the 12-day closest approach centered on the 1st perihelion. AWSoM (van der Holst et al., 2014) allows us to interpret the PSP data in the context of coronal heating via Alfv\'en wave turbulence. The coronal heating and acceleration is addressed via outward-propagating low-frequency Alfv\'en waves that are partially reflected by Alfv\'en speed gradients. The nonlinear interaction of these counter-propagating waves results in a turbulent energy cascade. To apportion the wave dissipation to the electron and anisotropic proton temperatures, we employ the results of the theories of linear wave damping and nonlinear stochastic heating as described by Chandran et al. (2011). We find that during the first encounter, PSP was in close proximity to the heliospheric current sheet (HCS) and in the slow wind. PSP crossed the HCS two times, namely at 2018/11/03 UT 01:02 and 2018/11/08 UT 19:09 with perihelion occuring on the south of side of the HCS. We predict the plasma state along the PSP trajectory, which shows a dominant proton parallel temperature causing the plasma to be firehose unstable.Comment: 16 pages, 5 figures; accepted for publication in the Astrophysical Journal Letter

A Bose-Einstein Approach to the Random Partitioning of an Integer

Consider N equally-spaced points on a circle of circumference N. Choose at random n points out of $N$ on this circle and append clockwise an arc of integral length k to each such point. The resulting random set is made of a random number of connected components. Questions such as the evaluation of the probability of random covering and parking configurations, number and length of the gaps are addressed. They are the discrete versions of similar problems raised in the continuum. For each value of k, asymptotic results are presented when n,N both go to infinity according to two different regimes. This model may equivalently be viewed as a random partitioning problem of N items into n recipients. A grand-canonical balls in boxes approach is also supplied, giving some insight into the multiplicities of the box filling amounts or spacings. The latter model is a k-nearest neighbor random graph with N vertices and kn edges. We shall also briefly consider the covering problem in the context of a random graph model with N vertices and n (out-degree 1) edges whose endpoints are no more bound to be neighbors

Semilinear mixed problems on Hilbert complexes and their numerical approximation

Arnold, Falk, and Winther recently showed [Bull. Amer. Math. Soc. 47 (2010), 281-354] that linear, mixed variational problems, and their numerical approximation by mixed finite element methods, can be studied using the powerful, abstract language of Hilbert complexes. In another recent article [arXiv:1005.4455], we extended the Arnold-Falk-Winther framework by analyzing variational crimes (a la Strang) on Hilbert complexes. In particular, this gave a treatment of finite element exterior calculus on manifolds, generalizing techniques from surface finite element methods and recovering earlier a priori estimates for the Laplace-Beltrami operator on 2- and 3-surfaces, due to Dziuk [Lecture Notes in Math., vol. 1357 (1988), 142-155] and later Demlow [SIAM J. Numer. Anal., 47 (2009), 805-827], as special cases. In the present article, we extend the Hilbert complex framework in a second distinct direction: to the study of semilinear mixed problems. We do this, first, by introducing an operator-theoretic reformulation of the linear mixed problem, so that the semilinear problem can be expressed as an abstract Hammerstein equation. This allows us to obtain, for semilinear problems, a priori solution estimates and error estimates that reduce to the Arnold-Falk-Winther results in the linear case. We also consider the impact of variational crimes, extending the results of our previous article to these semilinear problems. As an immediate application, this new framework allows for mixed finite element methods to be applied to semilinear problems on surfaces.Comment: 22 pages; v2: major revision, particularly sharpening of error estimates in Section

Far-from-constant mean curvature solutions of Einstein's constraint equations with positive Yamabe metrics

In this article we develop some new existence results for the Einstein constraint equations using the Lichnerowicz-York conformal rescaling method. The mean extrinsic curvature is taken to be an arbitrary smooth function without restrictions on the size of its spatial derivatives, so that it can be arbitrarily far from constant. The rescaled background metric belongs to the positive Yamabe class, and the freely specifiable part of the data given by the traceless-transverse part of the rescaled extrinsic curvature and the matter fields are taken to be sufficiently small, with the matter energy density not identically zero. Using topological fixed-point arguments and global barrier constructions, we then establish existence of solutions to the constraints. Two recent advances in the analysis of the Einstein constraint equations make this result possible: A new type of topological fixed-point argument without smallness conditions on spatial derivatives of the mean extrinsic curvature, and a new construction of global super-solutions for the Hamiltonian constraint that is similarly free of such conditions on the mean extrinsic curvature. For clarity, we present our results only for strong solutions on closed manifolds. However, our results also hold for weak solutions and for other cases such as compact manifolds with boundary; these generalizations will appear elsewhere. The existence results presented here for the Einstein constraints are apparently the first such results that do not require smallness conditions on spatial derivatives of the mean extrinsic curvature.Comment: 4 pages, no figures, accepted for publication in Physical Review Letters. (Abstract shortenned and other minor changes reflecting v4 version of arXiv:0712.0798

3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the Finite Element Method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies available upon reques

Impaired nutrient signaling and body weight control in a Na⁺ neutral amino acid cotransporter (Slc6a19)-deficient mouse

Amino acid uptake in the intestine and kidney is mediated by a variety of amino acid transporters. To understand the role of epithelial neutral amino acid uptake in whole body homeostasis, we analyzed mice lacking the apical broad-spectrum neutral (0) amino acid transporter BᴼAT1 (Slc6a19). A general neutral aminoaciduria was observed similar to human Hartnup disorder which is caused by mutations in SLC6A19. Na⁺ -dependent uptake of neutral amino acids into the intestine and renal brush-border membrane vesicles was abolished. No compensatory increase of peptide transport or other neutral amino acid transporters was detected. Mice lacking BᴼAT1 showed a reduced body weight. When adapted to a standard 20% protein diet, BᴼAT1-deficient mice lost body weight rapidly on diets containing 6 or 40% protein. Secretion of insulin in response to food ingestion after fasting was blunted. In the intestine, amino acid signaling to the mammalian target of rapamycin (mTOR) pathway was reduced, whereas the GCN2/ATF4 stress response pathway was activated, indicating amino acid deprivation in epithelial cells. The results demonstrate that epithelial amino acid uptake is essential for optimal growth and body weight regulation.This work was supported by National Health and Medical Research Council Grant 525415, Australian Research Council Grant DP0877897, University of Sydney Bridging Grant RIMS2009-02579), and by an anonymous foundatio

A Spinning Anti-de Sitter Wormhole

We construct a 2+1 dimensional spacetime of constant curvature whose spatial topology is that of a torus with one asymptotic region attached. It is also a black hole whose event horizon spins with respect to infinity. An observer entering the hole necessarily ends up at a "singularity"; there are no inner horizons. In the construction we take the quotient of 2+1 dimensional anti-de Sitter space by a discrete group Gamma. A key part of the analysis proceeds by studying the action of Gamma on the boundary of the spacetime.Comment: Latex, 28 pages, 7 postscript figures included in text, a Latex file without figures can be found at http://vanosf.physto.se/~stefan/spinning.html Replaced with journal version, minor change