Realistic Simulation of Local Solar Supergranulation

I represent results three-dimensional numerical simulation of solar surface convection on scales local supergranulation with realistic model physics. I study thermal structure of convective motions in photosphere, the range of convection cell sizes and the penetration depths of convection. A portion of the solar photosphere extending 100 x 100 Mm horizontally and from 0 Mm down to 20 Mm below the visible surface is considered. I take equation of state and opacities of stellar matter and distribution with radius of all physical variables from Solar Standard Model. The equations of fully compressible radiation hydrodynamics with dynamical viscosity and gravity are solved. The high order conservative PPML difference scheme for the hydrodynamics, the method of characteristic for the radiative transfer and dynamical viscosity from subgrid scale modeling are applied. The simulations are conducted on a uniform horizontal grid of 1000 x 1000, with 168 nonuniformly spaced vertical grid points, on 256 processors with distributed memory multiprocessors on supercomputer MVS5000 in Computational Centre of Russian Academy of Sciences.Comment: 4 pages, 3 figures. To appear in AIP Conference Proceedings, "Exploring the Solar System and the Universe", Apr 8-12 2008, Bucharest, Romania, eds. Vasile Mioc, Cristiana Dumitrache & Nedelia A. Popesc

Realistic Magnetohydrodynamical Simulation of Solar Local Supergranulation

Three-dimensional numerical simulations of solar surface magnetoconvection using realistic model physics are conducted. The thermal structure of convective motions into the upper radiative layers of the photosphere, the main scales of convective cells and the penetration depths of convection are investigated. We take part of the solar photosphere with size of 60x60 Mm in horizontal direction and by depth 20 Mm from level of the visible solar surface. We use a realistic initial model of the Sun and apply equation of state and opacities of stellar matter. The equations of fully compressible radiation magnetohydrodynamics with dynamical viscosity and gravity are solved. We apply: 1) conservative TVD difference scheme for the magnetohydrodynamics, 2) the diffusion approximation for the radiative transfer, 3) dynamical viscosity from subgrid scale modeling. In simulation we take uniform two-dimesional grid in gorizontal plane and nonuniform grid in vertical direction with number of cells 600x600x204. We use 512 processors with distributed memory multiprocessors on supercomputer MVS-100k in the Joint Computational Centre of the Russian Academy of Sciences.Comment: 6 pages, 5 figures, submitted to the proceedings of the GONG 2008 / SOHO XXI conferenc

Interstellar Turbulence and Star Formation

We provide a brief overview of recent advances and outstanding issues in simulations of interstellar turbulence, including isothermal models for interior structure of molecular clouds and larger-scale multiphase models designed to simulate the formation of molecular clouds. We show how self-organization in highly compressible magnetized turbulence in the multiphase ISM can be exploited in simple numerical models to generate realistic initial conditions for star formation.Comment: 8 pages, 5 color figures; submitted to Proceedings of IAU Symposium 270 "Computational Star Formation" held in Barcelona, May 31 - June 4, 201

Simulating Supersonic Turbulence in Magnetized Molecular Clouds

We present results of large-scale three-dimensional simulations of weakly magnetized supersonic turbulence at grid resolutions up to 1024^3 cells. Our numerical experiments are carried out with the Piecewise Parabolic Method on a Local Stencil and assume an isothermal equation of state. The turbulence is driven by a large-scale isotropic solenoidal force in a periodic computational domain and fully develops in a few flow crossing times. We then evolve the flow for a number of flow crossing times and analyze various statistical properties of the saturated turbulent state. We show that the energy transfer rate in the inertial range of scales is surprisingly close to a constant, indicating that Kolmogorov's phenomenology for incompressible turbulence can be extended to magnetized supersonic flows. We also discuss numerical dissipation effects and convergence of different turbulence diagnostics as grid resolution refines from 256^3 to 1024^3 cells.Comment: 10 pages, 3 figures, to appear in the proceedings of the DOE/SciDAC 2009 conferenc

Piecewise Parabolic Method on a Local Stencil for Magnetized Supersonic Turbulence Simulation

Stable, accurate, divergence-free simulation of magnetized supersonic turbulence is a severe test of numerical MHD schemes and has been surprisingly difficult to achieve due to the range of flow conditions present. Here we present a new, higher order-accurate, low dissipation numerical method which requires no additional dissipation or local "fixes" for stable execution. We describe PPML, a local stencil variant of the popular PPM algorithm for solving the equations of compressible ideal magnetohydrodynamics. The principal difference between PPML and PPM is that cell interface states are evolved rather that reconstructed at every timestep, resulting in a compact stencil. Interface states are evolved using Riemann invariants containing all transverse derivative information. The conservation laws are updated in an unsplit fashion, making the scheme fully multidimensional. Divergence-free evolution of the magnetic field is maintained using the higher order-accurate constrained transport technique of Gardiner and Stone. The accuracy and stability of the scheme is documented against a bank of standard test problems drawn from the literature. The method is applied to numerical simulation of supersonic MHD turbulence, which is important for many problems in astrophysics, including star formation in dark molecular clouds. PPML accurately reproduces in three-dimensions a transition to turbulence in highly compressible isothermal gas in a molecular cloud model. The low dissipation and wide spectral bandwidth of this method make it an ideal candidate for direct turbulence simulations.Comment: 28 pages, 18 figure

The Two States of Star Forming Clouds

We examine the effects of self-gravity and magnetic fields on supersonic turbulence in isothermal molecular clouds with high resolution simulations and adaptive mesh refinement. These simulations use large root grids (512^3) to capture turbulence and four levels of refinement to capture high density, for an effective resolution of 8,196^3. Three Mach 9 simulations are performed, two super-Alfv\'enic and one trans-Alfv\'enic. We find that gravity splits the clouds into two populations, one low density turbulent state and one high density collapsing state. The low density state exhibits properties similar to non-self-gravitating in this regime, and we examine the effects of varied magnetic field strength on statistical properties: the density probability distribution function is approximately lognormal; velocity power spectral slopes decrease with field strength; alignment between velocity and magnetic field increases with field; the magnetic field probability distribution can be fit to a stretched exponential. The high density state is characterized by self-similar spheres; the density PDF is a power-law; collapse rate decreases with increasing mean field; density power spectra have positive slopes, P({\rho},k) \propto k; thermal-to-magnetic pressure ratios are unity for all simulations; dynamic-to-magnetic pressure ratios are larger than unity for all simulations; magnetic field distribution is a power-law. The high Alfv\'en Mach numbers in collapsing regions explain recent observations of magnetic influence decreasing with density. We also find that the high density state is found in filaments formed by converging flows, consistent with recent Herschel observations. Possible modifications to existing star formation theories are explored.Comment: 19 pages, 20 figure

Comparing Numerical Methods for Isothermal Magnetized Supersonic Turbulence

We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss convergence of various characteristics for the turbulence decay test and impacts of various components of numerical schemes on the accuracy of solutions. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the magnetic field using the constrained transport method, and using little to no explicit artificial viscosity. Codes which fall short in one or more of these areas are still useful, but they must compensate higher numerical dissipation with higher numerical resolution. This paper is the largest, most comprehensive MHD code comparison on an application-like test problem to date. We hope this work will help developers improve their numerical algorithms while helping users to make informed choices in picking optimal applications for their specific astrophysical problems.Comment: 17 pages, 5 color figures, revised version to appear in ApJ, 735, July 201

Low level of expression of C-terminally truncated human FUS causes extensive changes in the spinal cord transcriptome of asymptomatic transgenic mice

A number of mutations in a gene encoding RNA-binding protein FUS have been linked to the development of a familial form of amyotrophic lateral sclerosis known as FUS-ALS. C-terminal truncations of FUS by either nonsense or frameshift mutations lead to the development of FUS-ALS with a particularly early onset and fast progression. However, even in patients bearing these highly pathogenic mutations the function of motor neurons is not noticeably compromised for at least a couple of decades, suggesting that until cytoplasmic levels of FUS lacking its C-terminal nuclear localisation signal reaches a critical threshold, motor neurons are able to tolerate its permanent production.In order to identify how the nervous system responds to low levels of pathogenic variants of FUS we produced and characterised a mouse line, L-FUS[1-359], with a low neuronal expression level of a highly aggregation-prone and pathogenic form of C-terminally truncated FUS. In contrast to mice that express substantially higher level of the same FUS variant and develop severe early onset motor neuron pathology, L-FUS[1-359] mice do not develop any clinical or histopathological signs of motor neuron deficiency even at old age. Nevertheless, we detected substantial changes in the spinal cord transcriptome of these mice compared to their wild type littermates. We suggest that at least some of these changes reflect activation of cellular mechanisms compensating for the potentially damaging effect of pathogenic FUS production. Further studies of these mechanism might reveal effective targets for therapy of FUS-ALS and possibly, other forms of ALS