On the viability of the shearing box approximation for numerical studies of MHD turbulence in accretion disks

Most of our knowledge on the nonlinear development of the magneto-rotational instability (MRI) relies on the results of numerical simulations employing the shearing box (SB) approximation. A number of difficulties arising from this approach have recently been pointed out in the literature. We thoroughly examine the effects of the assumptions made and numerical techniques employed in SB simulations. This is done in order to clarify and gain better understanding of those difficulties as well as of a number of additional serious problems, raised here for the first time, and of their impact on the results. Analytical derivations and estimates as well as comparative analysis to methods used in the numerical study of turbulence are used. Numerical experiments are performed to support some of our claims and conjectures. The following problems, arising from the (virtually exclusive) use of the SB simulations as a tool for the understanding and quantification of the nonlinear MRI development in disks, are analyzed and discussed: (i) inconsistencies in the application of the SB approximation itself; (ii) the limited spatial scale of the SB; (iii) the lack of convergence of most ideal MHD simulations; (iv) side-effects of the SB symmetry and the non-trivial nature of the linear MRI; (v) physical artifacts arising on the too small box scale due to periodic boundary conditions. The computational and theoretical challenge posed by the MHD turbulence problem in accretion disks cannot be met by the SB approximation, as it has been used to date. A new strategy to confront this challenge is proposed, based on techniques widely used in numerical studies of turbulent flows - developing (e.g., with the help of local numerical studies) a sub-grid turbulence model and implementing it in global calculations.Comment: Accepted for publication in Astronomy and Astrophysic

Ferromagnetism and Superconductivity in the multi-orbital Hubbard Model: Hund's Rule Coupling versus Crystal-Field Splitting

The multi-orbital Hubbard model in one dimension is studied using the numerical diagonalization method. Due to the effect of the crystal-field splitting $\Delta$, the fully polarized ferromagnetism which is observed in the strong coupling regime becomes unstable against the partially polarized ferromagnetism when the Hund's rule coupling $J$ is smaller than a certain critical value of order of $\Delta$. In the vicinity of the partially polarized ferromagnetism, the orbital fluctuation develops due to the competition between the Hund's rule coupling and the crystal-field splitting. The superconducting phase with the Luttinger liquid parameter $K_{\rho}>1$ is observed for the singlet ground state in this region.Comment: 4 pages,5 figures,submitted to J.Phys.Soc.Jp

Element Stratification in the Middle-Aged Type Ia Supernova Remnant G344.7-0.1

Despite their importance, a detailed understanding of Type Ia supernovae (SNe Ia) remains elusive. X-ray measurements of the element distributions in supernova remnants (SNRs) offer important clues for understanding the explosion and nucleosynthesis mechanisms for SNe Ia. However, it is challenging to observe the entire ejecta mass in X-rays for young SNRs, because the central ejecta may not have been heated by the reverse shock yet. Here we present over 200 kilosecond Chandra observations of the Type Ia SNR G344.7-0.1, whose age is old enough for the reverse shock to have reached the SNR center, providing an opportunity to investigate the distribution of the entire ejecta mass. We reveal a clear stratification of heavy elements with a centrally peaked distribution of the Fe ejecta surrounded by intermediate-mass elements (IMEs: Si, S, Ar Ca) with an arc-like structure. The centroid energy of the Fe K emission is marginally lower in the central Fe-rich region than in the outer IME-rich regions, suggesting that the Fe ejecta were shock-heated more recently. These results are consistent with the prediction for standard SN Ia models, where the heavier elements are synthesized in the interior of an exploding white dwarf. We find, however, that the peak location of the Fe K emission is slightly offset to the west with respect to the geometric center of the SNR. This apparent asymmetry is likely due to the inhomogeneous density distribution of the ambient medium, consistent with our radio observations of the ambient molecular and neutral gas.Comment: 16 pages, 10 figures, Accepted for publication in Astrophysical Journa

Synthetic induction of immunogenic cell death by genetic stimulation of endoplasmic reticulum stress.

Cis-diamminedichloridoplatinum(II) (CDDP), commonly referred to as cisplatin, is a chemotherapeutic drug used for the treatment of a wide range of solid cancers. CDDP is a relatively poor inducer of immunogenic cell death (ICD), a cell death modality that converts dying cells into a tumor vaccine, stimulating an immune response against residual cancer cells that permits long-lasting immunity and a corresponding reduction in tumor growth. The incapacity of CDDP to trigger ICD is at least partially due to its failure to stimulate the premortem endoplasmic reticulum (ER)-stress response required for the externalization of the "eat-me" signal calreticulin (CRT) on the surface of dying cancer cells. Here, we developed a murine cancer cell line genetically modified to express the ER resident protein reticulon-1c (Rtn-1c) by virtue of tetracycline induction and showed that enforced Rtn-1c expression combined with CDDP treatment promoted CRT externalization to the surface of cancer cells. In contrast to single agent treatments, the tetracycline-mediated Rtn-1c induction combined with CDDP chemotherapy stimulated ICD as measured by the capacity of dying tumor cells, inoculated into syngenic immunocompetent mice, to mount an immune response to tumor re-challenge 1 week later. More importantly, established tumors, forced to constitutively express Rtn-1c in vivo by continuous treatment with tetracycline, became responsive to CDDP and exhibited a corresponding reduction in the rate of tumor growth. The combined therapeutic effects of Rtn-1c induction with CDDP treatment was only detected in the context of an intact immune system and not in nu/nu mice lacking thymus-dependent T lymphocytes. Altogether, these results indicate that the artificial or "synthetic" induction of immunogenic cell death by genetic manipulation of the ER-stress response can improve the efficacy of chemotherapy with CDDP by stimulating anticancer immunity

Synthesis of Novel Phosphorus-Substituted Stable Isoindoles by a Three-Component Coupling Reaction of ortho-Phthalaldehyde, 9,10-Dihydro-9-oxa-10-phosphaphenanthrene 10-Oxide, and Primary Amines

A three-component coupling reaction of ortho-phthalaldehyde, 9,10-dihydro-9-oxa-10-phosphaphenanthrene 10-oxide, and various primary amines readily afforded novel phosphorus-substituted stable isoindoles in good to excellent yields. The importance of the reversible ring-opening of 9,10-dihydro-9-oxa-10-phosphaphenanthrene 10-oxide by methanolysis in the three-component coupling reaction became apparent

Kinetics of active surface-mediated diffusion in spherically symmetric domains

We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. We generalize the results of [J. Stat. Phys. {\bf 142}, 657 (2011)] and consider a biased diffusion in a general annulus with an arbitrary number of regularly spaced targets on a partially reflecting surface. The presented approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which provide more tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface.Comment: Published online in J. Stat. Phy

On the presence of mid-gap states in CaV4O9

Using exact diagonalizations of finite clusters with up to 32 sites, we study the $J_1-J_2$ model on the 1/5 depleted square lattice. Spin-spin correlation functions are consistent with plaquette order in the spin gap phase which exists for intermediate values of $J_2/J_1$. Besides, we show that singlet states will be present in the singlet-triplet gap if $J_2/J_1$ is not too small ($J_2/J_1 \gtrsim 0.47$). We argue that this property should play a central role in determining the exchange integrals in ${\rm CaV}_4{\rm O}_9$Comment: 4 pages, 5 postscript figure

Orbital Order Effect of Two-Dimensional Spin Gap System for CaV4O9

Effects of possible orbital order in magnetic properties of two-dimensional spin gap system for CaV$_4$O$_9$ are investigated theoretically. After analyzing experimental data, we show that single orbital models assumed in the literature are insufficient to reproduce the data. To understand the origin of the discrepancy, we assume that in $d^1$ state of V, $d_{xz}$ and $d_{yz}$ orbitals have substantial contributions in the lowest-energy atomic level which leads to a double-degeneracy. We study possible configurations of the orbital order. By exact diagonalization and perturbation expansion, we calculate the susceptibility, wavenumber dependence of low-lying excitations and equal-time spin-spin correlations which is related to integrated intensity of the neutron inelastic scattering. These quantities sensitively depend on the configuration of the orbital order. The calculated results for some configurations of the orbital order reproduce many experimental results much better than the previous single-orbital models. However some discrepancy still remains to completely reproduce all of the reported experimental results. To understand the origin of these discrepancies, we point out the possible importance of the partially occupied $d_{xy}$ orbital in addition to orbital order of partially filled $d_{xz}$ and $d_{yz}$ orbitals.Comment: 19 pages LATEX, 15 postscript figures, using jpsj.sty,to be published in J.Phys.Soc.Jpn. Vol.67 No.2 (1998