A course space construction based on local Dirichlet-to-Neumann maps

Coarse-grid correction is a key ingredient of scalable domain decomposition methods. In this work we construct coarse-grid space using the low-frequency modes of the subdomain Dirichlet-to-Neumann maps and apply the obtained two-level preconditioners to the extended or the original linear system arising from an overlapping domain decomposition. Our method is suitable for parallel implementation, and its efficiency is demonstrated by numerical examples on problems with large heterogeneities for both manual and automatic partitionings

The Mira-based distance to the Galactic centre

Mira variables are useful distance indicators, due to their high luminosities and well-defined period-luminosity relation. We select 1863 Miras from SAAO and MACHO observations to examine their use as distance estimators in the Milky Way. We measure a distance to the Galactic centre of $R_0 = 7.9 \pm 0.3$ kpc, which is in good agreement with other literature values. The uncertainty has two components of $\sim$0.2 kpc each: the first is from our analysis and predominantly due to interstellar extinction, the second is due to zero-point uncertainties extrinsic to our investigation, such as the distance to the Large Magellanic Cloud (LMC). In an attempt to improve existing period-luminosity calibrations, we use theoretical models of Miras to determine the dependence of the period-luminosity relation on age, metallicity, and helium abundance, under the assumption that Miras trace the bulk stellar population. We find that at a fixed period of $\log P = 2.4$, changes in the predicted $K_s$ magnitudes can be approximated by $\Delta M_{Ks} \approx -0.109(\Delta \rm{[Fe/H]}) + 0.033( {\Delta}t/\rm{Gyr}) + 0.021 ({\Delta}Y/0.01)$, and these coefficients are nearly independent of period. The expected overestimate in the Galactic centre distance from using an LMC-calibrated relation is $\sim$0.3 kpc. This prediction is not validated by our analysis; a few possible reasons are discussed. We separately show that while the predicted color-color diagrams of solar-neighbourhood Miras work well in the near-infrared, though there are offsets from the model predictions in the optical and mid-infrared.Comment: Accepted for publication in The Astrophysical Journal. 16 pages, 8 figures, 6 table

Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps

Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the PDE coefficients, especially for systems of PDEs. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems in the overlaps of subdomains that isolate the terms responsible for slow convergence. We prove a general theoretical result that rigorously establishes the robustness of the new coarse space and give some numerical examples on two and three dimensional heterogeneous PDEs and systems of PDEs that confirm this property

Magnetic properties of the honeycomb oxide Na2_2Co2_2TeO6_6

We have studied the magnetic properties of Na$_2$Co$_2$TeO$_6$, which features a honeycomb lattice of magnetic Co$^{2+}$ ions, through macroscopic characterization and neutron diffraction on a powder sample. We have shown that this material orders in a zig-zag antiferromagnetic structure. In addition to allowing a linear magnetoelectric coupling, this magnetic arrangement displays very peculiar spatial magnetic correlations, larger in the honeycomb planes than between the planes, which do not evolve with the temperature. We have investigated this behavior by Monte Carlo calculations using the $J_1$-$J_2$-$J_3$ model on a honeycomb lattice with a small interplane interaction. Our model reproduces the experimental neutron structure factor, although its absence of temperature evolution must be due to additional ingredients, such as chemical disorder or quantum fluctuations enhanced by the proximity to a phase boundary.Comment: 9 pages, 13 figure

Experimental study of super-rotation in a magnetostrophic spherical Couette flow

We report measurements of electric potentials at the surface of a spherical container of liquid sodium in which a magnetized inner core is differentially rotating. The azimuthal angular velocities inferred from these potentials reveal a strong super-rotation of the liquid sodium in the equatorial region, for small differential rotation. Super-rotation was observed in numerical simulations by Dormy et al. [1]. We find that the latitudinal variation of the electric potentials in our experiments differs markedly from the predictions of a similar numerical model, suggesting that some of the assumptions used in the model - steadiness, equatorial symmetry, and linear treatment for the evolution of both the magnetic and velocity fields - are violated in the experiments. In addition, radial velocity measurements, using ultrasonic Doppler velocimetry, provide evidence of oscillatory motion near the outer sphere at low latitude: it is viewed as the signature of an instability of the super-rotating region

Simulation of Laser Propagation in a Plasma with a Frequency Wave Equation

The aim of this work is to perform numerical simulations of the propagation of a laser in a plasma. At each time step, one has to solve a Helmholtz equation in a domain which consists in some hundreds of millions of cells. To solve this huge linear system, one uses a iterative Krylov method with a preconditioning by a separable matrix. The corresponding linear system is solved with a block cyclic reduction method. Some enlightments on the parallel implementation are also given. Lastly, numerical results are presented including some features concerning the scalability of the numerical method on a parallel architecture

D010 Mesenchymal stem cells protect cardiomyocytes from reperfusion injury through a paracrine activation of the PI3 kinase pathway

ObjectivesPrevious data suggest that implantation of mesenchymal stem cells (MSCs) improves heart function after myocardial infarction. We investigated whether protection afforded by MSCs might involve a paracrine activation of the PI3 kinase pathway in reperfused cardiomyocytes.MethodMSCs and neonatal rat cardiomyocytes (NRCs) were isolated and cultured separately. NRCs (2.106) were subjected to 5 hours of ischemia followed by 16 hours of reperfusion. At the time of reperfusion, NRCs (n=8-14/group) received either fresh medium (control group), or the following treatments: MSCs (2.105 MSCs in fresh medium), conditioned SN (MSCs supernatant alone (i.e. without MSCs) obtained after 8 hours of serum deprived culture), [conditioned SN + LY294002] (15 microM of LY294002 a specifi c inhibitor of PI3K), [conditioned SN + Wortmannin] (100 nM of wortmannin, a non specifi c inhibitor of PI3K), or CsA (200 nM in fresh medium) a potent inhibitor of the mitochondrial permeability transition pore. Cell death was assessed by LDH release in NRCs supernatant at the end of reperfusion.ResultsAs expected, LDH activity was dramatically reduced by CsA, averaging 4 % of control values. LDH activity was signifi cantly reduced by MSCs alone and by conditioned SN, averaging 29 % and 12 % of control value, respectively. Both LY294002 and wortmannin signifi cantly attenuated conditioned SN induced protection.Conclusionour data suggest that MSCs can protect NRCs from reperfusion injury through a paracrine activation of the PI3K pathway