Influence of adaptive mesh refinement and the hydro solver on shear-induced mass stripping in a minor-merger scenario

We compare two different codes for simulations of cosmological structure formation to investigate the sensitivity of hydrodynamical instabilities to numerics, in particular, the hydro solver and the application of adaptive mesh refinement (AMR). As a simple test problem, we consider an initially spherical gas cloud in a wind, which is an idealized model for the merger of a subcluster or galaxy with a big cluster. Based on an entropy criterion, we calculate the mass stripping from the subcluster as a function of time. Moreover, the turbulent velocity field is analyzed with a multi-scale filtering technique. We find remarkable differences between the commonly used PPM solver with directional splitting in the Enzo code and an unsplit variant of PPM in the Nyx code, which demonstrates that different codes can converge to systematically different solutions even when using uniform grids. For the test case of an unbound cloud, AMR simulations reproduce uniform-grid results for the mass stripping quite well, although the flow realizations can differ substantially. If the cloud is bound by a static gravitational potential, however, we find strong sensitivity to spurious fluctuations which are induced at the cutoff radius of the potential and amplified by the bow shock. This gives rise to substantial deviations between uniform-grid and AMR runs performed with Enzo, while the mass stripping in Nyx simulations of the subcluster is nearly independent of numerical resolution and AMR. Although many factors related to numerics are involved, our study indicates that unsplit solvers with advanced flux limiters help to reduce grid effects and to keep numerical noise under control, which is important for hydrodynamical instabilities and turbulent flows.Comment: 23 pages, 18 figures, accepted for publication by Astronomy and Computin

White Dwarf Mergers on Adaptive Meshes I. Methodology and Code Verification

The Type Ia supernova progenitor problem is one of the most perplexing and exciting problems in astrophysics, requiring detailed numerical modeling to complement observations of these explosions. One possible progenitor that has merited recent theoretical attention is the white dwarf merger scenario, which has the potential to naturally explain many of the observed characteristics of Type Ia supernovae. To date there have been relatively few self-consistent simulations of merging white dwarf systems using mesh-based hydrodynamics. This is the first paper in a series describing simulations of these systems using a hydrodynamics code with adaptive mesh refinement. In this paper we describe our numerical methodology and discuss our implementation in the compressible hydrodynamics code CASTRO, which solves the Euler equations, and the Poisson equation for self-gravity, and couples the gravitational and rotation forces to the hydrodynamics. Standard techniques for coupling gravitation and rotation forces to the hydrodynamics do not adequately conserve the total energy of the system for our problem, but recent advances in the literature allow progress and we discuss our implementation here. We present a set of test problems demonstrating the extent to which our software sufficiently models a system where large amounts of mass are advected on the computational domain over long timescales. Future papers in this series will describe our treatment of the initial conditions of these systems and will examine the early phases of the merger to determine its viability for triggering a thermonuclear detonation.Comment: Accepted for publication in the Astrophysical Journa

Zinc absorption in adult humans: the effect of iron fortification

The effect of Fe fortification on the absorption of Zn was studied by radioisotopic labelling of single meals, followed by measurements of whole-body retention of 65Zn at 14 d after intake. Healthy adult volunteers participated in the study. Weaning cereal, wheat bread and infant formula, foods that are all frequently Fe-fortified, were evaluated in the study. The amounts of Fe added as FeSO4 were similar to the levels in commercial products in Europe and the USA, and were 200 or 500 mg Fe/kg (weaning cereal), 65 mg Fe/kg (white wheat flour) and 12 mg Fe/1 (infant formula). For comparison, Zn absorption was measured in the same subjects, from identical test meals containing no added Fe. No statistically significant differences were found when Zn absorption from the Fe-fortified test meals was compared with that from non-Fe-fortified test meals. Fractional Zn-absorption values from Fe-fortified v. non-fortified meals were 31·1 (sd 1·19) v. 30·7 (SD 7·0)% (weaning cereal; 200 mg Fe/kg), 37·7 (SD 16·6) v. 30·2 (SD 9·9)% (weaning cereal; 500 mg Fe/kg), 36·5 (SD 14·4) v. 38·2 (SD 18·1)% (bread; 65 mg Fe/kg flour) and 41·6 (SD 8·1) v. 38·9 (SD 14·5)% (infant formula; 12 mg Fe/1). The addition of Fe to foods at the currently used fortification levels was thus not associated with impaired absorption of Zn and the consumption of these Fe-fortified foods would not be expected to have a negative effect on Zn nutritio

Existence of Least-perimeter Partitions

We prove the existence of a perimeter-minimizing partition of R^n into regions of unit volume. We conclude with a short tribute to the late Manuel A. Fortes.Comment: 5 pages; for submission to Fortes memorial isue of Philosphical Magazine Letter

Zinc absorption in adult humans: the effect of protein sources added to liquid test meals

The influence of different protein sources on Zn absorption was evaluated in healthy adults by radioisotopic labelling of single meals, followed by whole-body retention measurements 14 d after intake. Semi-synthetic liquid diets were used for the evaluation of different animal-protein sources and dephytinized soyabean-protein isolate ( ··01 g phytic acid/kg). Zn absorption was measured in the same subjects from identical test meals containing no added protein. No statistically significant differences were found in the Zn absorption from test meals containing bovine whey, casein or egg albumen when compared with test meals without added protein. Bovine serum albumin (BSA) and soyabean-protein isolate (< ··01 g phytic acid/kg) significantly reduced the mean absorption of Zn from 45-49% (no added protein) to 38·0 (SD 10·9) (BSA, P < ··05) and 33·9 (SD 12·6)% (soyabean-protein isolate < ··01 g phytic acid/kg, P < ··01). These results demonstrate that Zn absorption is inhibited by certain protein sources, such as BSA and dephytinized soyabean-protein isolate, while other proteins have little or no effec

Proof of the Double Bubble Conjecture in R^n

The least-area hypersurface enclosing and separating two given volumes in R^n is the standard double bubble.Comment: 20 pages, 22 figure

Constrained-Transport Magnetohydrodynamics with Adaptive-Mesh-Refinement in CHARM

We present the implementation of a three-dimensional, second order accurate Godunov-type algorithm for magneto-hydrodynamic (MHD), in the adaptive-mesh-refinement (AMR) cosmological code {\tt CHARM}. The algorithm is based on the full 12-solve spatially unsplit Corner-Transport-Upwind (CTU) scheme. The fluid quantities are cell-centered and are updated using the Piecewise-Parabolic-Method (PPM), while the magnetic field variables are face-centered and are evolved through application of the Stokes theorem on cell edges via a Constrained-Transport (CT) method. The multidimensional MHD source terms required in the predictor step for high-order accuracy are applied in a simplified form which reduces their complexity in three dimensions without loss of accuracy or robustness. The algorithm is implemented on an AMR framework which requires specific synchronization steps across refinement levels. These include face-centered restriction and prolongation operations and a {\it reflux-curl} operation, which maintains a solenoidal magnetic field across refinement boundaries. The code is tested against a large suite of test problems, including convergence tests in smooth flows, shock-tube tests, classical two- and three-dimensional MHD tests, a three-dimensional shock-cloud interaction problem and the formation of a cluster of galaxies in a fully cosmological context. The magnetic field divergence is shown to remain negligible throughout.Comment: 53 pages, 17 figs, under review by ApJ