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A time-dependent coordinate transformation of a constant coeffcient hyperbolic equation which results in a variable coeffcient problem is considered. By using the energy method, we derive well-posed boundary conditions for the continuous problem. It is shown that the number of boundary conditions depend on the coordinate transformation. By using Summation-by-Parts (SBP) operators for the space discretization and weak boundary conditions, an energy stable finite dieffrence scheme is obtained. We also show how to construct a time-dependent penalty formulation that automatically imposes the right number of boundary conditions. Numerical calculations corroborate the stability and accuracy of the approximations

Stellar substructures in the solar neighbourhood. III. Kinematic group 2 in the Geneva-Copenhagen survey

From correlations between orbital parameters, several new coherent groups of stars were recently identified in the Galactic disc and suggested to correspond to remnants of disrupted satellites. To reconstruct their origin at least three main observational parameters - kinematics, chemical composition and age - must be known. We determine detailed elemental abundances in stars belonging to the so-called Group 2 of the Geneva-Copenhagen Survey and compare the chemical composition with Galactic thin- and thick-disc stars, as well as with the Arcturus and AF06 streams. The aim is to search for chemical signatures that might give information about the formation history of this kinematic group of stars. High-resolution spectra were obtained with the FIES spectrograph at the Nordic Optical Telescope, La Palma, and were analysed with a differential model atmosphere method. Comparison stars were observed and analysed with the same method. The average value of [Fe/H] for the 32 stars of Group 2 is -0.42 +- 0.10 dex. The investigated group consists mainly of two 8- and 12-Gyr-old stellar populations. Abundances of oxygen, alpha-elements, and r-process-dominated elements are higher than in Galactic thin-disc dwarfs. This elemental abundance pattern has similar characteristics as that of the Galactic thick-disc. The similarity in chemical composition of stars in Group 2 with that in stars of the thick-disc might suggest that their formation histories are linked. The chemical composition together with the kinematic properties and ages of stars in the investigated stars provides evidence of their common origin and possible relation to an ancient merging event. A gas-rich satellite merger scenario is proposed as the most likely origin. Groups 2 and 3 of the Geneva-Copenhagen Survey might have originated in the same merging event.Comment: 17 pages, 13 figures, accepted for publication in Astronomy & Astrophysics, 201

The double-Reissner-Nordstrom solution and the interaction force between two spherically symmetric charged particles

The physical representation of the general double-Reissner-Nordstrom solution is obtained by rewriting the N=2 Breton-Manko-Aguilar electrostatic solution in the Varzugin-Chistyakov parametrization (M_i, Q_i, R). A concise analytical formula is derived for the interaction force between two arbitrary Reissner-Nordstrom constituents, and an example of the equilibrium configuration involving two oppositely charged particles which confirms earlier Bonnor's prediction of the existence of such configurations is given.Comment: 14 pages, 1 figure; submitted to Physical Review

Stellar substructures in the solar neighbourhood IV. Kinematic Group 1 in the Geneva-Copenhagen survey

We determine detailed elemental abundances in stars belonging to the so-called Group 1 of the Geneva-Copenhagen survey (GCS) and compare the chemical composition with the Galactic thin- and thick-disc stars, with the GCS Group 2 and Group 3 stars, as well as with several kinematic streams of similar metallicities. The aim is to search for chemical signatures that might give information about the formation history of this kinematic group of stars. High-resolution spectra were obtained with the Fibre-fed Echelle Spectrograph (FIES) spectrograph at the Nordic Optical Telescope, La Palma, and were analysed with a differential model atmosphere method. Comparison stars were observed and analysed with the same method. The average value of [Fe/H] for the 37 stars of Group 1 is -0.20 +- 0.14 dex. Investigated Group 1 stars can be separated into three age subgroups. Along with the main 8- and 12-Gyr-old populations, a subgroup of stars younger than 5 Gyr can be separated as well. Abundances of oxygen, alpha-elements, and r-process dominated elements are higher than in Galactic thin-disc dwarfs. This elemental abundance pattern has similar characteristics to that of the Galactic thick disc and differs slightly from those in Hercules, Arcturus, and AF06 stellar streams. The similar chemical composition of stars in Group 1, as well as in Group 2 and 3, with that in stars of the thick disc might suggest that their formation histories are linked. The chemical composition pattern together with the kinematic properties and ages of stars in the investigated GCS groups provide evidence of their common origin and possible relation to an ancient merging event. A gas-rich satellite merger scenario is proposed as the most likely origin.Comment: 17 pages, 13 figures, accepted for publication in Astronomy & Astrophysics, 201

Two kinds of procedural semantics for privative modification

In this paper we present two kinds of procedural semantics for privative modification. We do this for three reasons. The first reason is to launch a tough test case to gauge the degree of substantial agreement between a constructivist and a realist interpretation of procedural semantics; the second is to extend Martin-L ̈f’s Constructive Type Theory to privative modification, which is characteristic of natural language; the third reason is to sketch a positive characterization of privation

Atomistic spin dynamics of the CuMn spin glass alloy

We demonstrate the use of Langevin spin dynamics for studying dynamical properties of an archetypical spin glass system. Simulations are performed on CuMn (20% Mn) where we study the relaxation that follows a sudden quench of the system to the low temperature phase. The system is modeled by a Heisenberg Hamiltonian where the Heisenberg interaction parameters are calculated by means of first-principles density functional theory. Simulations are performed by numerically solving the Langevin equations of motion for the atomic spins. It is shown that dynamics is governed, to a large degree, by the damping parameter in the equations of motion and the system size. For large damping and large system sizes we observe the typical aging regime.Comment: 18 pages, 9 figure

Lead abundance in the uranium star CS 31082-001

In a previous paper we were able to measure the abundance of uranium and thorium in the very-metal poor halo giant BPS CS 31082-001, but only obtained an upper limit for the abundance of lead (Pb). We have got from ESO 17 hours of additional exposure on this star in order to secure a detection of the minimum amount of lead expected to be present in CS 31082-001, the amount arising from the decay of the original content of Th and U in the star. We report here this successful detection. We find an LTE abundance log(Pb/H)+12=-0.55 \pm 0.15 dex, one dex below the upper limits given by other authors for the similar stars CS 22892-052 and BD +17d3248, also enhanced in r-process elements. From the observed present abundances of Th and U in the star, the expected amount of Pb produced by the decay of 232Th, and 238U alone, over 12-15 Gyr is -0.73\pm 0.17 dex. The decay of 235U is more difficult to estimate, but is probably slightly below the contribution of 238U, making the contribution of the 3 actinides only slightly below, or even equal to, the measured abundance. The contribution from the decay of 234U has was not included, for lack of published data. In this sense our determination is a lower limit to the contribution of actinides to lead production. We comment this result, and we note that if a NLTE analysis, not yet possible, doubles our observed abundance, the decay of the 3 actinides will still represent 50 per cent of the total lead, a proportion higher than the values considered so far in the literature.Comment: 4 pages, LateX, A&A Letters Accepte

Dynamics of diluted magnetic semiconductors from atomistic spin dynamics simulations: Mn doped GaAs as a case study

The dynamical behavior of the magnetism of diluted magnetic semiconductors (DMS) has been investigated by means of atomistic spin dynamics simulations. The conclusions drawn from the study are argued to be general for DMS systems in the low concentration limit, although all simulations are done for 5% Mn-doped GaAs with various concentrations of As antisite defects. The magnetization curve, $M(T)$, and the Curie temperature $T_C$ have been calculated, and are found to be in good correspondence to results from Monte Carlo simulations and experiments. Furthermore, equilibrium and non-equilibrium behavior of the magnetic pair correlation function have been extracted. The dynamics of DMS systems reveals a substantial short ranged magnetic order even at temperatures at or above the ordering temperature, with a non-vanishing pair correlation function extending up to several atomic shells. For the high As antisite concentrations the simulations show a short ranged anti-ferromagnetic coupling, and a weakened long ranged ferromagnetic coupling. For sufficiently large concentrations we do not observe any long ranged ferromagnetic correlation. A typical dynamical response shows that starting from a random orientation of moments, the spin-correlation develops very fast ($\sim$ 1ps) extending up to 15 atomic shells. Above $\sim$ 10 ps in the simulations, the pair correlation is observed to extend over some 40 atomic shells. The autocorrelation function has been calculated and compared with ferromagnets like bcc Fe and spin-glass materials. We find no evidence in our simulations for a spin-glass behaviour, for any concentration of As antisites. Instead the magnetic response is better described as slow dynamics, at least when compared to that of a regular ferromagnet like bcc Fe.Comment: 24 pages, 15 figure