Highly accurate calculation of rotating neutron stars: Detailed description of the numerical methods

We give a detailed description of the recently developed multi-domain spectral method for constructing highly accurate general-relativistic models of rapidly rotating stars. For both "ordinary" and "critical" configurations, it is exhibited by means of representative examples, how the accuracy improves as the order of the approximation increases. Apart from homogeneous fluid bodies, we also discuss models of polytropic and strange stars.Comment: 22 pages, 4 figures, 9 tables, version accepted by A&

Equilibrium Configurations of Homogeneous Fluids in General Relativity

By means of a highly accurate, multi-domain, pseudo-spectral method, we investigate the solution space of uniformly rotating, homogeneous and axisymmetric relativistic fluid bodies. It turns out that this space can be divided up into classes of solutions. In this paper, we present two new classes including relativistic core-ring and two-ring solutions. Combining our knowledge of the first four classes with post-Newtonian results and the Newtonian portion of the first ten classes, we present the qualitative behaviour of the entire relativistic solution space. The Newtonian disc limit can only be reached by going through infinitely many of the aforementioned classes. Only once this limiting process has been consummated, can one proceed again into the relativistic regime and arrive at the analytically known relativistic disc of dust.Comment: 8 pages, colour figures, v3: minor additions including one reference, accepted by MNRA

Sulfur is limiting the glucosinolate accumulation in nasturtium in vitro plants (Tropaeolum majus L.)

It is well established that sulfate fertilisation significantly enhances the content of mustard oil glucosides in glucosinolate containing plants. However, with respect to tissue cultures and in vitro-plants, corresponding data are missing. In this study the influence of sulfur on the accumulation of glucosinolates was analyzed in nasturtium in vitro-plants (Tropaeolum majus). The glucotropaeolin content in plants grown on standard media (MS) varied between 10 and 50 μmol/g DW, corresponding to only about 20 % to 70 % of the glucotropaeolin content in earth grown plants. A fivefold enhancement of the sulfate concentration resulted in a massive increase in the glucotropaeolin content of the in vitro-plants. A decline of sulfate in the medium leads to corresponding diminutions of the glucosinolates accumulated. These data clearly demonstrate the high impact of sulfur availability on glucosinolate biosynthesis and accumulation

Collisions of rigidly rotating disks of dust in General Relativity

We discuss inelastic collisions of two rotating disks by using the conservation laws for baryonic mass and angular momentum. In particular, we formulate conditions for the formation of a new disk after the collision and calculate the total energy loss to obtain upper limits for the emitted gravitational energy.Comment: 30 pages, 9 figure

Relativistic Dyson Rings and Their Black Hole Limit

In this Letter we investigate uniformly rotating, homogeneous and axisymmetric relativistic fluid bodies with a toroidal shape. The corresponding field equations are solved by means of a multi-domain spectral method, which yields highly accurate numerical solutions. For a prescribed, sufficiently large ratio of inner to outer coordinate radius, the toroids exhibit a continuous transition to the extreme Kerr black hole. Otherwise, the most relativistic configuration rotates at the mass-shedding limit. For a given mass-density, there seems to be no bound to the gravitational mass as one approaches the black-hole limit and a radius ratio of unity.Comment: 13 pages, 1 table, 5 figures, v2: some discussion and two references added, accepted for publication in Astrophys. J. Let

Experimental field cultivation of in vitro propagated high-yield varieties of Tropaeolum majus L.

About 10,000 mass propagated clonal progenies of the medicinal plant Tropaeolum majus L. had been cultivated in an experimental field trial to analyze the large scale cultivation of nasturtium-plants for pharmaceutical utilization. The glucotropaeolin contents of the eight Tropaeolum-clones, which had been established and propagated by in vitro-culture techniques, had been monitored and compared with unselected plants from commercial seed mixtures (sm-plants). Whereas the intra-clonal variation of the glucosinolate levels was significantly lower than the variability of the sm-plants, the glucotropaeolin content in the clonal progenies was markedly lower than in both, in the clonal mother plants as well as in the sm-plants. The proposed explanation for this phenomenon is based on the fact that the genetically identical cloned plants reveal only a very narrow phenotypical amplitude, which accordingly resulted in designated glucosinolate levels due to the certain environmental situations. However, under changing conditions, the corresponding glucotropaeolin content might be much lower. In contrast, the sm-plants reveal – due to the strong genetic heterogeneity – a much broader phenotypical amplitude of their physiological characteristics. Consequently, under changing growth conditions various individual plants may accumulate high amounts of glucotropaeolin. These coherences explain both, firstly, the finding that the clonal mother plants revealed very high glucotropaeolin levels under the certain – maybe spatial limited cultivation conditions – whereas their progenies accumulate far less glucosinolates; and secondly, that the average content in the sm-plants is higher than the mean content of the clonal progenies.These data suggest that the much cheaper growing of nasturtium plants from seeds should be favoured over the more sophisticated in vitro-propagation techniques. Anyhow, for industrial farming there is one great advantage for the usage of in vitro generated Tropaeolum plants: the selected, high glucosinolate-nasturtium clones all reveal a compact growth with short tendrils. Therefore, the mechanical harvest of the corresponding clonal progenies, is quite unproblematic in comparison to the difficile harvest of sm-plants, most exhibiting tendrils of several meters

Differentially rotating disks of dust

We present a three-parameter family of solutions to the stationary axisymmetric Einstein equations that describe differentially rotating disks of dust. They have been constructed by generalizing the Neugebauer-Meinel solution of the problem of a rigidly rotating disk of dust. The solutions correspond to disks with angular velocities depending monotonically on the radial coordinate; both decreasing and increasing behaviour is exhibited. In general, the solutions are related mathematically to Jacobi's inversion problem and can be expressed in terms of Riemann theta functions. A particularly interesting two-parameter subfamily represents Baecklund transformations to appropriate seed solutions of the Weyl class.Comment: 14 pages, 3 figures. To appear in "General Relativity and Gravitation". Second version with minor correction

Phase transitions in open quantum systems

We consider the behaviour of open quantum systems in dependence on the coupling to one decay channel by introducing the coupling parameter $\alpha$ being proportional to the average degree of overlapping. Under critical conditions, a reorganization of the spectrum takes place which creates a bifurcation of the time scales with respect to the lifetimes of the resonance states. We derive analytically the conditions under which the reorganization process can be understood as a second-order phase transition and illustrate our results by numerical investigations. The conditions are fulfilled e.g. for a picket fence with equal coupling of the states to the continuum. Energy dependencies within the system are included. We consider also the generic case of an unfolded Gaussian Orthogonal Ensemble. In all these cases, the reorganization of the spectrum occurs at the critical value $\alpha_{crit}$ of the control parameter globally over the whole energy range of the spectrum. All states act cooperatively.Comment: 28 pages, 22 Postscript figure

Dirichlet Boundary Value Problems of the Ernst Equation

We demonstrate how the solution to an exterior Dirichlet boundary value problem of the axisymmetric, stationary Einstein equations can be found in terms of generalized solutions of the Backlund type. The proof that this generalization procedure is valid is given, which also proves conjectures about earlier representations of the gravitational field corresponding to rotating disks of dust in terms of Backlund type solutions.Comment: 22 pages, to appear in Phys. Rev. D, Correction of a misprint in equation (4

Spectral Decorrelation of Nuclear Levels in the Presence of Continuum Decay

The fluctuation properties of nuclear giant resonance spectra are studied in the presence of continuum decay. The subspace of quasi-bound states is specified by one-particle one-hole and two-particle two-hole excitations and the continuum coupling is generated by a scattering ensemble. It is found that, with increasing number of open channels, the real parts of the complex eigenvalues quickly decorrelate. This appears to be related to the transition from power-law to exponential time behavior of the survival probability of an initially non-stationary state.Comment: 10 Pages, REVTEX, 4 PostScript figure