Two-level Fourier analysis of a multigrid approach for discontinuous Galerkin discretisation

In this paper we study a multigrid method for the solution of a linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods, andwe give a detailed analysis of the convergence for different block-relaxation strategies.We find that point-wise block-partitioning gives much better results than the classical cell-wise partitioning.Both for the Baumann-Oden and for the symmetric DG method,with and without interior penalty, the block relaxation methods (Jacobi,Gauss-Seidel and symmetric Gauss-Seidel) give excellent smoothing procedures in a classical multigrid setting.Independent of the mesh size, simple MG cycles give convergence factors 0.075 -- 0.4 per iteration sweep for the different discretisation methods studied

Discontinuous Galerkin discretisation with embedded boundary conditions

The purpose of this paper is to introduce discretisation methods of discontinuous Galerkin type for solving second order elliptic PDEs on a structured, regular rectangular grid, while the problem is defined on a curved boundary. The methods aim at high-order accuracy and the difficulty arises since the regular grid cannot follow the curved boundary. Starting with the Lagrange multiplier formulation for the boundary conditions, we derive variational forms for the discretisation of 2-D elliptic problems with embedded Dirichlet boundary conditions. Within the framework of structured, regular rectangular grids, we treat curved boundaries according to the principles that underlie the discontinuous Galerkin method. Thus, the high-order DG-discretisation is adapted in the cells with embedded boundaries. We give examples of approximation with tensor products of cubic polynomials. As an illustration, we solve a convection dominated boundary value problem on a complex domain. Although, of course, it is impossible to accurately represent a boundary layer with a complex structure by means of a cubic polynomial, the boundary condition treatment appears quite effective in handling such complex situations

Fourier two-level analysis for discontinuous Galerkin discretization with linear elements

In this paper we study the convergence of a multigrid method for the solution of a linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods, and we give a detailed analysis of the convergence fordifferent block-relaxation strategies. In addition to an earlier paper where higher-order methods were studied, here we restrict ourselves to methods using piecewise linear approximations. It is well-known that these methods are unstable if no additional interior penalty is applied.As for the higher order methods, we find that point-wise block-relaxationsgive much better results than the classical cell-wise relaxations. Both for the Baumann-Oden and for the symmetric DG method, with a sufficient interior penalty, the block relaxation methods studied (Jacobi, Gauss-Seidel and symmetric Gauss-Seidel) all make excellent smoothing procedures in a classical multigrid setting. Independent of the mesh size, simple MG cycles give convergence factors 0.2 -- 0.4 per iteration sweep for the different discretizations studied

Discontinuous Galerkin discretisation with embedded boundary conditions

The purpose of this paper is to introduce discretisation methods of discontinuous Galerkin type for solving second order elliptic PDEs on a structured, regular rectangular grid, while the problem is defined on a curved boundary. The methods aim at high-order accuracy and the difficulty arises since the regular grid cannot follow the curved boundary. Starting with the Lagrange multiplier formulation for the boundary conditions, we derive variational forms for the discretisation of 2-D elliptic problems with embedded Dirichlet boundary conditions. Within the framework of structured, regular rectangular grids, we treat curved boundaries according to the principles that underlie the discontinuous Galerkin method. Thus, the high-order DG-discretisation is adapted in the cells with embedded boundaries. We give examples of approximation with tensor products of cubic polynomials. As an illustration, we solve a convection dominated boundary value problem on a complex domain. Although, of course, it is impossible to accurately represent a boundary layer with a complex structure by means of a cubic polynomial, the boundary condition treatment appears quite effective in handling such complex situations

Cloning and characterisation of a maize carotenoid cleavage dioxygenase (ZmCCD1) and its involvement in the biosynthesis of apocarotenoids with various roles in mutualistic and parasitic interactions

Colonisation of maize roots by arbuscular mycorrhizal (AM) fungi leads to the accumulation of apocarotenoids (cyclohexenone and mycorradicin derivatives). Other root apocarotenoids (strigolactones) are involved in signalling during early steps of the AM symbiosis but also in stimulation of germination of parasitic plant seeds. Both apocarotenoid classes are predicted to originate from cleavage of a carotenoid substrate by a carotenoid cleavage dioxygenase (CCD), but the precursors and cleavage enzymes are unknown. A Zea mays CCD (ZmCCD1) was cloned by RT-PCR and characterised by expression in carotenoid accumulating E. coli strains and analysis of cleavage products using GC¿MS. ZmCCD1 efficiently cleaves carotenoids at the 9, 10 position and displays 78% amino acid identity to Arabidopsis thaliana CCD1 having similar properties. ZmCCD1 transcript levels were shown to be elevated upon root colonisation by AM fungi. Mycorrhization led to a decrease in seed germination of the parasitic plant Striga hermonthica as examined in a bioassay. ZmCCD1 is proposed to be involved in cyclohexenone and mycorradicin formation in mycorrhizal maize roots but not in strigolactone formatio

Testing the Terminal Investment Hypothesis in California Oaks

The terminal investment hypothesis—which proposes that reproductive investment should increase with age-related declines in reproductive value—has garnered support in a range of animal species but has not been previously examined in long-lived plants, such as trees. We tested this hypothesis by comparing relative acorn production and radial growth among 1,0001 mature individuals of eight species of California oaks (genus Quercus) followed for up to 37 years, during which time 70 trees died apparently natural deaths. We found no significant differences in the radial growth, acorn production, or index of reproductive effort, taking into consideration both growth and reproduction among dying trees relative to either conspecific trees at the same site that did not die or growth and reproduction from earlier years for the focal trees that did eventually die. Furthermore, we found no consistent trade-off between growth and reproduction among trees that died, nor did dying trees significantly alter their relative investment in reproduction even as they underwent physical decline. Trees approaching the end of their lives are often in poor physical condition but do not appear to differentially invest more of their diminished resources in reproduction compared with healthy trees

The Magnificent Seven: Magnetic fields and surface temperature distributions

Presently seven nearby radio-quiet isolated neutron stars discovered in ROSAT data and characterized by thermal X-ray spectra are known. They exhibit very similar properties and despite intensive searches their number remained constant since 2001 which led to their name ``The Magnificent Seven''. Five of the stars exhibit pulsations in their X-ray flux with periods in the range of 3.4 s to 11.4 s. XMM-Newton observations revealed broad absorption lines in the X-ray spectra which are interpreted as cyclotron resonance absorption lines by protons or heavy ions and / or atomic transitions shifted to X-ray energies by strong magnetic fields of the order of 10^13 G. New XMM-Newton observations indicate more complex X-ray spectra with multiple absorption lines. Pulse-phase spectroscopy of the best studied pulsars RX J0720.4-3125 and RBS 1223 reveals variations in derived emission temperature and absorption line depth with pulse phase. Moreover, RX J0720.4-3125 shows long-term spectral changes which are interpreted as due to free precession of the neutron star. Modeling of the pulse profiles of RX J0720.4-3125 and RBS 1223 provides information about the surface temperature distribution of the neutron stars indicating hot polar caps which have different temperatures, different sizes and are probably not located in antipodal positions.Comment: 10 pages, 8 figures, to appear in Astrophysics and Space Science, in the proceedings of "Isolated Neutron Stars: from the Interior to the Surface", edited by D. Page, R. Turolla and S. Zan

The Randomized Shortened Dental Arch Study: Tooth Loss

The evidence concerning the management of shortened dental arch (SDA) cases is sparse. This multi-center study was aimed at generating data on outcomes and survival rates for two common treatments, removable dental prostheses (RDP) for molar replacement or no replacement (SDA). The hypothesis was that the treatments lead to different incidences of tooth loss. We included 215 patients with complete molar loss in one jaw. Molars were either replaced by RDP or not replaced, according to the SDA concept. First tooth loss after treatment was the primary outcome measure. This event occurred in 13 patients in the RDP group and nine patients in the SDA group. The respective Kaplan-Meier survival rates at 38 months were 0.83 (95% CI: 0.74-0.91) in the RDP group and 0.86 (95% CI: 0.78-0.95) in the SDA group, the difference being non-significant

Implications on zinc binding to S100A2

AbstractHuman S100A2 is an EF-hand calcium-binding S100 protein that is localized mainly in the nucleus and functions as tumor suppressor. In addition to Ca2+ S100A2 binds Zn2+ with a high affinity. Studies have been carried out to investigate whether Zn2+ acts as a regulatory ion for S100A2, as in the case of Ca2+. Using the method of competition with the Zn2+ chelator 4-(2-pyridylazo)-resorcinol, an apparent Kd of 25 nM has been determined for Zn2+ binding to S100A2. The affinity lies close to the range of intracellular free Zn2+ concentrations, suggesting that S100A2 is able to bind Zn2+ in the nucleus. Two Zn2+-binding sites have been identified using site directed mutagenesis and several spectroscopic techniques with Cd2+ and Co2+ as probes. In site 1 Zn2+ is bound by Cys21 and most likely by His 17. The binding of Zn2+ in site 2 induces the formation of a tetramer, whereby the Zn2+ is coordinated by Cys2 from each subunit. Remarkably, only binding of Zn2+ to site 2 substantially weakens the affinity of S100A2 for Ca2+. Analysis of the individual Ca2+-binding constants revealed that the Ca2+ affinity of one EF-hand is decreased about 3-fold, whereas the other EF-hand exhibits a 300-fold decrease in affinity. These findings imply that S100A2 is regulated by both Zn2+ and Ca2+, and suggest that Zn2+ might deactivate S100A2 by inhibiting response to intracellular Ca2+ signals