Hyperboloidal evolution of test fields in three spatial dimensions

We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on compactification at null infinity in hyperboloidal scri fixing coordinates. We report numerical tests for the particular example of a scalar wave equation on Minkowski and Schwarzschild backgrounds. We address issues related to the implementation of the hyperboloidal approach for the Einstein equations, such as nonlinear source functions, matching, and evaluation of formally singular terms at null infinity.Comment: 10 pages, 8 figure

Universality of global dynamics for the cubic wave equation

We consider the initial value problem for the spherically symmetric, focusing cubic wave equation in three spatial dimensions. We give numerical and analytical evidence for the existence of a universal attractor which encompasses both global and blowup solutions. As a byproduct we get an explicit description of the critical behavior at the threshold of blowup.Comment: 13 pages, 15 figures. Uses IOP-style. Updated to conform with published versio

Spacelike matching to null infinity

We present two methods to include the asymptotic domain of a background spacetime in null directions for numerical solutions of evolution equations so that both the radiation extraction problem and the outer boundary problem are solved. The first method is based on the geometric conformal approach, the second is a coordinate based approach. We apply these methods to the case of a massless scalar wave equation on a Kerr spacetime. Our methods are designed to allow existing codes to reach the radiative zone by including future null infinity in the computational domain with minor modifications. We demonstrate the flexibility of the methods by considering both Boyer-Lindquist and ingoing Kerr coordinates near the black hole. We also confirm numerically predictions concerning tail decay rates for scalar fields at null infinity in Kerr spacetime due to Hod for the first time.Comment: 12 pages, 9 figures; matches the published versio

The biological activities and phytochemical content of Ferulago humulis Boiss.

728-735Ferulago humulis Boiss. is an endemic species growing in Turkey. The aim of the study was to compare in vitro antioxidant and antimicrobial activities of the aerial parts (HFH) and rhizomes (RFH) of F. humulis. According to the results of antimicrobial and antioxidant activities of the extracts obtained from different parts of the plant, their phytochemical contents were evaluated. Petroleum ether (HFH-PE; RFH-PE), dichloromethane (HFH-DM; RFH-DM) and methanol (HFH-ME; RFH-ME) extracts from aerial parts (HFH) and rhizomes (RFH) of F. humulis were obtained for antimicrobial activity and examined by the agar hole diffusion and microdilution methods. Chromatographic and spectroscopic (1H NMR, LS-MS and UV) techniques were used for the isolation of coumarin compounds from petroleum ether (RFH-PE) and dichloromethane (RFH-DM) extracts. Furthermore, antioxidant activity were assayed by the 4 different methods in methanol extracts (HFH-ME; RFH-ME). HFH-PE (MIC=6.25 mg/mL), RFH-PE (MIC=12.5 mg/mL) and RFH-DM (MIC=11 mg/mL) extracts against Staphylococcus aureus, and RFH-PE (MIC= 3.125 mg/mL), HFH-PE (MIC=6.25 mg/mL) extracts showed antimicrobial activity against S. epidermidis. HFH-PE (MIC=1.56 mg/mL), RFH-PE (MIC= 6.25 mg/mL) extracts exhibited antifungal activity against Candida tropicalis. From the rhizomes of F. humulis isoimperatorin, bergapten, oxypeucedanin, marmesin senecioate and oxypeucedanin hydrate known as furanocoumarins derivatives were isolated

Intermediate behavior of Kerr tails

The numerical investigation of wave propagation in the asymptotic domain of Kerr spacetime has only recently been possible thanks to the construction of suitable hyperboloidal coordinates. The asymptotics revealed an apparent puzzle in the decay rates of scalar fields: the late-time rates seemed to depend on whether finite distance observers are in the strong field domain or far away from the rotating black hole, an apparent phenomenon dubbed "splitting". We discuss far-field "splitting" in the full field and near-horizon "splitting" in certain projected modes using horizon-penetrating, hyperboloidal coordinates. For either case we propose an explanation to the cause of the "splitting" behavior, and we determine uniquely decay rates that previous studies found to be ambiguous or immeasurable. The far-field "splitting" is explained by competition between projected modes. The near-horizon "splitting" is due to excitation of lower multipole modes that back excite the multipole mode for which "splitting" is observed. In both cases "splitting" is an intermediate effect, such that asymptotically in time strong field rates are valid at all finite distances. At any finite time, however, there are three domains with different decay rates whose boundaries move outwards during evolution. We then propose a formula for the decay rate of tails that takes into account the inter--mode excitation effect that we study.Comment: 16 page

The biological activities and phytochemical content of Ferulago humulis Boiss.

Ferulago humulis Boiss. is an endemic species growing in Turkey. The aim of the study was to compare in vitro antioxidant and antimicrobial activities of the aerial parts (HFH) and rhizomes (RFH) of F. humulis. According to the results of antimicrobial and antioxidant activities of the extracts obtained from different parts of the plant, their phytochemical contents were evaluated. Petroleum ether (HFH-PE; RFH-PE), dichloromethane (HFH-DM; RFH-DM) and methanol (HFH-ME; RFH-ME) extracts from aerial parts (HFH) and rhizomes (RFH) of F. humulis were obtained for antimicrobial activity and examined by the agar hole diffusion and microdilution methods. Chromatographic and spectroscopic (1H NMR, LS-MS and UV) techniques were used for the isolation of coumarin compounds from petroleum ether (RFH-PE) and dichloromethane (RFH-DM) extracts. Furthermore, antioxidant activity were assayed by the 4 different methods in methanol extracts (HFH-ME; RFH-ME). HFH-PE (MIC=6.25 mg/mL), RFH-PE (MIC=12.5 mg/mL) and RFH-DM (MIC=11 mg/mL) extracts against Staphylococcus aureus, and RFH-PE (MIC= 3.125 mg/mL), HFH-PE (MIC=6.25 mg/mL) extracts showed antimicrobial activity against S. epidermidis. HFH-PE (MIC=1.56 mg/mL), RFH-PE (MIC= 6.25 mg/mL) extracts exhibited antifungal activity against Candida tropicalis. From the rhizomes of F. humulis isoimperatorin, bergapten, oxypeucedanin, marmesin senecioate and oxypeucedanin hydrate known as furanocoumarins derivatives were isolated

Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem

We study gravitational perturbations of Schwarzschild spacetime by solving a hyperboloidal initial value problem for the Bardeen-Press equation. Compactification along hyperboloidal surfaces in a scri-fixing gauge allows us to have access to the gravitational waveform at null infinity in a general setup. We argue that this hyperboloidal approach leads to a more accurate and efficient calculation of the radiation signal than the common approach where a timelike outer boundary is introduced. The method can be generalized to study perturbations of Kerr spacetime using the Teukolsky equation.Comment: 14 pages, 9 figure

Hyperboloidal foliations and scri-fixing

We discuss a gauge choice which allows us to avoid the introduction of artificial timelike outer boundaries in numerical studies of test fields based on a 3+1 decomposition of asymptotically flat background spacetimes. The main idea is to include null infinity in the computational domain by conformally compactifying the metric on hyperboloidal foliations and fixing the spatial coordinate location of null infinity, i.e. scri-fixing. We construct such coordinates explicitly on Minkowski, Schwarzschild and Kerr spacetimes.Comment: 14 pages, 14 figures. Published versio

Hyperboloidal evolution with the Einstein equations

We consider an approach to the hyperboloidal evolution problem based on the Einstein equations written for a rescaled metric. It is shown that a conformal scale factor can be freely prescribed a priori in terms of coordinates in a well-posed hyperboloidal initial value problem such that the location of null infinity is independent of the time coordinate. With an appropriate choice of a single gauge source function each of the formally singular conformal source terms in the equations attains a regular limit at null infinity. The suggested approach could be beneficial in numerical relativity for both wave extraction and outer boundary treatment.Comment: 10 pages; uses iop styl