Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note: updated version of arXiv:gr-qc/050809

EGF increases expression and activity of PAs in preimplantation rat embryos and their implantation rate

BACKGROUND: Embryo implantation plays a major role in embryogenesis and the outcome of pregnancy. Plasminogen activators (PAs) have been implicated in mammalian fertilization, early stages of development and embryo implantation. As in-vitro developing embryos resulted in lower implantation rate than those developed in-vivo we assume that a reduced PAs activity may be involved. In the present work we studied the effect of EGF on PAs activity, quantity and embryo implantation. METHODS: Zygotes were flushed from rat oviducts on day one of pregnancy and grown in-vitro in R1ECM supplemented with EGF (10 ng/ml) and were grown up to the blastocyst stage. The control groups were grown in the same medium without EGF. The distribution and quantity of the PAs were examined using fluorescence immunohistochemistry followed by measurement of PAs activity using the chromogenic assay. Implantation rate was studied using the embryo donation model. RESULTS: PAs distribution in the embryos was the same in EGF treated and untreated embryos. Both PAs were localized in the blastocysts' trophectoderm, supporting the assumption that PAs play a role in the implantation process in rats. EGF increased the quantity of uPA at all stages studied but the 8-cell stage as compared with controls. The tissue type PA (tPA) content was unaffected except the 8-cell stage, which was increased. The activity of uPA increased gradually towards the blastocyst stage and more so due to the presence of EGF. The activity of tPA did not vary with the advancing developmental stages although it was also increased by EGF. The presence of EGF during the preimplantation development doubled the rate of implantation of the treated group as compared with controls

Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black spacetime. A prime application of characteristic evolution is to compute waveforms via Cauchy-characteristic matching, which is also reviewed.Comment: Published version http://www.livingreviews.org/lrr-2005-1