Toward stable 3D numerical evolutions of black-hole spacetimes

Three dimensional (3D) numerical evolutions of static black holes with excision are presented. These evolutions extend to about 8000M, where M is the mass of the black hole. This degree of stability is achieved by using growth-rate estimates to guide the fine tuning of the parameters in a multi-parameter family of symmetric hyperbolic representations of the Einstein evolution equations. These evolutions were performed using a fixed gauge in order to separate the intrinsic stability of the evolution equations from the effects of stability-enhancing gauge choices.Comment: 4 pages, 5 figures. To appear in Phys. Rev. D. Minor additions to text for clarification. Added short paragraph about inner boundary dependenc

How to make a blastocyst.

Several of the new reproductive technologies have been cultivated from our current understanding of the genetic programming and cellular processes that are involved in the major morphogenetic events of mammalian preimplantation development. Research directed at characterizing the patterns of gene expression during early development has shown that the embryo is initially under maternal control and later superseded by new transcriptional activity provided by the activation of the embryonic genome. Several embryonic transcripts encoding: (i) growth factors, (ii) cell junctions, (iii) plasma membrane ion transporters, and (iv) cell adhesion molecules have been identified as contributing directly to the progression of the embryo through the preimplantation interval of development. In this brief review, we have outlined the patterns of expression and the integral roles that these gene families play in the morphogenetic events of compaction and cavitation. Research of this type has greatly facilitate our understanding of the control processes that underlie preimplantation development and represent but one area of this exciting and vigorous field of research

Analytic Gradients for Complete Active Space Pair-Density Functional Theory

Analytic gradient routines are a desirable feature for quantum mechanical methods, allowing for efficient determination of equilibrium and transition state structures and several other molecular properties. In this work, we present analytical gradients for multiconfiguration pair-density functional theory (MC-PDFT) when used with a state-specific complete active space self-consistent field reference wave function. Our approach constructs a Lagrangian that is variational in all wave function parameters. We find that MC-PDFT locates equilibrium geometries for several small- to medium-sized organic molecules that are similar to those located by complete active space second-order perturbation theory but that are obtained with decreased computational cost

Evolution systems for non-linear perturbations of background geometries

The formulation of the initial value problem for the Einstein equations is at the heart of obtaining interesting new solutions using numerical relativity and still very much under theoretical and applied scrutiny. We develop a specialised background geometry approach, for systems where there is non-trivial a priori knowledge about the spacetime under study. The background three-geometry and associated connection are used to express the ADM evolution equations in terms of physical non-linear deviations from that background. Expressing the equations in first order form leads naturally to a system closely linked to the Einstein-Christoffel system, introduced by Anderson and York, and sharing its hyperbolicity properties. We illustrate the drastic alteration of the source structure of the equations, and discuss why this is likely to be numerically advantageous.Comment: 12 pages, 3 figures, Revtex v3.0. Revised version to appear in Physical Review

Application of energy and angular momentum balance to gravitational radiation reaction for binary systems with spin-orbit coupling

We study gravitational radiation reaction in the equations of motion for binary systems with spin-orbit coupling, at order (v/c)^7 beyond Newtonian gravity, or O(v/c)^2 beyond the leading radiation reaction effects for non-spinning bodies. We use expressions for the energy and angular momentum flux at infinity that include spin-orbit corrections, together with an assumption of energy and angular momentum balance, to derive equations of motion that are valid for general orbits and for a class of coordinate gauges. We show that the equations of motion are compatible with those derived earlier by a direct calculation.Comment: 12 pages, submitted to General Relativity and Gravitatio

Geometrical optics analysis of the short-time stability properties of the Einstein evolution equations

Many alternative formulations of Einstein's evolution have lately been examined, in an effort to discover one which yields slow growth of constraint-violating errors. In this paper, rather than directly search for well-behaved formulations, we instead develop analytic tools to discover which formulations are particularly ill-behaved. Specifically, we examine the growth of approximate (geometric-optics) solutions, studied only in the future domain of dependence of the initial data slice (e.g. we study transients). By evaluating the amplification of transients a given formulation will produce, we may therefore eliminate from consideration the most pathological formulations (e.g. those with numerically-unacceptable amplification). This technique has the potential to provide surprisingly tight constraints on the set of formulations one can safely apply. To illustrate the application of these techniques to practical examples, we apply our technique to the 2-parameter family of evolution equations proposed by Kidder, Scheel, and Teukolsky, focusing in particular on flat space (in Rindler coordinates) and Schwarzchild (in Painleve-Gullstrand coordinates).Comment: Submitted to Phys. Rev.

Einstein boundary conditions for the 3+1 Einstein equations

In the 3+1 framework of the Einstein equations for the case of vanishing shift vector and arbitrary lapse, we calculate explicitly the four boundary equations arising from the vanishing of the projection of the Einstein tensor along the normal to the boundary surface of the initial-boundary value problem. Such conditions take the form of evolution equations along (as opposed to across) the boundary for certain components of the extrinsic curvature and for certain space-derivatives of the intrinsic metric. We argue that, in general, such boundary conditions do not follow necessarily from the evolution equations and the initial data, but need to be imposed on the boundary values of the fundamental variables. Using the Einstein-Christoffel formulation, which is strongly hyperbolic, we show how three of the boundary equations should be used to prescribe the values of some incoming characteristic fields. Additionally, we show that the fourth one imposes conditions on some outgoing fields.Comment: Revtex 4, 6 pages, text and references added, typos corrected, to appear in Phys. Rev.

Gravity Waves, Chaos, and Spinning Compact Binaries

Spinning compact binaries are shown to be chaotic in the Post-Newtonian expansion of the two body system. Chaos by definition is the extreme sensitivity to initial conditions and a consequent inability to predict the outcome of the evolution. As a result, the spinning pair will have unpredictable gravitational waveforms during coalescence. This poses a challenge to future gravity wave observatories which rely on a match between the data and a theoretical template.Comment: Final version published in PR

Possible roles of insulin and insulin-like growth factors in rat preimplantation development: investigation of gene expression by reverse transcription-polymerase chain reaction.

The sensitive mRNA phenotyping technique of reverse transcription-polymerase chain reaction was used to demonstrate that insulin receptor mRNA is present in rat embryos during the preimplantation period. In addition, mRNA encoding insulin-like growth factor (IGF) type I and type II receptors have also been detected in rat preimplantation embryos. IGF-I mRNA was not detected in preimplantation embryos but was found in oviducts and uteri of prepubertal and early pregnant rats. IGF-II mRNA was present in both embryos and in oviducts and uteri during the preimplantation period. These findings suggest that insulin and IGF-I could influence early embryo development in endocrine or in paracrine fashions, whereas IGF-II may have an additional autocrine mode of action in affecting preimplantation embryos in rats