Robust evolution system for Numerical Relativity

The paper combines theoretical and applied ideas which have been previously considered separately into a single set of evolution equations for Numerical Relativity. New numerical ingredients are presented which avoid gauge pathologies and allow one to perform robust 3D calculations. The potential of the resulting numerical code is demonstrated by using the Schwarzschild black hole as a test-bed. Its evolution can be followed up to times greater than one hundred black hole masses.Comment: 11 pages, 4 figures; figure correcte

Cauchy boundaries in linearized gravitational theory

We investigate the numerical stability of Cauchy evolution of linearized gravitational theory in a 3-dimensional bounded domain. Criteria of robust stability are proposed, developed into a testbed and used to study various evolution-boundary algorithms. We construct a standard explicit finite difference code which solves the unconstrained linearized Einstein equations in the 3+1 formulation and measure its stability properties under Dirichlet, Neumann and Sommerfeld boundary conditions. We demonstrate the robust stability of a specific evolution-boundary algorithm under random constraint violating initial data and random boundary data.Comment: 23 pages including 3 figures and 2 tables, revte

The constraints as evolution equations for numerical relativity

The Einstein equations have proven surprisingly difficult to solve numerically. A standard diagnostic of the problems which plague the field is the failure of computational schemes to satisfy the constraints, which are known to be mathematically conserved by the evolution equations. We describe a new approach to rewriting the constraints as first-order evolution equations, thereby guaranteeing that they are satisfied to a chosen accuracy by any discretization scheme. This introduces a set of four subsidiary constraints which are far simpler than the standard constraint equations, and which should be more easily conserved in computational applications. We explore the manner in which the momentum constraints are already incorporated in several existing formulations of the Einstein equations, and demonstrate the ease with which our new constraint-conserving approach can be incorporated into these schemes.Comment: 10 pages, updated to match published versio

Constraint propagation in the family of ADM systems

The current important issue in numerical relativity is to determine which formulation of the Einstein equations provides us with stable and accurate simulations. Based on our previous work on "asymptotically constrained" systems, we here present constraint propagation equations and their eigenvalues for the Arnowitt-Deser-Misner (ADM) evolution equations with additional constraint terms (adjusted terms) on the right hand side. We conjecture that the system is robust against violation of constraints if the amplification factors (eigenvalues of Fourier-component of the constraint propagation equations) are negative or pure-imaginary. We show such a system can be obtained by choosing multipliers of adjusted terms. Our discussion covers Detweiler's proposal (1987) and Frittelli's analysis (1997), and we also mention the so-called conformal-traceless ADM systems.Comment: 11 pages, RevTeX, 2 eps figure

Generalized harmonic formulation in spherical symmetry

In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention in numerical relativity over the past few years, especially as applied to the problem of binary inspiral and merger. A key issue when using the technique is the choice of the gauge source functions, and recent work has provided several prescriptions for gauge drivers designed to evolve these functions in a controlled way. We numerically investigate the parameter spaces of some of these drivers in the context of fully non-linear collapse of a real, massless scalar field, and determine nearly optimal parameter settings for specific situations. Surprisingly, we find that many of the drivers that perform well in 3+1 calculations that use Cartesian coordinates, are considerably less effective in spherical symmetry, where some of them are, in fact, unstable.Comment: 47 pages, 15 figures. v2: Minor corrections, including 2 added references; journal version

Advantages of modified ADM formulation: constraint propagation analysis of Baumgarte-Shapiro-Shibata-Nakamura system

Several numerical relativity groups are using a modified ADM formulation for their simulations, which was developed by Nakamura et al (and widely cited as Baumgarte-Shapiro-Shibata-Nakamura system). This so-called BSSN formulation is shown to be more stable than the standard ADM formulation in many cases, and there have been many attempts to explain why this re-formulation has such an advantage. We try to explain the background mechanism of the BSSN equations by using eigenvalue analysis of constraint propagation equations. This analysis has been applied and has succeeded in explaining other systems in our series of works. We derive the full set of the constraint propagation equations, and study it in the flat background space-time. We carefully examine how the replacements and adjustments in the equations change the propagation structure of the constraints, i.e. whether violation of constraints (if it exists) will decay or propagate away. We conclude that the better stability of the BSSN system is obtained by their adjustments in the equations, and that the combination of the adjustments is in a good balance, i.e. a lack of their adjustments might fail to obtain the present stability. We further propose other adjustments to the equations, which may offer more stable features than the current BSSN equations.Comment: 10 pages, RevTeX4, added related discussion to gr-qc/0209106, the version to appear in Phys. Rev.

Towards an understanding of the stability properties of the 3+1 evolution equations in general relativity

We study the stability properties of the standard ADM formulation of the 3+1 evolution equations of general relativity through linear perturbations of flat spacetime. We focus attention on modes with zero speed of propagation and conjecture that they are responsible for instabilities encountered in numerical evolutions of the ADM formulation. These zero speed modes are of two kinds: pure gauge modes and constraint violating modes. We show how the decoupling of the gauge by a conformal rescaling can eliminate the problem with the gauge modes. The zero speed constraint violating modes can be dealt with by using the momentum constraints to give them a finite speed of propagation. This analysis sheds some light on the question of why some recent reformulations of the 3+1 evolution equations have better stability properties than the standard ADM formulation.Comment: 15 pages, 9 figures. Added a new section, plus incorporated many comments made by refere

Depletion of abscisic acid levels in roots of flooded Carrizo citrange (Poncirus trifoliata L. Raf. x Citrus sinensis L. Osb.) plants is a stress-specific response associated to the differential expression of PYR/PYL/RCAR receptors

[EN] Soil flooding reduces root abscisic acid (ABA) levels in citrus, conversely to what happens under drought. Despite this reduction, microarray analyses suggested the existence of a residual ABA signaling in roots of flooded Carrizo citrange seedlings. The comparison of ABA metabolism and signaling in roots of flooded and water stressed plants of Carrizo citrange revealed that the hormone depletion was linked to the upregulation of CsAOG, involved in ABA glycosyl ester (ABAGE) synthesis, and to a moderate induction of catabolism (CsCYP707A, an ABA 8'-hydroxylase) and buildup of dehydrophaseic acid (DPA). Drought strongly induced both ABA biosynthesis and catabolism (CsNCED1, 9-cis-neoxanthin epoxycarotenoid dioxygenase 1, and CsCYP707A) rendering a significant hormone accumulation. In roots of flooded plants, restoration of control ABA levels after stress release was associated to the upregulation of CsBGLU18 (an ABA beta-glycosidase) that cleaves ABAGE. Transcriptional profile of ABA receptor genes revealed a different induction in response to soil flooding (CsPYL5) or drought (CsPYL8). These two receptor genes along with CsPYL1 were cloned and expressed in a heterologous system. Recombinant CsPYL5 inhibited Delta NHAB1 activity in vitro at lower ABA concentrations than CsPYL8 or CsPYL1, suggesting its better performance under soil flooding conditions. Both stress conditions induced ABA-responsive genes CsABI5 and CsDREB2A similarly, suggesting the occurrence of ABA signaling in roots of flooded citrus seedlings. The impact of reduced ABA levels in flooded roots on CsPYL5 expression along with its higher hormone affinity reinforce the role of this ABA receptor under soil-flooding conditions and explain the expression of certain ABA-responsive genes.This work was supported by Ministerio de Economia y Competitividad (MINECO), Fondo Europeo de Desarrollo Regional (FEDER) and Universitat Jaume I through grants No. AGL201676574-R, UJI-B2016-23/UJI-B2016-24 to A.G-C. and V.A. and MINECO, FEDER and Consejo Superior de Investigaciones Cientificas (CSIC) through grant BIO2014-52537-R to P.L.R. S.I.Z. and M.M. were supported by predoctoral grants from Universitat Jaume I and Generalitat Valenciana, respectively. M.G.G. was recipient of a "JAE-DOC" contract from the CSIC. 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Persistent wheezing as manifestation of esophageal tubular duplication cyst

Duplications of esophagus are rare congenital anomalies and the second most common duplications of the gastrointestinal tract. This form of bronchopulmonary foregut malformation may appear as a cystic mediastinal mass. On chest radiographs they may be visible as middle or posterior masses. On CT they are well marginated and oppose the esophagus. Usually they are asymptomatic, unless they become infected or cause obstruction. We report a case of thoracic tubular duplication cyst in a 10-month-old boy who presented with persistent wheezing that was unsuccessfully treated in out-patient services