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

Management of wet age-related macular degeneration in Spain: challenges for treat and extend implementation in routine clinical practice

Age-related macular degeneration; Ophthalmology services; Anti-VEGFDegeneración macular relacionada con la edad; Servicios de oftalmología; Anti-VEGFDegeneració macular relacionada amb l’edat; Serveis d’oftalmologia; Anti-VEGFPurpose. To ascertain wet AMD (wAMD) management patterns in Spain. Methods. A two-round Delphi study conducted through a questionnaire-based survey designed from literature review and validated by an independent Steering Committee. Results. Forty-nine retina specialists experienced in wAMD participated by answering the two-round study questionnaire. Retina specialists are the main responsible for wAMD diagnosis and monitoring, including visits and associated procedures, with a median time per visit of 15 minutes. Standard treatment strategies are based on anti-VEGF administration, including standard loading dose administration followed by maintenance with aflibercept or ranibizumab (81% of patients). Although treat and extend (T&E) dosing strategy is considered as optimal for wAMD management (78% of the panelists), the main routine healthcare limitations (i.e., visits overload, reduced staff, short visit time, coordination issues, lack of facilities) conduct to self-defined “flexible” strategies, based on T&E and pro-re-nata (PRN) protocols. Conclusion. Proactive treatment patterns (T&E) are the preferred ones by the retina specialists in Spain. However, their proper implementation is difficult due to healthcare resource limitations, as well as organisation and logistic issues. The use of anti-VEGF agents with longer duration of action could facilitate the use of strict T&E approaches according to routine clinical practices

Management of wet age-related macular degeneration in Spain: Challenges for treat and extend implementation in routine clinical practice

Purpose. To ascertain wet AMD (wAMD) management patterns in Spain. Methods. A two-round Delphi study conducted through a questionnaire-based survey designed from literature review and validated by an independent Steering Committee. Results. Forty-nine retina specialists experienced in wAMD participated by answering the two-round study questionnaire. Retina specialists are the main responsible for wAMD diagnosis and monitoring, including visits and associated procedures, with a median time per visit of 15 minutes. Standard treatment strategies are based on anti-VEGF administration, including standard loading dose administration followed by maintenance with aflibercept or ranibizumab (81% of patients). Although treat and extend (T&E) dosing strategy is considered as optimal for wAMD management (78% of the panelists), the main routine healthcare limitations (i.e., visits overload, reduced staff, short visit time, coordination issues, lack of facilities) conduct to self-defined “flexible” strategies, based on T&E and pro-re-nata (PRN) protocols. Conclusion. Proactive treatment patterns (T&E) are the preferred ones by the retina specialists in Spain. However, their proper implementation is difficult due to healthcare resource limitations, as well as organisation and logistic issues. .e use of anti-VEGF agents with longer duration of action could facilitate the use of strict T&E approaches according to routine clinical practicesThe study has been sponsored by Bayer Hispania S.L. Logistic

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.

Strongly hyperbolic second order Einstein's evolution equations

BSSN-type evolution equations are discussed. The name refers to the Baumgarte, Shapiro, Shibata, and Nakamura version of the Einstein evolution equations, without introducing the conformal-traceless decomposition but keeping the three connection functions and including a densitized lapse. It is proved that a pseudo-differential first order reduction of these equations is strongly hyperbolic. In the same way, densitized Arnowitt-Deser-Misner evolution equations are found to be weakly hyperbolic. In both cases, the positive densitized lapse function and the spacelike shift vector are arbitrary given fields. This first order pseudodifferential reduction adds no extra equations to the system and so no extra constraints.Comment: LaTeX, 16 pages, uses revtex4. Referee corections and new appendix added. English grammar improved; typos correcte

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

A hyperbolic slicing condition adapted to Killing fields and densitized lapses

We study the properties of a modified version of the Bona-Masso family of hyperbolic slicing conditions. This modified slicing condition has two very important features: In the first place, it guarantees that if a spacetime is static or stationary, and one starts the evolution in a coordinate system in which the metric coefficients are already time independent, then they will remain time independent during the subsequent evolution, {\em i.e.} the lapse will not evolve and will therefore not drive the time lines away from the Killing direction. Second, the modified condition is naturally adapted to the use of a densitized lapse as a fundamental variable, which in turn makes it a good candidate for a dynamic slicing condition that can be used in conjunction with some recently proposed hyperbolic reformulations of the Einstein evolution equations.Comment: 11 page