Viscous wing theory development. Volume 1: Analysis, method and results

Viscous transonic flows at large Reynolds numbers over 3-D wings were analyzed using a zonal viscid-inviscid interaction approach. A new numerical AFZ scheme was developed in conjunction with the finite volume formulation for the solution of the inviscid full-potential equation. A special far-field asymptotic boundary condition was developed and a second-order artificial viscosity included for an improved inviscid solution methodology. The integral method was used for the laminar/turbulent boundary layer and 3-D viscous wake calculation. The interaction calculation included the coupling conditions of the source flux due to the wing surface boundary layer, the flux jump due to the viscous wake, and the wake curvature effect. A method was also devised incorporating the 2-D trailing edge strong interaction solution for the normal pressure correction near the trailing edge region. A fully automated computer program was developed to perform the proposed method with one scalar version to be used on an IBM-3081 and two vectorized versions on Cray-1 and Cyber-205 computers

Spin-squared Hamiltonian of next-to-leading order gravitational interaction

The static, i.e., linear momentum independent, part of the next-to-leading order (NLO) gravitational spin(1)-spin(1) interaction Hamiltonian within the post-Newtonian (PN) approximation is calculated from a 3-dim. covariant ansatz for the Hamilton constraint. All coefficients in this ansatz can be uniquely fixed for black holes. The resulting Hamiltonian fits into the canonical formalism of Arnowitt, Deser, and Misner (ADM) and is given in their transverse-traceless (ADMTT) gauge. This completes the recent result for the momentum dependent part of the NLO spin(1)-spin(1) ADM Hamiltonian for binary black holes (BBH). Thus, all PN NLO effects up to quadratic order in spin for BBH are now given in Hamiltonian form in the ADMTT gauge. The equations of motion resulting from this Hamiltonian are an important step toward more accurate calculations of templates for gravitational waves.Comment: REVTeX4, 10 pages, v2: minor improvements in the presentation, v3: added omission in Eq. (4) and corrected coefficients in the result, Eq. (9); version to appear in Phys. Rev.

Canonical formulation of self-gravitating spinning-object systems

Based on the Arnowitt-Deser-Misner (ADM) canonical formulation of general relativity, a canonical formulation of gravitationally interacting classical spinning-object systems is given to linear order in spin. The constructed position, linear momentum and spin variables fulfill standard Poisson bracket relations. A spatially symmetric time gauge for the tetrad field is introduced. The achieved formulation is of fully reduced form without unresolved constraints, supplementary, gauge, or coordinate conditions. The canonical field momentum is not related to the extrinsic curvature of spacelike hypersurfaces in standard ADM form. A new reduction of the tetrad degrees of freedom to the Einstein form of the metric field is suggested.Comment: 6 pages. v2: extended version; identical to the published one. v3: corrected misprints in (24) and (39); improved notation; added note regarding a further reference

Multidisciplinary Consideration of Potential Pathophysiologic Mechanisms of Paradoxical Erythema with Topical Brimonidine Therapy.

Rosacea is a chronic inflammatory disease with transient and non-transient redness as key characteristics. Brimonidine is a selective α2-adrenergic receptor (AR) agonist approved for persistent facial erythema of rosacea based on significant efficacy and good safety data. The majority of patients treated with brimonidine report a benefit; however, there have been sporadic reports of worsening erythema after the initial response. A group of dermatologists, receptor physiology, and neuroimmunology scientists met to explore potential mechanisms contributing to side effects as well as differences in efficacy. We propose the following could contribute to erythema after application: (1) local inflammation and perivascular inflammatory cells with abnormally functioning ARs may lead to vasodilatation; (2) abnormal saturation and cells expressing different AR subtypes with varying ligand affinity; (3) barrier dysfunction and increased skin concentrations of brimonidine with increased actions at endothelial and presynaptic receptors, resulting in increased vasodilation; and (4) genetic predisposition and receptor polymorphism(s) leading to different smooth muscle responses. Approximately 80% of patients treated with brimonidine experience a significant improvement without erythema worsening as an adverse event. Attention to optimizing skin barrier function, setting patient expectations, and strategies to minimize potential problems may possibly reduce further the number of patients who experience side effects.FundingGalderma International S.A.S., Paris, France

Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries

Within the post Newtonian framework the fully reduced Hamiltonian (i.e., with eliminated spin supplementary condition) for the next-to-leading order spin-squared dynamics of general compact binaries is presented. The Hamiltonian is applicable to the spin dynamics of all kinds of binaries with self-gravitating components like black holes and/or neutron stars taking into account spin-induced quadrupolar deformation effects in second post-Newtonian order perturbation theory of Einstein's field equations. The corresponding equations of motion for spin, position and momentum variables are given in terms of canonical Poisson brackets. Comparison with a nonreduced potential calculated within the Effective Field Theory approach is made.Comment: 11 pages, minor changes to match published version at CQ

Effective-action model for dynamical scalarization beyond the adiabatic approximation

In certain scalar-field extensions to general relativity, scalar charges can develop on compact objects in an inspiraling binary -- an effect known as dynamical scalarization. This effect can be modeled using effective-field-theory methods applied to the binary within the post-Newtonian approximation. Past analytic investigations focused on the adiabatic (or quasi-stationary) case for quasi-circular orbits. In this work, we explore the full dynamical evolution around the phase transition to the scalarized regime. This allows for generic (eccentric) orbits and to quantify nonadiabatic (e.g., oscillatory) behavior during the phase transition. We also find that even in the circular-orbit case, the onset of scalarization can only be predicted reliably when taking the full dynamics into account, i.e., the adiabatic approximation is not appropriate. Our results pave the way for accurate post-Newtonian predictions for dynamical scalarization effects in gravitational waves from compact binaries

Gravitational Quadratic-in-Spin Hamiltonian at NNNLO in the post-Newtonian framework

We present the result of the quadratic-in-spin interaction Hamiltonian forbinary systems of rotating compact objects with generic spins, up to NNNLOcorrections within the post-Newtonian expansion. The calculation is performedby employing the effective field theory diagrammatic approach, and it involvesFeynman integrals up to three loops, evaluated within the dimensionalregularization scheme. The gauge-invariant binding energy and the scatteringangle, in special kinematic regimes and spin configurations, are explicitlyderived. The results extend our earlier study on the spin-orbit interactioneffects.<br

Non-Relativistic Gravitation: From Newton to Einstein and Back

We present an improvement to the Classical Effective Theory approach to the non-relativistic or Post-Newtonian approximation of General Relativity. The "potential metric field" is decomposed through a temporal Kaluza-Klein ansatz into three NRG-fields: a scalar identified with the Newtonian potential, a 3-vector corresponding to the gravito-magnetic vector potential and a 3-tensor. The derivation of the Einstein-Infeld-Hoffmann Lagrangian simplifies such that each term corresponds to a single Feynman diagram providing a clear physical interpretation. Spin interactions are dominated by the exchange of the gravito-magnetic field. Leading correction diagrams corresponding to the 3PN correction to the spin-spin interaction and the 2.5PN correction to the spin-orbit interaction are presented.Comment: 10 pages, 3 figures. v2: published version. v3: Added a computation of Einstein-Infeld-Hoffmann in higher dimensions within our improved ClEFT which partially confirms and partially corrects a previous computation. See notes added at end of introductio

On the comparison of results regarding the post-Newtonian approximate treatment of the dynamics of extended spinning compact binaries

A brief review is given of all the Hamiltonians and effective potentials calculated hitherto covering the post-Newtonian (pN) dynamics of a two body system. A method is presented to compare (conservative) reduced Hamiltonians with nonreduced potentials directly at least up to the next-to-leading-pN order.Comment: Conference proceedings for the 7th International Conference on Gravitation and Cosmology (ICGC2011), 4 page