Effective source approach to self-force calculations

Numerical evaluation of the self-force on a point particle is made difficult by the use of delta functions as sources. Recent methods for self-force calculations avoid delta functions altogether, using instead a finite and extended "effective source" for a point particle. We provide a review of the general principles underlying this strategy, using the specific example of a scalar point charge moving in a black hole spacetime. We also report on two new developments: (i) the construction and evaluation of an effective source for a scalar charge moving along a generic orbit of an arbitrary spacetime, and (ii) the successful implementation of hyperboloidal slicing that significantly improves on previous treatments of boundary conditions used for effective-source-based self-force calculations. Finally, we identify some of the key issues related to the effective source approach that will need to be addressed by future work.Comment: Invited review for NRDA/Capra 2010 (Theory Meets Data Analysis at Comparable and Extreme Mass Ratios), Perimeter Institute, June 2010, CQG special issue - 22 pages, 8 figure

Quasi-local contribution to the scalar self-force: Geodesic Motion

We consider a scalar charge travelling in a curved background spacetime. We calculate the quasi-local contribution to the scalar self-force experienced by such a particle following a geodesic in a general spacetime. We also show that if we assume a massless field and a vacuum background spacetime, the expression for the self-force simplifies significantly. We consider some specific cases whose gravitational analog are of immediate physical interest for the calculation of radiation reaction corrected orbits of binary black hole systems. These systems are expected to be detectable by the LISA space based gravitational wave observatory. We also investigate how alternate techniques may be employed in some specific cases and use these as a check on our own results.Comment: Final Phys. Rev. D version. 24 pages, revtex4. Minor typos correcte

Generic effective source for scalar self-force calculations

A leading approach to the modelling of extreme mass ratio inspirals involves the treatment of the smaller mass as a point particle and the computation of a regularized self-force acting on that particle. In turn, this computation requires knowledge of the regularized retarded field generated by the particle. A direct calculation of this regularized field may be achieved by replacing the point particle with an effective source and solving directly a wave equation for the regularized field. This has the advantage that all quantities are finite and require no further regularization. In this work, we present a method for computing an effective source which is finite and continuous everywhere, and which is valid for a scalar point particle in arbitrary geodesic motion in an arbitrary background spacetime. We explain in detail various technical and practical considerations that underlie its use in several numerical self-force calculations. We consider as examples the cases of a particle in a circular orbit about Schwarzschild and Kerr black holes, and also the case of a particle following a generic time-like geodesic about a highly spinning Kerr black hole. We provide numerical C code for computing an effective source for various orbital configurations about Schwarzschild and Kerr black holes.Comment: 24 pages, 7 figures, final published versio

Quasi-local contribution to the scalar self-force: Non-geodesic Motion

We extend our previous calculation of the quasi-local contribution to the self-force on a scalar particle to general (not necessarily geodesic) motion in a general spacetime. In addition to the general case and the case of a particle at rest in a stationary spacetime, we consider as examples a particle held at rest in Reissner-Nordstrom and Kerr-Newman space-times. This allows us to most easily analyse the effect of non-geodesic motion on our previous results and also allows for comparison to existing results for Schwarzschild spacetime.Comment: 11 pages, 1 figure, corrected typo in Eq. 2.

Improving the triple bottom line returns from smallholder tree farms in the Philippines: A systems approach

This paper outlines the application of systems thinking in investigating ways to improve the returns to smallholder tree farmers in the Philippines. The paper illustrates how a systems approach was used in the conceptualisation of the project and how systems thinking facilitated a shared understanding of the how each individual’s research contributed to the broader project activities. Systems thinking has also been used in the design and implementation of various project activities. Three examples are provided. The first example illustrates how a systems diagram was developed which outlined the direct and indirect linkages between biophysical data on tree farms and various activities designed to increase returns. The second example illustrates how the suggested approach for improving the flow of information concerning tree registration, harvest and transportation regulations and approval mechanisms link with various project activities and have been informed by a series of action research workshops. The third example illustrates how systems thinking has been applied to understand the factors affecting the production of high quality tree seedlings and to investigate the effect of policy interventions on improving the quality of seedlings available to smallholders

1,3-Bis(4-bromo­phen­yl)imidazolium chloride dihydrate

In the title hydrated salt, C15H11Br2N2 +·Cl−·2H2O, the complete imidazolium cation is generated by a crystallographic twofold axis, with one C atom lying on the axis. The chloride ion and both water mol­ecules of crystallization also lie on a crystallographic twofold axis of symmetry. The cation is non-planar, the dihedral angle formed between the central imidazolium and benzene rings being 12.9 (3)°; the dihedral angle between the symmetry-related benzene rings is 25.60 (13)°. In the crystal, O—H⋯Cl hydrogen bonds result in supra­molecular chains along c mediated by eight-membered {⋯HOH⋯Cl}2 synthons. These are consolidated by C—H⋯O and π–π [centroid–centroid distance = 3.687 (3) Å] inter­actions

MEASUREMENT OF SMALLHOLDER TREE FARMS ON LEYTE ISLAND

This paper describes the field techniques used to measure timber volume and log quality from smallholder tree farms on Leyte Island conducted as part of ACIAR project ASEM/2003/052, Improving Financial Returns from Smallholder Tree Farms in the Philippines . Tree farms were included in the sample if they were 0.1 ha or greater in area and contained 100 or more trees. Paired circular blocks were chosen for measurement, one in the centre and one on the edge of the tree block. Where tree farms included multiple blocks of trees, two circular plots were established within each block. For each tree over 10 cm diameter at breast height (dbh) in the plot, measurements were made of dbh, diameter at the base (db), tree height, location, crown depth, crown radius, bearing and distance of each tree with reference to the plot centre. Estimates of log lengths and grade that each tree was expected to yield were also recorded, along with a sketch of each tree. In addition, data were collected on tree farm, block and plot characteristics, and were entered into an ACCESS database for subsequent analysis

Spin–orbit precession for eccentric black hole binaries at first order in the mass ratio

We consider spin–orbit ('geodetic') precession for a compact binary in strong-field gravity. Specifically, we compute ψ, the ratio of the accumulated spin-precession and orbital angles over one radial period, for a spinning compact body of mass m 1 and spin s 1, with ${{s}_{1}}\ll Gm_{1}^{2}/c$ , orbiting a non-rotating black hole. We show that ψ can be computed for eccentric orbits in both the gravitational self-force and post-Newtonian frameworks, and that the results appear to be consistent. We present a post-Newtonian expansion for ψ at next-to-next-to-leading order, and a Lorenz-gauge gravitational self-force calculation for ψ at first order in the mass ratio. The latter provides new numerical data in the strong-field regime to inform the effective one-body model of the gravitational two-body problem. We conclude that ψ complements the Detweiler redshift z as a key invariant quantity characterizing eccentric orbits in the gravitational two-body problem

Glycoprotein Ib activation by thrombin stimulates the energy metabolism in human platelets

<div><p>Thrombin-induced platelet activation requires substantial amounts of ATP. However, the specific contribution of each ATP-generating pathway <i>i</i>.<i>e</i>., oxidative phosphorylation (OxPhos) versus glycolysis and the biochemical mechanisms involved in the thrombin-induced activation of energy metabolism remain unclear. Here we report an integral analysis on the role of both energy pathways in human platelets activated by several agonists, and the signal transducing mechanisms associated with such activation. We found that thrombin, Trap-6, arachidonic acid, collagen, A23187, epinephrine and ADP significantly increased glycolytic flux (3–38 times <i>vs</i>. non-activated platelets) whereas ristocetin was ineffective. OxPhos (33 times) and mitochondrial transmembrane potential (88%) were increased only by thrombin. OxPhos was the main source of ATP in thrombin-activated platelets, whereas in platelets activated by any of the other agonists, glycolysis was the principal ATP supplier. In order to establish the biochemical mechanisms involved in the thrombin-induced OxPhos activation in platelets, several signaling pathways associated with mitochondrial activation were analyzed. Wortmannin and LY294002 (PI3K/Akt pathway inhibitors), ristocetin and heparin (GPIb inhibitors) as well as resveratrol, ATP (calcium-release inhibitors) and PP1 (Tyr-phosphorylation inhibitor) prevented the thrombin-induced platelet activation. These results suggest that thrombin activates OxPhos and glycolysis through GPIb-dependent signaling involving PI3K and Akt activation, calcium mobilization and protein phosphorylation.</p></div