Explicit solution of the linearized Einstein equations in TT gauge for all multipoles

We write out the explicit form of the metric for a linearized gravitational wave in the transverse-traceless gauge for any multipole, thus generalizing the well-known quadrupole solution of Teukolsky. The solution is derived using the generalized Regge-Wheeler-Zerilli formalism developed by Sarbach and Tiglio.Comment: 9 pages. Minor corrections, updated references. Final version to appear in Class. Quantum Gra

Three-dimensional adaptive evolution of gravitational waves in numerical relativity

Adaptive techniques are crucial for successful numerical modeling of gravitational waves from astrophysical sources such as coalescing compact binaries, since the radiation typically has wavelengths much larger than the scale of the sources. We have carried out an important step toward this goal, the evolution of weak gravitational waves using adaptive mesh refinement in the Einstein equations. The 2-level adaptive simulation is compared with unigrid runs at coarse and fine resolution, and is shown to track closely the features of the fine grid run.Comment: REVTeX, 7 pages, including three figures; submitted to Physical Review

An Axisymmetric Gravitational Collapse Code

We present a new numerical code designed to solve the Einstein field equations for axisymmetric spacetimes. The long term goal of this project is to construct a code that will be capable of studying many problems of interest in axisymmetry, including gravitational collapse, critical phenomena, investigations of cosmic censorship, and head-on black hole collisions. Our objective here is to detail the (2+1)+1 formalism we use to arrive at the corresponding system of equations and the numerical methods we use to solve them. We are able to obtain stable evolution, despite the singular nature of the coordinate system on the axis, by enforcing appropriate regularity conditions on all variables and by adding numerical dissipation to hyperbolic equations.Comment: 19 pages, 9 figure

Can rates of ocean primary production and biological carbon export be related through their probability distributions?

© The Author(s), 2018. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Global Biogeochemical Cycles 32 (2018): 954-970, doi:10.1029/2017GB005797.We describe the basis of a theory for interpreting measurements of two key biogeochemical fluxes—primary production by phytoplankton (p, μg C · L−1 · day−1) and biological carbon export from the surface ocean by sinking particles (f, mg C · m−2 · day−1)—in terms of their probability distributions. Given that p and f are mechanistically linked but variable and effectively measured on different scales, we hypothesize that a quantitative relationship emerges between collections of the two measurements. Motivated by the many subprocesses driving production and export, we take as a null model that large‐scale distributions of p and f are lognormal. We then show that compilations of p and f measurements are consistent with this hypothesis. The compilation of p measurements is extensive enough to subregion by biome, basin, depth, or season; these subsets are also well described by lognormals, whose log‐moments sort predictably. Informed by the lognormality of both p and f we infer a statistical scaling relationship between the two quantities and derive a linear relationship between the log‐moments of their distributions. We find agreement between two independent estimates of the slope and intercept of this line and show that the distribution of f measurements is consistent with predictions made from the moments of the p distribution. These results illustrate the utility of a distributional approach to biogeochemical fluxes. We close by describing potential uses and challenges for the further development of such an approach.National Science Foundation Grant Number: OCE-1315201; Simons Foundation Grant Numbers: 329108, 553242; National Aeronautics and Space Administration Grant Numbers: NNX16AR47G, NNX16AR49

Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations

We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and nonlinear waves, and are found to be both less reflective and constraint preserving than standard Sommerfeld-type boundary conditions.Comment: 18 pages, 7 figures, accepted in CQ

Sinking properties of some phytoplankton shapes and the relation of form resistance to morphological diversity of plankton – an experimental study

Form resistance (Phi) is a dimensionless number expressing how much slower or faster a particle of any form sinks in a fluid medium than the sphere of equivalent volume. Form resistance factors of PVC models of phytoplankton sinking in glycerin were measured in a large aquarium (0.6 x 0.6 x 0.95 m). For cylindrical forms, a positive relationship was found between Phi and length/ width ratio. Coiling decreased Phi in filamentous forms. Form resistance of Asterionella colonies increased from single cells up to 6-celled colonies than remained nearly constant. For Fragilaria crotonensis chains, no such upper limit to Phi was observed in chains of up to 20 cells ( longer ones were not measured). The effect of symmetry on Phi was tested in 1 - 6-celled Asterionella colonies, having variable angles between the cells, and in Tetrastrum staurogeniaeforme coenobia, having different spine arrangements. In all cases, symmetric forms had considerably higher form resistance than asymmetric ones. However, for Pediastrum coenobia with symmetric/asymmetric fenestration, no difference was observed with respect to symmetry. Increasing number and length of spines on Tetrastrum coenobia substantially increased Phi. For a series of Staurastrum forms, a significant positive correlation was found between arm-length/cell-width ratio and Phi: protuberances increased form resistance. Flagellates (Rhodomonas, Gymnodinium) had a Phi 1. The highest value ( Phi = 8.1) was established for a 20-celled Fragilaria crotonensis chain. Possible origin of the so-called 'vital component' ( a factor that shows how much slower viable populations sink than morphologically similar senescent or dead ones) is discussed, as is the role of form resistance in evolution of high diversity of plankton morphologies

Deep subcutaneous application of poly-L-lactic acid as a filler for facial lipoatrophy in HIV-infected patients

Introduction: Facial lipoatrophy is a crucial problem of HIV-infected patients undergoing highly active antiretroviral therapy (HAART). Poly-L-lactic acid (PLA), provided as New-Fill(R)/Sculptra(TM), is known as one possible treatment option. In 2004 PLA was approved by the FDA as Sculptra(TM) for the treatment of lipoatrophy of the face in HIV-infected patients. While the first trials demonstrated relevant efficacy, this was to some extent linked to unwanted effects. As the depth of injection was considered relevant in this context, the application modalities of the preparation were changed. The preparation was to be injected more deeply into subcutaneous tissue, after increased dilution. Material and Methods: To test this approach we performed a pilot study following the new recommendations in 14 patients. Results: While the efficacy turned out to be about the same, tolerability was markedly improved. The increase in facial dermal thickness was particularly obvious in those patients who had suffered from lipoatrophy for a comparatively small period of time. Conclusion: With the new recommendations to dilute PLA powder and to inject it into the deeper subcutaneous tissue nodule formation is a minor problem. However, good treatment results can only be achieved if lipoatrophy is not too intense; treatment intervals should be about 2 - 3 weeks. Copyright (C) 2005 S. Karger AG, Basel

Symmetry without Symmetry: Numerical Simulation of Axisymmetric Systems using Cartesian Grids

We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used, particularly in simulating tensor partial differential equations like those of 3+1 numerical relativity. For a system axisymmetric about the z axis, the basic idea is to use a 3-dimensional Cartesian (x,y,z) coordinate grid which covers (say) the y=0 plane, but is only one finite-difference-molecule--width thick in the y direction. The field variables in the central y=0 grid plane can be updated using normal (x,y,z)--coordinate finite differencing, while those in the y \neq 0 grid planes can be computed from those in the central plane by using the axisymmetry assumption and interpolation. We demonstrate the effectiveness of the approach on a set of fully nonlinear test computations in 3+1 numerical general relativity, involving both black holes and collapsing gravitational waves.Comment: 17 pages, 4 figure

Dynamics of Gravitational Waves in 3D: Formulations, Methods, and Tests

The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge degrees of freedom. Using gravitational waves with amplitudes low enough that one has a good understanding of the physics involved, but large enough to enable non-linear effects to emerge, we study the coupling between numerical errors, coordinate effects, and the nonlinearities of the theory. We discuss the various strategies used in identifying specific features of the evolution. We show the importance of the flexibility of being able to use different numerical schemes, different slicing conditions, different formulations of the Einstein equations (standard ADM vs. first order hyperbolic), and different sets of equations (linearized vs. full Einstein equations). A non-linear scalar field equation is presented which captures some properties of the full Einstein equations, and has been useful in our understanding of the coupling between finite differencing errors and non-linearites. We present a set of monitoring devices which have been crucial in our studying of the waves, including Riemann invariants, pseudo-energy momentum tensor, hamiltonian constraint violation, and fourier spectrum analysis.Comment: 34 pages, 14 figure