The self-consistent gravitational self-force

I review the problem of motion for small bodies in General Relativity, with an emphasis on developing a self-consistent treatment of the gravitational self-force. An analysis of the various derivations extant in the literature leads me to formulate an asymptotic expansion in which the metric is expanded while a representative worldline is held fixed; I discuss the utility of this expansion for both exact point particles and asymptotically small bodies, contrasting it with a regular expansion in which both the metric and the worldline are expanded. Based on these preliminary analyses, I present a general method of deriving self-consistent equations of motion for arbitrarily structured (sufficiently compact) small bodies. My method utilizes two expansions: an inner expansion that keeps the size of the body fixed, and an outer expansion that lets the body shrink while holding its worldline fixed. By imposing the Lorenz gauge, I express the global solution to the Einstein equation in the outer expansion in terms of an integral over a worldtube of small radius surrounding the body. Appropriate boundary data on the tube are determined from a local-in-space expansion in a buffer region where both the inner and outer expansions are valid. This buffer-region expansion also results in an expression for the self-force in terms of irreducible pieces of the metric perturbation on the worldline. Based on the global solution, these pieces of the perturbation can be written in terms of a tail integral over the body's past history. This approach can be applied at any order to obtain a self-consistent approximation that is valid on long timescales, both near and far from the small body. I conclude by discussing possible extensions of my method and comparing it to alternative approaches.Comment: 44 pages, 4 figure

Trade-offs between morphology and thermal niches mediate adaptation in response to competing selective pressures

The effects of climate change—such as increased temperature variability and novel predators—rarely happen in isolation, but it is unclear how organisms cope with mul- tiple stressors simultaneously. To explore this, we grew replicate Paramecium caudatum populations in either constant or variable temperatures and exposed half to predation. We then fit thermal performance curves (TPCs) of intrinsic growth rate (rmax) for each replicate population (N = 12) across seven temperatures (10°C–38°C). TPCs of P. caudatum exposed to both temperature variability and predation re- sponded only to one or the other (but not both), resulting in unpredictable outcomes. These changes in TPCs were accompanied by changes in cell morphology. Although cell volume was conserved across treatments, cells became narrower in response to temperature variability and rounder in response to predation. Our findings sug- gest that predation and temperature variability produce conflicting pressures on both thermal performance and cell morphology. Lastly, we found a strong correlation between changes in cell morphology and TPC parameters in response to predation, suggesting that responses to opposing selective pressures could be constrained by trade-offs. Our results shed new light on how environmental and ecological pressures interact to elicit changes in characteristics at both the individual and population levels. We further suggest that morphological responses to interactive environmen- tal forces may modulate population-level responses, making prediction of long-term responses to environmental change challenging

Trade-Offs Between Morphology and Thermal Niches Mediate Adaptation in Response to Competing Selective Pressures

Abstract The effects of climate change—such as increased temperature variability and novel predators—rarely happen in isolation, but it is unclear how organisms cope with multiple stressors simultaneously. To explore this, we grew replicate Paramecium caudatum populations in either constant or variable temperatures and exposed half to predation. We then fit thermal performance curves (TPCs) of intrinsic growth rate (rmax) for each replicate population (N = 12) across seven temperatures (10°C–38°C). TPCs of P. caudatum exposed to both temperature variability and predation responded only to one or the other (but not both), resulting in unpredictable outcomes. These changes in TPCs were accompanied by changes in cell morphology. Although cell volume was conserved across treatments, cells became narrower in response to temperature variability and rounder in response to predation. Our findings suggest that predation and temperature variability produce conflicting pressures on both thermal performance and cell morphology. Lastly, we found a strong correlation between changes in cell morphology and TPC parameters in response to predation, suggesting that responses to opposing selective pressures could be constrained by trade-offs. Our results shed new light on how environmental and ecological pressures interact to elicit changes in characteristics at both the individual and population levels. We further suggest that morphological responses to interactive environmental forces may modulate population-level responses, making prediction of long-term responses to environmental change challenging

Gestational age at delivery and special educational need: retrospective cohort study of 407,503 schoolchildren

<STRONG>Background</STRONG> Previous studies have demonstrated an association between preterm delivery and increased risk of special educational need (SEN). The aim of our study was to examine the risk of SEN across the full range of gestation. <STRONG>Methods and Findings</STRONG> We conducted a population-based, retrospective study by linking school census data on the 407,503 eligible school-aged children resident in 19 Scottish Local Authority areas (total population 3.8 million) to their routine birth data. SEN was recorded in 17,784 (4.9%) children; 1,565 (8.4%) of those born preterm and 16,219 (4.7%) of those born at term. The risk of SEN increased across the whole range of gestation from 40 to 24 wk: 37–39 wk adjusted odds ratio (OR) 1.16, 95% confidence interval (CI) 1.12–1.20; 33–36 wk adjusted OR 1.53, 95% CI 1.43–1.63; 28–32 wk adjusted OR 2.66, 95% CI 2.38–2.97; 24–27 wk adjusted OR 6.92, 95% CI 5.58–8.58. There was no interaction between elective versus spontaneous delivery. Overall, gestation at delivery accounted for 10% of the adjusted population attributable fraction of SEN. Because of their high frequency, early term deliveries (37–39 wk) accounted for 5.5% of cases of SEN compared with preterm deliveries (<37 wk), which accounted for only 3.6% of cases. <STRONG>Conclusions</STRONG> Gestation at delivery had a strong, dose-dependent relationship with SEN that was apparent across the whole range of gestation. Because early term delivery is more common than preterm delivery, the former accounts for a higher percentage of SEN cases. Our findings have important implications for clinical practice in relation to the timing of elective delivery

Equation level matching: An extension of the method of matched asymptotic expansion for problems of wave propagation

We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we propose to match at the level of the equations involved, via a "uniform expansion" whose equations enfold those of the approximations to be matched. This has the advantage that one does not need to explicitly solve the asymptotic equations to do the matching, which can be quite impossible for some problems. In addition, it allows matching to proceed in certain wave situations where the traditional approach fails because the time behaviors differ (e.g., one of the expansions does not include dissipation). On the other hand, this approach does not provide the fairly explicit approximations resulting from standard matching. In fact, this is not even its aim, which to produce the "simplest" set of equations that capture the behavior

Singular perturbation techniques in the gravitational self-force problem

Much of the progress in the gravitational self-force problem has involved the use of singular perturbation techniques. Yet the formalism underlying these techniques is not widely known. I remedy this situation by explicating the foundations and geometrical structure of singular perturbation theory in general relativity. Within that context, I sketch precise formulations of the methods used in the self-force problem: dual expansions (including matched asymptotic expansions), for which I identify precise matching conditions, one of which is a weak condition arising only when multiple coordinate systems are used; multiscale expansions, for which I provide a covariant formulation; and a self-consistent expansion with a fixed worldline, for which I provide a precise statement of the exact problem and its approximation. I then present a detailed analysis of matched asymptotic expansions as they have been utilized in calculating the self-force. Typically, the method has relied on a weak matching condition, which I show cannot determine a unique equation of motion. I formulate a refined condition that is sufficient to determine such an equation. However, I conclude that the method yields significantly weaker results than do alternative methods.Comment: 39 pages, 5 figures, final version to be published in Phys. Rev. D, several typos corrected, added discussion of order-reductio

Simple Viscous Flows: from Boundary Layers to the Renormalization Group

The seemingly simple problem of determining the drag on a body moving through a very viscous fluid has, for over 150 years, been a source of theoretical confusion, mathematical paradoxes, and experimental artifacts, primarily arising from the complex boundary layer structure of the flow near the body and at infinity. We review the extensive experimental and theoretical literature on this problem, with special emphasis on the logical relationship between different approaches. The survey begins with the developments of matched asymptotic expansions, and concludes with a discussion of perturbative renormalization group techniques, adapted from quantum field theory to differential equations. The renormalization group calculations lead to a new prediction for the drag coefficient, one which can both reproduce and surpass the results of matched asymptotics

Finite size effects near the onset of the oscillatory instability

A system of two complex Ginzburg - Landau equations is considered that applies at the onset of the oscillatory instability in spatial domains whose size is large (but finite) in one direction; the dependent variables are the slowly modulated complex amplitudes of two counterpropagating wavetrains. In order to obtain a well posed problem, four boundary conditions must be imposed at the boundaries. Two of them were already known, and the other two are first derived in this paper. In the generic case when the group velocity is of order unity, the resulting problem has terms that are not of the same order of magnitude. This fact allows us to consider two distinguished limits and to derive two associated (simpler) sub-models, that are briefly discussed. Our results predict quite a rich variety of complex dynamics that is due to both the modulational instability and finite size effects

The Adhesion GPCR GPR125 is specifically expressed in the choroid plexus and is upregulated following brain injury

<p>Abstract</p> <p>Background</p> <p>GPR125 belongs to the family of <it>Adhesion </it>G protein-coupled receptors (GPCRs). A single copy of GPR125 was found in many vertebrate genomes. We also identified a <it>Drosophila </it>sequence, DmCG15744, which shares a common ancestor with the entire Group III of <it>Adhesio</it>n GPCRs, and also contains Ig, LRR and HBD domains which were observed in mammalian GPR125.</p> <p>Results</p> <p>We found specific expression of GPR125 in cells of the choroid plexus using <it>in situ </it>hybridization and protein-specific antibodies and combined <it>in situ</it>/immunohistochemistry co-localization using cytokeratin, a marker specific for epithelial cells. Induction of inflammation by LPS did not change GPR125 expression. However, GPR125 expression was transiently increased (almost 2-fold) at 4 h after traumatic brain injury (TBI) followed by a decrease (approximately 4-fold) from 2 days onwards in the choroid plexus as well as increased expression (2-fold) in the hippocampus that was delayed until 1 day after injury.</p> <p>Conclusion</p> <p>These findings suggest that GPR125 plays a functional role in choroidal and hippocampal response to injury.</p