Effective stress-energy tensors, self-force, and broken symmetry

Deriving the motion of a compact mass or charge can be complicated by the presence of large self-fields. Simplifications are known to arise when these fields are split into two parts in the so-called Detweiler-Whiting decomposition. One component satisfies vacuum field equations, while the other does not. The force and torque exerted by the (often ignored) inhomogeneous "S-type" portion is analyzed here for extended scalar charges in curved spacetimes. If the geometry is sufficiently smooth, it is found to introduce effective shifts in all multipole moments of the body's stress-energy tensor. This greatly expands the validity of statements that the homogeneous R field determines the self-force and self-torque up to renormalization effects. The forces and torques exerted by the S field directly measure the degree to which a spacetime fails to admit Killing vectors inside the body. A number of mathematical results related to the use of generalized Killing fields are therefore derived, and may be of wider interest. As an example of their application, the effective shift in the quadrupole moment of a charge's stress-energy tensor is explicitly computed to lowest nontrivial order.Comment: 22 pages, fixed typos and simplified discussio

Mechanics of extended masses in general relativity

The "external" or "bulk" motion of extended bodies is studied in general relativity. Compact material objects of essentially arbitrary shape, spin, internal composition, and velocity are allowed as long as there is no direct (non-gravitational) contact with other sources of stress-energy. Physically reasonable linear and angular momenta are proposed for such bodies and exact equations describing their evolution are derived. Changes in the momenta depend on a certain "effective metric" that is closely related to a non-perturbative generalization of the Detweiler-Whiting R-field originally introduced in the self-force literature. If the effective metric inside a self-gravitating body can be adequately approximated by an appropriate power series, the instantaneous gravitational force and torque exerted on it is shown to be identical to the force and torque exerted on an appropriate test body moving in the effective metric. This result holds to all multipole orders. The only instantaneous effect of a body's self-field is to finitely renormalize the "bare" multipole moments of its stress-energy tensor. The MiSaTaQuWa expression for the gravitational self-force is recovered as a simple application. A gravitational self-torque is obtained as well. Lastly, it is shown that the effective metric in which objects appear to move is approximately a solution to the vacuum Einstein equation if the physical metric is an approximate solution to Einstein's equation linearized about a vacuum background.Comment: 39 pages, 2 figures; fixed equation satisfied by the Green function used to construct the effective metri

Self-forces from generalized Killing fields

A non-perturbative formalism is developed that simplifies the understanding of self-forces and self-torques acting on extended scalar charges in curved spacetimes. Laws of motion are locally derived using momenta generated by a set of generalized Killing fields. Self-interactions that may be interpreted as arising from the details of a body's internal structure are shown to have very simple geometric and physical interpretations. Certain modifications to the usual definition for a center-of-mass are identified that significantly simplify the motions of charges with strong self-fields. A derivation is also provided for a generalized form of the Detweiler-Whiting axiom that pointlike charges should react only to the so-called regular component of their self-field. Standard results are shown to be recovered for sufficiently small charge distributions.Comment: 21 page

Electromagnetic self-forces and generalized Killing fields

Building upon previous results in scalar field theory, a formalism is developed that uses generalized Killing fields to understand the behavior of extended charges interacting with their own electromagnetic fields. New notions of effective linear and angular momenta are identified, and their evolution equations are derived exactly in arbitrary (but fixed) curved spacetimes. A slightly modified form of the Detweiler-Whiting axiom that a charge's motion should only be influenced by the so-called "regular" component of its self-field is shown to follow very easily. It is exact in some interesting cases, and approximate in most others. Explicit equations describing the center-of-mass motion, spin angular momentum, and changes in mass of a small charge are also derived in a particular limit. The chosen approximations -- although standard -- incorporate dipole and spin forces that do not appear in the traditional Abraham-Lorentz-Dirac or Dewitt-Brehme equations. They have, however, been previously identified in the test body limit.Comment: 20 pages, minor typos correcte

Methodological insights from a study using video-ethnography to conduct interdisciplinary research in the study of birth unit design

© eContent Management Pty Ltd. Little is known about how the physical design of a birthing unit can influence the experiences of labour and birth for women, their supporters and midwives. We proposed that an interdisciplinary approach (disciplines of midwifery, architecture, design, communication and public health) was likely to be the most effective way to better understand the complexities and interactions of design, behaviour, communication and experiences. In this methodological paper we aim to provide a roadmap that other researchers may find helpful when considering the use of video as a data collection technique, especially in the study of the powerful and intimate setting of childbirth. The paper also outlines our process for engaging both researchers and participants in reviewing video footage with the aim to contribute multiple perspectives to the analysis process

Spatial Scaling in Model Plant Communities

We present an analytically tractable variant of the voter model that provides a quantitatively accurate description of beta-diversity (two-point correlation function) in two tropical forests. The model exhibits novel scaling behavior that leads to links between ecological measures such as relative species abundance and the species area relationship.Comment: 10 pages, 3 figure

Seasonal patterns of carbon dioxide and water fluxes in three representative tundra ecosystems in northern Alaska

© The Author(s), 2012. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Ecosphere 3, no 1 (2012): art4, doi:10.1890/ES11-00202.1.Understanding the carbon dioxide and water fluxes in the Arctic is essential for accurate assessment and prediction of the responses of these ecosystems to climate change. In the Arctic, there have been relatively few studies of net CO2, water, and energy exchange using micrometeorological methods due to the difficulty of performing these measurements in cold, remote regions. When these measurements are performed, they are usually collected only during the short summer growing season. We established eddy covariance flux towers in three representative Alaska tundra ecosystems (heath tundra, tussock tundra, and wet sedge tundra), and have collected CO2, water, and energy flux data continuously for over three years (September 2007–May 2011). In all ecosystems, peak CO2 uptake occurred during July, with accumulations of 51–95 g C/m2 during June–August. The timing of the switch from CO2 source to sink in the spring appears to be regulated by the number of growing degree days early in the season, indicating that warmer springs may promote increased net CO2 uptake. However, this increased uptake in the spring may be lost through warmer temperatures in the late growing season that promote respiration, if this respiration is not impeded by large amounts of precipitation or cooler temperatures. Net CO2 accumulation during the growing season was generally lost through respiration during the snow covered months of September–May, turning the ecosystems into net sources of CO2 over measurement period. The water balance from June to August at the three ecosystems was variable, with the most variability observed in the heath tundra, and the least in the tussock tundra. These findings underline the importance of collecting data over the full annual cycle and across multiple types of tundra ecosystems in order to come to a more complete understanding of CO2 and water fluxes in the Arctic.This research was funded by the National Science Foundation Office of Polar Programs (OPP 0632264), with a grant during the International Polar Year, ‘Collaborative Research on Carbon, Water, and Energy Balance of the Arctic Landscape at Flagship Observatories and in a PanArctic Network’. Trac

Universal Fluctuations in Correlated Systems

The probability density function (PDF) of a global measure in a large class of highly correlated systems has been suggested to be of the same functional form. Here, we identify the analytical form of the PDF of one such measure, the order parameter in the low temperature phase of the 2D-XY model. We demonstrate that this function describes the fluctuations of global quantities in other correlated, equilibrium and non-equilibrium systems. These include a coupled rotor model, Ising and percolation models, models of forest fires, sand-piles, avalanches and granular media in a self organized critical state. We discuss the relationship with both Gaussian and extremal statistics.Comment: 4 pages, 2 figure

Self-forces on extended bodies in electrodynamics

In this paper, we study the bulk motion of a classical extended charge in flat spacetime. A formalism developed by W. G. Dixon is used to determine how the details of such a particle's internal structure influence its equations of motion. We place essentially no restrictions (other than boundedness) on the shape of the charge, and allow for inhomogeneity, internal currents, elasticity, and spin. Even if the angular momentum remains small, many such systems are found to be affected by large self-interaction effects beyond the standard Lorentz-Dirac force. These are particularly significant if the particle's charge density fails to be much greater than its 3-current density (or vice versa) in the center-of-mass frame. Additional terms also arise in the equations of motion if the dipole moment is too large, and when the `center-of-electromagnetic mass' is far from the `center-of-bare mass' (roughly speaking). These conditions are often quite restrictive. General equations of motion were also derived under the assumption that the particle can only interact with the radiative component of its self-field. These are much simpler than the equations derived using the full retarded self-field; as are the conditions required to recover the Lorentz-Dirac equation.Comment: 30 pages; significantly improved presentation; accepted for publication in Phys. Rev.