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

Optimal Rebuilding of Fish Stocks in Different Nations: Bioeconomic Lessons for Regulators

Under the rubric of sustainable fisheries, nations are mandated to rebuild overfished stocks. Although rebuilding strategies are almost universally directed by the available biological information, approaches vary depending on fishery laws, management objectives, and technical guidelines. For example, rebuilding schedules in the United States are primarily designed to achieve rapid rebuilding of biomass and spawning stocks consistent with the biological characteristics of the resource. In contrast, New Zealand has greater flexibility in rebuilding stocks in order to consider economic, social, and cultural needs. In this paper we investigate potential economic costs to the fishery that result by limiting the US manager’s flexibility in choosing a recovery trajectory. Using numerical models for moderate- and long-lived stocks, the analysis reveals that depending on productivity of the stock and the discount rate, extending the rebuilding timeframe can substantially increase annual harvests and economic benefits. The results underscore the importance of economic analysis in crafting flexible rebuilding schedules that account for the unique characteristics of the fisheries, including economic and social needs.Fisheries economics, fisheries management, K-selective species, rebuilding., Resource /Energy Economics and Policy, Q22, C61,

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

Multipole structure of current vectors in curved spacetime

A method is presented which allows the exact construction of conserved (i.e. divergence-free) current vectors from appropriate sets of multipole moments. Physically, such objects may be taken to represent the flux of particles or electric charge inside some classical extended body. Several applications are discussed. In particular, it is shown how to easily write down the class of all smooth and spatially-bounded currents with a given total charge. This implicitly provides restrictions on the moments arising from the smoothness of physically reasonable vector fields. We also show that requiring all of the moments to be constant in an appropriate sense is often impossible; likely limiting the applicability of the Ehlers-Rudolph-Dixon notion of quasirigid motion. A simple condition is also derived that allows currents to exist in two different spacetimes with identical sets of multipole moments (in a natural sense).Comment: 13 pages, minor changes, accepted to J. Math. Phy

Promoting Excellence within Early Care and Education Providers: A Teacher Education Program Story--RESEARCH

This paper shares the process and experience of a university community partnership to improve the quality of care and education in the region by enhancing teachers’ early childhood knowledge. A hybrid course for both university students and childcare providers, The Academy for Early Childhood Excellence sought to provide intense and supportive professional development for early care and education providers as well as access and an introduction to the university setting. The hybrid format necessitated some level of competence with technology and more emphasis on writing as a mode of communication. Some of the Academy participants, especially the more experienced and older providers, were not as comfortable with different computer software needed to open information provided or to complete the assignments through the Blackboard system. For some participants, navigating the online sessions was a bit difficult and they had to seek assistance from others about how and where to go on the Bb site for their postings. Participants reported increased reflection and intentionality in practices. Challenges included navigation of and access to technology as well as lack of university orientation for the transition to the university setting after the course ended. The paper ends with recommendations for higher education institutions thinking about offering professional development courses

Insulin mediated upregulation of the renin angiotensin system in human subcutaneous adipocytes is reduced by Rosiglitazone

Background: Obesity associated hypertension is likely to be due to multiple mechanisms. Identification of the renin-angiotensin system (RAS) within adipose tissue does, however, suggest a potential causal role for it in obesity-associated hypertension. Obese patients are often hyperinsulinaemic, but mechanisms underlying insulin upregulation of the RAS in adipose tissue are unclear. TNFα, an inducer of angiotensinogen in hepatocytes, is elevated in hyperinsulinaemic, obese individuals, and may provide a link in mediating insulin upregulation of the RAS in adipose tissue. Further, thiazolidinediones lower blood pressure in vivo and downregulation of the RAS in adipose tissue may contribute to this effect. We therefore examined the effect of rosiglitazone (RSG), on the insulin mediated upregulation of the RAS. Methods and Results: Sera were obtained from the arterial circulation and from venous blood draining subcutaneous abdominal adipose tissue. Isolated human abdominal subcutaneous adipocytes (n=12) were treated with insulin (1-1000nM) and insulin in combination with RSG (10nM), and RSG (10nM) alone to determine angiotensinogen expression, angiotensin II, bradykinin and TNFα secretion. Subcutaneous adipocytes were also treated with TNFα (10-100ng/mL) to examine the direct effect on angiotensinogen expression and angiotensin II secretion. The findings showed that the arterio-venous difference in angiotensin II levels was significant (↑23%; p<0.001). Insulin increased TNFα secretion in a concentration-dependent manner (p<0.01) whilst RSG (10nM) significantly reduced the insulin mediated rise in TNFα (p<0.001), as well as AGT and angiotensin II. TNFα also increased angiotensinogen and angiotensin II in isolated adipocytes. Conclusions: Our in vivo data suggest that human subcutaneous adipose tissue is a significant source of angiotensin II. This study also demonstrates a potential TNFα mediated mechanism through which insulin may stimulate the RAS and may contribute to explain obesity associated hypertension. RSG downregulates the RAS in subcutaneous adipose tissue and this effect may contribute to the long-term effect of RSG on blood pressure

How geckos stick in nature: ecology and biomechanics of gecko feet

Phenotype and performance play a fundamental role in evolution and ecology. Studies of form and function often use correlations between morphology, performance, and habitat use to examine patterns of ecomorphology and morphological adaptation. Geckos, of the taxonomic group Gekkota, are an understudied yet diverse clade of lizards in which studies of form and function would greatly improve our understanding of their evolution. Geckos have the rather unique trait of adhesive toe pads, enabling them to use arboreal and rocky environments in a way few other creatures can. Gecko toe pad morphology and adhesive abilities are highly variable across species, suggesting ecological adaptations may have driven their evolution, yet few studies has considered gecko adhesive morphology and performance in an ecological context. In this study, we quantified morphology, adhesive performance, and habitat use of 13 gecko species from Queensland, Australia including tropical, arid, arboreal, and rock-dwelling species. We found toe detachment angle to be correlated with residual limb length. We also found residual limb length to be correlated with the use of arboreal and rock microhabitats as well as negatively correlated with perch diameter. This study is one of the first examples investigating gecko adhesive performance and specific microhabitat parameters. We suggest additional comparative studies investigating gecko limb kinematics and setal mechanics to corroborate our observational results