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

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

The distribution of species range size: a stochastic process

The major role played by environmental factors in determining the geographical range sizes of species raises the possibility of describing their long-term dynamics in relatively simple terms, a goal which has hitherto proved elusive. Here we develop a stochastic differential equation to describe the dynamics of the range size of an individual species based on the relationship between abundance and range size, derive a limiting stationary probability model to quantify the stochastic nature of the range size for that species at steady state, and then generalize this model to the species-range size distribution for an assemblage. The model fits well to several empirical datasets of the geographical range sizes of species in taxonomic assemblages, and provides the simplest explanation of species-range size distributions to date

Down In Jungle Town : A Monkey Ditty

https://digitalcommons.library.umaine.edu/mmb-vp/1347/thumbnail.jp

Acoustic measurement differences on trees and logs from hardwoods in wet and dry condition

peer-reviewedAcoustic velocities measured on standing trees using time-of-flight (TOF) devices have been found to be between 7% and 36% higher for softwoods than those in logs using resonance techniques based on longitudinal frequencies. This effect was explained in three different ways: (1) TOF devices on standing trees measure outerwood containing more mature wood while resonance methods assess the whole crosssection, (2) the variation in the velocity is due to loading conditions in standing trees, while logs are free of loads and (3) the acoustic waves are dilatational waves in the case of TOF measurements on standing trees and one-dimensional longitudinal waves in the case of resonance on logs. This is an important topic considering the fact that resonance methods are considered more accurate for predicting mechanical properties and it has been proposed that correction factors should be applied on TOF measurements. In the present work, four hardwoods from Irish forests were studied and, on average, TOF velocities measured in the forest above fibre saturation point (FSP) were 19.8% higher than those from resonance measurements taken on logs immediately after felling. However, this difference reduced to 5.4% when the measurements were repeated at a moisture content (MC) of about 18% in the laboratory. Therefore, there is a MC effect on the velocity differences. Furthermore, higher differences were systematically found in older specimens in wet condition. However, this age effect was small in most cases

Characterization and improvement of rheological properties of sodium caseinate glycated with galactose, lactose and dextran

10 páginas, 7 figuras, 2 tablas.-- El pdf del artículo es la versión de autor.The aim of this work was to investigate the effect of non-enzymatic glycosylation with galactose, lactose, and 10 kDa dextran on the rheological properties of sodium caseinate. To promote the formation of covalent complexes, the reaction was done in solid state (aw = 0.67), pH 7.0 (0.1 M sodium phosphate buffer), and temperature set at 50 and 60 °C. The progress of Maillard reaction was indirectly traced by measuring the formation of the Amadori compound, through furosine (2-furoylmethyl-lysine) analysis, and brown polymers, and the resulting glycoconjugates were characterized by LC/ESI-MS and SEC. Results showed a higher reactivity of galactose than lactose and dextran to form the glycoconjugates, due to its smaller molecular weight. Glycation with galactose and lactose increased the viscosity of caseinate and also altered its flow characteristics from Newtonian to shear-thinning. Oscillatory testing showed a higher elastic modulus (G′) in glycoconjugates when compared to non-glycated caseinate, especially with galactose, where a gel-like behaviour was observed after long incubation times. Glycation with dextran did not produce substantial improvements in the rheological properties of caseinate, probably due to the limited extent of the reaction. Our results show that by controlling the rate and extent of the Maillard reaction is a technologically feasible operation to improve the viscosity and gelling properties of sodium caseinate-based ingredients.This work was supported by projects Consolider Ingenio 2010 FUN-C-FOOD CSD2007-00063 (Ministerio de Educación y Ciencia), ALIBIRD S-0505/AGR/000153 (Comunidad de Madrid) and Hatch project TEN00332 (University of Tennessee Institute of Agriculture). M. Corzo-Martínez thanks the CSIC for an I3P PhD-grant.Peer reviewe

Relating relational networks: An initial experimental analysis

Studying relating of relational networks is a complex and challenging task. The main objective of the present study was to demonstrate relating within and across relational networks based on same/opposite and bigger/smaller contextual cues and establish antecedent control. After nonarbitrary pretraining of the contextual cues, two nonsense stimulus classes were established based on comparative relations. Participants were trained to select stimuli from an array of options based on a symbolic rule that established a relation between two stimuli: one of Network 1 and one of Network 2. Training involved relating Network 1 to Network 2, and testing assessed relating Network 2 to Network 1. Seven of eight participants reached the mastery criterion in training and responded accordingly in test. In a final stage, reinforcing and punishing consequences were varied systematically in the presence of two novel stimuli and antecedent control was observed for all 7 participants. Experiment 2 replicated the results of Experiment 1 but using contextual cues taken from natural language, and Experiment 3 sought to understand the effects of pretraining relational responding using natural language. The mastery criteria were reached by four of seven participants in Experiment 2 and by all eight participants in Experiment 3. Future studies could develop and refine the methods employed here in analyzing the relating of relational networks, thus allowing for an increasingly sophisticated behavior-analytic account of human language and cognition

Effects of coherence on speaker preference and rule-following

Rule-following is affected by multiple variables. A relevant aspect of rules regards whether they “make sense”, that is, the extent to which the instruction coheres with previously reinforced patterns of relational responding. The present study aimed to evaluate the influence of relational coherence upon rule-following. After mastering a particular set of conditional relations (e.g., A1B1, A2B2), the participants were exposed to two speakers, one of which would “state” relations that cohered (e.g., A1B1, A2B2) with the participant’s previous relational training and the other that would present relations that were incoherent (e.g., A1B2, A2B1). Then, rule-following was measured in a preference test in which the participant would have to choose which of the two speakers would provide instructions in each test trial. Results show that the participants preferred the coherent speaker to provide instructions and followed the rules presented by that speaker throughout the test. Coherence is discussed as a critical aspect of rule following and preference for particular narratives