A Phase Space Approach to Gravitational Enropy

We examine the definition S = ln Omega as a candidate "gravitational entropy" function. We calculate its behavior for gravitationl and density perturbations in closed, open and flat cosmologies and find that in all cases it increases monotonically. Using the formalism to calculate the gravitational entropy produced during inflation gives the canonical answer. We compare the behavior of S with the behavior of the square of the Weyl tensor. Applying the formalism to black holes has proven more problematical.Comment: Talk delivered at South African Relativistic Cosmology Symposium, Feb 1999. Some new results over Rothman and Anninos 97. To appear in GRG, 17 page

General properties of cosmological models with an Isotropic Singularity

Much of the published work regarding the Isotropic Singularity is performed under the assumption that the matter source for the cosmological model is a barotropic perfect fluid, or even a perfect fluid with a $\gamma$-law equation of state. There are, however, some general properties of cosmological models which admit an Isotropic Singularity, irrespective of the matter source. In particular, we show that the Isotropic Singularity is a point-like singularity and that vacuum space-times cannot admit an Isotropic Singularity. The relationships between the Isotropic Singularity, and the energy conditions, and the Hubble parameter is explored. A review of work by the authors, regarding the Isotropic Singularity, is presented.Comment: 18 pages, 1 figur

The effect of duration of exercise at the ventilation threshold on subjective appetite and short-term food intake in 9 to 14 year old boys and girls

<p>Abstract</p> <p>Background</p> <p>The effect of exercise on subjective appetite and short-term food intake has received little investigation in children. Despite a lack of reported evaluation of short-duration activity programs, they are currently being implemented in schools as a means to benefit energy balance. The purpose of this study was to determine the effect of duration of exercise at the ventilation threshold (VeT) on subjective appetite and short-term food intake in normal weight boys and girls aged 9 to 14 years.</p> <p>Methods</p> <p>On 4 separate mornings and in random order, boys (n = 14) and girls (n = 15) completed 2 rest or 2 exercise treatments for 15 (short-duration; SD) or 45 min (long-duration; LD) at their previously measured VeT, 2 h after a standardized breakfast. Subjective appetite was measured at regular intervals during the study sessions and food intake from a pizza meal was measured 30 min after rest or exercise.</p> <p>Results</p> <p>An increase in average appetite, desire to eat, and hunger (p < 0.05) was attenuated by SD exercise, but was further increased (p < 0.05) by LD exercise. However, food intake after SD and LD exercise was similar to after rest in both boys and girls (p = 0.55). The energy cost of SD and LD exercise resulted in a lower net energy balance compared to resting during the study measurement period in boys (SD: Δ = -418 ± 301 kJ; LD: Δ = -928 ± 196 kJ) and in girls (SD: Δ = -297 ± 105 kJ; LD: Δ = -432 ± 115 kJ).</p> <p>Conclusion</p> <p>Neither SD nor LD exercise at the VeT increased short-term food intake and SD exercise attenuated increases in appetite. Thus, SD exercise programs in schools may be an effective strategy for maintaining healthier body weights in children.</p

EB1 directly regulates APC-mediated actin nucleation

EB1 was discovered 25 years ago as a binding partner of the tumor suppressor Adenomatous Polyposis Coli (APC) [1]; however, the significance of EB1-APC interactions has remained poorly understood. EB1 functions at the center of a network of microtubule end-tracking proteins (+TIPs) [2–5], and APC binding to EB1 promotes EB1 association with microtubule ends and microtubule stabilization [6, 7]. Whether or not EB1 interactions govern functions of APC beyond microtubule regulation has not been explored. The C-terminal Basic domain of APC (APC-B) directly nucleates actin assembly, and this activity is required in vivo for directed cell migration and for maintaining normal levels of F-actin [8–10]. Here, we show that EB1 binds APC-B and inhibits its actin nucleation function by blocking actin monomer recruitment. Consistent with these biochemical observations, knocking down EB1 increases F-actin levels in cells, and this can be rescued by disrupting APC-mediated actin nucleation. Conversely, overexpressing EB1 decreases F-actin levels and impairs directed cell migration, without altering microtubule organization and independent of its direct binding interactions with microtubules. Overall, our results define a new function for EB1 in negatively regulating APC-mediated actin assembly. Combining these findings with other recent studies showing that APC interactions regulate EB1-dependent effects on microtubule dynamics [7], we propose that EB1-APC interactions govern bidirectional cytoskeletal crosstalk by coordinating microtubule and actin dynamics

Structure formation in the Lemaitre-Tolman model

Structure formation within the Lemaitre-Tolman model is investigated in a general manner. We seek models such that the initial density perturbation within a homogeneous background has a smaller mass than the structure into which it will develop, and the perturbation then accretes more mass during evolution. This is a generalisation of the approach taken by Bonnor in 1956. It is proved that any two spherically symmetric density profiles specified on any two constant time slices can be joined by a Lemaitre-Tolman evolution, and exact implicit formulae for the arbitrary functions that determine the resulting L-T model are obtained. Examples of the process are investigated numerically.Comment: LaTeX 2e plus 14 .eps & .ps figure files. 33 pages including figures. Minor revisions of text and data make it more precise and consistent. Currently scheduled for Phys Rev D vol 64, December 15 issu

On the evolution of a large class of inhomogeneous scalar field cosmologies

The asymptotic behaviour of a family of inhomogeneous scalar field cosmologies with exponential potential is studied. By introducing new variables we can perform an almost complete analysis of the evolution of these cosmologies. Unlike the homogeneous case (Bianchi type solutions), when k^2<2 the models do not isotropize due to the presence of the inhomogeneitiesComment: 23 pages, 1 figure. Submitted to Classical and Quantum Gravit

A fully covariant description of CMB anisotropies

Starting from the exact non-linear description of matter and radiation, a fully covariant and gauge-invariant formula for the observed temperature anisotropy of the cosmic microwave background (CBR) radiation, expressed in terms of the electric ($E_{ab}$) and magnetic ($H_{ab}$) parts of the Weyl tensor, is obtained by integrating photon geodesics from last scattering to the point of observation today. This improves and extends earlier work by Russ et al where a similar formula was obtained by taking first order variations of the redshift. In the case of scalar (density) perturbations, $E_{ab}$ is related to the harmonic components of the gravitational potential $\Phi_k$ and the usual dominant Sachs-Wolfe contribution $\delta T_R/\bar{T}_R\sim\Phi_k$ to the temperature anisotropy is recovered, together with contributions due to the time variation of the potential (Rees-Sciama effect), entropy and velocity perturbations at last scattering and a pressure suppression term important in low density universes. We also explicitly demonstrate the validity of assuming that the perturbations are adiabatic at decoupling and show that if the surface of last scattering is correctly placed and the background universe model is taken to be a flat dust dominated Friedmann-Robertson-Walker model (FRW), then the large scale temperature anisotropy can be interpreted as being due to the motion of the matter relative to the surface of constant temperature which defines the surface of last scattering on those scales.Comment: 18 pages LaTeX, 1 figure. Submitted to Classical and Quantum Gravity. Also available at http://shiva.mth.uct.ac.za/preprints/9705.htm

Conformal regularization of Einstein's field equations

To study asymptotic structures, we regularize Einstein's field equations by means of conformal transformations. The conformal factor is chosen so that it carries a dimensional scale that captures crucial asymptotic features. By choosing a conformal orthonormal frame we obtain a coupled system of differential equations for a set of dimensionless variables, associated with the conformal dimensionless metric, where the variables describe ratios with respect to the chosen asymptotic scale structure. As examples, we describe some explicit choices of conformal factors and coordinates appropriate for the situation of a timelike congruence approaching a singularity. One choice is shown to just slightly modify the so-called Hubble-normalized approach, and one leads to dimensionless first order symmetric hyperbolic equations. We also discuss differences and similarities with other conformal approaches in the literature, as regards, e.g., isotropic singularities.Comment: New title plus corrections and text added. To appear in CQ