Gravitational waves in vacuum spacetimes with cosmological constant. II. Deviation of geodesics and interpretation of non-twisting type N solutions

In a suitably chosen essentially unique frame tied to a given observer in a general spacetime, the equation of geodesic deviation can be decomposed into a sum of terms describing specific effects: isotropic (background) motions associated with the cosmological constant, transverse motions corresponding to the effects of gravitational waves, longitudinal motions, and Coulomb-type effects. Conditions under which the frame is parallelly transported along a geodesic are discussed. Suitable coordinates are introduced and an explicit coordinate form of the frame is determined for spacetimes admitting a non-twisting null congruence. Specific properties of all non-twisting type N vacuum solutions with cosmological constant Lambda (non-expanding Kundt class and expanding Robinson-Trautman class) are then analyzed. It is demonstrated that these spacetimes can be understood as exact transverse gravitational waves of two polarization modes "+" and "x", shifted by pi/4, which propagate "on" Minkowski, de Sitter, or anti-de Sitter backgrounds. It is also shown that the solutions with Lambda>0 may serve as exact demonstrations of the cosmic "no-hair" conjecture in radiative spacetimes with no symmetry.Comment: 16 pages, no figures, LaTeX, To appear in J. Math. Phy

Estimating total momentum at finite distances

We study the difficulties associated with the evaluation of the total Bondi momentum at finite distances around the central source of a general (asymptotically flat) spacetime. Since the total momentum is only rigorously defined at future null infinity, both finite distance and gauge effects must be taken into account for a correct computation of this quantity. Our discussion is applicable in general contexts but is particularly relevant in numerically constructed spacetimes for both extracting important physical information and assessing the accuracy of additional quantities.Comment: 10 pages, 1 figure. Typos corrected. Comments added and a new Appendix. To be published in PR

Child labour: a public health issue

Child labour is a global practice and has many negative outcomes. According to International Labour Organization, child labour is the important source of child exploitation and child abuse in the world today. The Human Rights Commission of Pakistan has estimated the number of Pakistani working children to be around 11-12 millions, out of which, at least, half the children are under the age of ten years. It portrays the society\u27s attitude towards child care. It is therefore, essential to break this vicious cycle and hence, enable the society to produce healthy citizens. This article analyzes the determinants of child labour in the Pakistani context and its implications for child\u27s life, in specific, and for the nation, in general, utilizing the model developed by Clemen-stone & McGuire (1991). Since this practice has complex web of causation, a multidisciplinary approach is required to combat this issue through proposed recommendations

Dirac equations in curved space-time versus Papapetrou spinning particles

We find out classical particles, starting from Dirac quantum fields on a curved space-time, by an eikonal approximation and a localization hypothesis for amplitudes. We recover the results by Mathisson-Papapetrou, hence establishing a fundamental correspondence between the coupling of classical and quantum spinning particles with the gravitational field.Comment: 6 pages, 1 figure, accepted for publication in Europhysics Letter

Consensus-based Networked Tracking in Presence of Heterogeneous Time-Delays

We propose a distributed (single) target tracking scheme based on networked estimation and consensus algorithms over static sensor networks. The tracking part is based on linear time-difference-of-arrival (TDOA) measurement proposed in our previous works. This paper, in particular, develops delay-tolerant distributed filtering solutions over sparse data-transmission networks. We assume general arbitrary heterogeneous delays at different links. This may occur in many realistic large-scale applications where the data-sharing between different nodes is subject to latency due to communication-resource constraints or large spatially distributed sensor networks. The solution we propose in this work shows improved performance (verified by both theory and simulations) in such scenarios. Another privilege of such distributed schemes is the possibility to add localized fault-detection and isolation (FDI) strategies along with survivable graph-theoretic design, which opens many follow-up venues to this research. To our best knowledge no such delay-tolerant distributed linear algorithm is given in the existing distributed tracking literature.Comment: ICRoM2

Modelling macronutrient dynamics in the Hampshire Avon river: a Bayesian approach to estimate seasonal variability and total flux

The macronutrients nitrate and phosphate are aquatic pollutants that arise naturally, however, in excess concentrations they can be harmful to human health and ecosystems. These pollutants are driven by river currents and show dynamics that are affected by weather patterns and extreme rainfall events. As a result, the nutrient budget in the receiving estuaries and coasts can change suddenly and seasonally, causing ecological damage to resident wildlife and fish populations. In this paper, we propose a statistical change-point model with interactions between time and river flow, to capture the macronutrient dynamics and their responses to river flow threshold behaviour. It also accounts for the nonlinear effect of water quality properties via nonparametric penalised splines. This model enables us to estimate the daily levels of riverine macronutrient fluxes and their seasonal and annual totals. In particular, we present a study of macronutrient dynamics on the Hampshire Avon River, which flows to the southern coast of the UK through the Christchurch Harbour estuary. We model daily data for more than a year during 2013-14 in which period there were multiple severe meteorological conditions leading to localised flooding. Adopting a Bayesian inference framework, we have quantified riverine macronutrient fluxes based on input river flow values. Out of sample empirical validation methods justify our approach, which captures also the dependencies of macronutrient concentrations with water body characteristics

Gravitational lens optical scalars in terms of energy-momentum distributions

This is a general work on gravitational lensing. We present new expressions for the optical scalars and the deflection angle in terms of the energy-momentum tensor components of matter distributions. Our work generalizes standard references in the literature where normally stringent assumptions are made on the sources. The new expressions are manifestly gauge invariant, since they are presented in terms of curvature components. We also present a method of approximation for solving the lens equations, that can be applied to any order.Comment: 17 pages, 2 figures. Titled changed. Small improvements. References added. Final version published in Phys.Rev.