A Simplified Mathematical Model for the Formation of Null Singularities Inside Black Holes I - Basic Formulation and a Conjecture

Einstein's equations are known to lead to the formation of black holes and spacetime singularities. This appears to be a manifestation of the mathematical phenomenon of finite-time blowup: a formation of singularities from regular initial data. We present a simple hyperbolic system of two semi-linear equations inspired by the Einstein equations. We explore a class of solutions to this system which are analogous to static black-hole models. These solutions exhibit a black-hole structure with a finite-time blowup on a characteristic line mimicking the null inner horizon of spinning or charged black holes. We conjecture that this behavior - namely black-hole formation with blow-up on a characteristic line - is a generic feature of our semi-linear system. Our simple system may provide insight into the formation of null singularities inside spinning or charged black holes in the full system of Einstein equations.Comment: 39 pages, 3 figures, extended versio

VAT: Is it Suitable for the Caribbean Community?

The Caribbean Community is in transition, moving toward a liberalized trade environment with low tariffs. Tax reform is at the forefront of the policy response since traditional sources of tax revenue such as import duties are on the decline. This paper evaluates the suitability of the VAT to countries of the Caribbean Community. We examine theoretical arguments, practical experiences of the Caribbean with the VAT and the economic and tax characteristics of the Caribbean. We conclude by supporting VAT implementation in the Caribbean Community. This paper also reflects a comprehensive survey of tax reform efforts in the Caribbean.Value Added Tax; Caribbean Community

Fabrication and test of a space power boiler feed electromagnetic pump. 3: Endurance and final performance tests

A three-phase helical induction electromagnetic pump designed for the boiler feed pump of a potassium Rankine cycle space power system was developed and built. It was mounted in a liquid metal test loop and successfully tested over a range of potassium temperatures from 900 to 1400 F, flow rates from 0.75 to 4.85 lb/sec, developed pressures up to 340 psi, net positive suction head from 1 to 22 psi, and NaK coolant temperatures from 800 to 950 F. Maximum efficiency at design point conditions of 3.25 lb/sec flow rate, 240 psi developed head, 1000 F potassium inlet temperature, and 800 F NaK coolant inlet temperature was 16.3 percent. After the performance tests the pump was operated without any difficulty at design point for 10,000 hours, and then a limited number of repeat performance tests were made. There was no appreciable change in pump performance after 10,000 hours of operation. A supplementary series of tests using the quasi-square wave power output of a dc to three-phase ac inverter showed that the pump would operate without difficulty at a frequency as low as 25 Hz, with little loss in efficiency

Determination of the forward slope in p pp~p and pˉ p\bar p~p elastic scattering up to LHC energy

In the analysis of experimental data on $p p$ (or $\bar p p$) elastic differential cross section it is customary to define an average forward slope $b$ in the form $\exp{(-b|t|)}$, where $t$ is the momentum transfer. Taking as working example the results of experiments at Tevatron and SPS, we will show with the help of the impact picture approach, that this simplifying assumption hides interesting information on the complex non-flip scattering amplitude, and that the slope $b$ is not a constant. We investigate the variation of this slope parameter, including a model-independent way to extract this information from an accurate measurement of the elastic differential cross section. An extension of our results to the LHC energy domain is presented in view of future experiments.Comment: 12 pages, 6 figures, to appear in EPJ

Zenithal bistable device: comparison of modeling and experiment

A comparative modeling and experimental study of the zenithal bistable liquid crystal device is presented. A dynamic Landau de Gennes theory of nematic liquid crystals is solved numerically to model the electric field induced latching of the device and the results are compared with experimental measurements and theoretical approximations. The study gives a clear insight into the latching mechanism dynamics and enables the dependence of the device latching on both material parameters and surface shape to be determined. Analytical approximation highlights a route to optimize material selection in terms of latching voltages and the numerical model, which includes an accurate surface representation, recovers the complex surface shape effects. Predictions of device performance are presented as a function of both surface anchoring strength and surface shape and grating pitch. A measurement of the homeotropic anchoring energy has been undertaken by comparing the voltage response as a function of cell gap; we find the homeotropic anchoring energies can be varied in the range 0.5 to 4 (10-44 J m-2)

Eikonal profile functions and amplitudes for pp\rm pp and pˉp\bar{\rm p}{\rm p} scattering

The eikonal profile function $J(b)$ obtained from the Model of the Stochastic Vacuum is parametrized in a form suitable for comparison with experiment. The amplitude and the extended profile function (including imaginary and real parts) are determined directly from the complete pp and $\bar{\rm p}$p elastic scattering data at high energies. Full and accurate representation of the data is presented, with smooth energy dependence of all parameters. The changes needed in the original profile function required for description of scattering beyond the forward direction are described.Comment: Latex, 28 pages and 16 figure

A new time-machine model with compact vacuum core

We present a class of curved-spacetime vacuum solutions which develope closed timelike curves at some particular moment. We then use these vacuum solutions to construct a time-machine model. The causality violation occurs inside an empty torus, which constitutes the time-machine core. The matter field surrounding this empty torus satisfies the weak, dominant, and strong energy conditions. The model is regular, asymptotically-flat, and topologically-trivial. Stability remains the main open question.Comment: 7 page

Surface Functionalization of Polymer Vesicles with Dendritic Groups: Effects on Physical and Biological Properties

Polymer vesicles (polymersomes) are spherical assemblies with aqueous cores, formed by the self-assembly of amphiphilic polymers in an aqueous environment. They resemble phospholipid vesicles, but typically exhibit much greater stabilities. The chemical versatility of the polymer synthesis makes it possible to tune the vesicle characteristics such as vesicle size and: circulation time in vivo. As such, they are highly promising materials for various applications including drug delivery. Our research group recently developed a versatile approach for the conjugation of dendritic groups to the surfaces of polymer vesicles which allows the surface properties to be readily tuned for specific biological properties or applications. This thesis will investigate the effects of different dendron functionalities, both neutral and cationic, on the rate of release of encapsulated small molecules and larger biomacromolecules, cytotoxicity and the cell uptake properties of polymer vesicles. These properties were explored in both non-biodegradable vesicles based on polybutadiene-poly(ethylene oxide) (PBD-PEO) and biodegradable vesicles based on polycaprolactone-poly(ethylene\u27oxide) (PEOPCL). The rate of release of an encapsulated small molecule, rhodamine B, was founk to be dependent on the absence or presence of dendritic functionality. Unlike with small molecules, the release of encapsulated protein, bovine serum albumin (BSA), depends on the charge of the dendritic functionalization since both cationic systems exhibited faster, similar release profiles. The cytotoxicity of the vesicle systems was found to be dependent on their surface charge as toxicity was observed with both cationic systems at higher concentrations. Finally, the cell uptake was found to be dependent on the functional group displayed on the vesicle surface and guanidine functionalized vesicles had significantly increased cell uptake relative to the other samples

Study of an attitude reference system utilizing an electrically suspended gyro final report, 1 aug. 1964 - 31 mar. 1965

Miniature electrically suspended gyroscope for spacecraft attitude reference syste

Rainwater storage systems and household agriculture for the sustainable provision of food & water in developing and developed countries

Food and water are at the heart of every community, form significant aspects of cultural identity, and must be in good supply for healthy and sustainable development. Not surprisingly, food and water feature directly as part of the recent UN sustainable development goals (SDGs) as Goal 2, Zero Hunger, and Goal 6, Clean Water and Sanitation. Household agriculture (HA) and rainwater storage systems (RSS) have grown in popularity in recent years and have the potential to increase yields and supplement household nutrition. Yet there is a significant lack of research into this potential. Domestic RSS studies usually focus on water savings rather than on crop production. There is also little research on the economic analysis of RSS systems in developing countries where home gardens often fail due to insufficient rainfall and water supply. Promoting green cities in general, begs the question of whether there is enough water available to support it. The recent COVID-19 crisis and keeping safe by isolation at home only strengthens the argument for HA. This study investigates the potential of using RSS in water, sanitation and hygiene (WASH) and particularly for HA. It also looks at economic issues associated with RSS, which are particularly relevant to developing countries. The work focuses mainly on Australia, Bangladesh, and Kenya, but is relevant to most other regions. The findings of this study, and the consequent publications are intended to serve as a key reference on modelling and economic aspects of RWH in urban agriculture and greening of cities. They are expected to be useful to modellers and researchers, water engineers, environmentalists, town planners, and policy makers concerned with sustainable development and dealing with integrated water management and the water-energy-food-ecosystem nexus by bringing together knowledge gaps and potential solutions. It is hoped that the challenge of providing food and water for all be met with the same vigour as was the space race, circumnavigation of and landing on the moon