Commercial equity: the Quistclose trust and asset recovery

This paper examines the impact of equitable principles on the sphere of commercial law. It will make particular reference to the effect of the incursion of equity on ordinary creditors with regard to obtaining priorities in cases of insolvency. It will analyze the Quistclose trust and show how this type of trust may be used to obtain an advantage by those who would otherwise be ordinary creditors. It will refer to the use of equitable tracing to recover assets in a money-laundering scheme The paper will suggest that judicial acceptance of the concept of the remedial constructive trusts has enhanced the development of proprietary restitutionary remedies in commercial transactions where no proprietary remedy would have previously existed

AROMA: Automatic Generation of Radio Maps for Localization Systems

WLAN localization has become an active research field recently. Due to the wide WLAN deployment, WLAN localization provides ubiquitous coverage and adds to the value of the wireless network by providing the location of its users without using any additional hardware. However, WLAN localization systems usually require constructing a radio map, which is a major barrier of WLAN localization systems' deployment. The radio map stores information about the signal strength from different signal strength streams at selected locations in the site of interest. Typical construction of a radio map involves measurements and calibrations making it a tedious and time-consuming operation. In this paper, we present the AROMA system that automatically constructs accurate active and passive radio maps for both device-based and device-free WLAN localization systems. AROMA has three main goals: high accuracy, low computational requirements, and minimum user overhead. To achieve high accuracy, AROMA uses 3D ray tracing enhanced with the uniform theory of diffraction (UTD) to model the electric field behavior and the human shadowing effect. AROMA also automates a number of routine tasks, such as importing building models and automatic sampling of the area of interest, to reduce the user's overhead. Finally, AROMA uses a number of optimization techniques to reduce the computational requirements. We present our system architecture and describe the details of its different components that allow AROMA to achieve its goals. We evaluate AROMA in two different testbeds. Our experiments show that the predicted signal strength differs from the measurements by a maximum average absolute error of 3.18 dBm achieving a maximum localization error of 2.44m for both the device-based and device-free cases.Comment: 14 pages, 17 figure

General relativistic Poynting-Robertson effect to diagnose wormholes existence: static and spherically symmetric case

We derive the equations of motion of a test particle in the equatorial plane around a static and spherically symmetric wormhole influenced by a radiation field including the general relativistic Poynting-Robertson effect. From the analysis of this dynamical system, we develop a diagnostic to distinguish a black hole from a wormhole, which can be timely supported by several and different observational data. This procedure is based on the possibility of having some wormhole metrics, which smoothly connect to the Schwarzschild metric in a small transition surface layer very close to the black hole event horizon. To detect such a metric-change, we analyse the emission proprieties from the critical hypersurface (stable region where radiation and gravitational fields balance) together with those from an accretion disk in the Schwarzschild spacetime toward a distant observer. Indeed, if the observational data are well fitted within such model, it immediately implies the existence of a black hole; while in case of strong departures from such description it means that a wormhole could be present. Finally, we discuss our results and draw the conclusions.Comment: 17 pages, 11 figures, 1 Table. Paper accepted on April 30, 2020 on Physical Review

General Relativistic Ray-Tracing Method for Estimating the Energy and Momentum Deposition by Neutrino Pair Annihilation in Collapsars

Bearing in mind the application to the collapsar models of gamma-ray bursts (GRBs), we develop a numerical scheme and code for estimating the deposition of energy and momentum due to the neutrino pair annihilation ($\nu + {\bar \nu} \rightarrow e^{-} + e^{+}$) in the vicinity of accretion tori around a Kerr black hole. Our code is designed to solve the general relativistic neutrino transfer by a ray-tracing method. To solve the collisional Boltzmann equation in curved spacetime, we numerically integrate the so-called rendering equation along the null geodesics. For the neutrino opacity, the charged-current $\beta$-processes are taken into account, which are dominant in the vicinity of the accretion tori. The numerical accuracy of the developed code is certificated by several tests, in which we show comparisons with the corresponding analytic solutions. Based on the hydrodynamical data in our collapsar simulation, we estimate the annihilation rates in a post-processing manner. Increasing the Kerr parameter from 0 to 1, it is found that the general relativistic effect can increase the local energy deposition rate by about one order of magnitude, and the net energy deposition rate by several tens of percents. After the accretion disk settles into a stationary state (typically later than $\sim 9$ s from the onset of gravitational collapse), we point out that the neutrino-heating timescale in the vicinity of the polar funnel region can be shorter than the dynamical timescale. Our results suggest the neutrino pair annihilation has a potential importance equal to the conventional magnetohydrodynamic mechanism for igniting the GRB fireballs.Comment: 33 pages, 15 figures, accepted to the Ap

Interplay between multiple scattering, emission, and absorption of light in the phosphor of a white light-emitting diode

We study light transport in phosphor plates of white light-emitting diodes (LEDs). We measure the broadband diffuse transmission through phosphor plates of varying YAG:Ce$^{3+}$ density. We distinguish the spectral ranges where absorption, scattering, and re-emission dominate. Using diffusion theory, we derive the transport and absorption mean free paths from first principles. We find that both transport and absorption mean free paths are on the order of the plate thickness. This means that phosphors in commercial LEDs operate well within an intriguing albedo range around 0.7. We discuss how salient parameters that can be derived from first principles control the optical properties of a white LED.Comment: 14 pages, 9 figure

A Self-Assembled Microlensing Rotational Probe

A technique to measure microscopic rotational motion is presented. When a small fluorescent polystyrene microsphere is attached to a larger polystyrene microsphere, the larger sphere acts as a lens for the smaller microsphere and provides an optical signal that is a strong function of the azimuthal angle. We demonstrate the technique by measuring the rotational diffusion constant of the microsphere in solutions of varying viscosity and discuss the feasibility of using this probe to measure rotational motion of biological systems.Comment: 3 pages with 2 figures (eps format). Paper has been submitted to Applied Physics Letter

Tracing magnetic separators and their dependence on IMF clock angle in global magnetospheric simulations

A new, efficient, and highly accurate method for tracing magnetic separators in global magnetospheric simulations with arbitrary clock angle is presented. The technique is to begin at a magnetic null and iteratively march along the separator by finding where four magnetic topologies meet on a spherical surface. The technique is verified using exact solutions for separators resulting from an analytic magnetic field model that superposes dipolar and uniform magnetic fields. Global resistive magnetohydrodynamic simulations are performed using the three-dimensional BATS-R-US code with a uniform resistivity, in eight distinct simulations with interplanetary magnetic field (IMF) clock angles ranging from 0 (parallel) to 180 degrees (anti-parallel). Magnetic nulls and separators are found in the simulations, and it is shown that separators traced here are accurate for any clock angle, unlike the last closed field line on the Sun-Earth line that fails for southward IMF. Trends in magnetic null locations and the structure of magnetic separators as a function of clock angle are presented and compared with those from the analytic field model. There are many qualitative similarities between the two models, but quantitative differences are also noted. Dependence on solar wind density is briefly investigated.Comment: 10 pages, 10 figures, Presented at 2012 AGU Fall Meeting and 2013 Geospace Environment Modeling (GEM) Worksho