Modelling of automotive fuel droplets heating and evaporation - mathematical tools and approximations

New mathematical tools and approximations developed for the analysis of automotive fuel droplet heating and evaporation are summarised. The approach to modelling biodiesel fuel droplets is based on the application of the Discrete Component Model (DCM), while the approach to modelling Diesel fuel droplets is based on the application of the recently developed multi-dimensional quasi-discrete model. In both cases, the models are applied in combination with the Eective Thermal Conductivity/Eective Diusivity model and the implementation in the numerical code of the analytical solutions to heat transfer and species diusion equations inside droplets. It is shown that the approximation of biodiesel fuel by a single component leads to under-prediction of droplet evaporation time by up to 13% which can be acceptable as a crude approximation in some applications. The composition of Diesel fuel was simpli ed and reduced to only 98 components. The approximation of 98 components of Diesel fuel with 15 quasi-components/components leads to under-prediction of droplet evaporation time by about 3% which is acceptable in most engineering applications. At the same time, the approximation of Diesel fuel by a single component and 20 alkane components leads to a decrease in the evaporation time by about 19%, compared with the case of approximation of Diesel fuel with 98 components. The approximation of Diesel fuel with a single alkane quasi-component (C14:763H31:526) leads to under-prediction of the evaporation time by about 35% which is not acceptable even for qualitative analysis of the process. In the case when n-dodecane is chosen as the single alkane component, the above-mentioned under-prediction increases to about 44%

Gravitational strings. Do we see one?

I present a class of objects called gravitational strings (GS) for their similarity to the conventional cosmic strings: even though the former are just singularities in flat spacetime, both varieties are equally "realistic", they may play equally important cosmological r\^ole and their lensing properties are akin. I argue that the enigmatic object CSL-1 is an evidence in favor of the existence of GS.Comment: The published version. Minor correction

Massive graviton as a testable cold dark matter candidate

We construct a consistent model of gravity where the tensor graviton mode is massive, while linearized equations for scalar and vector metric perturbations are not modified. The Friedmann equation acquires an extra dark-energy component leading to accelerated expansion. The mass of the graviton can be as large as $\sim (10^{15}{cm})^{-1}$, being constrained by the pulsar timing measurements. We argue that non-relativistic gravitational waves can comprise the cold dark matter and may be detected by the future gravitational wave searches.Comment: 4 pages, final version to appear in PR

Gravitons and Lightcone Fluctuations II: Correlation Functions

A model of a fluctuating lightcone due to a bath of gravitons is further investigated. The flight times of photons between a source and a detector may be either longer or shorter than the light propagation time in the background classical spacetime, and will form a Gaussian distribution centered around the classical flight time. However, a pair of photons emitted in rapid succession will tend to have correlated flight times. We derive and discuss a correlation function which describes this effect. This enables us to understand more fully the operational significance of a fluctuating lightcone. Our results may be combined with observational data on pulsar timing to place some constraints on the quantum state of cosmological gravitons.Comment: 16 pages and two figures, uses eps

Black Hole Relics in String Gravity: Last Stages of Hawking Evaporation

One of the most intriguing problem of modern physics is the question of the endpoint of black hole evaporation. Based on Einstein-dilaton-Gauss-Bonnet four dimensional string gravity model we show that black holes do not disappear and that the end of the evaporation process leaves some relic. The possibility of experimental detection of the remnant black holes is investigated. If they really exist, such objects could be a considerable part of the non baryonic dark matter in our Universe.Comment: 15 pages, accepted to Class. Quant. Gra

Peaks in the Cosmic Microwave Background: flat versus open models

We present properties of the peaks (maxima) of the CMB anisotropies expected in flat and open CDM models. We obtain analytical expressions of several topological descriptors: mean number of maxima and the probability distribution of the gaussian curvature and the eccentricity of the peaks. These quantities are calculated as functions of the radiation power spectrum, assuming a gaussian distribution of temperature anisotropies. We present results for angular resolutions ranging from 5' to 20' (antenna FWHM), scales that are relevant for the MAP and COBRAS/SAMBA space missions and the ground-based interferometer experiments. Our analysis also includes the effects of noise. We find that the number of peaks can discriminate between standard CDM models, and that the gaussian curvature distribution provides a useful test for these various models, whereas the eccentricity distribution can not distinguish between them.Comment: 13 pages latex file using aasms4.sty + 3 tables + 2 postscript figures, to appear in ApJ (March 1997

The BaR-SPOrt Experiment

BaR-SPOrt (Balloon-borne Radiometers for Sky Polarisation Observations) is an experiment to measure the linearly polarized emission of sky patches at 32 and 90 GHz with sub-degree angular resolution. It is equipped with high sensitivity correlation polarimeters for simultaneous detection of both the U and Q stokes parameters of the incident radiation. On-axis telescope is used to observe angular scales where the expected polarization of the Cosmic Microwave Background (CMBP) peaks. This project shares most of the know-how and sophisticated technology developed for the SPOrt experiment onboard the International Space Station. The payload is designed to flight onboard long duration stratospheric balloons both in the Northern and Southern hemispheres where low foreground emission sky patches are accessible. Due to the weakness of the expected CMBP signal (in the range of microK), much care has been spent to optimize the instrument design with respect to the systematics generation, observing time efficiency and long term stability. In this contribution we present the instrument design, and first tests on some components of the 32 GHz radiometer.Comment: 12 pages, 10 figures, Astronomical Telescopes and Instrumentation (Polaimetry in Astronomy) Hawaii August 2002 SPIE Meetin