Linear and fractal diffusion coefficients in a family of one dimensional chaotic maps

We analyse deterministic diffusion in a simple, one-dimensional setting consisting of a family of four parameter dependent, chaotic maps defined over the real line. When iterated under these maps, a probability density function spreads out and one can define a diffusion coefficient. We look at how the diffusion coefficient varies across the family of maps and under parameter variation. Using a technique by which Taylor-Green-Kubo formulae are evaluated in terms of generalised Takagi functions, we derive exact, fully analytical expressions for the diffusion coefficients. Typically, for simple maps these quantities are fractal functions of control parameters. However, our family of four maps exhibits both fractal and linear behavior. We explain these different structures by looking at the topology of the Markov partitions and the ergodic properties of the maps.Comment: 21 pages, 19 figure

Promoting the emotional wellbeing and mental health of unaccompanied young people seeking asylum in the UK - Research Summary

This research summary provides an overview of findings from an 18-month, in-depth research project: The social functioning, emotional wellbeing and mental health of unaccompanied young people seeking asylum in the UK. The research was conducted by the Thomas Coram Research Unit, at the Institute of Education, University of London. It was commissioned and funded by the Department of Health, although the views expressed in this summary do not necessarily reflect those of the Department. The key findings from the study are presented and some of the specific implications for policy and practice for those working with unaccompanied children and young people in a range of health, social care, education, immigration and legal settings are discussed

On the Preparation of Pure States in Resonant Microcavities

We consider the time evolution of the radiation field (R) and a two-level atom (A) in a resonant microcavity in terms of the Jaynes-Cummings model with an initial general pure quantum state for the radiation field. It is then shown, using the Cauchy-Schwarz inequality and also a Poisson resummation technique, that {\it perfect} coherence of the atom can in general never be achieved. The atom and the radiation field are, however, to a good approximation in a pure state $|\psi >_A\otimes|\psi >_R$ in the middle of what has been traditionally called the ``collapse region'', independent of the initial state of the atoms, provided that the initial pure state of the radiation field has a photon number probability distribution which is sufficiently peaked and phase differences that do not vary significantly around this peak. An approximative analytic expression for the quantity \Tr[\rho^2_{A}(t)], where $\rho_{A}(t)$ is the reduced density matrix for the atom, is derived. We also show that under quite general circumstances an initial entangled pure state will be disentangled to the pure state $|\psi >_{A\otimes R}$.Comment: 14 pages and 3 figure

Electrical phase change of CVD-grown Ge-Sb-Te thin film device

A prototype Ge-Sb-Te thin film phase-change memory device has been fabricated and reversible threshold and phase change switching demonstrated electrically, with a threshold voltage of 1.5 – 1.7 V. The Ge-Sb-Te thin film was fabricated by chemical vapour deposition (CVD) at atmospheric pressure using GeCl4, SbCl5, and Te precursors with reactive gas H2 at reaction temperature 780 °C and substrate temperature 250 °C. The surface morphology and composition of the CVD-grown Ge-Sb-Te thin film has been characterized by scanning electron microscopy (SEM) and energy dispersive X-ray analysis (EDX). The CVD-grown Ge-Sb-Te thin film shows promise for the phase change memory applications

Atmospheric structure determined from satellite data

The capabilities of the Nimbus 6 satellite sounding data for use in synoptic analysis were considered and interpreted. An evaluation of the ability of the satellite sounding data to detect and depict structural features of the atmosphere was made on the basis of vertical profiles of average difference and standard deviation of differences between satellite and rawinsonde data at nine pressure levels from 850 to 100 mb; and constant pressure charts and cross sections of satellite, rawinsonde and difference values. Results indicate that satellite measurements of temperature as well as the vertical lapse rate and horizontal gradient of temperature are accurate enough to show large scale patterns but not to precisely define fronts or tropopauses; satellite measurements of dew point temperature are smoothed enough to severely reduce contrasts between air masses across fronts; the magnitude of the standard deviation of differences between rawinsonde and satellite data for most variables increases with the synoptic activity in the region; and the most reliable variables to examine from satellite data for depiction of synoptic features are the temperature equivalent potential temperature and mixing ratio

Linear quantum trajectories: Applications to continuous projection measurements

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