A fast 2D image reconstruction algorithm from 1D data for the Gaia mission

A fast 2-dimensional image reconstruction method is presented, which takes as input 1-dimensional data acquired from scans across a central source in different orientations. The resultant reconstructed images do not show artefacts due to non-uniform coverage in the orientations of the scans across the central source, and are successful in avoiding a high background due to contamination of the flux from the central source across the reconstructed image. Due to the weighting scheme employed this method is also naturally robust to hot pixels. This method was developed specifically with Gaia data in mind, but should be useful in combining data with mismatched resolutions in different directions.Comment: accepted (18 pages, 13 figures) will appear in Experimental Astronom

From Hipparcos to Gaia

The measurement of the positions, distances, motions and luminosities of stars represents the foundations of modern astronomical knowledge. Launched at the end of the eighties, the ESA Hipparcos satellite was the first space mission dedicated to such measurements. Hipparcos improved position accuracies by a factor of 100 compared to typical ground-based results and provided astrometric and photometric multi-epoch observations of 118,000 stars over the entire sky. The impact of Hipparcos on astrophysics has been extremely valuable and diverse. Building on this important European success, the ESA Gaia cornerstone mission promises an even more impressive advance. Compared to Hipparcos, it will bring a gain of a factor 50 to 100 in position accuracy and of a factor of 10,000 in star number, collecting photometric, spectrophotometric and spectroscopic data for one billion celestial objects. During its 5-year flight, Gaia will measure objects repeatedly, up to a few hundred times, providing an unprecedented database to study the variability of all types of celestial objects. Gaia will bring outstanding contributions, directly or indirectly, to most fields of research in astrophysics, such as the study of our Galaxy and of its stellar constituents, the search for planets outside the solar system.Comment: 6 pages. New Horizons in Time Domain Astronomy Proceedings IAU Symposium No. 285, 2012, E. Griffin, B. Hanisch & R. Seaman, ed

Free energies in the presence of electric and magnetic fields

We discuss different free energies for materials in static electric and magnetic fields. We explain what the corresponding Hamiltonians are, and describe which choice gives rise to which result for the free energy change, dF, in the thermodynamic identity. We also discuss which Hamiltonian is the most appropriate for calculations using statistical mechanics, as well as the relationship between the various free energies and the "Landau function", which has to be minimized to determine the equilibrium polarization or magnetization, and is central to Landau's theory of second order phase transitions

Many-body Green's function theory for electron-phonon interactions: the Kadanoff-Baym approach to spectral properties of the Holstein dimer

We present a Kadanoff-Baym formalism to study time-dependent phenomena for systems of interacting electrons and phonons in the framework of many-body perturbation theory. The formalism takes correctly into account effects of the initial preparation of an equilibrium state, and allows for an explicit time-dependence of both the electronic and phononic degrees of freedom. The method is applied to investigate the charge neutral and non-neutral excitation spectra of a homogeneous, two-site, two-electron Holstein model. This is an extension of a previous study of the ground state properties in the Hartree (H), partially self-consistent Born (Gd) and fully self-consistent Born (GD) approximations published in Ref. [arXiv:1403.2968]. We show that choosing a homogeneous ground state solution leads to unstable dynamics for a sufficiently strong interaction, and that allowing a symmetry-broken state prevents this. The instability is caused by the bifurcation of the ground state and understood physically to be connected with the bipolaronic crossover of the exact system. This mean-field instability persists in the partially self-consistent Born approximation but is not found for the fully self-consistent Born approximation. By understanding the stability properties, we are able to study the linear response regime by calculating the density-density response function by time-propagation. This functions amounts to a solution of the Bethe-Salpeter equation with a sophisticated kernel. The results indicate that none of the approximations is able to describe the response function during or beyond the bipolaronic crossover for the parameters investigated. Overall, we provide an extensive discussion on when the approximations are valid, and how they fail to describe the studied exact properties of the chosen model system.Comment: 12 figure

Relating starch structure in breakfast cereals and rice to their digestibility

Grain based food products are rich in the complex carbohydrate starch and represent a major source of dietary energy for the majority of the world’s population. These products play a significant role in digestive health, making them ideal targets for weight management and the prevention and management of obesity related illnesses such as type 2 diabetes and cardiovascular disease. Understanding the digestibility of grain products and improving their dietary quality is important for improving dietary management. However, the complex matrices of these products have resulted in poorly understood digestibility mechanisms. This project aims to characterise starch structure in grain foods to improve our understanding of their digestibility. In this work starches were employed as model samples with which to set up and optimise characterisation methods. Rice flour samples were then characterised. Rice has a relatively simple composition (90% starch) allowing for a less complex model with which to understand the relationship between starch structure and functional properties of starch such as digestibility. Breakfast cereals were also explored, allowing for an investigation into the characterisation of starch in a more complex sample matrix. Starch has multiple hierarchical structural levels on both the molecular and supramolecular level that need to be understood to comprehend the various models for starch digestibility. This has involved the mastering of a variety of techniques to characterise different structural levels of starch. Free solution capillary electrophoresis (CE) was employed in characterising the molecular of starch structure through the determination of amylose content and the investigation of heterogeneity of branching. The supramolecular structure of starch must also be characterised, with supramolecular arrangements introducing steric factors to digestibility. Both short- and long-range crystallinity were explored by a variety of techniques. Short-range order was investigated by Fourier-transform infrared (FTIR) spectroscopy, while long-range order was explored using X-ray diffraction (XRD) and small angle X-ray scattering (SAXS). CE is a powerful separation technique that has been shown to be useful for the separation of amylose and amylopectin, the two macromolecular components of starch, by taking advantage of iodine binding and visible light detection. The amylose content of starch has been linked with digestive properties; therefore, accurate characterisation is an important step in understanding digestive properties. Separation approaches overcome the interference caused by overlapping absorbance bands in traditional approaches, allowing for a more accurate quantification. Previous applications of the CE method in the literature had employed non-ideal dissolution conditions, introducing inaccuracy into analysis. In this thesis the incorporation of improved dissolution conditions in the methodology was explored. A reduced sample concentration was found to be ideal, reducing aggregation. The use of anhydrous DMSO with the addition of a hydrogen bond disruptor, as well as high dissolution temperatures were also determined to be essential in obtaining a complete dissolution thus allowing for accurate characterisation. Using a new methodology developed by our research team, the heterogeneity of branching in starch was also explored by CE, assessing the broadness of resulting electrophoretic mobility distributions through the value of their dispersity. Results using this methodology indicated an extremely high degree of heterogeneity of branching in starch. Further optimisation of the separation method will allow the heterogeneity of amylose and amylopectin to be investigated independently. The determination of short-range order by FTIR spectroscopy is based on the ratio of infrared bands; however, the assignments of these bands are poorly understood. In this work, the improvement of spectral resolution, and the correlation of crystalline index values with published crystallinity values were explored. Transmission mode FTIR spectra measured at cryogenic temperatures yielded the best resolution of the peaks of interest with deconvolution also yielding slight improvements to spectral resolution. The influence of improved spectral resolution on the determined crystalline index was highly variable. Crystalline index values had a loose correlation with published crystallinity values in some cases; however, as a measure of crystallinity, this method was deemed to be suitable in cases where only an estimate is required. The determination of long-range order by XRD was also explored, investigating the influence of data processing and software packages in peak fitting approaches for crystallinity determinations. The different algorithms that the software packages employed impacted on the peak fitting, baseline fitting and resulting crystallinity determinations. SAXS has proven to be a valuable tool in the analysis of lamellar structures in starch. The relation between lamellar structure of maize starches and amylose content was explored. A decrease in the relative amount and size of semi-crystalline structure was observed with increasing amylose content. This trend is similar to those found in the literature in other plant starches. The same trend between varying amylose content and semi-crystalline structural features was also observed in rice flour for the first time. Degree of branching (as measured by another member of our research team) was also investigated in relation to other structural features. Degree of branching showed a trend with varying amylose content as well as a relationship with semi-crystalline structure. These relationships are expected to rely heavily on the amylose content itself and also on the branching structure of the amylases present. In conclusion, the starch structure is complex and every structural level influences digestive properties. A number of characterisation methods were explored in this work, aiming to develop a set of tools that may be used in understanding how starch structure at different levels relates to digestibility. Identifying the links between starch structure and digestibility creates opportunities for applications within the food industry to alter the digestion rates of foods and food ingredients. These relationships may then be used in more efficiently producing healthier food products to combat the issue of rising obesity rates and associated illnesses

Image charge dynamics in time-dependent quantum transport

In this work we investigate the effects of the electron-electron interaction between a molecular junction and the metallic leads in time-dependent quantum transport. We employ the recently developed embedded Kadanoff-Baym method [Phys. Rev. B 80, 115107 (2009)] and show that the molecule-lead interaction changes substantially the transient and steady-state transport properties. We first show that the mean-field Hartree-Fock (HF) approximation does not capture the polarization effects responsible for the renormalization of the molecular levels neither in nor out of equilibrium. Furthermore, due to the time-local nature of the HF self-energy there exists a region in parameter space for which the system does not relax after the switch-on of a bias voltage. These and other artifacts of the HF approximation disappear when including correlations at the second-Born or GW levels. Both these approximations contain polarization diagrams which correctly account for the screening of the charged molecule. We find that by changing the molecule-lead interaction the ratio between the screening and relaxation time changes, an effect which must be properly taken into account in any realistic time-dependent simulation. Another important finding is that while in equilibrium the molecule-lead interaction is responsible for a reduction of the HOMO-LUMO gap and for a substantial redistribution of the spectral weight between the main spectral peaks and the induced satellite spectrum, in the biased system it can have the opposite effect, i.e., it sharpens the spectral peaks and opens the HOMO-LUMO gap.Comment: 18 pages, 26 figure

Kadanoff-Baym approach to time-dependent quantum transport in AC and DC fields

We have developed a method based on the embedded Kadanoff-Baym equations to study the time evolution of open and inhomogeneous systems. The equation of motion for the Green's function on the Keldysh contour is solved using different conserving many-body approximations for the self-energy. Our formulation incorporates basic conservation laws, such as particle conservation, and includes both initial correlations and initial embedding effects, without restrictions on the time-dependence of the external driving field. We present results for the time-dependent density, current and dipole moment for a correlated tight binding chain connected to one-dimensional non-interacting leads exposed to DC and AC biases of various forms. We find that the self-consistent 2B and GW approximations are in extremely good agreement with each other at all times, for the long-range interactions that we consider. In the DC case we show that the oscillations in the transients can be understood from interchain and lead-chain transitions in the system and find that the dominant frequency corresponds to the HOMO-LUMO transition of the central wire. For AC biases with odd inversion symmetry odd harmonics to high harmonic order in the driving frequency are observed in the dipole moment, whereas for asymmetric applied bias also even harmonics have considerable intensity. In both cases we find that the HOMO-LUMO transition strongly mixes with the harmonics leading to harmonic peaks with enhanced intensity at the HOMO-LUMO transition energy.Comment: 16 pages, 9 figures. Submitted at "Progress in Nonequilibrium Green's Functions IV" conferenc