Evaluation and test of xenon lamps, phase 4, volume 1 Final report

Anode configurations for xenon lamp

Ultrashort echo time (UTE) imaging using gradient pre-equalization and compressed sensing.

Ultrashort echo time (UTE) imaging is a well-known technique used in medical MRI, however, the implementation of the sequence remains non-trivial. This paper introduces UTE for non-medical applications and outlines a method for the implementation of UTE to enable accurate slice selection and short acquisition times. Slice selection in UTE requires fast, accurate switching of the gradient and r.f. pulses. Here a gradient "pre-equalization" technique is used to optimize the gradient switching and achieve an effective echo time of 10μs. In order to minimize the echo time, k-space is sampled radially. A compressed sensing approach is used to minimize the total acquisition time. Using the corrections for slice selection and acquisition along with novel image reconstruction techniques, UTE is shown to be a viable method to study samples of cork and rubber with a shorter signal lifetime than can typically be measured. Further, the compressed sensing image reconstruction algorithm is shown to provide accurate images of the samples with as little as 12.5% of the full k-space data set, potentially permitting real time imaging of short T2(*) materials.HTF would like to acknowledge the financial support of the Gates-Cambridge Trust and all authors of the EPSRC (EP/K008218/1). In addition, we would like to thank SoftPoint Industries Inc. for providing samples of rubber.This version is final published version, distributed under a Creative Commons Attribution License 2.0. This can also be viewed on the publisher's website at: http://www.sciencedirect.com/science/article/pii/S1090780714001840

Learning filter functions in regularisers by minimising quotients

Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learning to high-dimensional machine learning techniques. Most learning approaches, however, only aim at fitting parametrised models to favourable training data whilst ignoring misfit training data completely. In this paper, we follow up on the idea of learning parametrised regularisation functions by quotient minimisation as established in [3]. We extend the model therein to include higher-dimensional filter functions to be learned and allow for fit- and misfit-training data consisting of multiple functions. We first present results resembling behaviour of well-established derivative-based sparse regularisers like total variation or higher-order total variation in one-dimension. Our second and main contribution is the introduction of novel families of non-derivative-based regularisers. This is accomplished by learning favourable scales and geometric properties while at the same time avoiding unfavourable ones

Nonlinear lensing mechanisms in a cloud of cold atoms

We present an experimental study of nonlinear lensing of near-resonant light by a cloud of laser-cooled rubidium atoms, specifically aimed at understanding the role of the interaction time between the light and the atomic vapor. We identify four different nonlinear mechanisms, each associated with a different time constant: electronic nonlinearity, Zeeman optical pumping, hyperfine optical pumping and radiation pressure. Our observations can be quite accurately reproduced using a simple rate equation model which allows for a straightforward discussion of the various effects. The results are important for planning more refined experiments on transverse nonlinear optics and self-organization in samples of cold atoms

Reaction pathways and textural aspects of the replacement of anhydrite by calcite at 25 °C

The replacement of sulfate minerals by calcium carbonate polymorphs (carbonation) has important implications in various geological processes occurring in Earth surface environments. In this paper we report the results of an experimental study of the interaction between anhydrite (100), (010), and (001) surfaces and Na₂CO₃ aqueous solutions under ambient conditions. Carbonation progress was monitored by glancing incidence X-ray diffraction (GIXRD) and scanning electron microscopy (SEM). We show that the reaction progresses through the dissolution of anhydrite and the simultaneous growth of calcite. The growth of calcite occurs oriented on the three anhydrite cleavage surfaces and its formation is accompanied by minor vaterite. The progress of the carbonation always occurs from the outer-ward to the inner-ward surfaces and its rate depends on the anhydrite surface considered, with the (001) surface being much more reactive than the (010) and (100) surfaces. The thickness of the formed carbonate layer grows linearly with time. The original external shape of the anhydrite crystals and their surface details (e.g., cleavage steps) are preserved during the carbonation reaction. Textural characteristics of the transformed regions, such as the gradation in the size of calcite crystals, from ~2 μm in the outer region to ~17 μm at the calcite-anhydrite interface, the local preservation of calcite crystalographic orientation with respect to anhydrite and the distribution of the microporosity mainly within the carbonate layer without development of any significant gap at the calcite-anhydrite interface. Finally, we compare these results on anhydrite carbonation with those on gypsum carbonation and can explain the differences on the basis of four parameters: (1) the molar volume change involved in the replacement process in each case, (2) the lack/existence of epitactic growth between parent and product phases, (3) the kinetics of dissolution of the different surfaces, and (4) the chemical composition (amount of structural water) of the parent phases

Not just fractal surfaces, but surface fractal aggregates: Derivation of the expression for the structure factor and its applications

Densely packed surface fractal aggregates form in systems with high local volume fractions of particles with very short diffusion lengths, which effectively means that particles have little space to move. However, there are no prior mathematical models, which would describe scattering from such surface fractal aggregates and which would allow the subdivision between inter- and intraparticle interferences of such aggregates. Here, we show that by including a form factor function of the primary particles building the aggregate, a finite size of the surface fractal interfacial sub-surfaces can be derived from a structure factor term. This formalism allows us to define both a finite specific surface area for fractal aggregates and the fraction of particle interfacial sub-surfaces at the perimeter of an aggregate. The derived surface fractal model is validated by comparing it with an ab initio approach that involves the generation of a "brick-in-a-wall" von Koch type contour fractals. Moreover, we show that this approach explains observed scattering intensities from in situ experiments that followed gypsum (CaSO4 · 2H2O) precipitation from highly supersaturated solutions. Our model of densely packed "brick-in-a-wall" surface fractal aggregates may well be the key precursor step in the formation of several types of mosaic- and meso-crystals

Metagenomic insights into diazotrophic communities across Arctic glacier forefields

Microbial nitrogen fixation is crucial for building labile nitrogen stocks and facilitating higher plant colonization in oligotrophic glacier forefield soils. Here, the diazotrophic bacterial community structure across four Arctic glacier forefields was investigated using metagenomic analysis. In total, 70 soil metagenomes were used for taxonomic interpretation based on 185 nitrogenase (nif) sequences, extracted from assembled contigs. The low number of recovered genes highlights the need for deeper sequencing in some diverse samples, to uncover the complete microbial populations. A key group of forefield diazotrophs, found throughout the forefields, was identified using a nifH phylogeny, associated with nifH Cluster I and III. Sequences related most closely to groups including Alphaproteobacteria, Betaproteobacteria, Cyanobacteria and Firmicutes. Using multiple nif genes in a Last Common Ancestor analysis revealed a diverse range of diazotrophs across the forefields. Key organisms identified across the forefields included Nostoc, Geobacter, Polaromonas and Frankia. Nitrogen fixers which are symbiotic with plants were also identified, through the presence of root associated diazotrophs, which fix nitrogen in return for reduced carbon. Additional nitrogen fixers identified in forefield soils were metabolically diverse, including fermentative and sulphur cycling bacteria, halophiles and anaerobes

A combined first and second order variational approach for image reconstruction

In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a non-smooth second order regulariser. It combines convex functions of the total variation and the total variation of the first derivatives. In what follows, we prove existence and uniqueness of minimisers of the combined model and present the numerical solution of the corresponding discretised problem by employing the split Bregman method. The paper is furnished with applications of our model to image denoising, deblurring as well as image inpainting. The obtained numerical results are compared with results obtained from total generalised variation (TGV), infimal convolution and Euler's elastica, three other state of the art higher-order models. The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images -- a known disadvantage of the ROF model -- while being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure

ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation

Quantitative mapping of chemical compositions with MRI using compressed sensing.

In this work, a magnetic resonance (MR) imaging method for accelerating the acquisition time of two dimensional concentration maps of different chemical species in mixtures by the use of compressed sensing (CS) is presented. Whilst 2D-concentration maps with a high spatial resolution are prohibitively time-consuming to acquire using full k-space sampling techniques, CS enables the reconstruction of quantitative concentration maps from sub-sampled k-space data. First, the method was tested by reconstructing simulated data. Then, the CS algorithm was used to reconstruct concentration maps of binary mixtures of 1,4-dioxane and cyclooctane in different samples with a field-of-view of 22mm and a spatial resolution of 344μm×344μm. Spiral based trajectories were used as sampling schemes. For the data acquisition, eight scans with slightly different trajectories were applied resulting in a total acquisition time of about 8min. In contrast, a conventional chemical shift imaging experiment at the same resolution would require about 17h. To get quantitative results, a careful weighting of the regularisation parameter (via the L-curve approach) or contrast-enhancing Bregman iterations are applied for the reconstruction of the concentration maps. Both approaches yield relative errors of the concentration map of less than 2mol-% without any calibration prior to the measurement. The accuracy of the reconstructed concentration maps deteriorates when the reconstruction model is biased by systematic errors such as large inhomogeneities in the static magnetic field. The presented method is a powerful tool for the fast acquisition of concentration maps that can provide valuable information for the investigation of many phenomena in chemical engineering applications.The authors thank for the financial support by the following grants: Microsoft Research Cambridge, and EPSRC (EP/K039318/1 and EP/K008218/1). Erik von Harbou was the recipient of a scholarship from the German Academic Exchange Service (DAAD).This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.jmr.2015.09.01