Band dispersion in C60(111): An angle-resolved photoemission study

Angle-resolved photoemission studies of single-crystal C60(111) films grown on GeS(001) reveal changes in valence feature line shape with emission angle and photon energy that are indicative of band dispersion. For an excitation energy (hν) of 10 eV, normal emission spectra show four sharp structures within the ∼1.1-eV-wide valence feature derived from the second highest molecular orbital (HOMO-1) of C60. For hν=8.1 eV, the 1-eV-wide HOMO-derived feature exhibits changes with emission angle mainly due to dispersion of 0.6 eV in the unoccupied bands. The distribution of electronic states underlying HOMO and HOMO-1 indicates that vibronic loss structures are not necessary to explain the width of these valence features

Convergence rates in expectation for Tikhonov-type regularization of Inverse Problems with Poisson data

In this paper we study a Tikhonov-type method for ill-posed nonlinear operator equations \gdag = F( ag) where \gdag is an integrable, non-negative function. We assume that data are drawn from a Poisson process with density t\gdag where $t>0$ may be interpreted as an exposure time. Such problems occur in many photonic imaging applications including positron emission tomography, confocal fluorescence microscopy, astronomic observations, and phase retrieval problems in optics. Our approach uses a Kullback-Leibler-type data fidelity functional and allows for general convex penalty terms. We prove convergence rates of the expectation of the reconstruction error under a variational source condition as $t\to\infty$ both for an a priori and for a Lepski{\u\i}-type parameter choice rule

Vivianite-parasymplesite solid solution: A sink for arsenic in ferruginous environments?

Vivianite, a hydrated ferrous phosphate [FeII3(PO4)2 · 8 H2O] that forms in oxygen-poor, but Fe2+-rich conditions is important in nutrient cycling in anoxic environments. In natural vivianites, isomorphic substitution of divalent cations for structural Fe(II) are typical. However, anion substitution is rare; in particular, arsenate (AsVO43−) substitution has never been documented in natural vivianites. Only partial substitution has been reported in synthetic analogues, and parasymplesite [FeII3(AsO4)2 · 8 H2O], the arsenic end member of the vivianite mineral group, is found in hydrothermal deposits. In this study, we detail structural changes in synthesised As-vivianites (FeII3[(PO4)1−x(AsO4)x]2 · 8 H2O) with systematically increased degrees of As(V) substitution (0.22 ≤ x ≤ 0.95). As(V) was successfully incorporated into the vivianite crystal structure, creating a homogenous, solid solution between AsVO43− and PO43−. Like both end members, the intermediate As-vivianites crystallised in the monoclinic system (C2/m space group), and retained the platelet crystal habit of As-free vivianite, even at the highest As(V) substitution. This uniform incorporation of As(V), and its replacement of PO43−, provides a potentially stable sink for arsenic in anoxic soils and sediments, and may have implications in ferruginous early Earth oceans

Necessary conditions for variational regularization schemes

We study variational regularization methods in a general framework, more precisely those methods that use a discrepancy and a regularization functional. While several sets of sufficient conditions are known to obtain a regularization method, we start with an investigation of the converse question: How could necessary conditions for a variational method to provide a regularization method look like? To this end, we formalize the notion of a variational scheme and start with comparison of three different instances of variational methods. Then we focus on the data space model and investigate the role and interplay of the topological structure, the convergence notion and the discrepancy functional. Especially, we deduce necessary conditions for the discrepancy functional to fulfill usual continuity assumptions. The results are applied to discrepancy functionals given by Bregman distances and especially to the Kullback-Leibler divergence.Comment: To appear in Inverse Problem

Two-Stage Rotational Disordering of a Molecular Crystal Surface: C60

We propose a two-stage mechanism for the rotational surface disordering phase transition of a molecular crystal, as realized in C$_{60}$ fullerite. Our study, based on Monte Carlo simulations, uncovers the existence of a new intermediate regime, between a low temperature ordered $(2 \times 2)$ state, and a high temperature $(1 \times 1)$ disordered phase. In the intermediate regime there is partial disorder, strongest for a subset of particularly frustrated surface molecules. These concepts and calculations provide a coherent understanding of experimental observations, with possible extension to other molecular crystal surfaces.Comment: 4 pages, 2 figure

Organic synthesis on Mars by electrochemical reduction of CO2

The sources and nature of organic carbon on Mars have been a subject of intense research. Steele et al. (2012) showed that 10 martian meteorites contain macromolecular carbon phases contained within pyroxene- and olivine-hosted melt inclusions. Here, we show that martian meteorites Tissint, Nakhla, and NWA 1950 have an inventory of organic carbon species associated with fluid-mineral reactions that are remarkably consistent with those detected by the Mars Science Laboratory (MSL) mission. We advance the hypothesis that interactions among spinel-group minerals, sulfides, and a brine enable the electrochemical reduction of aqueous CO2 to organic molecules. Although documented here in martian samples, a similar process likely occurs wherever igneous rocks containing spinel-group minerals and/or sulfides encounter brines

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

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