116 research outputs found

    Symmetry of the Atomic Electron Density in Hartree, Hartree-Fock, and Density Functional Theory

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    The density of an atom in a state of well-defined angular momentum has a specific finite spherical harmonic content, without and with interactions. Approximate single-particle schemes, such as the Hartree, Hartree-Fock, and Local Density Approximations, generally violate this feature. We analyze, by means of perturbation theory, the degree of this violation and show that it is small. The correct symmetry of the density can be assured by a constrained-search formulation without significantly altering the calculated energies. We compare our procedure to the (different) common practice of spherically averaging the self-consistent potential. Kohn-Sham density functional theory with the exact exchange-correlation potential has the correct finite spherical harmonic content in its density; but the corresponding exact single particle potential and wavefunctions contain an infinite number of spherical harmonics.Comment: 11 pages, 6 figures. Expanded discussion of spherical harmonic expansion of Hartree density. Some typos corrected, references adde

    Occupation numbers in density-functional calculations

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    It is the intention of this paper to rigorously clarify the role of the occupation numbers in the current practical applications of the density functional formalism. In these calculations one has to decide how to distribute a given, fixed number of electrons over a set of single-particle orbitals. The conventional choice is to have orbitals below the Fermi level completely occupied and the orbitals above the Fermi level empty. Although there is a certain confusion in literature why this choice is superior to any others, the general belief is that it can justified by treating the occupation numbers as variational parameters and then applying Janak's theorem or similar reasoning. We demonstrate that there is a serious flaw in those arguments,mainly the kinetic energy and therefore the exchange-correlation potential are not differentiable with respect to density for arbitrary occupation numbers. It is rigorously shown that in the present context of the density functional calculations there is no freedom to vary the occupation numbers. The occupation numbers cannot be considered as variational parameters.Comment: 10 pages, Revtex, accepted for publication by Phys.Rev.

    Density functional theories and self-energy approaches

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    A purpose-designed microarray platform (Stressgenes, Phase 1) was utilised to investigate the changes in gene expression within the liver of rainbow trout during exposure to a prolonged period of confinement. Tissue and blood samples were collected from trout at intervals up to 648 h after transfer to a standardised confinement stressor, together with matched samples from undisturbed control fish. Plasma ACTH, cortisol, glucose and lactate were analysed to confirm that the neuroendocrine response to confinement was consistent with previous findings and to provide a phenotypic context to assist interpretation of gene expression data. Liver samples for suppression subtractive hybridisation (SSH) library construction were selected from within the experimental groups comprising “early” stress (2–48 h) and “late” stress (96–504 h). In order to reduce redundancy within the four SSH libraries and yield a higher number of unique clones an additional subtraction was carried out. After printing of the arrays a series of 55 hybridisations were executed to cover 6 time points. At 2 h, 6 h, 24 h, 168 h and 504 h 5 individual confined fish and 5 individual control fish were used with control fish only at 0 h. A preliminary list of 314 clones considered differentially regulated over the complete time course was generated by a combination of data analysis approaches and the most significant gene expression changes were found to occur during the 24 h to 168 h time period with a general approach to control levels by 504 h. Few changes in expression were apparent over the first 6 h. The list of genes whose expression was significantly altered comprised predominantly genes belonging to the biological process category (response to stimulus) and one cellular component category (extracellular region) and were dominated by so-called acute phase proteins. Analysis of the gene expression profile in liver tissue during confinement revealed a number of significant clusters. The major patterns comprised genes that were up-regulated at 24 h and beyond, the primary examples being haptoglobin, β-fibrinogen and EST10729. Two representative genes from each of the six k-means clusters were validated by qPCR. Correlations between microarray and qPCR expression patterns were significant for most of the genes tested. qPCR analysis revealed that haptoglobin expression was up-regulated approximately 8-fold at 24 h and over 13-fold by 168 h.This project was part funded by the European Commission (Q5RS-2001-02211), Enterprise Ireland and the Natural Environment Research Council of the United Kingdom

    Overview of fast particle experiments in the first MAST Upgrade experimental campaigns

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    MAST-U is equipped with on-axis and off-axis neutral beam injectors (NBI), and these external sources of super-Alfvénic deuterium fast-ions provide opportunities for studying a wide range of phenomena relevant to the physics of alpha-particles in burning plasmas. The MeV range D-D fusion product ions are also produced but are not confined. Simulations with the ASCOT code show that up to 20% of fast ions produced by NBI can be lost due to charge exchange (CX) with edge neutrals. Dedicated experiments employing low field side (LFS) gas fuelling show a significant drop in the measured neutron fluxes resulting from beam-plasma reactions, providing additional evidence of CX-induced fast-ion losses, similar to the ASCOT findings. Clear evidence of fast-ion redistribution and loss due to sawteeth (ST), fishbones (FB), long-lived modes (LLM), Toroidal Alfvén Eigenmodes (TAE), Edge Localised Modes (ELM) and neoclassical tearing modes (NTM) has been found in measurements with a Neutron Camera (NCU), a scintillator-based Fast-Ion Loss Detector (FILD), a Solid-State Neutral Particle Analyser (SSNPA) and a Fast-Ion Deuterium-α (FIDA) spectrometer. Unprecedented FILD measurements in the range of 1–2 MHz indicate that fast-ion losses can be also induced by the beam ion cyclotron resonance interaction with compressional or global Alfvén eigenmodes (CAEs or GAEs). These results show the wide variety of scenarios and the unique conditions in which fast ions can be studied in MAST-U, under conditions that are relevant for future devices like STEP or ITER
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