119 research outputs found

    Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings

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    Recent studies of the thermodynamic phase diagrams of the Gross-Neveu model (GN2), and its chiral cousin, the NJL2 model, have shown that there are phases with inhomogeneous crystalline condensates. These (static) condensates can be found analytically because the relevant Hartree-Fock and gap equations can be reduced to the nonlinear Schr\"odinger equation, whose deformations are governed by the mKdV and AKNS integrable hierarchies, respectively. Recently, Thies et al have shown that time-dependent Hartree-Fock solutions describing baryon scattering in the massless GN2 model satisfy the Sinh-Gordon equation, and can be mapped directly to classical string solutions in AdS3. Here we propose a geometric perspective for this result, based on the generalized Weierstrass spinor representation for the embedding of 2d surfaces into 3d spaces, which explains why these well-known integrable systems underlie these various Gross-Neveu gap equations, and why there should be a connection to classical string theory solutions. This geometric viewpoint may be useful for higher dimensional models, where the relevant integrable hierarchies include the Davey-Stewartson and Novikov-Veselov systems.Comment: 27 pages, 1 figur

    The role of neuronavigation in intracranial endoscopic procedures

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    In occlusive hydrocephalus, cysts and some ventricular tumours, neuroendoscopy has replaced shunt operations and microsurgery. There is an ongoing discussion if neuronavigation should routinely accompany neuroendoscopy or if its use should be limited to selected cases. In this prospective clinical series, the role of neuronavigation during intracranial endoscopic procedures was investigated. In 126 consecutive endoscopic procedures (endoscopic third ventriculostomy, ETV, n = 65; tumour biopsy/resection, n = 36; non-tumourous cyst fenestration, n = 23; abscess aspiration and hematoma removal, n = 1 each), performed in 121 patients, neuronavigation was made available. After operation and videotape review, the surgeon had to categorize the role of neuronavigation: not beneficial; beneficial, but not essential; essential. Overall, neuronavigation was of value in more than 50% of the operations, but its value depended on the type of the procedure. Neuronavigation was beneficial, but not essential in 16 ETVs (24.6%), 19 tumour biopsies/resections (52.7%) and 14 cyst fenestrations (60.9%). Neuronavigation was essential in 1 ETV (2%), 11 tumour biopsies/resections (30.6%) and 8 cyst fenestrations (34.8%). Neuronavigation was not needed/not used in 48 ETVs (73.9%), 6 endoscopic tumour operations (16.7%) and 1 cyst fenestration (4.3%). For ETV, neuronavigation mostly is not required. In the majority of the remaining endoscopic procedures, however, neuronavigation is at least beneficial. This finding suggests integrating neuronavigation into the operative routine in endoscopic tumour operations and cyst fenestrations

    Corrosion of the International Simple Glass under acidic to hyperalkaline conditions

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    Assessment of glass dissolution kinetics, under disposal relevant temperature and pH environments, is required to credibly estimate radionuclide release rates from vitrified radioactive waste. Leaching of the International Simple Glass (ISG) under acidic to hyperalkaline conditions was examined. Forward rate measurements have been obtained using the dynamic leaching SPFT protocol and rate parameters for B, Na and Si in the basic regime; errors in rates predicted using these parameters at high pH and temperature are significant because the fitting uses logarithmic data. Longer term behaviour under hyperalkaline conditions, representative of some disposal environments, was investigated using the PCT and MCC-1 static leaching protocols with Ca(OH)2 solutions for up to 120 days (PCT) and 720 days (MCC-1). In hyperalkaline conditions dissolution was incongruent for all elements and the presence of alternating zirconia-rich and zirconia-poor alteration layers was observed on all leached monoliths, indicating the occurrence of a self-organisation phenomenon during leaching

    Global burden of 369 diseases and injuries in 204 countries and territories, 1990-2019: a systematic analysis for the Global Burden of Disease Study 2019

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