A gyrokinetic model for the plasma periphery of tokamak devices

A gyrokinetic model is presented that can properly describe strong flows, large and small amplitude electromagnetic fluctuations occurring on scale lengths ranging from the electron Larmor radius to the equilibrium perpendicular pressure gradient scale length, and large deviations from thermal equilibrium. The formulation of the gyrokinetic model is based on a second order description of the single charged particle dynamics, derived from Lie perturbation theory, where the fast particle gyromotion is decoupled from the slow drifts, assuming that the ratio of the ion sound Larmor radius to the perpendicular equilibrium pressure scale length is small. The collective behavior of the plasma is obtained by a gyrokinetic Boltzmann equation that describes the evolution of the gyroaveraged distribution function and includes a non-linear gyrokinetic Dougherty collision operator. The gyrokinetic model is then developed into a set of coupled fluid equations referred to as the gyrokinetic moment hierarchy. To obtain this hierarchy, the gyroaveraged distribution function is expanded onto a velocity-space Hermite-Laguerre polynomial basis and the gyrokinetic equation is projected onto the same basis, obtaining the spatial and temporal evolution of the Hermite-Laguerre expansion coefficients. The Hermite-Laguerre projection is performed accurately at arbitrary perpendicular wavenumber values. Finally, the self-consistent evolution of the electromagnetic fields is described by a set of gyrokinetic Maxwell's equations derived from a variational principle, with the velocity integrals of the gyroaveraged distribution function explicitly evaluated

A construction of integer-valued polynomials with prescribed sets of lengths of factorizations

For an arbitrary finite set S of natural numbers greater 1, we construct an integer-valued polynomial f, whose set of lengths in Int(Z) is S. The set of lengths of f is the set of all natural numbers n, such that f has a factorization as a product of n irreducibles in Int(Z)={g in Q[x] | g(Z) contained in Z}.Comment: To appear in Monatshefte f\"ur Mathematik; 11 page

Topische Therapie bei chronisch-entzündlichen Darmerkrankungen: Ein häufig unterschätzter Therapiebaustein

Zusammenfassung: Die Inzidenz und Prävalenz der Colitis ulcerosa nimmt sowohl in westlichen Ländern als auch in Entwicklungsländern zu. Grundstein der Behandlung ist die Anwendung von Aminosalicylaten (5-ASA). Alternativ können auch steroidhaltige topische Therapien eingesetzt werden. Häufig werden 5-ASA-Präparate nur peroral verabreicht, obschon insbesondere bei Proktitis und linksseitiger Kolitis topische (oder rektale) 5-ASA-Präparate sogar effizienter sind als perorale/systemische. Dies gilt sowohl für die Remissionsinduktion wie auch für die remissionserhaltende Therapie. Zahlreiche Untersuchungen in Kohorten oder größeren Behandlungszentren zeigen, dass topische Therapien zu selten eingesetzt werden. Insbesondere bei der ausgedehnten Kolitis sollten perorale und topische Therapien kombiniert Anwendung finden. In diesem Übersichtsartikel fassen wir die Evidenz der topischen Therapie bei der Colitis ulcerosa mit 5-ASA und Steroiden zusammen. Damit kann die Therapie optimiert und die Akzeptanz einer topischen Therapie bei den Patienten verbessert werden. Diese ist nach entsprechender Aufklärung höher als generell vermutet wird. Nur bei schweren Kolitisverläufen hat eine topische Therapie keinen Stellenwert, da sie zum einen bei häufigen Darmentleerungen nicht ausreichend wirksam wäre und zum anderen von den Patienten schlecht toleriert wird. Die Evidenz für die Anwendung topischer Therapien bei Morbus Crohn ist unzureichen

Vinogradov's three primes theorem with primes having given primitive roots

The first purpose of our paper is to show how Hooley's celebrated method leading to his conditional proof of the Artin conjecture on primitive roots can be combined with the Hardy-Littlewood circle method. We do so by studying the number of representations of an odd integer as a sum of three primes, all of which have prescribed primitive roots. The second purpose is to analyse the singular series. In particular, using results of Lenstra, Stevenhagen and Moree, we provide a partial factorisation as an Euler product and prove that this does not extend to a complete factorisation

A statistical method to search for recoiling supermassive black holes in active galactic nuclei

We propose an observational test for gravitationally recoiling supermassive black holes (BHs) in active galactic nuclei, based on a correlation between the velocities of BHs relative to their host galaxies, |Δv|, and their obscuring dust column densities, Σdust (both measured along the line of sight). We use toy models for the distribution of recoil velocities, BH trajectories, and the geometry of obscuring dust tori in galactic centres, to simulate 2.5 × 105 random observations of recoiling quasars. BHs with recoil velocities comparable to the escape velocity from the galactic centre remain bound to the nucleus, and do not fully settle back to the centre of the torus due to dynamical friction in a typical quasar lifetime. We find that |Δv| and Σdust for these BHs are positively correlated. For obscured (Σdust > 0) and for partially obscured (0 < Σdust ≲ 2.3 g m−2) quasars with |Δv| ≥ 45 km s−1, the sample correlation coefficient between log10(|Δv|) and Σdust is r45 = 0.28 ± 0.02 and r45 = 0.13 ± 0.02, respectively. Allowing for random ± 100 km s− 1 errors in |Δv| unrelated to the recoil dilutes the correlation for the partially obscured quasars to r45 = 0.026 ± 0.004 measured between |Δv| and Σdust. A random sample of ≳ 3500 obscured quasars with |Δv| ≥ 45 km s−1 would allow rejection of the no-correlation hypothesis with 3σ significance 95 per cent of the time. Finally, we find that the fraction of obscured quasars, obs (|Δv|), decreases with |Δv| from obs (103 km s−1) ≲ 0.4. This predicted trend can be compared to the observed fraction of type II quasars, and can further test combinations of recoil, trajectory, and dust torus models

Granite-hosted gold mineralization in the Midlands greenstone belt: a new type of low-grade gold deposit in Zimbabwe

In 1992, the Ford gold deposit was rediscovered during field work in the Kwekwe district near the Indarama mine, approximately 200 km southwest of Harare, Zimbabwe. Based on diamond drilling and open pit operations, estimated ore reserves are at least 3 Mt with an average gold content of 2.5 g/t. The gold deposit is located within a porphyritic granite dike with a thickness of 20–50 m, striking 800 m NNW-SSE. It dips 60–70° to the NE and intrudes a volcano-sedimentary sequence of tholeiitic basalts, acid volcanics, and banded iron formations of the Bulawayan Group (2900–2700 Ma). The intrusion of the dike occurred at 2541 ± 17 Ma (Pb/Pb step leaching technique) within a second order structure and is related to displacement along transcrustal deformation zones such as the Sherwood- and Taba-Mali deformation zones. Gold mineralization is confined to the s-shaped part of the dike intrusion. At the present stage of mining, the deposit is characterized by the absence of major veins, the occurrence of disseminated pyrite throughout the orebody, and a distinct alteration pattern comparable to that of porphyry copper deposits. The central zone of the dike shows a typical K-feldspar-albite-sericite-pyrite (±biotite?) alteration, followed by a narrow external propylitic zone. Native gold with an average Ag content of 5 wt.% and a grain size of 5–100 μm is rare and occurs within pyrite and secondary K-feldspar. Sulphide mineral separates of pyrite and minor arsenopyrite probably contain invisible gold (up to 120 ppm) amenable to cyanidation. Anomalously high gold values of ∼7 ppm have been found in the transition between the K-feldspar-albite-sericite-pyrite alteration and the propylitic zone, indicating that the mineralizing fluids have experienced major physico-chemical changes in the transition zone. The regional tectonic position of the orebody suggests that the emplacement of the granite and the gold mineralization are structurally controlled. The Pb isotope composition of several leachates of pyrite indicate isotope disequilibrium with magmatic minerals and point to a contamination of the mineralizing fluid by Pb from older (sedimentary?) sources. Stable isotope geochemistry of sulphides and carbonates as well as the metallogeny of the deposit compare to shear-zone hosted gold mineralization in the Kwekwe district, for which a deep crustal origin has been discussed. Although this study documents contrasting evidence for a porphyry-gold versus a shear-zone type of mineralization, it is suggested that gold-bearing fluids were syntectonically introduced into a ductile shear zone within the granite dike either during cooling of the intrusion or later in Archaean or early Proterozoic times

InSPIREd - advances in Conformal Printing: 3D printing onto unknown uneven surfaces

The term Conformal Printing refers to 3D printing onto uneven surfaces. Whilst some very high priced solutions exist for known uneven surfaces, where the toolpath is generated in advance, based on CAD data of the object to be printed onto, there is nothing available yet for conformal printing onto unknown uneven surfaces that are scanned on-the-fly. A low-cost prototype named 'InSPIREd' was recently developed to achieve this, made possible with a combination of multi-disciplinary expertise, ingenuity and problem tackling knowhow, and the latest improvements are presented in this paper. The prototype now includes more capable scanning technology and a simplified calibration procedure

Full-F Turbulent Simulation in a Linear Device using a Gyro-Moment Approach

Simulations of plasma turbulence in a linear plasma device configuration are presented. These simulations are based on a simplified version of the gyrokinetic (GK) model proposed by B. J. Frei et al. [J. Plasma Phys. 86, 905860205 (2020)] where the full-F distribution function is expanded on a velocity-space polynomial basis allowing us to reduce its evolution to the solution of an arbitrary number of fluid-like equations for the expansion coefficients, denoted as the gyro-moments (GM). By focusing on the electrostatic and neglecting finite Larmor radius effects, a full-F GM hierarchy equation is derived to evolve the ion dynamics, which includes a nonlinear Dougherty collision operator, localized sources, and Bohm sheath boundary conditions. An electron fluid Braginskii model is used to evolve the electron dynamics, coupled to the full-F ion GM hierarchy equation via a vorticity equation where the Boussinesq approximation is used. A set of full-F turbulent simulations are then performed using the parameters of the LArge Plasma Device (LAPD) experiments with different numbers of ion GMs and different values of collisionality. The ion distribution function is analyzed illustrating the convergence properties of the GM approach. In particular, we show that higher-order GMs are damped by collisions in the high-collisional regime relevant to LAPD experiments. The GM results are then compared with those from two-fluid Braginskii simulations, finding qualitative agreement in the time-averaged profiles and statistical turbulent properties