Provably stable numerical method for the anisotropic diffusion equation in toroidally confined magnetic fields

We present a novel numerical method for solving the anisotropic diffusion equation in toroidally confined magnetic fields which is efficient, accurate and provably stable. The continuous problem is written in terms of a derivative operator for the perpendicular transport and a linear operator, obtained through field line tracing, for the parallel transport. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing both boundary conditions and parallel diffusion operator obtained by field line tracing. We prove that the fully-discrete approximation is unconditionally stable and asymptotic preserving. Discrete energy estimates are shown to match the continuous energy estimate given the correct choice of penalty parameters. Convergence tests are shown for the perpendicular operator by itself, and the ``NIMROD benchmark" problem is used as a manufactured solution to show the full scheme converges even in the case where the perpendicular diffusion is zero. Finally, we present a magnetic field with chaotic regions and islands and show the contours of the anisotropic diffusion equation reproduce key features in the field.Comment: 33 pages, 8 figure

An efficient method for the anisotropic diffusion equation in magnetic fields

We solve the anisotropic diffusion equation in 2D, where the dominant direction of diffusion is defined by a vector field which does not conform to a Cartesian grid. Our method uses operator splitting to separate the diffusion perpendicular and parallel to the vector field. The slow time scale is solved using a provably stable finite difference formulation in the perpendicular to the vector field, and an integral operator for the diffusion parallel to it. Energy estimates are shown to for the continuous and semi-discrete cases. Numerical experiments are performed showing convergence of the method, and examples is given to demonstrate the capabilities of the method

Biomarkers for identifying the early phases of osteoarthritis secondary to medial patellar luxation in dogs

The levels of tartrate resistant acid phosphatase (TRAP), matrix metalloproteinase-2 (MMP-2), and tissue inhibitor of matrix metalloproteinase-2 (TIMP-2) in synovial fluid (SF) and serum in cases of canine osteoarthritis (OA) were measured. OA was induced by a surgically-created medial patellar luxation in the left stifle of 24 dogs. SF and blood samples were collected at 1.5- and 3-month intervals, respectively. Every 3 months, one dog was euthanatized to collect tissue samples from both stifles. TRAP levels in SF and serum were measured using a spectrophotometer, and TRAP-positive cells in joint tissues were identified by enzyme histochemistry. MMP-2 and TIMP-2 in SF and serum were detected by Western blotting and ELISA, respectively. TRAP in SF from the stifles and serum was significantly increased (p < 0.05) after 3 months. TIMP-2 in SF and serum was significantly decreased (p < 0.05), whereas MMP-2 in SF was significantly increased (p < 0.05) during the progression of OA. Histochemistry revealed an increased number of TRAP-positive cells in tissues from OA-affected joints. Assays measuring TRAP, MMP-2, and TIMP-2 in SF and serum, and methods that detect increased numbers of TRAP-positive cells in the joint tissues can play an important role in identifying the early phases of degenerative changes in canine joint components

Writing in Britain and Ireland, c. 400 to c. 800

No abstract available

Effects of antiplatelet therapy on stroke risk by brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases: subgroup analyses of the RESTART randomised, open-label trial

Background Findings from the RESTART trial suggest that starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. Brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases (such as cerebral microbleeds) are associated with greater risks of recurrent intracerebral haemorrhage. We did subgroup analyses of the RESTART trial to explore whether these brain imaging features modify the effects of antiplatelet therapy

An integrative approach to understanding microbial diversity: from intracellular mechanisms to community structure

Trade-offs have been put forward as essential to the generation and maintenance of diversity. However, variation in trade-offs is often determined at the molecular level, outside the scope of conventional ecological inquiry. In this study, we propose that understanding the intracellular basis for trade-offs in microbial systems can aid in predicting and interpreting patterns of diversity. First, we show how laboratory experiments and mathematical models have unveiled the hidden intracellular mechanisms underlying trade-offs key to microbial diversity: (i) metabolic and regulatory trade-offs in bacteria and yeast; (ii) life-history trade-offs in bacterial viruses. Next, we examine recent studies of marine microbes that have taken steps toward reconciling the molecular and the ecological views of trade-offs, despite the challenges in doing so in natural settings. Finally, we suggest avenues for research where mathematical modelling, experiments and studies of natural microbial communities provide a unique opportunity to integrate studies of diversity across multiple scales

Jet energy measurement with the ATLAS detector in proton-proton collisions at root s=7 TeV

The jet energy scale and its systematic uncertainty are determined for jets measured with the ATLAS detector at the LHC in proton-proton collision data at a centre-of-mass energy of √s = 7TeV corresponding to an integrated luminosity of 38 pb-1. Jets are reconstructed with the anti-kt algorithm with distance parameters R=0. 4 or R=0. 6. Jet energy and angle corrections are determined from Monte Carlo simulations to calibrate jets with transverse momenta pT≥20 GeV and pseudorapidities {pipe}η{pipe}<4. 5. The jet energy systematic uncertainty is estimated using the single isolated hadron response measured in situ and in test-beams, exploiting the transverse momentum balance between central and forward jets in events with dijet topologies and studying systematic variations in Monte Carlo simulations. The jet energy uncertainty is less than 2. 5 % in the central calorimeter region ({pipe}η{pipe}<0. 8) for jets with 60≤pT<800 GeV, and is maximally 14 % for pT<30 GeV in the most forward region 3. 2≤{pipe}η{pipe}<4. 5. The jet energy is validated for jet transverse momenta up to 1 TeV to the level of a few percent using several in situ techniques by comparing a well-known reference such as the recoiling photon pT, the sum of the transverse momenta of tracks associated to the jet, or a system of low-pT jets recoiling against a high-pT jet. More sophisticated jet calibration schemes are presented based on calorimeter cell energy density weighting or hadronic properties of jets, aiming for an improved jet energy resolution and a reduced flavour dependence of the jet response. The systematic uncertainty of the jet energy determined from a combination of in situ techniques is consistent with the one derived from single hadron response measurements over a wide kinematic range. The nominal corrections and uncertainties are derived for isolated jets in an inclusive sample of high-pT jets. Special cases such as event topologies with close-by jets, or selections of samples with an enhanced content of jets originating from light quarks, heavy quarks or gluons are also discussed and the corresponding uncertainties are determined. © 2013 CERN for the benefit of the ATLAS collaboration

Measurement of the inclusive and dijet cross-sections of b-jets in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

The inclusive and dijet production cross-sections have been measured for jets containing b-hadrons (b-jets) in proton-proton collisions at a centre-of-mass energy of sqrt(s) = 7 TeV, using the ATLAS detector at the LHC. The measurements use data corresponding to an integrated luminosity of 34 pb^-1. The b-jets are identified using either a lifetime-based method, where secondary decay vertices of b-hadrons in jets are reconstructed using information from the tracking detectors, or a muon-based method where the presence of a muon is used to identify semileptonic decays of b-hadrons inside jets. The inclusive b-jet cross-section is measured as a function of transverse momentum in the range 20 < pT < 400 GeV and rapidity in the range |y| < 2.1. The bbbar-dijet cross-section is measured as a function of the dijet invariant mass in the range 110 < m_jj < 760 GeV, the azimuthal angle difference between the two jets and the angular variable chi in two dijet mass regions. The results are compared with next-to-leading-order QCD predictions. Good agreement is observed between the measured cross-sections and the predictions obtained using POWHEG + Pythia. MC@NLO + Herwig shows good agreement with the measured bbbar-dijet cross-section. However, it does not reproduce the measured inclusive cross-section well, particularly for central b-jets with large transverse momenta.Comment: 10 pages plus author list (21 pages total), 8 figures, 1 table, final version published in European Physical Journal