An Unsplit Godunov Method for Ideal MHD via Constrained Transport in Three Dimensions

We present a single step, second-order accurate Godunov scheme for ideal MHD which is an extension of the method described by Gardiner & Stone (2005) to three dimensions. This algorithm combines the corner transport upwind (CTU) method of Colella for multidimensional integration, and the constrained transport (CT) algorithm for preserving the divergence-free constraint on the magnetic field. We describe the calculation of the PPM interface states for 3D ideal MHD which must include multidimensional ``MHD source terms'' and naturally respect the balance implicit in these terms by the ${\bf\nabla\cdot B}=0$ condition. We compare two different forms for the CTU integration algorithm which require either 6- or 12-solutions of the Riemann problem per cell per time-step, and present a detailed description of the 6-solve algorithm. Finally, we present solutions for test problems to demonstrate the accuracy and robustness of the algorithm.Comment: Extended version of the paper accepted for publication in JC

Hydrodynamical Non-radiative Accretion Flows in Two-Dimensions

Two-dimensional (axially symmetric) numerical hydrodynamical calculations of accretion flows which cannot cool through emission of radiation are presented. The calculations begin from an equilibrium configuration consisting of a thick torus with constant specific angular momentum. Accretion is induced by the addition of a small anomalous azimuthal shear stress which is characterized by a function \nu. We study the flows generated as the amplitude and form of \nu are varied. A spherical polar grid which spans more than two orders of magnitude in radius is used to resolve the flow over a wide range of spatial scales. We find that convection in the inner regions produces significant outward mass motions that carry away both the energy liberated by, and a large fraction of the mass participating in, the accretion flow. Although the instantaneous structure of the flow is complex and dominated by convective eddies, long time averages of the dynamical variables show remarkable correspondence to certain steady-state solutions. Near the equatorial plane, the radial profiles of the time-averaged variables are power-laws with an index that depends on the radial scaling of the shear stress. We find that regardless of the adiabatic index of the gas, or the form or magnitude of the shear stress, the mass inflow rate is a strongly increasing function of radius, and is everywhere nearly exactly balanced by mass outflow. The net mass accretion rate through the disc is only a fraction of the rate at which mass is supplied to the inflow at large radii, and is given by the local, viscous accretion rate associated with the flow properties near the central object.Comment: 33 pages, 12 figures, accepted by MNRA

Energy Dependence of the Breit-Wheeler process in Heavy-Ion Collisions and its Application to Nuclear Charge Radius Measurements

The energy dependence of the cross section and the transverse momentum distribution of dielectrons from the Breit-Wheeler process in heavy-ion collisions are computed in the lowest-order QED and found to be sensitive to the nuclear charge distribution and the infrared-divergence of the ultra-Lorentz boosted Coulomb field. Within a given experimental kinematic acceptance, the cross section is found to increase while the pair average transverse momentum decreases with increasing beam energy. We demonstrate that the transverse-momentum component of Weizs\"acker-Williams photons is due to the finite extent of the charge source and electric field component in the longitudinal direction. We further clarify the connection between the nuclear charge distribution and the kinematics of produced $e^+e^-$ from the Breit-Wheeler process, and propose a criterion for the validity of the Breit-Wheeler process in relativistic heavy-ion collisions. Following this approach we demonstrate that the experimental measurements of the Breit-Wheeler process in ultra-relativistic heavy-ion collisions can be used to quantitatively constrain the nuclear charge radius. The extracted parameters show potential centrality dependence, and can be used to study the initial charge fluctuation and final-state magnetic field effect in hadronic interactions.Comment: 3 figure

Sustained Magnetorotational Turbulence in Local Simulations of Stratified Disks with Zero Net Magnetic Flux

We examine the effects of density stratification on magnetohydrodynamic turbulence driven by the magnetorotational instability in local simulations that adopt the shearing box approximation. Our primary result is that, even in the absence of explicit dissipation, the addition of vertical gravity leads to convergence in the turbulent energy densities and stresses as the resolution increases, contrary to results for zero net flux, unstratified boxes. The ratio of total stress to midplane pressure has a mean of ~0.01, although there can be significant fluctuations on long (>~50 orbit) timescales. We find that the time averaged stresses are largely insensitive to both the radial or vertical aspect ratio of our simulation domain. For simulations with explicit dissipation, we find that stratification extends the range of Reynolds and magnetic Prandtl numbers for which turbulence is sustained. Confirming the results of previous studies, we find oscillations in the large scale toroidal field with periods of ~10 orbits and describe the dynamo process that underlies these cycles.Comment: 13 pages, 18 figures, submitted to Ap

Self-similar turbulent dynamo

The amplification of magnetic fields in a highly conducting fluid is studied numerically. During growth, the magnetic field is spatially intermittent: it does not uniformly fill the volume, but is concentrated in long thin folded structures. Contrary to a commonly held view, intermittency of the folded field does not increase indefinitely throughout the growth stage if diffusion is present. Instead, as we show, the probability-density function (PDF) of the field strength becomes self-similar. The normalized moments increase with magnetic Prandtl number in a powerlike fashion. We argue that the self-similarity is to be expected with a finite flow scale and system size. In the nonlinear saturated state, intermittency is reduced and the PDF is exponential. Parallels are noted with self-similar behavior recently observed for passive-scalar mixing and for map dynamos.Comment: revtex, 4 pages, 5 figures; minor changes to match published versio

Novel hepatoselective insulin analog

Cel pracy. Zbadanie, czy tyroksylowy analog insuliny z ograniczonym dostępem do receptora w tkankach obwodowych wykazuje względnie wybiórcze powinowactwo do wątroby u ludzi. MATERIAŁ i metody. Pięć zdrowych osób otrzymywało podskórnie Na B1L-thyroksyl-insulinę (B1-T4-Ins) lub insulinę NPH w przypadkowej kolejności. Posługując się metodą klamry euglikemicznej i rozcieńczania znacznika izotopowego([D-6,6-2H2] glukozy), badano kinetykę insuliny oraz jej względny wpływ na wątrobową produkcję i obwodowy wychwyt glukozy. Pobierano próbki krwi w celu oznaczenia całkowitego stężenia insuliny immunoreaktywnej (bądź jej analogu) oraz w celu określenia stopnia wiązania analogu insuliny z białkami krwi, który badano metodą chromatografii cieczowej. Wyniki. Po podskórnym podaniu B1-T4-Ins była dobrze tolerowana i szybko wchłaniana. Analog cechował się długim czasem półtrwania w surowicy oraz wysokim stopniem wiązania (ok. 86%) z białkami. Jego czas działania, mierzony czasem wlewu glukozy niezbędnym do utrzymania euglikemii, był podobny do czasu działania insuliny NPH. Wpływ analogu na wątrobową produkcję glukozy był podobny do wpływu insuliny NPH, co wskazuje na podobny stopień oddziaływania. Analog w mniejszym stopniu działał na obwodowy wychwyt insuliny w porównaniu z insuliną NPH (p = 0,025), nie wpływał na szybkość przemian metabolicznych glukozy oraz wykazywał zmniejszoną zdolność do hamowania lipolizy (p < 0,05). Wnioski. U osób zdrowych B1-T4-Ins po podaniu podskórnym jest dobrze tolerowana, szybko się wchłania i ma wysoki stopień związania z białkami krwi, co odpowiada za długi czas połowicznego zaniku w surowicy. Analog ten wydaje się bardziej wybiórczy w oddziaływaniu na komórki wątroby, a zatem potencjalnie ma bardziej fizjologiczny profil działania w porównaniu z dotychczas stosowanymi preparatami insuliny.OBJECTIVE. To test whether a thyroxyl-insulin analog with restricted access to receptor sites in peripheral tissues displays relative hepatoselectivity in humans. RESEARCH DESIGN AND METHODS. Five normal human subjects received a subcutaneous bolus injection of either N B1 L-thyroxyl-insulin (B1-T4-Ins) or NPH insulin in random order. Insulin kinetics, relative effects on hepatic glucose production, and peripheral glucose uptake were studied using euglycemic clamp and stable isotope [D-6,6-2H2]glucose) dilution techniques. Blood samples were taken for the determination of total immunoreactive insulin/analog concentrations and for liquid chromatography to assess the protein binding of the analog in the circulation. RESULTS. After subcutaneous administration, B1-T4-Ins was well tolerated and rapidly absorbed. The analog had a long serum half-life and was highly protein bound (~86%). Its duration of action, as judged by the duration of infusion of exogenous glucose to maintain euglycemia, was similar to that of NPH insulin. The effect of the analogs on hepatic glucose production was similar to that of NPH insulin, indicating equivalent hepatic potency. The analog demonstrated less effect on peripheral glucose uptake than NPH insulin (P = 0,025), had no effect on metabolic clearance rate of glucose, and exhibited a reduced capacity to inhibit lipolysis (P < 0,05). CONCLUSIONS. When injected subcutaneously into normal human subjects, B1-T4-Ins is well tolerated, quickly absorbed, and highly protein bound, resulting in a long plasma half-life. This analog appears to have a hepatoselective action, and, therefore, has the potential to provide more physiological insulin action than the insulin preparations currently used