Accretion Disc Theory: From the Standard Model Until Advection

Accretion disc theory was first developed as a theory with the local heat balance, where the whole energy produced by a viscous heating was emitted to the sides of the disc. One of the most important new invention of this theory was a phenomenological treatment of the turbulent viscosity, known as ''alpha'' prescription, when the (r$\phi$) component of the stress tensor was approximated by ($\alpha$ P) with a unknown constant $\alpha$. This prescription played the role in the accretion disc theory as well important as the mixing-length theory of convection for stellar evolution. Sources of turbulence in the accretion disc are discussed, including nonlinear hydrodynamical turbulence, convection and magnetic field role. In parallel to the optically thick geometrically thin accretion disc models, a new branch of the optically thin accretion disc models was discovered, with a larger thickness for the same total luminosity. The choice between these solutions should be done of the base of a stability analysis. The ideas underlying the necessity to include advection into the accretion disc theory are presented and first models with advection are reviewed. The present status of the solution for a low-luminous optically thin accretion disc model with advection is discussed and the limits for an advection dominated accretion flows (ADAF) imposed by the presence of magnetic field are analysed.Comment: Roceeding of the Int. Workshop "Observational Evidence for Black Holes in the Universe". Calcutta, 11-17 January 1998. Kluwer Acad. Pu

Early

Arthritis Rheum. 2004 Dec;50(12):3934-40. Early response to immunosuppressive therapy predicts good renal outcome in lupus nephritis: lessons from long-term followup of patients in the Euro-Lupus Nephritis Trial. Houssiau FA, Vasconcelos C, D'Cruz D, Sebastiani GD, de Ramon Garrido E, Danieli MG, Abramovicz D, Blockmans D, Mathieu A, Direskeneli H, Galeazzi M, Gül A, Levy Y, Petera P, Popovic R, Petrovic R, Sinico RA, Cattaneo R, Font J, Depresseux G, Cosyns JP, Cervera R. Université Catholique de Louvain, Brussels, Belgium. [email protected] Abstract OBJECTIVE: In the Euro-Lupus Nephritis Trial (ELNT), 90 patients with lupus nephritis were randomly assigned to a high-dose intravenous cyclophosphamide (IV CYC) regimen (6 monthly pulses and 2 quarterly pulses with escalating doses) or a low-dose IV CYC regimen (6 pulses of 500 mg given at intervals of 2 weeks), each of which was followed by azathioprine (AZA). After a median followup of 41 months, a difference in efficacy between the 2 regimens was not observed. The present analysis was undertaken to extend the followup and to identify prognostic factors. METHODS: Renal function was prospectively assessed quarterly in all 90 patients except 5 who were lost to followup. Survival curves were derived using the Kaplan-Meier method. RESULTS: After a median followup of 73 months, there was no significant difference in the cumulative probability of end-stage renal disease or doubling of the serum creatinine level in patients who received the low-dose IV CYC regimen versus those who received the high-dose regimen. At long-term followup, 18 patients (8 receiving low-dose and 10 receiving high-dose treatment) had developed permanent renal impairment and were classified as having poor long-term renal outcome. We demonstrated by multivariate analysis that early response to therapy at 6 months (defined as a decrease in serum creatinine level and proteinuria <1 g/24 hours) was the best predictor of good long-term renal outcome. CONCLUSION: Long-term followup of patients from the ELNT confirms that, in lupus nephritis, a remission-inducing regimen of low-dose IV CYC followed by AZA achieves clinical results comparable with those obtained with a high-dose regimen. Early response to therapy is predictive of good long-term renal outcome. PMID: 15593207 [PubMed - indexed for MEDLINE

Fuchs versus Painlev\'e

We briefly recall the Fuchs-Painlev\'e elliptic representation of Painlev\'e VI. We then show that the polynomiality of the expressions of the correlation functions (and form factors) in terms of the complete elliptic integral of the first and second kind, $K$ and $E$, is a straight consequence of the fact that the differential operators corresponding to the entries of Toeplitz-like determinants, are equivalent to the second order operator $L_E$ which has $E$ as solution (or, for off-diagonal correlations to the direct sum of $L_E$ and $d/dt$). We show that this can be generalized, mutatis mutandis, to the anisotropic Ising model. The singled-out second order linear differential operator $L_E$ being replaced by an isomonodromic system of two third-order linear partial differential operators associated with $\Pi_1$, the Jacobi's form of the complete elliptic integral of the third kind (or equivalently two second order linear partial differential operators associated with Appell functions, where one of these operators can be seen as a deformation of $L_E$). We finally explore the generalizations, to the anisotropic Ising models, of the links we made, in two previous papers, between Painlev\'e non-linear ODE's, Fuchsian linear ODE's and elliptic curves. In particular the elliptic representation of Painlev\'e VI has to be generalized to an ``Appellian'' representation of Garnier systems.Comment: Dedicated to the : Special issue on Symmetries and Integrability of Difference Equations, SIDE VII meeting held in Melbourne during July 200

Large PT Double Photon Production in Hadronic Collisions - Beyond Leading Logarithm QCD Calculation

Aurenche P, Douiri A, Baier R, Fontannaz M, Schiff D. Large PT Double Photon Production in Hadronic Collisions - Beyond Leading Logarithm QCD Calculation. Zeitschrift für Physik C: Particles and fields. 1985;29(3):459-475

Gravitational Lensing by Black Holes

We review the theoretical aspects of gravitational lensing by black holes, and discuss the perspectives for realistic observations. We will first treat lensing by spherically symmetric black holes, in which the formation of infinite sequences of higher order images emerges in the clearest way. We will then consider the effects of the spin of the black hole, with the formation of giant higher order caustics and multiple images. Finally, we will consider the perspectives for observations of black hole lensing, from the detection of secondary images of stellar sources and spots on the accretion disk to the interpretation of iron K-lines and direct imaging of the shadow of the black hole.Comment: Invited article for the GRG special issue on lensing (P. Jetzer, Y. Mellier and V. Perlick Eds.). 31 pages, 12 figure

Immunosuppressive therapy in lupus nephritis: the Euro-Lupus Nephritis Trial, a randomized trial of low-dose versus high-dose intravenous cyclophosphamide.

OBJECTIVE: Glomerulonephritis is a severe manifestation of systemic lupus erythematosus (SLE) that is usually treated with an extended course of intravenous (IV) cyclophosphamide (CYC). Given the side effects of this regimen, we evaluated the efficacy and the toxicity of a course of low-dose IV CYC prescribed as a remission-inducing treatment, followed by azathioprine (AZA) as a remission-maintaining treatment. METHODS: In this multicenter, prospective clinical trial (the Euro-Lupus Nephritis Trial [ELNT]), we randomly assigned 90 SLE patients with proliferative glomerulonephritis to a high-dose IV CYC regimen (6 monthly pulses and 2 quarterly pulses; doses increased according to the white blood cell count nadir) or a low-dose IV CYC regimen (6 fortnightly pulses at a fixed dose of 500 mg), each of which was followed by AZA. Intent-to-treat analyses were performed. RESULTS: Followup continued for a median of 41.3 months in the low-dose group and 41 months in the high-dose group. Sixteen percent of those in the low-dose group and 20% of those in the high-dose group experienced treatment failure (not statistically significant by Kaplan-Meier analysis). Levels of serum creatinine, albumin, C3, 24-hour urinary protein, and the disease activity scores significantly improved in both groups during the first year of followup. Renal remission was achieved in 71% of the low-dose group and 54% of the high-dose group (not statistically significant). Renal flares were noted in 27% of the low-dose group and 29% of the high-dose group. Although episodes of severe infection were more than twice as frequent in the high-dose group, the difference was not statistically significant. CONCLUSION: The data from the ELNT indicate that in European SLE patients with proliferative lupus nephritis, a remission-inducing regimen of low-dose IV CYC (cumulative dose 3 gm) followed by AZA achieves clinical results comparable to those obtained with a high-dose regimen