Viscous accretion discs around rotating black holes

The stationary hydrodynamic equations for transonic viscous accretion discs in Kerr geometry are derived. The consistent formulation is given for the viscous angular momentum transport and the boundary conditions on the horizon of a central black hole. An expression for the thickness of the disc is obtained from the vertical Euler equation for general accretion flows with vanishing vertical velocity. Different solution topologies are identified, characterized by a sonic transition close to or far from the marginally stable orbit. A numerical method is presented that allows to integrate the structure equations of transonic accretion flows. Global polytropic solutions for the disc structure are calculated, covering each topology and a wide range of physical conditions. These solutions generally possess a sub-Keplerian angular momentum distribution and have maximum temperatures in the range $10^{11}-10^{12}$ K. Accretion discs around rotating black holes are hotter and deposit less angular momentum on the central object than accretion discs around Schwarzschild black holes.Comment: 15 pages LateX, requires mn.sty, accepted for publication in the MNRAS, figures available at http://www.lsw.uni-heidelberg.de/~jpeitz/PV

Pressure-driven Instabilities in Cylindrical Geometry: A New General Criterion

A new criterion for pressure-driven interchange instabilities in cylindrical geometry is derived, based on an alternate use of the Energy Principle. This criterion is inequivalent to Suydam's criterion and does not contain the magnetic shear. In fact, it is shown that Suydam's criterion relates to the instability of the slow magnetosonic branch, while the present criterion relates to the Alfv\'enic one, which is the most dangerous of the two. These findings explain why pressure-driven modes nearly always exist even if Suydam's criterion is satisfied by a large margin.Comment: 4 pages. Submitted to Phys. Rev. Let

3+1 formulation of non-ideal hydrodynamics

The equations governing dissipative relativistic hydrodynamics are formulated within the 3+1 approach for arbitrary spacetimes. Dissipation is accounted for by applying the theory of extended causal thermodynamics (Israel-Stewart theory). This description eliminates the causality violating infinite signal speeds present in the conventional Navier-Stokes equation. As an example we treat the astrophysically relevant case of stationary and axisymmetric spacetimes, including the Kerr metric. The equations take a simpler form whenever the inertia due to the dissipative contributions can be neglected.Comment: 24 pages, LateX, uses mn.sty and AMS fonts, no figures, accepted for publication in the MNRAS, also available via http://www.lsw.uni-heidelberg.de/~jpeitz/Personal.htm

Dynamics and Structure of Three-Dimensional Trans-Alfvenic Jets. II. The Effect of Density and Winds

Two three-dimensional magnetohydrodynamical simulations of strongly magnetized conical jets, one with a poloidal and one with a helical magnetic field, have been performed. In the poloidal simulation a significant sheath (wind) of magnetized moving material developed and partially stabilized the jet to helical twisting. The fundamental pinch mode was not similarly affected and emission knots developed in the poloidal simulation. Thus, astrophysical jets surrounded by outflowing winds could develop knotty structures along a straight jet triggered by pinching. Where helical twisting dominated the dynamics, magnetic field orientation along the line-of-sight could be organized by the toroidal flow field accompanying helical twisting. On astrophysical jets such structure could lead to a reversal of the direction of Faraday rotation in adjacent zones along a jet. Theoretical analysis showed that the different dynamical behavior of the two simulations could be entirely understood as a result of dependence on the velocity shear between jet and wind which must exceed a surface Alfven speed before the jet becomes unstable to helical and higher order modes of jet distortion.Comment: 25 pages, 15 figures, in press Astrophysical Journal (September

Plasma physics in clusters of galaxies

Clusters of galaxies are the largest self-gravitating structures in the universe. Each cluster is filled with a large-scale plasma atmosphere, in which primordial matter is mixed with matter that has been processed inside stars. This is a wonderful plasma physics laboratory. Our diagnostics are the data we obtain from X-ray and radio telescopes. The thermal plasma is a strong X-ray source; from this we determine its density and temperature. Radio data reveal a relativistic component in the plasma, and first measurements of the intracluster magnetic field have now been made. Energization of the particles and the field must be related to the cosmological evolution of the cluster. The situation is made even richer by the few galaxies in each cluster which host radio jets. In these galaxies, electrodynamics near a massive black hole in the core of the galaxy lead to a collimated plasma beam which propagates from the nucleus out to supergalactic scales. These jets interact with the cluster plasma to form the structures known as radio galaxies. The interaction disturbs and energizes the cluster plasma. This complicates the story but also helps us understand both the radio jets and the cluster plasma.Comment: 12 pages, 6 figures, 3 in color. Invited review, to appear in Physics of Plasmas, May 2003. After publication it can be found at http://ojps.aip.org/po

Two-dimensional vortex behavior in highly underdoped YBa_2Cu_3O_{6+x} observed by scanning Hall probe microscopy

We report scanning Hall probe microscopy of highly underdoped superconducting YBa_2Cu_3O_{6+x} with T_c ranging from 5 to 15 K which showed distinct flux bundles with less than one superconducting flux quantum (Phi_0) through the sample surface. The sub-Phi_0 features occurred more frequently for lower T_c, were more mobile than conventional vortices, and occurred more readily when the sample was cooled with an in-plane field component. We show that these features are consistent with kinked stacks of pancake vortices.Comment: 11 pages, 8 figures, accepted for publication in Physical Review

A new digital twin for enzymatic hydrolysis processes applied to model-based process design

Renewable raw materials containing starch and proteins are split into their main components using enzymatic hydrolysis processes. However, even small changes in temperature, pH or pressure may strongly affect the enzyme activity and stability. At the same time, natural fluctuations may lead to changes in the substrate composition. These mutually influencing factors place enormous demands on the design and control of enzymatic hydrolysis processes. Individual enzymatic hydrolysis processes have already been modelled, but models for the hydrolysis of potato starch by α-amylase and glucoamylase and the proteolysis of organic sunflower seed meal by endopeptidase and exopeptidase in a stirred tank reactor, or even digital twins, are unavailable. Therefore, a new mechanistic model for the combined starch hydrolysis and proteolysis was developed. Sigmoidal and double sigmoidal functions were implemented to map the temperature and pH-dependent enzyme activity. The model can simulate the enzymatic hydrolysis processes with an agreement of more than 90%. The new model was integrated into an existing digital twin of a 20 L stirred tank reactor to create a new stand-alone digital twin for enzymatic hydrolysis processes. Applying the new digital twin core model, a model-based process design strategy based on the open-loop-feedback-optimal and model-based design of experiment strategies was established. By applying the new strategy, the amount of α-amylase and glucoamylase required for starch hydrolysis could be reduced by more than 30%. In addition, the required amount of endopeptidase and exopeptidase for proteolysis could be reduced by more than 50%. Compared to the classic design of experiments approach, the number of experiments required for process optimisation could be reduced by more than 50%. The strategies resulting from this work can soon be used for the optimisation of the industrial organic nutrient media production from regenerative substrates for the cultivation of microorganisms such as Saccharomyces cerevisiae

On the Dynamics and Structure of Three-Dimensional Trans-Alfvenic Jets

Three-dimensional magnetohydrodynamical simulations of strongly magnetized ``light'' conical jets have been performed. An investigation of the transition from sub-Alfv\'enic to super-Alfv\'enic flow has been made for nearly poloidal and for helical magnetic fields. The jets are stable to asymmetric modes of jet distortion provided they are sub-Alfv\'enic over most of their interior but destabilize rapidly when they become on average super-Alfv\'enic. The jets are precessed at the origin and the resulting small amplitude azimuthal motion is communicated down the jet to the Alfv\'en point where it couples to a slowly moving and rapidly growing helical twist. Significant jet rotation can contribute to destabilization via increase in the velocity shear between the jet and the external medium. Destabilization is accompanied by significant mass entrainment and the jets slow down significantly as denser external material is entrained. Synchrotron intensity images satisfactorily reveal large scale helical structures but have trouble distinguishing a large amplitude elliptical jet distortion that appears as an apparent pinching in an intensity image. Smaller scale jet distortions are not clearly revealed in intensity images, largely as a result of the relatively small total pressure variations that accompany destabilization and growing distortions. Fractional polarization is high as a result of the strong ordered magnetic fields except where the intensity image suggests cancellation of polarization vectors by integration through twisted structures.Comment: 27 pages, 11 figures, AASTeX, to appear in Oct 20 issue of ApJ, postscript versions of Figures 5 and 6 are available at this URL http://crux.astr.ua.edu/~rosen/tralf/hr.htm