Continuous Time Random Walks (CTRWs): Simulation of continuous trajectories

Continuous time random walks have been developed as a straightforward generalisation of classical random walk processes. Some 10 years ago, Fogedby introduced a continuous representation of these processes by means of a set of Langevin equations [H. C. Fogedby, Phys. Rev. E 50 (1994)]. The present work is devoted to a detailed discussion of Fogedby's model and presents its application for the robust numerical generation of sample paths of continuous time random walk processes.Comment: 7 pages, 7 figure

General Relativistic Scalar Field Models in the Large

For a class of scalar fields including the massless Klein-Gordon field the general relativistic hyperboloidal initial value problems are equivalent in a certain sense. By using this equivalence and conformal techniques it is proven that the hyperboloidal initial value problem for those scalar fields has an unique solution which is weakly asymptotically flat. For data sufficiently close to data for flat spacetime there exist a smooth future null infinity and a regular future timelike infinity.Comment: 22 pages, latex, AGG 1

Do Magnetic Fields Prevent Hydrogen from Accreting onto Cool Metal-line White Dwarf Stars?

It is generally assumed that metals detected in the spectra of a few cool white dwarfs cannot be of primordial origin and must be accreted from the interstellar medium. However, the observed abundances of hydrogen, which should also be accreted from the interstellar medium, are lower than expected from metal accretion. Magnetic fields are thought to be the reason for this discrepancy. We have therefore obtained circular polarization spectra of the helium-rich white dwarfs GD40 and L745-46A, which both show strong metal lines as well as hydrogen. Whereas L745-46A might have a magnetic field of about -6900 G, which is about two times the field strength of 3000G necessary to repell hydrogen at the Alfen radius, only an upper limit for the field strength of GD40 of 4000G (with 99% confidence) can be set which is far off the minimum field strength of 144000G to repell hydrogen.Comment: 4 LaTeX pages, 4 eps figures, to appear in the proceedings of the 14th European Workshop on White Dwarfs, eds. D. Koester and S. Moehler, ASP Conf. Serie

Curvature dependent lower bounds for the first eigenvalue of the Dirac operator

Using Weitzenb\"ock techniques on any compact Riemannian spin manifold we derive inequalities that involve a real parameter and join the eigenvalues of the Dirac operator with curvature terms. The discussion of these inequalities yields vanishing theorems for the kernel of the Dirac operator $D$ and lower bounds for the spectrum of $D^2$ if the curvature satisfies certain conditions.Comment: Latex2e, 14p

Quasi-geostrophic approximation of anelastic convection

The onset of convection in a rotating cylindrical annulus with parallel ends filled with a compressible fluid is studied in the anelastic approximation. Thermal Rossby waves propagating in the azimuthal direction are found as solutions. The analogy to the case of Boussinesq convection in the presence of conical end surfaces of the annular region is emphasised. As in the latter case, the results can be applied as an approximation for the description of the onset of anelastic convection in rotating spherical fluid shells. Reasonable agreement with three-dimensional numerical results published by Jones, Kuzanyan & Mitchell (J. Fluid Mech., vol. 634, 2009, pp. 291–319) for the latter problem is found. As in those results, the location of the onset of convection shifts outwards from the tangent cylinder with increasing number Nρof density scale heights until it reaches the equatorial boundary. A new result is that at a much higher number Nρ the onset location returns to the interior of the fluid shell

Gaussian Subordination for the Beurling-Selberg Extremal Problem

We determine extremal entire functions for the problem of majorizing, minorizing, and approximating the Gaussian function $e^{-\pi\lambda x^2}$ by entire functions of exponential type. This leads to the solution of analogous extremal problems for a wide class of even functions that includes most of the previously known examples (for instance \cite{CV2}, \cite{CV3}, \cite{GV} and \cite{Lit}), plus a variety of new interesting functions such as $|x|^{\alpha}$ for $-1 < \alpha$; \,$\log \,\bigl((x^2 + \alpha^2)/(x^2 + \beta^2)\bigr)$, for $0 \leq \alpha < \beta$;\, $\log\bigl(x^2 + \alpha^2\bigr)$; and $x^{2n} \log x^2$\,, for $n \in \N$. Further applications to number theory include optimal approximations of theta functions by trigonometric polynomials and optimal bounds for certain Hilbert-type inequalities related to the discrete Hardy-Littlewood-Sobolev inequality in dimension one

Dynamo Effects Near The Transition from Solar to Anti-Solar Differential Rotation

Numerical MHD simulations play increasingly important role for understanding mechanisms of stellar magnetism. We present simulations of convection and dynamos in density-stratified rotating spherical fluid shells. We employ a new 3D simulation code for the solution of a physically consistent anelastic model of the process with a minimum number of parameters. The reported dynamo simulations extend into a "buoyancy-dominated" regime where the buoyancy forcing is dominant while the Coriolis force is no longer balanced by pressure gradients and strong anti-solar differential rotation develops as a result. We find that the self-generated magnetic fields, despite being relatively weak, are able to reverse the direction of differential rotation from anti-solar to solar-like. We also find that convection flows in this regime are significantly stronger in the polar regions than in the equatorial region, leading to non-oscillatory dipole-dominated dynamo solutions, and to concentration of magnetic field in the polar regions. We observe that convection has different morphology in the inner and at the outer part of the convection zone simultaneously such that organized geostrophic convection columns are hidden below a near-surface layer of well-mixed highly-chaotic convection. While we focus the attention on the buoyancy-dominated regime, we also demonstrate that conical differential rotation profiles and persistent regular dynamo oscillations can be obtained in the parameter space of the rotation-dominated regime even within this minimal model.Comment: Published in the Astrophysical Journa