Induced decay of composite JPC=1++ particles in atomic Coulomb fields

The electron-positron pairs observed in heavy-ion collisions at Gesellschaft für Schwerionen-forschung Darmstadt mbH have been interpreted as the decay products of yet unknown particles with masses around 1.8 MeV. The negative results of resonant Bhabha scattering experiments, however, do not support such an interpretation. Therefore we focus on a more complex decay scenario, where the e+e- lines result from a two-collision process. We discuss the induced decay of a metastable 1++ state into e+e- pairs. For most realizations of a 1++ state such a decay in leading order can only take place in the Coulomb field of a target atom. This fact has the attractive consequence that for such a state the Bhabha bounds are no longer valid. However, the absolute value of the e+e- production cross section turns out to be unacceptably small

Class number approximation in cubic function fields

We develop explicitly computable bounds for the order of the Jacobian of a cubic function field. We use approximations via truncated Euler products and thus derive effective methods of computing the order of the Jacobian of a cubic function field. Also, a detailed discussion of the zeta function of a cubic function field extension is included

Numerical analysis for time-dependent advection-diffusion problems with random discontinuous coefficients

Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media, the parameters of the equation are spatially discontinuous. Specifically, a scenario with coupled advection- and diffusion coefficients that are modeled as sums of continuous random fields and discontinuous jump components are considered. For the numerical approximation of the solution, an adaptive, pathwise discretization scheme based on a Finite Element approach is introduced. To stabilize the numerical approximation and accelerate convergence, the discrete space-time grid is chosen with respect to the varying discontinuities in each sample of the coefficients, leading to a stochastic formulation of the Galerkin projection and the Finite Element basis

Stochastic Transport with L\'evy Noise -- Fully Discrete Numerical Approximation

Semilinear hyperbolic stochastic partial differential equations have various applications in the natural and engineering sciences. From a modeling point of view the Gaussian setting may be too restrictive, since applications in mathematical finance and phenomena such as porous media or pollution models indicate an influence of noise of a different nature. In order to capture temporal discontinuities and allow for heavy-tailed distributions, Hilbert space-valued L\'evy processes (or L\'evy fields) as driving noise terms are considered. The numerical discretization of the corresponding SPDE involves several difficulties: Low spatial and temporal regularity of the solution to the problem entails slow convergence rates and instabilities for space/time-discretization schemes. Furthermore, the L\'evy process admits values in a possibly infinite-dimensional Hilbert space, hence projections onto a finite-dimensional subspace for each discrete point in time are necessary. Finally, unbiased sampling from the resulting L\'evy field may not be possible. We introduce a novel fully discrete approximation scheme that addresses all of these aspects. Our central contribution is a novel discontinuous Petrov-Galerkin scheme for the spatial approximation that naturally arises from the weak formulation of the SPDE. We prove optimal convergence of this approach and couple it with a suitable time stepping scheme to avoid numerical oscillations. Moreover, we approximate the driving noise process by truncated Karhunen-Lo\'eve expansions. The latter essentially yields a sum of scaled and uncorrelated one-dimensional L\'evy processes, which may be simulated with controlled bias by Fourier inversion techniques