A semi-implicit Hall-MHD solver using whistler wave preconditioning

The dispersive character of the Hall-MHD solutions, in particular the whistler waves, is a strong restriction to numerical treatments of this system. Numerical stability demands a time step dependence of the form $\Delta t\propto (\Delta x)^2$ for explicit calculations. A new semi--implicit scheme for integrating the induction equation is proposed and applied to a reconnection problem. It it based on a fix point iteration with a physically motivated preconditioning. Due to its convergence properties, short wavelengths converge faster than long ones, thus it can be used as a smoother in a nonlinear multigrid method

Numerical Simulation of Current Sheet Formation in a Quasi-Separatrix Layer using Adaptive Mesh Refinement

The formation of a thin current sheet in a magnetic quasi-separatrix layer (QSL) is investigated by means of numerical simulation using a simplified ideal, low-$\beta$, MHD model. The initial configuration and driving boundary conditions are relevant to phenomena observed in the solar corona and were studied earlier by Aulanier et al., A&A 444, 961 (2005). In extension to that work, we use the technique of adaptive mesh refinement (AMR) to significantly enhance the local spatial resolution of the current sheet during its formation, which enables us to follow the evolution into a later stage. Our simulations are in good agreement with the results of Aulanier et al. up to the calculated time in that work. In a later phase, we observe a basically unarrested collapse of the sheet to length scales that are more than one order of magnitude smaller than those reported earlier. The current density attains correspondingly larger maximum values within the sheet. During this thinning process, which is finally limited by lack of resolution even in the AMR studies, the current sheet moves upward, following a global expansion of the magnetic structure during the quasi-static evolution. The sheet is locally one-dimensional and the plasma flow in its vicinity, when transformed into a co-moving frame, qualitatively resembles a stagnation point flow. In conclusion, our simulations support the idea that extremely high current densities are generated in the vicinities of QSLs as a response to external perturbations, with no sign of saturation.Comment: 6 Figure

Adaptive modeling of the femtosecond inscription in silica

We present an adaptive mesh approach to high performance comprehensive investigation of dynamics of light and plasma pattens during the process of direct laser inscription. The results reveal extreme variations of spatial and temporal scales and tremendous complexity of these patterns which was not feasible to study previously

Impact of the floating-point precision and interpolation scheme on the results of DNS of turbulence by pseudo-spectral codes

In this paper we investigate the impact of the floating-point precision and interpolation scheme on the results of direct numerical simulations (DNS) of turbulence by pseudo-spectral codes. Three different types of floating-point precision configurations show no differences in the statistical results. This implies that single precision computations allow for increased Reynolds numbers due to the reduced amount of memory needed. The interpolation scheme for obtaining velocity values at particle positions has a noticeable impact on the Lagrangian acceleration statistics. A tri-cubic scheme results in a slightly broader acceleration probability density function than a tri-linear scheme. Furthermore the scaling behavior obtained by the cubic interpolation scheme exhibits a tendency towards a slightly increased degree of intermittency compared to the linear one.Comment: to appear in Comp. Phys. Com

Numerical simulations of possible finite time singularities in the incompressible Euler equations: comparison of numerical methods

The numerical simulation of the 3D incompressible Euler equation is analyzed with respect to different integration methods. The numerical schemes we considered include spectral methods with different strategies for dealiasing and two variants of finite difference methods. Based on this comparison, a Kida-Pelz like initial condition is integrated using adaptive mesh refinement and estimates on the necessary numerical resolution are given. This estimate is based on analyzing the scaling behavior similar to the procedure in critical phenomena and present simulations are put into perspective.Comment: Euler equations: 250 years o

A Parallel Mesh-Adaptive Framework for Hyperbolic Conservation Laws

We report on the development of a computational framework for the parallel, mesh-adaptive solution of systems of hyperbolic conservation laws like the time-dependent Euler equations in compressible gas dynamics or Magneto-Hydrodynamics (MHD) and similar models in plasma physics. Local mesh refinement is realized by the recursive bisection of grid blocks along each spatial dimension, implemented numerical schemes include standard finite-differences as well as shock-capturing central schemes, both in connection with Runge-Kutta type integrators. Parallel execution is achieved through a configurable hybrid of POSIX-multi-threading and MPI-distribution with dynamic load balancing. One- two- and three-dimensional test computations for the Euler equations have been carried out and show good parallel scaling behavior. The Racoon framework is currently used to study the formation of singularities in plasmas and fluids.Comment: late submissio

Femtosecond laser microfabrication of subwavelength structures in photonics

This paper describes experimental and numerical results of the plasma-assisted microfabrication of subwavelength structures by means of point-by point femtosecond laser inscription. It is shown that the spatio-temporal evolution of light and plasma patterns critically depend on input power. Subwavelength inscription corresponds to the supercritical propagation regimes when pulse power is several times self-focusing threshold. Experimental and numerical profiles show quantitative agreement

Optimization of carbon ion and proton treatment plans using the raster-scanning technique for patients with unresectable pancreatic cancer

Background: The aim of the thesis is to improve radiation plans of patients with locally advanced, unresectable pancreatic cancer by using carbon ion and proton beams. Patients and methods: Using the treatment planning system Syngo RT Planning (Siemens, Erlangen, Germany) a total of 50 treatment plans have been created for five patients with the dose schedule 15 × 3 Gy(RBE). With reference to the anatomy, five field configurations were considered to be relevant. The plans were analyzed with respect to dose distribution and individual anatomy, and compared using a customized index. Results: Within the index the three-field configurations yielded the best results, though with a high variety of score points (field setup 5, carbon ion: median 74 (range 48–101)). The maximum dose in the myelon is low (e.g. case 3, carbon ion: 21.5 Gy(RBE)). A single posterior field generally spares the organs at risk, but the maximum dose in the myelon is high (e.g. case 3, carbon ion: 32.9 Gy(RBE)). Two oblique posterior fields resulted in acceptable maximum doses in the myelon (e.g. case 3, carbon ion: 26.9 Gy(RBE)). The single-field configuration and the two oblique posterior fields had a small score dispersion (carbon ion: median 66 and 58 (range 62–72 and 40–69)). In cases with topographic proximity of the organs at risk to the target volume, the single-field configuration scored as well as the three-field configurations. Conclusion: In summary, the three-field configurations showed the best dose distributions. A single posterior field seems to be robust and beneficial in case of difficult topographical conditions and topographical proximity of organs at risk to the target volume. A setup with two oblique posterior fields is a reasonable compromise between three-field and single-field configurations

Phänomenologie und Soziologie:Theoretische Positionen, aktuelle Problemfelder und empirische Umsetzungen

Der Band erörtert die Bedeutung der Phänomenologie für die Soziologie. Die 35 Autorinnen und Autoren erkunden und diskutieren die Anregungen, Chancen und Erträge phänomenologischen Denkens für die Sozialtheorie ebenso wie für die empirische Sozialforschung. Hierzu werden in dem Band Beiträge zu soziologischen Begriffs- und Theorieproblemen, zu methodisch-methodologischen Aspekten und zu aktuellen Gegenwartsfragen versammelt. Diese vermitteln nicht nur einen umfassenden Überblick über den augenblicklichen Stand einer in der Soziologie in jüngster Zeit wieder verstärkt geführten Auseinandersetzung mit der Phänomenologie, sondern sie beziehen auch pointiert Stellung innerhalb dieser Debatte. Denn bei aller Unterschiedlichkeit der Fragestellungen und Herangehensweisen eint die Autorinnen und Autoren die Einsicht in die konstitutive Bedeutung der Subjektivität für aktuelle soziologische Frage- und Problemstellunge