Reaction-diffusion systems and nonlinear waves

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation. The importance of the derived results lies in the fact that numerous results on fractional reaction, fractional diffusion, anomalous diffusion problems, and fractional telegraph equations scattered in the literature can be derived, as special cases, of the results investigated in this article.Comment: LaTeX, 16 pages, corrected typo

Design of the AGIPD sensor for the European XFEL

For experiments at the European X-Ray Free-Electron Laser (XFEL) the Adaptive Gain Integrating Pixel Detector (AGIPD) is under development. The particular requirements for the detector are a high dynamic range of 0, 1 - to more than 10E4 12.4 keV photons per pixel within an XFEL pulse duration of < 100 fs, and a radiation tolerance of doses up to 1 GGy for 3 years of operation. The detector will have 1024 x 1024 p+ pixels with a pixel size of 200 um x 200 um and will be manufactured on 500 um thick n-type silicon. The design value for the operating voltage is 500 V, however, for special applications an operation up to ~ 1000 V should be possible. Experimental data on the dose dependence of the surface density of oxide charges at the Si-SiO2 interface and the surface-current density have been implemented in the SYNOPSYS TCAD simulation program in order to optimize the design of the pixel and guard-ring layout. The methodology of the sensor design, the optimization of the most relevant parameters and the layout are demonstrated. Finally the simulated performance, in particular the breakdown voltage, dark current and inter-pixel capacitance as function of the X-ray dose will be presented