Empirical efficiency and volume relationships for HPGe detectors

We have extended the empirical work of Vano et al.[1] relating the slope of the detector efficiency curve to the active volume for Ge detectors. The analysis was carried out using Monte Carlo techniques and covered a wide range of incident energies (200 keV-20 MeV) and active volumes (19.6 cm³–396 cm³). It is shown that the expression of Vano et al.[1] is only valid over the energy range 200 keV-3 MeV for active volumes <50 cm³. The upper bound decreases to 2 MeV for volumes of a few hundred cm³. The usable energy range can, however, be extended to 6 MeV by introducing higher order terms into the polynomial. Above this energy, the shape of the efficiency curve is better described by a non-linear function since linear forms fail simultaneously to fit large active volumes and high energies. We therefore propose a composite function which reduces to the form given in Vano et al. in the low energy/active volume limit. By comparison with the Monte Carlo results, it is estimated that relative efficiencies can be calculated to within 6% over the energy range 200 keV-20 MeV and active volumes 20 cm³–400 cm³. Since the largest errors occur for the smallest volumes, we recommend that for energies <3 MeV a two-fold approach be followed, i.e. using the expression of Vano et al.[1] for active volumes less than 50 cm³ and the proposed non-linear form for larger volumes. For high energy work (E > 3 MeV), we advocate the non-linear form. In this way, average errors can be kept 3%. Finally, we point out that the real power of the expression of Vano et al. lies not in predicting efficiencies, but active volumes.     

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Computability of Countable Subshifts in One Dimension

We investigate the computability of countable subshifts in one dimension, and their members. Subshifts of Cantor?CBendixson rank two contain only eventually periodic elements. Any rank two subshift in 2^? is decidable. Subshifts of rank three may contain members of arbitrary Turing degree. In contrast, effectively closed ( $\Pi^{0}_{1}$ ) subshifts of rank three contain only computable elements, but $\Pi^{0}_{1}$ subshifts of rank four may contain members of arbitrary $\Delta^{0}_{2}$ degree. There is no subshift of rank ??+1.     

Preparation of grids for simulations of groundwater flow in fractured porous media

This work presents an extension of grid generation techniques for finite-volume discretizations of density-driven flow in fractured porous media, in which fractures are considered as low-dimensional manifolds and are resolved by sides of grid elements. The proposed technique introduces additional degrees of freedom for the unknowns assigned to the fractures and thus allows to reconstruct jumps of the solution over a fracture. Through the concept of degenerated elements, the proposed technique can be used for arbitrary junctions of fractures but is sufficiently simple regarding the implementation and allows for the application of conventional numerical solvers. Numerical experiments presented at the end of the paper demonstrate the applicability of this technique in two and three dimensions for complicated fracture networks.