Constrained correlation functions from the Millennium Simulation

Context. In previous work, we developed a quasi-Gaussian approximation for the likelihood of correlation functions, which, in contrast to the usual Gaussian approach, incorporates fundamental mathematical constraints on correlation functions. The analytical computation of these constraints is only feasible in the case of correlation functions of one-dimensional random fields. Aims. In this work, we aim to obtain corresponding constraints in the case of higher-dimensional random fields and test them in a more realistic context. Methods. We develop numerical methods to compute the constraints on correlation functions which are also applicable for two- and three-dimensional fields. In order to test the accuracy of the numerically obtained constraints, we compare them to the analytical results for the one-dimensional case. Finally, we compute correlation functions from the halo catalog of the Millennium Simulation, check whether they obey the constraints, and examine the performance of the transformation used in the construction of the quasi-Gaussian likelihood. Results. We find that our numerical methods of computing the constraints are robust and that the correlation functions measured from the Millennium Simulation obey them. Despite the fact that the measured correlation functions lie well inside the allowed region of parameter space, i.e. far away from the boundaries of the allowed volume defined by the constraints, we find strong indications that the quasi-Gaussian likelihood yields a substantially more accurate description than the Gaussian one.Comment: 11 pages, 13 figures, updated to match version accepted by A&

Computer simulation of pulsed field gel runs allows the quantitation of radiation-induced double-strand breaks in yeast

A procedure for the quantification of double-strand breaks in yeast is presented that utilizes pulsed field gel electrophoresis (PFGE) and a comparison of the observed DNA mass distribution in the gel lanes with calculated distributions. Calculation of profiles is performed as follows. If double-strand breaks are produced by sparsely ionizing radiation, one can assume that they are distributed randomly in the genome, and the resulting DNA mass distribution in molecular length can be predicted by means of a random breakage model. The input data for the computation of molecular length profiles are the breakage frequency per unit length, , as adjustable parameter, and the molecular lengths of the intact chromosomes. The obtained DNA mass distributions in molecular length must then be transformed into distributions of DNA mass in migration distance. This requires a calibration of molecular length vs. migration distance that is specific for the gel lane in question. The computed profiles are then folded with a Lorentz distribution with adjusted spread parameter to account for and broadening. The DNA profiles are calculated for different breakage frequencies and for different values of , and the parameters resulting in the best fit of the calculated to the observed profile are determined

Rigorous FEM-Simulation of EUV-Masks: Influence of Shape and Material Parameters

We present rigorous simulations of EUV masks with technological imperfections like side-wall angles and corner roundings. We perform an optimization of two different geometrical parameters in order to fit the numerical results to results obtained from experimental scatterometry measurements. For the numerical simulations we use an adaptive finite element approach on irregular meshes. This gives us the opportunity to model geometrical structures accurately. Moreover we comment on the use of domain decomposition techniques for EUV mask simulations. Geometric mask parameters have a great influence on the diffraction pattern. We show that using accurate simulation tools it is possible to deduce the relevant geometrical parameters of EUV masks from scatterometry measurements. This work results from a collaboration between Advanced Mask Technology Center (AMTC, mask fabrication), Physikalisch-Technische Bundesanstalt (PTB, scatterometry), Zuse Institute Berlin (ZIB), and JCMwave (numerical simulation).Comment: 8 pages, 8 figures (see original publication for images with a better resolution

A closer look at the uncertainty relation of position and momentum

We consider particles prepared by the von Neumann-L\"uders projection. For those particles the standard deviation of the momentum is discussed. We show that infinite standard deviations are not exceptions but rather typical. A necessary and sufficient condition for finite standard deviations is given. Finally, a new uncertainty relation is derived and it is shown that the latter cannot be improved.Comment: 3 pages, introduction shortened, content unchange

Computation of effective dynamic properties of naturally fractured reservoirs: Comparison and validation of methods

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