Based on Friedberg and Lee's geometric picture by which the tribimaximal Pontecorvo-MakiNakawaga-Sakata leptonic mixing matrix is constructed, namely, corresponding mixing angles correspond to the geometric angles among the sides of a cube. We suggest that the three realistic mixing angles, which slightly deviate from the values determined for the cube, are due to a viable deformation from the perfectly cubic shape. Taking the best-fitted results of θ 12 and θ 23 as inputs, we determine the central value of sin 2 2θ 13 should be 0.0238, with a relatively large error tolerance;this value lies in the range of measurement precision of the Daya Bay experiment and is consistent with recent results from the T2K Collaboration.PACS: 14.60.Pq Neutrino mass and mixing

For direct dark matter detections, to extract useful information about the fundamental interaction from data, it is crucial to properly determine the nuclear form factor. The form factor for spinindependent cross section of collisions between dark matter particle and nucleus is thoroughly studied by many authors. When the analysis was carried out, the nuclei are always supposed to be spherically symmetric. In this work, we investigate the effects of deformation of nuclei from a spherical shape to an elliptical shape on the form factor. Our results indicate that as long as the ellipticity is not too large, such effects cannot cause any substantial effects, especially as the nuclei are randomly orientated in a room temperature circumstance one can completely neglect them.

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