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In this paper we handle the problem of filling the hole in the graphic of a surface by means of a patch that joins the original surface with $$\mathcal {C}^{1}$$ C 1 -smoothness and fulfills an additional non-linear geometrical constraint regarding its area or its mean curvature at some points. Furthermore, we develop a technique to estimate the optimum area that the filling patch is expected to have that will allow us to determine optimum filling patches by means of a system of linear and quadratic equations. We present several numerical and graphical examples showing the effectiveness of the proposed method.

Passive nuclear track methodology (NTM) is applied to study charged particles products of the reaction 7Li+Pb at ~ 31 MeV. It is a contribution to the 8pLP Project (LNL-INFN-Italy) in where we show an alternative approach to register charged particle from reaction fragments by PADC detection. The main advantage is that the passive system integrates data over the whole experiment and has its importance for low rate reaction processes. Reaction products as well as scattered beam particles are determined from track shape analysis. Some limitations are inherent to NTM since a priori knowledge is required to correlate track size distribution given by each type of particle emerging from the target. Results show that the passive technique gives useful information when applied in reaction data interpretation for a relatively large range of particle types.