Crossing-effect in non-isolated and non-symmetric systems of patches

The main result of this article is the crossing-effect between two fragments with no isolation on its sides. The crossing-effect term is given to the phenomenon of relative inversion between the minimum sizes of two patches, only varying the growth rate equally in both. This phenomenon was found from the determination of the minimal size prediction for the general case of problems with two identical patches. This prediction is presented in the explicit form, which allows to recuperate all the cases found in the literature as particular cases, namely, one isolated fragment, one single fragment communicating with its neighborhood, a system with two identical fragments isolated from the matrix but mutually communicating and a system of two identical fragments inserted in a homogeneous matrix. To find the crossing-effect, a particular case of the general solution is approached, which is a single fragment communicating with the matrix with different life difficulties on each side. To verify this statement, it is proposed an experiment, which is an adaptation of other experiments in the literature. The confirmation of the phenomenon presented in this work would be new and unexpected, on the other hand, the refutation of this phenomenon would bring worries to the minimum size models using FKPP equation.