Using an asymptotic analysis, we obtain an eigenvalue equation for the general mode dispersion in Bragg fibers. The asymptotic analysis is applied to calculate the dispersion relation and the field distribution of TE modes in a Bragg fiber. We compare the asymptotic results with exact solutions and find excellent agreement between them. This asymptotic approach greatly simplifies the analysis a...

We introduce and analyze a random tree model associated to Hoppe’s urn. The tree is built successively by adding nodes to the existing tree when starting with the single root node. In each step a node is added to the tree as a child of an existing node where these parent nodes are chosen randomly with probabilities proportional to their weights. The root node has weight θ > 0, a given fixed par...

We consider a perforated half-cylindrical thin shell and investigate the limit behavior when period thickness simultaneously go to zero. By using decomposition of displacements presented in Griso [ JMPA 89 (2008) 199–223] we obtain priori estimates. With unfolding rescaling operator transform problem reference configuration. In end this yields homogenized for shell.