Ricerc@Sapienza

A general geometric phase singularity array structure is presented and discussed. For any two-dimensional point lattice, a singularity array is defined as a summation of helical phase singularities with alternating handedness. The phase angle is the slow-axis orientation of a varying half-waveplate. Arrays are demonstrated in photoaligned polymer liquid crystal films. Simple square and biomimetic spiral lattices are characterized for diffraction behavior. Pattern selection rules based on topological charge are discovered.

The formulation of transport models in polymeric systems starting from the theory of stochastic processes possessing finite propagation velocity is here presented. Hyperbolic continuous equations are shown to be derived from Poisson-Kac stochastic processes and the extension to higher dimensions is discussed. We analyze the physical implications of this approach, namely: non-Markovian nature, admissible boundary conditions, breaking of concentration-flux paradigm and extension to nonlinear case.