Monte Carlo modeling of polarized light propagation: Stokes vs Jones - Part I

This bipartite comparative study aims at inspecting the similarities and differences between the Jones and Stokes–Mueller formalisms when modeling polarized light propagation with numerical simulations of the Monte Carlo type. In this first part, we review the theoretical concepts that concern light propagation and detection with both pure and partially/totally unpolarized states. The latter case involving fluctuations, or “depolarizing effects,” is of special interest here: Jones and Stokes–Mueller are equally apt to model such effects and are expected to yield identical results. In a second, ensuing paper, empirical evidence is provided by means of numerical experiments, using both formalisms.

Monte Carlo modeling of polarized light propagation: Stokes vs Jones - Part II

In this second part of our comparative study inspecting the (dis)similarities between “Stokes” and “Jones,” we present simulation results yielded by two independent Monte Carlo programs: (i) one developed in Bern with the Jones formalism and (ii) the other implemented in Ulm with the Stokes notation. The simulated polarimetric experiments involve suspensions of polystyrene spheres with varying size. Reflection and refraction at the sample/air interfaces are also considered. Both programs yield identical results when propagating pure polarization states, yet, with unpolarized illumination, second order statistical differences appear, thereby highlighting the pre-averaged nature of the Stokes parameters. This study serves as a validation for both programs and clarifies the misleading belief according to which “Jones cannot treat depolarizing effects.”

Daily and seasonal thermal stresses in tilings: a field survey combined with numeric modeling

This study investigates thermally induced tensile stresses in ceramic tilings. Daily and seasonal thermal cycles, as well as, rare but extreme events, such as a hail-storm striking a heated terrace tiling, were studied in the field and by numerical modeling investigations. The field surveys delivered temperature– time diagrams and temperature profiles across tiling systems. These data were taken as input parameters for modeling the stress distribution in the tiling system in order to detect potential sites for material failure. Dependent on the thermal scenario (e.g., slow heating of the entire structure during morning and afternoon, or a rapid cooling of the tiles by a rain storm) the modeling indicates specific locations with high tensile stresses. Typically regions along the rim of the tiling field showed stresses, which can become critical with respect to the adhesion strength. Over the years, ongoing cycles of thermal expansion–contraction result in material fatigue promoting the propagation of cracks. However, the installation of flexible waterproofing membranes (applied between substrate and tile adhesive) represents an efficient technical innovation to reduce such crack propagation as confirmed by both numerical modeling results and microstructural studies on real systems.