An interferometer in which all of its components are treated as quantum bodies is examined with the standard interpretation and with a model in which its uncoupled spatially separated components act collectively. These models utilize superposition principles that differ when applied to systems composed of three or more bodies. Interferometric disparities between them involving frequency shifts and recoil are shown to be difficult to measure. More pronounced discrepancies involve correlated interference. The collective model is shown to provide a missing connection between quantum and semiclassical theories. Scattering from an entangled state, which cannot be divided into disjoint parts, is discussed in relation to collective recoil. Collective scattering is shown to be a viable alternative to the standard model, thereby providing insight into constructing tests of the superposition principle in systems with three or more bodies.

We present a mathematical formulation of a multiscale model for solidification with convective flow in the liquid phase. The model is an extension of the dendritic needle network approach for crystal growth in a binary alloy. We propose a simple numerical implementation based on finite differences and step-wise approximations of parabolic dendritic branches of arbitrary orientation. Results of the two-dimensional model are verified against reference benchmark solutions for steady, unsteady, and buoyant flow, as well as steady-state dendritic growth in the diffusive regime. Simulations of equiaxed growth under forced flow yield dendrite tip velocities within 10% of quantitative phase-field results from the literature. Finally, we perform illustrative simulations of polycrystalline solidification using physical parameters for an aluminum-10wt%copper alloy. Resulting microstructures show notable differences when taking into account natural buoyancy in comparison to a purely diffusive transport regime. The resulting model opens new avenues for computationally and quantitatively investigating the influence of fluid flow and gravity-induced buoyancy upon the selection of dendritic microstructures. Further ongoing developments include an equivalent formulation for directional solidification conditions and the implementation of the model in three dimensions, which is critical for quantitative comparison to experimental measurements.