Health SPHere

Alumni magazine of the Boston University School of Public Healt

Integrating-sphere coating

Sodium chloride, used with proper solvent-dispersant combination, forms very durable reflective coatings. Several other inorganic salts, such as barium sulfate, barium carbonate, sodium fluoride, potassium chloride, sodium hexafluorosilicate, and aluminum oxide, are also suitable. Sodium chloride may also be used with other formulations to produce same type of coating

The Moyal Sphere

We construct a family of constant curvature metrics on the Moyal plane and compute the Gauss-Bonnet term for each of them. They arise from the conformal rescaling of the metric in the orthonormal frame approach. We find a particular solution, which corresponds to the Fubini-Study metric and which equips the Moyal algebra with the geometry of a noncommutative sphere.Comment: 16 pages, 3 figure

Affine sphere relativity

We investigate spacetimes whose light cones could be anisotropic. We prove the equivalence of the structures: (a) Lorentz-Finsler manifold for which the mean Cartan torsion vanishes, (b) Lorentz-Finsler manifold for which the indicatrix (observer space) at each point is a convex hyperbolic affine sphere centered on the zero section, and (c) pair given by a spacetime volume and a sharp convex cone distribution. The equivalence suggests to describe {\em (affine sphere) spacetimes} with this structure, so that no algebraic-metrical concept enters the definition. As a result, this work shows how the metric features of spacetime emerge from elementary concepts such as measure and order. Non-relativistic spacetimes are obtained replacing proper spheres with improper spheres, so the distinction does not call for group theoretical elements. In physical terms, in affine sphere spacetimes the light cone distribution and the spacetime measure determine the motion of massive and massless particles (hence the dispersion relation). Furthermore, it is shown that, more generally, for Lorentz-Finsler theories non-differentiable at the cone, the lightlike geodesics and the transport of the particle momentum over them are well defined though the curve parametrization could be undefined. Causality theory is also well behaved. Several results for affine sphere spacetimes are presented. Some results in Finsler geometry, for instance in the characterization of Randers spaces, are also included.Comment: Latex, 56 pages, one figur

Casimir interaction between a sphere and a grating

We derive the explicit expression for the Casimir energy between a sphere and a 1D grating, in terms of the sphere and grating reflection matrices, and valid for arbitrary materials, sphere radius, and grating geometric parameters. We then numerically calculate the Casimir energy between a metallic (gold) sphere and a dielectric (fused silica) lamellar grating at room temperature, and explore its dependence on the sphere radius, grating-sphere separation, and lateral displacement. We quantitatively investigate the geometrical dependence of the interaction, which is sensitive to the grating height and filling factor, and show how the sphere can be used as a local sensor of the Casimir force geometric features. To this purpose we mostly concentrate on separations and sphere radii of the same order of the grating parameters (here of the order of one micrometer). We also investigate the lateral component of the Casimir force, resulting from the absence of translational invariance. We compare our results with those obtained within the proximity force approximation (PFA). When applied to the sphere only, PFA overestimates the strength of the attractive interaction, and we find that the discrepancy is larger in the sphere-grating than in the sphere-plane geometry. On the other hand, when PFA is applied to both sphere and grating, it provides a better estimate of the exact results, simply because the effect of a single grating is underestimated, thus leading to a partial compensation of errors.Comment: 16 pages, 7 figure