Rigidity of Scattering Lengths and Traveling Times for Disjoint Unions of Convex Bodies

Obstacles $K$ and $L$ in $R^d$ ($d\geq 2$) are considered that are finite disjoint unions of strictly convex domains with $C^3$ boundaries. We show that if $K$ and $L$ have (almost) the same scattering length spectrum, or (almost) the same traveling times, then $K = L$

Applying the Wells-Riley equation to the risk of airborne infection in hospital environments: The importance of stochastic and proximity effects

Although the Wells-Riley equation for airborne infection is used to estimate infection risk in a range of environments, researchers generally assume complete air mixing and don’t consider either the stochastic effects in a small population or the proximity of susceptible people to an infectious source. This study presents stochastic simulations using the Wells-Riley model to evaluate the infection risk and variability among small populations such as hospital patients. This is linked with a simple multi-zone ventilation model to demonstrate the influence of airflow patterns and proximity to an infectious source on the risk of infection for an individual. The results also highlight that risk assessments made using data derived using complete mixing assumptions may significantly underestimate the real risk for those close to the infectious source