Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

CHARACTERIZATION AND THERMAL-HYDRAULIC MODELING OF ENGINEERED BARRIERS FOR A CANADIAN DEEP GEOLOGICAL REPOSITORY FOR USED NUCLEAR FUEL

Within Canada there are more than 2.5 million bundles of spent nuclear fuel with another approximately 2 million bundles to be generated in the future. Canada, and every country around the world that has taken a decision on management of spent nuclear fuel, has decided on long-term containment and isolation of the fuel within a deep geological repository. At depth, a deep geological repository consists of a network of placement rooms where the bundles will be located within a multi-layered system that incorporates engineered and natural barriers. The barriers will be placed in a complex thermal-hydraulic-mechanical-chemical-biological (THMCB) environment. A large database of material properties for all components in the repository are required to construct representative models. Within the repository, the sealing materials will experience elevated temperatures due to the thermal gradient produced by radioactive decay heat from the waste inside the container. Furthermore, high porewater pressure due to the depth of repository along with possibility of elevated salinity of groundwater would cause the bentonite-based materials to be under transient hydraulic conditions. Therefore it is crucial to characterize the sealing materials over a wide range of thermal-hydraulic conditions. A comprehensive experimental program has been conducted to measure properties (mainly focused on thermal properties) of all sealing materials involved in Mark II concept at plausible thermal-hydraulic conditions. The thermal response of Canada’s concept for a deep geological repository has been modelled using experimentally measured thermal properties. Plausible scenarios are defined and the effects of these scenarios are examined on the container surface temperature as well as the surrounding geosphere to assess whether they meet design criteria for the cases studied. The thermal response shows that if all the materials even being at dried condition, repository still performs acceptably as long as sealing materials remain in contact.