Elliptic operators and their symbols

We consider special elliptic operators in functional spaces on manifolds with a boundary which has some singular points. Such an operator can be represented by a sum of operators, and for a Fredholm property of an initial operator one needs a Fredholm property for each operator from this sum.

MARINE MODELLING IN SUPPORT OF KOOLAN ISLAND MINE RECOMMENCEMENT AND EVENTUAL DECOMMISSIONING

Koolan Island is located in a remote macrotidal (9m mean spring range) area of the Buccaneer Archipelago of NW Australia. High-quality hematite has been mined from the island since the 1940s, with direct export by ore carriers from a dedicated marine terminal. Mining in recent decades has focused on an open pit immediately adjacent to the ocean. The initial operator decommissioned the site in 1993, at which time a channel connecting the pit to the sea was excavated, the pit was flooded and a productive marine ecosystem developed within the photic zone of the former mine. The site was subsequently acquired by Mt. Gibson Iron, which drained the pit in 2007 and constructed a protective seawall to facilitate additional ore extraction through the extension of the pit both in depth as well as closer to the historical shoreline. A catastrophic failure of a section of the seawall in 2014 re-flooded the pit, which resulted in no injuries as the site was successfully evacuated in response to instrumented movements in the seawall structure. Construction of a strengthened seawall has recently been completed, and pit dewatering activities will be initiated during the week of the ICCE conference to enable in-Pit mining activities to recommence by the end of 2018. The presentation will present a summary of the unique history of the site, as well as supporting numerical modelling performed to describe a) the complex regional and local macrotidal dynamics, b) sediment spillage in connection with the reconstruction of the seawall following the 2014 failure, and c) coupled 2D/1D model calculations optimizing channel geometry to ensure adequate flushing of the pit following its eventual re-flooding in connection with final decommissioning.

Stability and Regularization of Difference Schemes in Banach and Hilbert Spaces

The necessary and sufficient conditions for stability of abstract difference schemes in Hilbert and Banach spaces are formulated. Contrary to known stability results we give stability conditions for schemes with non-self-adjoint operator coefficients in a Hilbert space and with strongly positive operator coefficients in a Banach space. It is shown that the parameters of the sectorial spectral domain play the crucial role. As an application we consider the Richardson iteration scheme for an operator equation in a Banach space, in particulary the Richardson iteration with precondition for a finite element scheme for a non-selfadjoint operator. The theoretical results are also the basis when using the regularization principle to construct stable difference schemes. For this aim we start from some simple scheme (even unstable) and derive stable schemes by perturbing the initial operator coefficients and by taking into account the stability conditions. Our approach is also valid for schemes with unbounded operator coefficients.

CT7-6: The Most Recent T700 Growth Derivative Engine

In June 1988, the most recent growth derivative of the successful T700 family of turboshaft/turboprop engines, the CT7–6, received its FAA type certificate. The CT7–6 is the latest model in the extensive T700/CT7 family of engines. Its design and certification program were the result of the growth derivative approach to meeting the customers’ demand for more power. This approach has been successfully used by GE Aircraft Engines to grow the T700/CT7 family to meet the needs of a wide variety of customers and aircraft applications around the world. T700/CT7 engines provide power to 14 different aircraft applications and have accumulated over 4.5 million hours of operation on nearly 6,000 engines. This paper traces the evolution of the CT7–6 model and discusses the technology enhancements which were incorporated to make it the most powerful member of the T700/CT7 family. A description is given of the synergism in the design and test phase of the CT7–6, which resulted from the derivative approach in combination with an integrated development program that simultaneously qualified/certified four T700/CT7 engine models. The paper also reviews the initial operator experience with the CT7–6 in a unique new European aircraft, the EH Industries EH101 helicopter.