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http://hdl.handle.net/2440/299
Thu, 22 Jun 2017 14:18:55 GMT2017-06-22T14:18:55ZSufficient conditions for holomorphic linearisation
http://hdl.handle.net/2440/106155
Title: Sufficient conditions for holomorphic linearisation
Author: Kutzschebauch, F.; Larusson, F.; Schwarz, G.
Abstract: Let G be a reductive complex Lie group acting holomorphically on X = ℂn. The (holomorphic) Linearisation Problem asks if there is a holomorphic change of coordinates on ℂn such that the G-action becomes linear. Equivalently, is there a G-equivariant biholomorphism Φ: X → V where V is a G-module? There is an intrinsic stratification of the categorical quotient QX, called the Luna stratification, where the strata are labeled by isomorphism classes of representations of reductive subgroups of G. Suppose that there is a Φ as above. Then Φ induces a biholomorphism φ: QX → QV which is stratified, i.e., the stratum of QX with a given label is sent isomorphically to the stratum of QV with the same label. The counterexamples to the Linearisation Problem construct an action of G such that QX is not stratified biholomorphic to any QV.Our main theorem shows that, for most X, a stratified biholomorphism of QX to some QV is sufficient for linearisation. In fact, we do not have to assume that X is biholomorphic to ℂn, only that X is a Stein manifold.Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/2440/1061552016-01-01T00:00:00ZUnsteadily manipulating internal flow barriers
http://hdl.handle.net/2440/106154
Title: Unsteadily manipulating internal flow barriers
Author: Balasuriya, S.
Abstract: Typical flows contain internal flow barriers: specialised time-moving Lagrangian entities which demarcate distinct motions. Examples include the boundary between an oceanic eddy and a nearby jet, the edge of the Antarctic circumpolar vortex or the interface between two fluids which are to be mixed together in an microfluidic assay. The ability to control the locations of these barriers in a user-specified time-varying (unsteady) way can profoundly impact fluid transport between the coherent structures which are separated by the barriers. A condition on the unsteady Eulerian velocity required to achieve this objective is explicitly derived, thereby solving an ‘inverse Lagrangian coherent structure’ problem. This is an important first step in developing flow-barrier control in realistic flows, and in providing a postprocessing tool for observational/experimental velocity data. The excellent accuracy of the method is demonstrated using the Kelvin–Stuart cats-eyes flow and the unsteady double gyre, utilising finite-time Lyapunov exponents.Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/2440/1061542017-01-01T00:00:00ZPressure drop in pipelines due to pump trip event
http://hdl.handle.net/2440/106045
Title: Pressure drop in pipelines due to pump trip event
Author: Stokes, Y.; Miller, A.; Hocking, G.
Abstract: We consider the pressure pulse or surge in a pipeline due to an unplanned sudden shutdown of a pump system in the pipeline network. This is known as water hammer. Our primary focus is the negative pressure pulse that travels downstream from the pump(s), is reflected with a sign reversal from the end, and travels back to the pump(s). As part of the preliminary design of a pipeline it is necessary to determine the minimum head envelope associated with such an event, which is used to determine where surge protection will be needed in the pipeline. Of particular interest is whether the initial head drop at the pump(s) due to a sudden drop of the flow speed to zero, as given by the Joukowski formula, gives a sufficiently accurate prediction of the minimum head at the pump(s). This minimum head is used to construct the minimum head envelope for the downstream pipeline. An examination of the relevant literature along with solution of the water hammer equations shows that, assuming the flow speed falls instantaneously to zero at the pump(s), the total drop in head at the pump(s) is given by the sum of the initial Joukowski head change and the friction loss under normal operating conditions. While the friction loss may not be significant in short pipelines, in long pipelines it cannot be neglected.
Description: Published October 6, 2016, as part of the Proceedings of the 2015 Mathematics and Statistics in Industry Study Group.Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/2440/1060452015-01-01T00:00:00ZGood coupling for the multiscale patch scheme on systems with microscale heterogeneity
http://hdl.handle.net/2440/105867
Title: Good coupling for the multiscale patch scheme on systems with microscale heterogeneity
Author: Bunder, J.; Roberts, A.; Kevrekidis, I.
Description: Available online 16 February 2017Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/2440/1058672017-01-01T00:00:00Z