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Faculty of Engineering and Biult Enviroment School of Mechanical,Industrial And Aeronautical Engineering 9807537d efunemarc@hotmail.com / Drag over a wide range of shapes is well established for steady flow conditions. Drag in unsteady flow, however, is for the most part not well understood. The research presented herein examines the drag over cones in unsteady compressible flow. This was achieved by constraining cones, with half-vertex angles ranging from 15° to 30°, in a shock tube and passing shock waves over them. The resulting drag was measured directly using a stress wave drag balance (SWDB). Tests were run at shock Mach numbers between 1.12 and 1.31 with corresponding post-shock Reynolds numbers between 2 × 105 and 6 × 105. The drag on the four cone geometries as well as one sphere geometry was modelled numerically. Density contours of the flow fields, obtained from the numerical simulations were used to visualise the shock/model interactions and deduce the causes of any variations in drag. It was thus proved that post-shock fluctuations are due to shock wave reflections off the shock tube walls and the model support. The maximum unsteady drag values measured experimentally ranged from 53.5 N for the 15° cone at a Mach number of 1.14 to 148.6 N for the 30° cone at a Mach number of 1.29. The drag obtained numerically agreed well with experimental results, showing a maximum deviation in peak drag of 9.6%. The drag forces on the conical models peaked as the shock wave reached the base of the cone whereas the drag on the sphere peaked just before the shock reached the equator of the sphere. The negative drag and large post-shock drag fluctuations on a sphere measured by Bredin (2002) were present in the numerical results and thus confirm that these features were not due to balance error. The large post-shock drag fluctuations were also present on the cones. The unsteady drag was shown to increase as both the shock wave Mach number and the cone angle were increased. The ratio of the maximum unsteady drag to the compressible steady state drag varied from v 4.4:1 to 9.8:1, while the ratio of the maximum unsteady drag to the incompressible steady state drag varied from 8.3:1 to 22.2:1. The steady state drag values were shown to be of the same order of magnitude as the post shock unsteady drag. Further numerical work is recommended to confirm that drag fluctuations are in fact due to shock reflections and to better establish the relationship between the unsteady drag and the cone angle.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 111-116).

Thesis (Ph.D.)--Tufts University, 2000. / Adviser: Lawrence H. Ford. Submitted to the Dept. of Physics and Astronomy. Includes bibliographical references (leaves 99-105). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

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<p> The major results of this work include an isomorphism theorem for B-complete barrelled spaces with similar bases and a theorem which shows that the cone associated with a separating biorthogonal system in a perfect C.N.S. has a basis. We also obtain some applications of the former result in the case of dual generalized bases and some results concerning Schauder bases in countably barrelled spaces.</p> / Thesis / Doctor of Philosophy (PhD)

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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Neste trabalho generalizaremos para o caso de curvatura escalar zero, os resultados de Simmons [14] para cones mÃnimos em Rn+1. Se Mn&#8722;1 à uma hipersuperf&#305;cie da esfera Sn(1) representamos por C(M)" o cone truncado com base em M e centro na origem. à fÃcil ver que M tem curvatura escalar zero se, e somente se, o cone com base em M tambÃm tem curvatura escalar zero. Hounie e Leite [10] recentemente deram condiÃÃes para a elipticidade da equaÃÃo diferencial parcial da curvatura escalar. Para mostrar isto temos que assumir n maior ou igual a 4 e que a 3 â curvatura de M à diferente de zero. Para tais cones,provaremos que, para n menor ou igual a 7 existe um " para o qual o cone truncado C(M)" nÃo à estÃvel. TambÃm mostraremos que para n maior ou igual a 8 existem hipersuperfÃcies compactas e orientÃveis Mn&#8722;1 da esfera com curvatura escalar zero e S3 diferente de zero, para as quais todos os cones truncados com base em M sÃo estÃveis.

Thesis (Ph. D.)--Case Western Reserve University, 2009. / [School of Medicine] Department of Neurosciences. Includes bibliographical references.

There are various notions of positivity for matrices and linear matrix-valued maps that play important roles in quantum information theory. The cones of positive semidefinite matrices and completely positive linear maps, which represent quantum states and quantum channels respectively, are the most ubiquitous positive cones. There are also many natural cones that can been regarded as "more" or "less" positive than these standard examples. In particular, entanglement theory deals with the cones of separable operators and entanglement witnesses, which satisfy very strong and weak positivity properties respectively. Rather complementary to the various cones that arise in entanglement theory are norms. The trace norm (or operator norm, depending on context) for operators and the diamond norm (or completely bounded norm) for superoperators are the typical norms that are seen throughout quantum information theory. In this work our main goal is to develop a family of norms that play a role analogous to the cone of entanglement witnesses. We investigate the basic mathematical properties of these norms, including their relationships with other well-known norms, their isometry groups, and their dual norms. We also make the place of these norms in entanglement theory rigorous by showing that entanglement witnesses arise from minimal operator systems, and analogously our norms arise from minimal operator spaces. Finally, we connect the various cones and norms considered here to several seemingly unrelated problems from other areas. We characterize the problem of whether or not non-positive partial transpose bound entangled states exist in terms of one of our norms, and provide evidence in favour of their existence. We also characterize the minimum gate fidelity of a quantum channel, the maximum output purity and its completely bounded counterpart, and the geometric measure of entanglement in terms of these norms. / Natural Sciences and Engineering Research Council (Canada Graduate Scholarship), Brock Scholarship