Numerical Analysis of Hypersonic Inlet Flows

The research uses CFD to investigate the internal flow of two hypersonic engine inlets: the Hypersonic Research Engine (HRE), a dual-mode ramjet/scramjet, and the Sustained Hypersonic Flight Experiment (SHyFE), a ramjet developed by QinetiQ. Various interactions are considered, namely shock-expansion, shock-shock and shock-boundary layer interactions. To isolate the different interactions, both inviscid and viscous turbulent computations are considered. For the HRE, axisymmetric computations are performed at Mach numbers of 5, 6 and 7, consistent with ground testing conditions used by NASA. The HRE was designed to cruise at a range of Mach numbers; for a given set of freestream flow conditions, dramatically different internal flow characteristics have been found depending on whether the engine arrived at the flow conditions through either acceleration or deceleration. CFD surface data and throat profiles have been compared to, and agree well with, experimental data obtained by. NASA. 'I\vo flow conditions are investigated for the SHyFE inlet. Firstly, the self-starting characteristics of the SHyFE intake are examined, where the effect of increased internal compression is considered. The findings show undesirable wave interactions, which lead to flow non-uniformities, and decreased shock stabilization properties have adverse effects on the performance of the engine. Secondly, the effect of freestream incidence on the inlet is examined..The SHyFE engine is designed to cruise at a mean incidence of between 2???????? and 3????????, however, it is conceivable that the engine will, at times, operate at 5????????. Fully three dimensional computations are performed at an angle of attack of 5???????? where the resulting flows show that Mach reflections on the inner surface of the cowl can lead to shock-detachment, as well as showing that shock-boundary layer interactions on the centrebody can cause centrebody flow separation which can unstart the engine. By aul1ing a rear-ward fdl-~l1b btep tU the CClltfCUUtly geometry, the centrebody separation is shown to be stabilised and does not unstart the engine. CFD results are compared to, and agree with, experimental data produced externally by QinetiQ, namely schlieren and surface pressure data.Imperial Users onl

Functional Analysis and Exterior Calculus on Mixed-Dimensional Geometries

We are interested in differential forms on mixed-dimensional geometries, in the sense of a domain containing sets of $d$-dimensional manifolds, structured hierarchically so that each $d$-dimensional manifold is contained in the boundary of one or more $d + 1$ dimensional manifolds. On any given $d$-dimensional manifold, we then consider differential operators tangent to the manifold as well as discrete differential operators (jumps) normal to the manifold. The combined action of these operators leads to the notion of a semi-discrete differential operator coupling manifolds of different dimensions. We refer to the resulting systems of equations as mixed-dimensional, which have become a popular modeling technique for physical applications including fractured and composite materials. We establish analytical tools in the mixed-dimensional setting, including suitable inner products, differential and codifferential operators, Poincar\'e lemma, and Poincar\'e--Friedrichs inequality. The manuscript is concluded by defining the mixed-dimensional minimization problem corresponding to the Hodge-Laplacian, and we show that this minimization problem is well-posed

Screening of heterogeneous surfaces: charge renormalization of Janus particles

Nonlinear ionic screening theory for heterogeneously charged spheres is developed in terms of a mode-decomposition of the surface charge. A far-field analysis of the resulting electrostatic potential leads to a natural generalization of charge renormalization from purely monopolar to dipolar, quadropolar, etc., including mode-couplings. Our novel scheme is generally applicable to large classes of surface heterogeneities, and is explicitly applied here to Janus spheres with differently charged upper and lower hemispheres, revealing strong renormalization effects for all multipoles.Comment: 2 figure

Coining a New Jurisdiction: The Security Council as Economic Peacekeeper

Economic conditions are linked to international peace and security. Financial crises, mismanagement of natural resources, food shortages, and climate change can create transnational effects, including conflict. The Security Council is the executive organ of the United Nations, with primary jurisdiction over the maintenance of international peace and security. This Article explores the extent to which the Security Council can and should assert jurisdiction over economic and financial issues. In the past decade, the economic dimensions of conflict, including the economic causes of war, economic agendas of state and nonstate actors, and economic measures for reconstruction have become central to the Security Council\u27s work and to contemporary concepts of collective security. This Article argues that the Security Council\u27s increasing engagement with economic and financial issues is proper and permissible under Article 39, provided that certain thresholds are met. For example, purely internal disruptions such as bankruptcies would be unlikely to rise to the level of a threat to peace and security, whereas the manipulation of natural resources destined for, or regulated by, international markets may well create threats within the Council\u27s jurisdiction. The Security Council\u27s enforcement jurisdiction under Article 41 has similarly evolved, shifting from the wholesale restriction of economic opportunities via trade embargoes and sanctions to the promotion of prospective measures such as good economic governance. If the Council\u27s economic interventions continue, it will become a player of some significance in applying and developing international economic norms

The United Nations as Good Samaritan: Immunity and Responsibility

Since the U.N.’s founding, its need for immunity from the jurisdiction of member states courts has been understood as necessary to achieve its purposes. Immunities, however, conflict with an individual’s right to a remedy and the law’s ordinary principles of responsibility for causing harm. This inherent conflict at the center of the immunity doctrine has evolved into a very public rift in the Haiti Cholera, Kosovo Lead Poisoning, and Mothers of Srebrenica cases against the U.N. In these three cases alleging mass torts by the U.N., the independence of the organization is perceived by some to have trumped the dignity of affected individuals. Due to a combination of factors, including the U.N.’s broad immunities, the limited jurisdiction rationae personae of courts over international organizations (IOs), and the nascent state of the U.N.’s own internal review mechanisms, not to mention continuing debate over whether human rights obligations bind the U.N. directly under international law, these cases of human tragedy have resulted in neither compensation by the U.N. to the victims nor access to domestic courts. This article argues that the threshold problem with the position that the U.N. is absolutely immune is that it severs ordinary legal principles: an organization is responsible for the harm it causes by its negligence. Absolute immunity also stands in contrast to the U.N.’s programmatic promotion of the Rule of Law and to the standards expected of member states. While partial immunity is justified under certain circumstances, the categorical assertion of absolute U.N. immunity does not survive an assessment of accountability, distributive justice, or economics. U.N. Member States should join the conversation about what immunities mean to the U.N. today given its contemporary mandate and impact on individuals. If they do not, there may be consequences for the U.N. that are disadvantageous for its future work

The Cellient System for Paraffin Histology Can Be Combined with HPV Testing and Morphotyping the Vaginal Microbiome Thanks to BoonFixing

The Cellient Automated Cell Block System (Hologic) can be used to process cervical scrapes to paraffin sections. For the first study on this subject, cervical scrapes were fixed in the formalin-free fixative BoonFix. This pilot study was limited to cases classified as atypical squamous lesion of unknown significance (ASCUS) and high-grade squamous lesion (HSIL) as diagnosed in the ThinPrep slide. The Cellient paraffin sections were classified into negative, atypical, CIN 1, CIN 2, and CIN 3. Multiple HPV genotypes were encountered in 79% of the scrapes. This study showed that the Cellient system for paraffin sections can be combined with HPV testing thanks to the formalin-free BoonFix. In two additional studies it was shown that such samples can also be used for morphotyping the vaginal microbiome and preparing cytologic ThinPrep slides

Propagation and organization in lattice random media

We show that a signal can propagate in a particular direction through a model random medium regardless of the precise state of the medium. As a prototype, we consider a point particle moving on a one-dimensional lattice whose sites are occupied by scatterers with the following properties: (i) the state of each site is defined by its spin (up or down); (ii) the particle arriving at a site is scattered forward (backward) if the spin is up (down); (iii) the state of the site is modified by the passage of the particle, i.e. the spin of the site where a scattering has taken place, flips ($\uparrow \Leftrightarrow \downarrow$). We consider one dimensional and triangular lattices, for which we give a microscopic description of the dynamics, prove the propagation of a particle through the scatterers, and compute analytically its statistical properties. In particular we prove that, in one dimension, the average propagation velocity is $= 1/(3-2q)$, with $q$ the probability that a site has a spin $\uparrow$, and, in the triangular lattice, the average propagation velocity is independent of the scatterers distribution: $= 1/8$. In both cases, the origin of the propagation is a blocking mechanism, restricting the motion of the particle in the direction opposite to the ultimate propagation direction, and there is a specific re-organization of the spins after the passage of the particle. A detailed mathematical analysis of this phenomenon is, to the best of our knowledge, presented here for the first time.Comment: 30 pages, 15 separate figures (in PostScript); submitted to J. Stat. Phy