The Dirac operator on untrapped surfaces

We establish a sharp extrinsic lower bound for the first eigenvalue of the Dirac operator of an untrapped surface in initial data sets without apparent horizon in terms of the norm of its mean curvature vector. The equality case leads to rigidity results for the constraint equations with spherical boundary as well as uniqueness results for constant mean curvature surfaces in Minkowski space.Comment: 16 page

Towards displacing domestic air conditioning in KSA, an assessment of hybrid cooling strategies integrated with 'Fabric First' passive design measures

Reducing energy use and CO2 emissions to curb global warming and climate change are the greatest challenges now facing mankind. The vast majority of energy generated from fossil fuels is burned to run vehicles, fuel power stations and cool or heat homes. Saudi Arabia, the world's largest producer and exporter of petroleum, currently consumes almost three times higher than the world average energy use and hence; ranked ninth among nations for CO2 emissions. Among all fossil energy consumers, residential buildings use almost half of the Saudi's prime energy sources and are responsible for almost 50% of the emitted CO2. In such a hot climate region, air conditioning (AC) of dwellings is by far the major consumer representing 69% of domestic energy use and drives peak loading. Future projections predict a continuous increase in energy use as the majority of existing buildings are poorly designed for the prevailing climate, leading to excessive use of mechanical AC. Therefore, it is crucial for Saudi Arabia to consider a horizon where hydrocarbons are not the dominant energy resource. The adoption of energy efficiency measures and low carbon cooling strategies may have the potential to displace a substantial percentage of oil currently used to run conventional AC plants. Therefore, the current study investigates the viability of 'fabric first' intelligent architectural design measures, in combination with hybrid ground cooling pipes integrated with black-body radiant night cooling systems, with a specific purpose to displace AC systems and decrease the carbon footprint while sustaining year-round thermal comfort. The interrogation of this hypothesis was addressed in three stages. The first stage was to generate a baseline analysis of the thermo-physical and energy performance of a typical residential block in Jeddah. The second stage involved developing an alternative low energy cooling approach that could handle high ambient temperatures. The task involved designing ground pipe ventilation integrated with high emissivity blackbody radiator to displace AC systems. The design of such 'hybrid' system required a parametric analysis combined with testing prototypes in field trials to establish actual ground temperatures at various depths and black body emissivity ranges under different sky conditions. This hybrid system became the subject of numerical modelling and simulation using DesignBuilder software in conjunction with EnergyPlus simulation engine. The third stage was to assess the simulation results and validate the cooling efficiency and cost-effectiveness of the hybrid system compared to the baseline. The preliminary results of prototype thermal simulation and field trials suggest that 'fabric first' passive designs and measures (PDMs), combined with night hydronic radiant cooling (HRCS) and supply ventilation via ground pipes (GPCS), can negate the necessity for a standard AC system by displacing over 80% of cooling demand and lower the carbon footprint of a typical housing block by over 75%. Such passive and hybrid system applications also have a remarkably short payback period with energy savings offsetting the capital costs associated with building thermo-physical enhancement.Reducing energy use and CO2 emissions to curb global warming and climate change are the greatest challenges now facing mankind. The vast majority of energy generated from fossil fuels is burned to run vehicles, fuel power stations and cool or heat homes. Saudi Arabia, the world's largest producer and exporter of petroleum, currently consumes almost three times higher than the world average energy use and hence; ranked ninth among nations for CO2 emissions. Among all fossil energy consumers, residential buildings use almost half of the Saudi's prime energy sources and are responsible for almost 50% of the emitted CO2. In such a hot climate region, air conditioning (AC) of dwellings is by far the major consumer representing 69% of domestic energy use and drives peak loading. Future projections predict a continuous increase in energy use as the majority of existing buildings are poorly designed for the prevailing climate, leading to excessive use of mechanical AC. Therefore, it is crucial for Saudi Arabia to consider a horizon where hydrocarbons are not the dominant energy resource. The adoption of energy efficiency measures and low carbon cooling strategies may have the potential to displace a substantial percentage of oil currently used to run conventional AC plants. Therefore, the current study investigates the viability of 'fabric first' intelligent architectural design measures, in combination with hybrid ground cooling pipes integrated with black-body radiant night cooling systems, with a specific purpose to displace AC systems and decrease the carbon footprint while sustaining year-round thermal comfort. The interrogation of this hypothesis was addressed in three stages. The first stage was to generate a baseline analysis of the thermo-physical and energy performance of a typical residential block in Jeddah. The second stage involved developing an alternative low energy cooling approach that could handle high ambient temperatures. The task involved designing ground pipe ventilation integrated with high emissivity blackbody radiator to displace AC systems. The design of such 'hybrid' system required a parametric analysis combined with testing prototypes in field trials to establish actual ground temperatures at various depths and black body emissivity ranges under different sky conditions. This hybrid system became the subject of numerical modelling and simulation using DesignBuilder software in conjunction with EnergyPlus simulation engine. The third stage was to assess the simulation results and validate the cooling efficiency and cost-effectiveness of the hybrid system compared to the baseline. The preliminary results of prototype thermal simulation and field trials suggest that 'fabric first' passive designs and measures (PDMs), combined with night hydronic radiant cooling (HRCS) and supply ventilation via ground pipes (GPCS), can negate the necessity for a standard AC system by displacing over 80% of cooling demand and lower the carbon footprint of a typical housing block by over 75%. Such passive and hybrid system applications also have a remarkably short payback period with energy savings offsetting the capital costs associated with building thermo-physical enhancement

On a spin conformal invariant on manifolds with boundary

On a n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric, a spin structure and a chirality operator, we study some properties of a spin conformal invariant defined from the first eigenvalue of the Dirac operator under the chiral bag boundary condition. More precisely, we show that we can derive a spinorial analogue of Aubin's inequality.Comment: 26 page

Nonexistence of Generalized Apparent Horizons in Minkowski Space

We establish a Positive Mass Theorem for initial data sets of the Einstein equations having generalized trapped surface boundary. In particular we answer a question posed by R. Wald concerning the existence of generalized apparent horizons in Minkowski space

Effectiveness of BaTiO3 dielectric patches on YBa2Cu3O7 thin films for MEM switches

A micro-electro-mechanical (MEM) switch built on a superconducting microstrip filter will be utilized to investigate BaTiO3 dielectric patches for functional switching points of contact. Actuation voltage resulting from the MEM switch provokes static friction between the bridge membrane and BaTiO3 insulation layer. The dielectric patch crystal structure and roughness affect the ability of repetitively switching cycles and lifetime. A series of experiments have been performed using different deposition methods and RF magnetron sputtering was found to be the best deposition process for the BaTiO3 layer. The effect examination of surface morphology will be presented using characterization techniques as x-ray diffraction, SEM and AFM for an optimum switching device. The thin film is made of YBa2Cu3O7 deposited on LaAlO3 substrate by pulsed laser deposition. For this work, the dielectric material sputtering pressure is set at 9.5x10-6 Torr. The argon gas is released through a mass-flow controller to purge the system prior to deposition. RF power is 85 W at a distance of 9 cm. The behavior of Au membranes built on ultimate BaTiO3 patches will be shown as part of the results. These novel surface patterns will in turn be used in modelling other RF MEM switch devices such as distributed-satellite communication system operating at cryogenic temperatures

A Reilly formula and eigenvalue estimates for differential forms

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a Riemannian manifold. The equality case of our inequality gives rise to a number of rigidity results, when the geometry of the boundary has special properties and the domain is non-negatively curved. Finally we also obtain, as a by-product of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.Comment: 22 page

La Inversión europea en el Consejo de Cooperación del Golfo (CCG)

De hecho, nadie puede negar que la inversión europea en el Consejo de Cooperación del Golfo es una de las cuestiones más importantes. En realidad, vale la pena debatir este tema. Me despierta tanto interés que considero un gran placer escribir sobre él. Este trabajo tiene como objetivo evaluar la evolución de los países del CCG en el aspecto económico como base para alcanzar la plena unión económica. Se pretende analizar, además, el acceso y el fortalecimiento de las relaciones de estos países con la Unión Europea. De la necesidad de examinar los logros alcanzados, los obstáculos, oportunidades y amenazas (DAFO) se plantea un modelo tentativo de relación que incremente las relaciones económicas de todos los países estudiados. Resultados previstos - Contribuir al fortalecimiento de la estabilidad en una región de importancia estratégica y facilitar las relaciones políticas, económicas y comerciales. - Ampliar la cooperación económica y técnica, así como la cooperación en los ámbitos de la energía, el comercio, los servicios, la agricultura, la industria pesquera, la inversión, la ciencia, la tecnología y el medio ambiente

Generic metrics and the mass endomorphism on spin three-manifolds

Let $(M,g)$ be a closed Riemannian spin manifold. The constant term in the expansion of the Green function for the Dirac operator at a fixed point $p\in M$ is called the mass endomorphism in $p$ associated to the metric $g$ due to an analogy to the mass in the Yamabe problem. We show that the mass endomorphism of a generic metric on a three-dimensional spin manifold is nonzero. This implies a strict inequality which can be used to avoid bubbling-off phenomena in conformal spin geometry.Comment: 8 page

Surgery and the spinorial tau-invariant

We associate to a compact spin manifold M a real-valued invariant \tau(M) by taking the supremum over all conformal classes over the infimum inside each conformal class of the first positive Dirac eigenvalue, normalized to volume 1. This invariant is a spinorial analogue of Schoen's $\sigma$-constant, also known as the smooth Yamabe number. We prove that if N is obtained from M by surgery of codimension at least 2, then $\tau(N) \geq \min\{\tau(M),\Lambda_n\}$ with $\Lambda_n>0$. Various topological conclusions can be drawn, in particular that \tau is a spin-bordism invariant below $\Lambda_n$. Below $\Lambda_n$, the values of $\tau$ cannot accumulate from above when varied over all manifolds of a fixed dimension.Comment: to appear in CPD