The Energy-Momentum tensor on low dimensional Spin^c manifolds

On a compact surface endowed with any \Spinc structure, we give a formula involving the Energy-Momentum tensor in terms of geometric quantities. A new proof of a B\"{a}r-type inequality for the eigenvalues of the Dirac operator is given. The round sphere $\mathbb{S}^2$ with its canonical \Spinc structure satisfies the limiting case. Finally, we give a spinorial characterization of immersed surfaces in $\mathbb{S}^2\times \mathbb{R}$ by solutions of the generalized Killing spinor equation associated with the induced \Spinc structure on $\mathbb{S}^2\times \mathbb{R}

Simple system to measure the Earth's magnetic field

Our aim in this proposal is by using the Faraday's law of induction as a simple lecture demonstration to measure the Earth's magnetic field (B). This will also enable the students to learn about how electric power is generated from the rotational motion. Obviously the idea is not original, yet it may be attractive in the sense that no sophisticated devices are used

Basin-level use and productivity of water: examples from South Asia

Water managementWater conservationRiver basinsWater useProductivityCase studiesIrrigated farmingIndicatorsWater scarcity

The central elliptical galaxy in fossil groups and formation of BCGs

We study the dominant central giant elliptical galaxies in ``Fossil groups'' using deep optical (R-band) and near infrared (Ks-band) photometry. These galaxies are as luminous as the brightest cluster galaxies (BCGs), raising immediate interest in their link to the formation of BCGs and galaxy clusters. However, despite apparent similarities, the dominant fossil galaxies show non-boxy isophotes, in contrast to the most luminous BCGs. This study suggests that the structure of the brightest group galaxies produced in fossil groups are systematically different to the majority of BCGs. If the fossils do indeed form from the merger of major galaxies including late-types within a group, then their disky nature is consistent with the results of recent numerical simulations of semi-analytical models which suggest that gas rich mergers result in disky isophote ellipticals. We show that fossils form a homogeneous population in which the velocity dispersion of the fossil group is tightly correlated with the luminosity of the dominant elliptical galaxy. This supports the scenario in which the giant elliptical galaxies in fossils can grow to the size and luminosity of BCGs in a group environment. However, the boxy structure of luminous BCGs indicate that they are either not formed as fossils, or have undergone later gas-free mergers within the cluster environment.Comment: 5 pages, 4 figures, Accepted for publication in MNRAS letter

Quasi-dynamic Load and Battery Sizing and Scheduling for Stand-Alone Solar System Using Mixed-integer Linear Programming

Considering the intermittency of renewable energy systems, a sizing and scheduling model is proposed for a finite number of static electric loads. The model objective is to maximize solar energy utilization with and without storage. For the application of optimal load size selection, the energy production of a solar photovoltaic is assumed to be consumed by a finite number of discrete loads in an off-grid system using mixed-integer linear programming. Additional constraints are battery charge and discharge limitations and minimum uptime and downtime for each unit. For a certain solar power profile the model outputs optimal unit size as well as the optimal scheduling for both units and battery charge and discharge (if applicable). The impact of different solar power profiles and minimum up and down time constraints on the optimal unit and battery sizes are studied. The battery size required to achieve full solar energy utilization decreases with the number of units and with increased flexibility of the units (shorter on and off-time). A novel formulation is introduced to model quasi-dynamic units that gradually start and stop and the quasi-dynamic units increase solar energy utilization. The model can also be applied to search for the optimal number of units for a given cost function.Comment: 6 pages, 3 figures, accepted at The IEEE Conference on Control Applications (CCA