Projective duals to algebraic and tropical hypersurfaces

We study a tropical analogue of the projective dual variety of a hypersurface. When $X$ is a curve in $\mathbb{P}^2$ or a surface in $\mathbb{P}^3$, we provide an explicit description of $\text{Trop}(X^*)$ in terms of $\text{Trop}(X)$, as long as $\text{Trop}(X)$ is smooth and satisfies a mild genericity condition. As a consequence, when $X$ is a curve we describe the transformation of Newton polygons under projective duality, and recover classical formulas for the degree of a dual plane curve. For higher dimensional hypersurfaces $X$, we give a partial description of $\text{Trop}(X^*)$.Comment: 47 pages, 13 figures; v2 minor revisions; accepted to PLM

An Entrepreneurship Model for Energy Empowerment of Indian Households - Economic and Policy Analysis

Provision of modern energy services for cooking (gaseous fuels) and lighting (electricity) is an essential component of any policy aiming to address health, education or welfare issues; yet it gets little attention from policymakers. Secure, adequate, low-cost energy of quality and convenience is core to the delivery of these services. The present study analyses the energy consumption pattern of Indian domestic sector and conceptualizes availability, accessibility, and affordability indicators of modern energy services to households and describes the practical ways of evaluating them. A comprehensive analysis is done to estimate the cost for providing modern energy services to everyone by 2030. A publicprivate partnership-driven business model, with entrepreneurship at the core, is developed with innovative institutional, financing and pricing mechanisms for diffusion of energy services. This approach facilitates largescale dissemination of energy efficient and renewable technologies like smallscale biogas/biofuel plants, and solar water heating systems to provide clean, safe, reliable and sustainable energy to rural households and urban poor. It is expected to integrate the processes of market transformation and entrepreneurship development involving government, NGOs, financial institutions and community groups as stakeholders.Energy Service, Electricity, Biogas, Availability, Accessibility, Affordability

From Registration to Recounts Revisited: Developments in the Election Ecosystems of Five Midwestern States

As a follow-up to a study of problems during the 2006 elections, examines the states' continuing adjustments to institutional arrangements, voter registration databases, convenience voting, and post-election processes in the 2008 elections

Solar energy conversion

If solar energy is to become a practical alternative to fossil fuels, we must have efficient ways to convert photons into electricity, fuel, and heat. The need for better conversion technologies is a driving force behind many recent developments in biology, materials, and especially nanoscience

The Behavior of Granular Materials under Cyclic Shear

The design and development of a parallel plate shear cell for the study of large scale shear flows in granular materials is presented. The parallel plate geometry allows for shear studies without the effects of curvature found in the more common Couette experiments. A system of independently movable slats creates a well with side walls that deform in response to the motions of grains within the pack. This allows for true parallel plate shear with minimal interference from the containing geometry. The motions of the side walls also allow for a direct measurement of the velocity profile across the granular pack. Results are presented for applying this system to the study of transients in granular shear and for shear-induced crystallization. Initial shear profiles are found to vary from packing to packing, ranging from a linear profile across the entire system to an exponential decay with a width of approximately 6 bead diameters. As the system is sheared, the velocity profile becomes much sharper, resembling an exponential decay with a width of roughly 3 bead diameters. Further shearing produces velocity profiles which can no longer be fit to an exponential decay, but are better represented as a Gaussian decay or error function profile. Cyclic shear is found to produce large scale ordering of the granular pack, which has a profound impact on the shear profile. There exist periods of time in which there is slipping between layers as well as periods of time in which the layered particles lock together resulting in very little relative motion.Comment: 10 pages including 12 figure

Maximum elastic deformations of relativistic stars

We present a method for calculating the maximum elastic quadrupolar deformations of relativistic stars, generalizing the previous Newtonian, Cowling approximation integral given by [G. Ushomirsky et al., Mon. Not. R. Astron. Soc. 319, 902 (2000)]. (We also present a method for Newtonian gravity with no Cowling approximation.) We apply these methods to the m = 2 quadrupoles most relevant for gravitational radiation in three cases: crustal deformations, deformations of crystalline cores of hadron-quark hybrid stars, and deformations of entirely crystalline color superconducting quark stars. In all cases, we find suppressions of the quadrupole due to relativity compared to the Newtonian Cowling approximation, particularly for compact stars. For the crust these suppressions are up to a factor ~6, for hybrid stars they are up to ~4, and for solid quark stars they are at most ~2, with slight enhancements instead for low mass stars. We also explore ranges of masses and equations of state more than in previous work, and find that for some parameters the maximum quadrupoles can still be very large. Even with the relativistic suppressions, we find that 1.4 solar mass stars can sustain crustal quadrupoles of a few times 10^39 g cm^2 for the SLy equation of state or close to 10^40 g cm^2 for equations of state that produce less compact stars. Solid quark stars of 1.4 solar masses can sustain quadrupoles of around 10^44 g cm^2. Hybrid stars typically do not have solid cores at 1.4 solar masses, but the most massive ones (~2 solar masses) can sustain quadrupoles of a few times 10^41 g cm^2 for typical microphysical parameters and a few times 10^42 g cm^2 for extreme ones. All of these quadrupoles assume a breaking strain of 0.1 and can be divided by 10^45 g cm^2 to yield the fiducial "ellipticities" quoted elsewhere.Comment: 21 pages, 11 figures, version accepted by PRD, including the corrected maximum hybrid star quadrupoles (from the erratum to the shear modulus calculation) and the corrected binding energy computatio

Pathologic Femur Fracture through Osteoid Osteoma after Radiofrequency Ablation: Case Report and Review of the Literature.

This is a case report of a 4-year-old girl who sustained a femoral shaft fracture 2 weeks after radiofrequency ablation of an osteoid osteoma. The fracture occurred after a relatively low-energy impact, jumping off the second to last step of a staircase. The pathologic fracture was successfully treated with closed reduction and spica casting, with full return to activities. Cases have been reported in the literature of femoral shaft fractures in older patients after radiofrequency ablation, but all are farther out than 2 weeks and none in patients as young as 4 years

Method for carbon dioxide splitting

A method for splitting carbon dioxide via a two-step metal oxide thermochemical cycle by heating a metal oxide compound selected from an iron oxide material of the general formula AxFe3-xO4, where 0≦x≦1 and A is a metal selected from Mg, Cu, Zn, Ni, Co, and Mn, or a ceria oxide compound of the general formula MaCebOc, where