Calibrated Sub-Bundles in Non-Compact Manifolds of Special Holonomy

This paper is a continuation of math.DG/0408005. We first construct special Lagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) on the cotangent bundle of S^n by looking at the conormal bundle of appropriate submanifolds of S^n. We find that the condition for the conormal bundle to be special Lagrangian is the same as that discovered by Harvey-Lawson for submanifolds in R^n in their pioneering paper. We also construct calibrated submanifolds in complete metrics with special holonomy G_2 and Spin(7) discovered by Bryant and Salamon on the total spaces of appropriate bundles over self-dual Einstein four manifolds. The submanifolds are constructed as certain subbundles over immersed surfaces. We show that this construction requires the surface to be minimal in the associative and Cayley cases, and to be (properly oriented) real isotropic in the coassociative case. We also make some remarks about using these constructions as a possible local model for the intersection of compact calibrated submanifolds in a compact manifold with special holonomy.Comment: 20 pages; for Revised Version: Minor cosmetic changes, some paragraphs rewritten for improved clarit

Closed trajectories of a particle model on null curves in anti-de Sitter 3-space

We study the existence of closed trajectories of a particle model on null curves in anti-de Sitter 3-space defined by a functional which is linear in the curvature of the particle path. Explicit expressions for the trajectories are found and the existence of infinitely many closed trajectories is proved.Comment: 12 pages, 1 figur

Pressure perturbations from geologic carbon sequestration: Area-of-review boundaries and borehole leakage driving forces

We investigate the possibility that brine could be displaced upward into potable water through wells. Because of the large volumes of CO2 to be injected, the influence of the zone of elevated pressure on potential conduits such as well boreholes could extend many kilometers from the injection site—farther than the CO2 plume itself. The traditional approach to address potential brine leakage related to fluid injection is to set an area of fixed radius around the injection well/zone and to examine wells and other potentially open pathways located in the “Area-of-Review” (AoR). This suggests that the AoR needs to be defined in terms of the potential for a given pressure perturbation to drive upward fluid flow in any given system rather than on some arbitrary pressure rise. We present an analysis that focuses on the changes in density/salinity of the fluids in the potentially leaking wellbore.Bureau of Economic Geolog

The Impact of Rising Energy Costs on Representative Farms

Recent increases in natural gas and fossil fuel based energy sources have had a negative impact on the financial condition of agricultural producers across the nation. • In addition to higher fuel costs for trucks, equipment, and irrigation motors, the cost of nitrogen fertilizer is closely linked to energy prices and has also increased significantly. • This study quantifies the impacts of these increases on the economic viability of representative farms located throughout the United States for the years 2005 and 2006.Crop Production/Industries,

A review of virtual reality technologies in the field of communication disability: implications for practice and research.

BACKGROUND: Technology devices and applications including virtual reality (VR) are increasingly used in healthcare research and practice as tools to promote health and wellbeing. However, there is limited research examining the potential for VR to enable improved communication for people with communication disability. AIMS: To review: (a) current research using VR in speech-language pathology; and (b) the ethical and safety considerations of VR research, to inform an agenda for future research applying VR in the field of speech-language pathology. MAIN CONTRIBUTION: This review reveals that there is an emergent body of literature applying VR to improve or develop physical, psychological and communication interventions. Use of non-immersive virtual environments to provide speech-language pathology assessment or intervention for people with communication disability has demonstrated positive outcomes, with emerging evidence of the transfer of functional communication skills from virtual to real-world environments. However, the use of VR technology and immersive virtual environments in communication disability practice and research introduces safety and ethical issues that must be carefully considered. CONCLUSIONS: Research employing VR is in its infancy in the field of speech-language pathology. Early evidence from other healthcare disciplines suggests that VR is an engaging means of delivering immersive and interactive training to build functional skills that can be generalized to the real world. While the introduction of new technology requires careful consideration of research ethics and patient safety, future VR communication research could proceed safely with adequate engagement of interdisciplinary teams and technology specialists. Implications for rehabilitation Immersive virtual reality may be used in rehabilitation to simulate natural environments to practice and develop communication skills. The sense of immersion that can be achieved using virtual reality may promote the generalization of skills learnt during clinical rehabilitation to real-world situations. Ethical and safety considerations, including cybersecurity and cybersickness, must be carefully monitored during all virtual reality research

Towards Verifying Nonlinear Integer Arithmetic

We eliminate a key roadblock to efficient verification of nonlinear integer arithmetic using CDCL SAT solvers, by showing how to construct short resolution proofs for many properties of the most widely used multiplier circuits. Such short proofs were conjectured not to exist. More precisely, we give n^{O(1)} size regular resolution proofs for arbitrary degree 2 identities on array, diagonal, and Booth multipliers and quasipolynomial- n^{O(\log n)} size proofs for these identities on Wallace tree multipliers.Comment: Expanded and simplified with improved result