Spectral analysis and zeta determinant on the deformed spheres

We consider a class of singular Riemannian manifolds, the deformed spheres $S^N_k$, defined as the classical spheres with a one parameter family $g[k]$ of singular Riemannian structures, that reduces for $k=1$ to the classical metric. After giving explicit formulas for the eigenvalues and eigenfunctions of the metric Laplacian $\Delta_{S^N_k}$, we study the associated zeta functions $\zeta(s,\Delta_{S^N_k})$. We introduce a general method to deal with some classes of simple and double abstract zeta functions, generalizing the ones appearing in $\zeta(s,\Delta_{S^N_k})$. An application of this method allows to obtain the main zeta invariants for these zeta functions in all dimensions, and in particular $\zeta(0,\Delta_{S^N_k})$ and $\zeta'(0,\Delta_{S^N_k})$. We give explicit formulas for the zeta regularized determinant in the low dimensional cases, $N=2,3$, thus generalizing a result of Dowker \cite{Dow1}, and we compute the first coefficients in the expansion of these determinants in powers of the deformation parameter $k$.Comment: 1 figur

Electromagnetic Casimir densities for a wedge with a coaxial cylindrical shell

Vacuum expectation values of the field square and the energy-momentum tensor for the electromagnetic field are investigated for the geometry of a wedge with a coaxal cylindrical boundary. All boundaries are assumed to be perfectly conducting and both regions inside and outside the shell are considered. By using the generalized Abel-Plana formula, the vacuum expectation values are presented in the form of the sum of two terms. The first one corresponds to the geometry of the wedge without the cylindrical shell and the second term is induced by the presence of the shell. The vacuum energy density induced by the shell is negative for the interior region and is positive for the exterior region. The asymptotic behavior of the vacuum expectation values are investigated in various limiting cases. It is shown that the vacuum forces acting on the wedge sides due to the presence of the cylindrical boundary are always attractive.Comment: 21 pages, 7 figure

Buoyancy Effects on Upward Brine Displacement Caused by CO2 Injection

Upward displacement of brine from deep reservoirs driven by pressure increases resulting from CO{sub 2} injection for geologic carbon sequestration may occur through improperly sealed abandoned wells, through permeable faults, or through permeable channels between pinch-outs of shale formations. The concern about upward brine flow is that, upon intrusion into aquifers containing groundwater resources, the brine may degrade groundwater. Because both salinity and temperature increase with depth in sedimentary basins, upward displacement of brine involves lifting fluid that is saline but also warm into shallower regions that contain fresher, cooler water. We have carried out dynamic simulations using TOUGH2/EOS7 of upward displacement of warm, salty water into cooler, fresher aquifers in a highly idealized two-dimensional model consisting of a vertical conduit (representing a well or permeable fault) connecting a deep and a shallow reservoir. Our simulations show that for small pressure increases and/or high-salinity-gradient cases, brine is pushed up the conduit to a new static steady-state equilibrium. On the other hand, if the pressure rise is large enough that brine is pushed up the conduit and into the overlying upper aquifer, flow may be sustained if the dense brine is allowed to spread laterally. In this scenario, dense brine only contacts the lower-most region of the upper aquifer. In a hypothetical case in which strong cooling of the dense brine occurs in the upper reservoir, the brine becomes sufficiently dense that it flows back down into the deeper reservoir from where it came. The brine then heats again in the lower aquifer and moves back up the conduit to repeat the cycle. Parameter studies delineate steady-state (static) and oscillatory solutions and reveal the character and period of oscillatory solutions. Such oscillatory solutions are mostly a curiosity rather than an expected natural phenomenon because in nature the geothermal gradient prevents the cooling in the upper aquifer that occurs in the model. The expected effect of upward brine displacement is either establishment of a new hydrostatic equilibrium or sustained upward flux into the bottom-most region of the upper aquifer

Environmental variation, vegetation distribution, carbon dynamics and water/energy exchange at high latitudes

The responses of high latitude ecosystems to global change involve complex interactions among environmental variables, vegetation distribution, carbon dynamics, and water and energy exchange. These responses may have important consequences for the earth system. In this study, we evaluated how vegetation distribution, carbon stocks and turnover, and water and energy exchange are related to environmental variation spanned by the network of the IGBP high latitude transects. While the most notable feature of the high latitude transects is that they generally span temperature gradients from southern to northern latitudes, there are substantial differences in temperature among the transects. Also, along each transect temperature co-varies with precipitation and photosynthetically active radiation, which are also variable among the transects. Both climate and disturbance interact to influence latitudinal patterns of vegetation and soil carbon storage among the transects, and vegetation distribution appears to interact with climate to determine exchanges of heat and moisture in high latitudes. Despite limitations imposed by the data we assembled, the analyses in this study have taken an important step toward clarifying the complexity of interactions among environmental variables, vegetation distribution, carbon stocks and turnover, and water and energy exchange in high latitude regions. This study reveals the need to conduct coordinated global change studies in high latitudes to further elucidate how interactions among climate, disturbance, and vegetation distribution influence carbon dynamics and water and energy exchange in high latitudes

Developing Canada's National Forest Carbon Monitoring, Accounting and Reporting System to Meet the Reporting Requirements of the Kyoto Protocol

accounting, carbon budget model, CBM-CFS, greenhouse gas emissions, Kyoto Protocol, monitoring, natural disturbances, reporting, NFCMARS,