650 research outputs found
Witten Genus and String Complete Intersections
In this note, we prove that the Witten genus of nonsingular string complete
intersections in product of complex projective spaces vanishes. Our result
generalizes a known result of Landweber and Stong (cf. [HBJ]).Comment: Some materials and references are adde
Generalized Witten Genus and Vanishing Theorems
We construct a generalized Witten genus for spin manifolds, which takes
values in level 1 modular forms with integral Fourier expansion on a class of
spin manifolds called string manifolds. We also construct a mod 2
analogue of the Witten genus for dimensional spin manifolds. The
Landweber-Stong type vanishing theorems are proven for the generalized Witten
genus and the mod 2 Witten genus on string and string (generalized)
complete intersections in (product of) complex projective spaces respectively.Comment: 28 page
Developing Critical Loads and Dynamic Critical Loads for Acidification for Watersheds in the Adirondack region of New York and Great Smoky Mountain National Park (GRSM)
Critical loads (CLs) and dynamic critical loads (DCLs) are important tools for the management of ecosystems that are impacted by high sulfate, nitrate and ammonium deposition. In this study, a biogeochemical model (PnET-BGC) was applied to 20 watersheds in the Adirondack region and 12 watersheds in Great Smoky Mountain National Park (GRSM) to calculate CLs and DCLs. I evaluated ecosystem changes in response to historical and potential future changes in acidic deposition. I analyzed factors affecting CLs and DCLs for acidification in the acid impacted Constable Pond Watershed in the Adirondack region, specifically evaluating trade-offs of sulfate and nitrate deposition, supply of dissolved organic carbon, land disturbance and lake hydrological residence time. I also calculated CLs and DCLs for 20 watersheds in the Adirondack Region. Based on chemical indicators (acid neutralizing capacity-ANC and soil base saturation) and biological indicators (fish and total zooplankton species richness). I defined two metrics - historical acidification and maximum recovery based on changes in ANC. I explored the factors affecting historical acidification and maximum recovery. I determined the conditions where acidified lakes can recover and the long-term sustained deposition loads that would be required to achieve such recovery and identified the types of watersheds for which recovery is unlikely, regardless of the emission reductions. I also projected the response of aquatic species (fish and total zooplankton species richness) to historical and potential future changes in acidic deposition. Using methods similar to those developed for the Adirondack region, I also applied PnET-BGC to the GRSM region to obtain CLs and DCLs and evaluated how watershed-ecosystems changed in response to historical and future decreases in NO3-, SO42- and NH4+ deposition.
Results from Constable Pond watershed showed that ANC increased more in response to equivalent decreases in SO42- deposition than NO3- deposition. Moreover, DOC in the surface water, lake hydrological residence time and forest cutting disturbance had substantial effects on historical acidification and the recovery of lake ANC.
Results from lakes of the Adirondack region also showed that future increases in ANC will be accomplished more effectively in response to further decreases in SO42- deposition than in NO3- deposition. Historical acidification was related to the current deposition of SO42-+NO3-, Ca2+ weathering rate, and pre-industrial ANC (~1850). Lake recovery was likewise related with the current deposition of SO42-+NO3-, Ca2+ weathering rate and current ANC. Fish and total zooplankton species richness are projected to increase under decreases in SO42- or NO3- deposition. However, complete chemical and biological recovery will not be attainable by 2200 even under decreases in atmospheric deposition to pre-industrial conditions.
Results from the GRSM showed that ANC in the future will also increase in response to decreases in acidic deposition. However, ANC increases will be accomplished more effectively with decreases in NO3- than in SO42- deposition. This difference in response is due to the strong retention of SO42- by soil adsorption in this unglaciated landscape, coupled with the limited watershed retention of atmospheric N deposition. Historical acidification and maximum recovery were also related to Ca2+ weathering rate and pre-industrial ANC. Some watersheds are projected to achieve target ANC in the future under different DCLs for SO42-+NO3- deposition. Other GRSM watersheds will not be able to achieve target ANC in the future due to sensitive soil conditions and are experiencing watershed N saturatio
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