Solution to the Equations of the Moment Expansions

We develop a formula for matching a Taylor series about the origin and an asymptotic exponential expansion for large values of the coordinate. We test it on the expansion of the generating functions for the moments and connected moments of the Hamiltonian operator. In the former case the formula produces the energies and overlaps for the Rayleigh-Ritz method in the Krylov space. We choose the harmonic oscillator and a strongly anharmonic oscillator as illustrative examples for numerical test. Our results reveal some features of the connected-moments expansion that were overlooked in earlier studies and applications of the approach

Absorption Spectral Slopes and Slope Ratios as Indicators of Molecular Weight, Source, and Photobleaching of Chromophoric Dissolved Organic Matter

A new approach for parameterizing dissolved organic matter ( DOM) ultraviolet-visible absorption spectra is presented. Two distinct spectral slope regions ( 275-295 nm and 350-400 nm) within log-transformed absorption spectra were used to compare DOM from contrasting water types, ranging from wetlands (Great Dismal Swamp and Suwannee River) to photobleached oceanic water ( Atlantic Ocean). On the basis of DOM size-fractionation studies ( ultrafiltration and gel filtration chromatography), the slope of the 275-295- nm region and the ratio of these slopes (SR; 275-295- nm slope : 350-400- nm slope) were related to DOM molecular weight ( MW) and to photochemically induced shifts in MW. Dark aerobic microbial alteration of chromophoric DOM ( CDOM) resulted in spectral slope changes opposite of those caused by photochemistry. Along an axial transect in the Delaware Estuary, large variations in SR were measured, probably due to mixing, photodegradation, and microbial alteration of CDOM as terrestrially derived DOM transited through the estuary. Further, SR varied by over a factor of 13 between DOM-rich wetland waters and Sargasso Sea surface waters. Currently, there is no consensus on a wavelength range for log-transformed absorption spectra. We propose that the 275-295- nm slope be routinely reported in future DOM studies, as it can be measured with high precision, it facilitates comparison among dissimilar water types including CDOM-rich wetland and CDOM-poor marine waters, and it appears to be a good proxy for DOM MW. © 2008, by the American Society of Limnology and Oceanography, Inc

Contextualizing Wetlands Within a River Network to Assess Nitrate Removal and Inform Watershed Management

Aquatic nitrate removal depends on interactions throughout an interconnected network of lakes, wetlands, and river channels. Herein, we present a network‐based model that quantifies nitrate‐nitrogen and organic carbon concentrations through a wetland‐river network and estimates nitrate export from the watershed. This model dynamically accounts for multiple competing limitations on nitrate removal, explicitly incorporates wetlands in the network, and captures hierarchical network effects and spatial interactions. We apply the model to the Le Sueur Basin, a data‐rich 2,880 km2 agricultural landscape in southern Minnesota and validate the model using synoptic field measurements during June for years 2013–2015. Using the model, we show that the overall limits to nitrate removal rate via denitrification shift between nitrate concentration, organic carbon availability, and residence time depending on discharge, characteristics of the waterbody, and location in the network. Our model results show that the spatial context of wetland restorations is an important but often overlooked factor because nonlinearities in the system, e.g., deriving from switching of resource limitation on denitrification rate, can lead to unexpected changes in downstream biogeochemistry. Our results demonstrate that reduction of watershed‐scale nitrate concentrations and downstream loads in the Le Sueur Basin can be most effectively achieved by increasing water residence time (by slowing the flow) rather than by increasing organic carbon concentrations (which may limit denitrification). This framework can be used toward assessing where and how to restore wetlands for reducing nitrate concentrations and loads from agricultural watersheds.This research was funded by NSF grant EAR-1209402 under the Water Sustainability and Climate Program (WSC): REACH (REsilience under Accelerated CHange)NSF grant EAR-1242458 under Science Across Virtual Institutes (SAVI): LIFE (Linked Institutions for Future EarthA.T.H. acknowledges support provided by NSF grant EAR- 1415206 under the Science, Engineering and Education for Sustainability (SEES

High--order connected moments expansion for the Rabi Hamiltonian

We analyze the convergence properties of the connected moments expansion (CMX) for the Rabi Hamiltonian. To this end we calculate the moments and connected moments of the Hamiltonian operator to a sufficiently large order. Our large--order results suggest that the CMX is not reliable for most practical purposes because the expansion exhibits considerable oscillations.Comment: 12 pages, 5 figures, 1 tabl

Assessing the Role of Photochemistry in Driving the Composition of Dissolved Organic Matter in Glacier Runoff

Dissolved organic matter (DOM) in glacier runoff is aliphatic-rich, yet studies have proposed that DOM originates mainly from allochthonous, aromatic, and often aged material. Allochthonous organic matter (OM) is exposed to ultraviolet radiation both in atmospheric transport and post-deposition on the glacier surface. Thus, we evaluate photochemistry as a mechanism to account for the compositional disconnect between allochthonous OM sources and glacier runoff DOM composition. Six endmember OM sources (including soils and diesel particulate matter) were leached and photo-irradiated for 28 days in a solar simulator, until >90% of initial chromophoric DOM was removed. Ultrahigh-resolution mass spectrometry was used to compare the molecular composition of endmember leachates pre- and post-irradiation to DOM in supraglacial and bulk runoff from the Greenland Ice Sheet and Juneau Icefield (Alaska), respectively. Photoirradiation drove molecular level convergence between the initially aromatic-rich leachates and aromatic-poor glacial samples, selectively removing aromatic compounds (−80 ± 19% relative abundance) and producing aliphatics (+75 ± 35% relative abundance). Molecular level glacier runoff DOM composition was statistically indistinguishable to post-irradiation leachates. Bray-Curtis analysis showed substantial similarity in the molecular formulae present between glacier samples and post-irradiation leachates. Post-irradiation leachates contained 84 ± 7.4% of the molecular formulae, including 72 ± 17% of the aliphatic formulae, detected in glacier samples. Our findings suggest that photodegradation, either in transit to or on glacier surfaces, could provide a mechanistic pathway to account for the disconnect between proposed aromatic, aged sources of OM and the aliphatic-rich fingerprint of glacial DOM.Megan I. Behnke is thanked for collecting the Alaskan soil samples, Stephanie McColaugh for collecting the Russell Glacier samples, Casey Luzius for help with leachate preparations, and Sarah Ellen Johnston for assistance with DOC analyses. Funding Source: This study was supported by NSF, DEB 1145932 and OCE 1333157 to R. G. M. Spencer. Funding was provided by Alaska EPSCoR (OIA-1757348). A portion of this work was performed in the Ion Cyclotron Resonance User Facility at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Division of Chemistry and Division of Materials Research through DMR 16-44779, and the State of Florida.Ye

Dirac equation with coupling to 1/r singular vector potentials for all angular momenta

We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term in the Dirac equation itself not for the traditional and more singular 1/r^2 term in the resulting second order differential equation. Consequently, the validity of the solution is for a wider energy spectrum. As examples, we consider the Hulthen and Eckart potentials.Comment: 7 page

Shedding light on plant litter decomposition: Advances, implications and new directions in understanding the role of photodegradation

Litter decomposition contributes to one of the largest fluxes of carbon (C) in the terrestrial biosphere and is a primary control on nutrient cycling. The inability of models using climate and litter chemistry to predict decomposition in dry environments has stimulated investigation of non-traditional drivers of decomposition, including photodegradation, the abiotic decomposition of organic matter via exposure to solar radiation. Recent work in this developing field shows that photodegradation may substantially influence terrestrial C fluxes, including abiotic production of carbon dioxide, carbon monoxide and methane, especially in arid and semi-arid regions. Research has also produced contradictory results regarding controls on photodegradation. Here we summarize the state of knowledge about the role of photodegradation in litter decomposition and C cycling and investigate drivers of photodegradation across experiments using a meta-analysis. Overall, increasing litter exposure to solar radiation increased mass loss by 23% with large variation in photodegradation rates among and within ecosystems. This variation was tied to both litter and environmental characteristics. Photodegradation increased with litter C to nitrogen (N) ratio, but not with lignin content, suggesting that we do not yet fully understand the underlying mechanisms. Photodegradation also increased with factors that increased solar radiation exposure (latitude and litter area to mass ratio) and decreased with mean annual precipitation. The impact of photodegradation on C (and potentially N) cycling fundamentally reshapes our thinking of decomposition as a solely biological process and requires that we define the mechanisms driving photodegradation before we can accurately represent photodegradation in global C and N models. © 2012 US Government

Identification of dissolved organic matter size components in freshwater and marine environments

Dissolved organic matter (DOM) in the transition zone from freshwater to marine systems was analyzed with a new approach for parameterizing the size distribution of organic compounds. We used size-exclusion chromatography for molecular size analysis and quantified colored DOM (CDOM) on samples from two coastal environments in the Baltic Sea (Roskilde Fjord, Denmark and Gulf of Gdansk, Poland). We applied a Gaussian decomposition method to identify peaks from the chromatograms, providing information beyond bulk size properties. This approach complements methods where DOM is separated into size classes with pre-defined filtering cutoffs, or methods where chromatograms are used only to infer average molecular weight. With this decomposition method, we extracted between three and five peaks from each chromatogram and clustered these into three size groups. To test the applicability of our method, we linked our decomposed peaks with salinity, a major environmental driver in the freshwater-marine continuum. Our results show that when moving from freshwater to low-salinity coastal waters, the observed steep decrease of apparent molecular weight is mostly due to loss of the high-molecular-weight fraction (HMW; >2 kDa) of CDOM. Furthermore, most of the CDOM absorbance in freshwater originates from HMW DOM, whereas the absorbing moieties are more equally distributed along the smaller size range (<2 kDa) in marine samples.Peer reviewe