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A graph theoretical approach to the analysis, comparison, and enumeration of crystal structures
(2008)
As an alternative approach to lattices and space groups, this work explores graph theory as a means to model crystal structures. The approach uses quotient graphs and nets - the graph theoretical equivalent of cells and lattices - to represent crystal structures. After a short review of related work, new classes of cycles in nets are introduced and their ability to distinguish between non-isomorphic nets and their computational complexity are evaluated. Then, two methods to estimate a structure’s density from the corresponding net are proposed. The first uses coordination sequences to estimate the number of nodes in a sphere, whereas the second method determines the maximal volume of a unit cell. Based on the quotient graph only, methods are proposed to determine whether nets consist of islands, chains, planes, or penetrating, disconnected sub-nets. An algorithm for the enumeration of crystal structures is revised and extended to a search for structures possessing certain properties. Particular attention is given to the exclusion of redundant nets and those, which, by the nature of their connectivity, cannot correspond to a crystal structure. Nets with four four-coordinated nodes, corresponding to sp3 hybridised carbon polymorphs with four atoms per unit cell, are completely enumerated in order to demonstrate the approach. In order to render quotient graphs and nets independent from crystal structures, they are reintroduced in a purely graph-theoretical way. Based on this, the issue of iso- and automorphism of nets is reexamined. It is shown that the topology of a net (that is the bonds in a crystal) constrains severely the symmetry of the embedding (that is the crystal), and in the case of connected nets the space group except for the setting. Several examples are studied and conclusions on phases are drawn (pseudo-cubic FeS2 versus pyrite; α- versus β- quartz; marcasite- versus rutile-like phases). As the automorphisms of certain quotient graphs stipulate a translational symmetry higher than an arbitrary embedding of the corresponding net would show, they are examined in more detail and a method to reduce the size of such quotient graphs is proposed. Besides two instructional examples with 2-dimensional graphs, the halite, calcite, magnesite, barytocalcite, and a strontium feldspar structures are discussed. For some of the structures it is shown that the quotient graph which is equivalent to a centred cell is reduced to a quotient graph equivalent to the primitive cell. For the partially disordered strontium feldspar, it is shown that even if it could be annealed to an ordered structure, the unit cell would likely remain unchanged. For the calcite and barytocalcite structures it is shown that the equivalent nets are not isomorphic.
The Late Tertiary to Quaternary evolution of the Ntem interior delta in SW Cameroon shall be modelled. A step fault was formed along neotectonically remobilized Precambrian structures. Uncalibrated 14C-datations in this ‘sediment trap’ show Pleistocene to Holocene ages. Both within and below the interior delta pebbles and clasts which are cemented in an iron and manganese matrix were found. These ‘fanglomerates’ are used to discuss different processes of the younger evolution also concerning climatic fluctuations in the study area.
Appropriate precautions in the case of flood occurrence often require long lead times (several days) in hydrological forecasting. This in turn implies large uncertainties that are mainly inherited from the meteorological precipitation forecast. Here we present a case study of the extreme flood event of August 2005 in the Swiss part of the Rhine catchment (total area 34 550 km2). This event caused tremendous damage and was associated with precipitation amounts and flood peaks with return periods beyond 10 to 100 years. To deal with the underlying intrinsic predictability limitations, a probabilistic forecasting system is tested, which is based on a hydrological-meteorological ensemble prediction system. The meteorological component of the system is the operational limited-area COSMO-LEPS that downscales the ECMWF ensemble prediction system to a horizontal resolution of 10 km, while the hydrological component is based on the semi-distributed hydrological model PREVAH with a spatial resolution of 500 m. We document the setup of the coupled system and assess its performance for the flood event under consideration. We show that the probabilistic meteorological-hydrological ensemble prediction chain is quite effective and provides additional guidance for extreme event forecasting, in comparison to a purely deterministic forecasting system. For the case studied, it is also shown that most of the benefits of the probabilistic approach may be realized with a comparatively small ensemble size of 10 members.
In order to quantitatively analyse the chemical and dynamical evolution of the polar vortex it has proven extremely useful to work with coordinate systems that follow the vortex flow. We propose here a two-dimensional quasi-Lagrangian coordinate system {X i, delta X i}, based on the mixing ratio of a long-lived stratospheric trace gas i, and its systematic use with i = N2O, in order to describe the structure of a well-developed Antarctic polar vortex. In the coordinate system {X i, delta X i} the mixing ratio X i is the vertical coordinate and delta X i = X i(theta) - X i vort(theta) is the meridional coordinate (X i vort(theta) being a vertical reference profile in the vortex core). The quasi-Lagrangian coordinates {X i, delta X i} persist for much longer time than standard isentropic coordinates, potential temperature theta and equivalent latitude Phi e, do not require explicit reference to geographic space, and can be derived directly from high-resolution in situ measurements. They are therefore well-suited for studying the evolution of the Antarctic polar vortex throughout the polar winter with respect to the relevant chemical and microphysical processes. By using the introduced coordinate system {X N2O, delta X N2O} we analyze the well-developed Antarctic vortex investigated during the APE-GAIA (Airborne Polar Experiment – Geophysica Aircraft in Antarctica – 1999) campaign (Carli et al., 2000). A criterion, which uses the local in-situ measurements of X i=X i(theta) and attributes the inner vortex edge to a rapid change (delta-step) in the meridional profile of the mixing ratio X i, is developed to determine the (Antarctic) inner vortex edge. In turn, we suggest that the outer vortex edge of a well-developed Antarctic vortex can be attributed to the position of a local minimum of the X H2O gradient in the polar vortex area. For a well-developed Antarctic vortex, the delta X N2O-parametrization of tracer-tracer relationships allows to distinguish the tracer inter-relationships in the vortex core, vortex boundary region and surf zone and to examine their meridional variation throughout these regions. This is illustrated by analyzing the tracer-tracer relationships X i : X N2O obtained from the in-situ data of the APE-GAIA campaign for i = CFC-11, CFC-12, H-1211 and SF6. A number of solitary anomalous points in the CFC-11 : N2O correlation, observed in the Antarctic vortex core, are interpreted in terms of small-scale cross-isentropic dispersion.
Large-scale hydrological modelling has become increasingly wide-spread during the last decade. An annual workshop series on large-scale hydrological modelling has provided, since 1997, a forum to the German-speaking community for discussing recent developments and achievements in this research area. In this paper we present the findings from the 2007 workshop which focused on advances and visions in large-scale hydrological modelling. We identify the state of the art, difficulties and research perspectives with respect to the themes "sensitivity of model results", "integrated modelling" and "coupling of processes in hydrosphere, atmosphere and biosphere". Some achievements in large-scale hydrological modelling during the last ten years are presented together with a selection of remaining challenges for the future.
In 1998 the German Universities of Kassel and Giessen organised a workshop on water and solute transport in large drainage basins. The workshop focused on analysing and summarising the state of research, existing problems and perspectives in this research area. It was the second of a series of annual workshops since 1997 that became an important discussion forum for the German-speaking research community in the field of hydrological modelling. Now the 11th Workshop on Large-scale Hydrological Modelling referred to the same questions as posed in 1998 in order to evaluate the developments and advances of the last ten years. Based on keynote presentations, the workshop focused on discussion in working groups where also posters were presented. This volume of "Advances in Geosciences" comprises seven papers referring to the poster contributions. At the end of the volume, an overview paper summarises the outcome of the workshop presentations and discussions (Doll et al.). ...
The crude oil constituents benzene, toluene, ethylbenzene, and the three xylene isomers (BTEX) are the dominating groundwater contaminants originating from surface spill accidents by oil production facilities and with gasoline and jet fuel. Thereby BTEX posing a threat to the world´s scarce drinking water resources due to their water solubility and toxicity. An active remediation cleanup involving a BTEX event proves not only to be very expensive but almost impossible when it comes to the complete removal of contaminants from the subsurface. A favoured and common practice is combining an active remediation process focussing on the source of contamination coupled together with the monitoring of the residual contamination in the subsurface (monitored natural attenuation; MNA). MNA include all naturally occuring biological, chemical and physical processes in the subsurface. The general goal of this work was to improve the knowledge of biodegradation of aromatic hydrocarbons under anaerobic conditions in groundwater. For this groundwater and soil at the former military underground storage tank (UST) site Schäferhof – Süd near Nienburg/Weser (Niedersachsen, Germany) were sampled and analysed. The investigations were done in collaboration of the Umweltbundesamt, the universitys of Frankfurt and Bremen and the alphacon GmbH Ganderkesee. To investigate the extent of groundwater contamination, the terminal electron acceptor processes (TEAPs) and the metabolites of BTEX degradation in groundwater, six observation wells were sampled at regular intervals between January 2002 and September 2004. The wells were positioned in order to cover the upstream, the source area and the downstream of the presumed contamination source. Additionally, vertical sediment profiles were sampled and investigated with respect to spreading and concentration of BTEX in the subsurface. A large residual contamination involving BTEX is present in soil and groundwater at the studied locality. Maximum BTEX concentration values of 17 mg/kg were recorded in analysing sediment in the unsaturated zone. In the capillary fringe, values of 450 mg/kg were recorded (October 2004) and in the saturated zone maximum values of 6.7 mg/kg BTEX were detected. The groundwater samples indicate increasing BTEX concentrations in the groundwater flow direction (from 532 µg/l up to 3300 µg/l (mean values)). Biodegradation of aromatic hydrocarbons under anaerobic conditions in the sub surface at contaminated sites is characterised by generation of metabolites. From the monoaromatic hydrocarbons BTEX metabolites such as benzoic acid (BA) and the methylated homologs and C1-and C2-benzyl-succinic acids (BSA) are generated as intermediates. A solid-phase extraction method based on octadecyl-bonded silica sorbent has been developed to concentrate such metabolite compounds from water samples followed by derivatization and gas chromatography/mass spectrometry (GC/MS) of the extracts. The recovery rate range between 75 and 97%. The method detection limit was 0.8 µg/l. Organic acids were identified as metabolic by-products of biodegradation. Benzoic acid, C1-, C2- and C3-benzoic acid were determined in all contaminated wells with considerable concentrations. Furthermore, the depletion of the dominant terminal electron acceptors (TEAs) oxygen, nitrate, and sulphate and the production of dissolved ferrous iron and methane in groundwater indicate biological mediated processes in the plume evidently proving the occurrence of NA. A large overlap of different redox zones at the studied part of the plume has been observed. A important finding in this study is the strong influence of groundwater level fluctuations on the BTEX concentration in groundwater. A very dry summer in 2003 was recorded during the monitoring period, resulting on site in a drop of the groundwater level to 1.7 m and a concomitant increase of BTEX concentrations from 240 µg/l to 1300 µg/l. The groundwater level fluctuations, natural degradation and retention processes essentially influence BTEX concentrations in the groundwater. Groundwater level fluctuations have by far a stronger influence than the influence of biological degradation. Increasing BTEX concentrations are hence not a consequence of limited biological degradation. Another part of the study was to observe the isotopic fractionation of the electron acceptor Fe(III), due to biologically mediated reduction of Fe(III) to the watersoluble Fe(II) at the site and first field data are presented. Both groundwater and sediment samples were analysed with respect to their Fe isotopic compositions using high mass resolution Multi Collector-Inductively Coupled Plasma-Mass Spectrometry (MC-ICP-MS). The delta56Fe -values of groundwater samples taken from observation wells located downstream of the source area were isotopically lighter than delta56Fe -values obtained from groundwater in the uncontaminated well. The Fe isotopic composition of most parts of the sediment profile was similar to the Fe isotopic composition of uncontaminated groundwater. Thus, a significant iron isotope fractionation can be observed between sediment and groundwater downstream of the BTEX contamination.
This study presents an evaluation of a pulse height condensation particle counter (PH-CPC) and an expansion condensation particle counter (E-CPC) in terms of measuring ambient and laboratory-generated molecular and ion clusters. Ambient molecular cluster concentrations were measured with both instruments as they were deployed in conjunction with an ion spectrometer and other aerosol instruments in Hyytiälä, Finland at the SMEAR II station between 1 March and 30 June 2007. The observed cluster concentrations varied and ranged from some thousands to 100 000 cm -3. Both instruments showed similar (within a factor of ~5) concentrations. An average size of the detected clusters was approximately 1.8 nm. As the atmospheric measurement of sub 2-nm particles and molecular clusters is a challenging task, we conclude that most likely we were unable to detect the smallest clusters. Nevertheless, the reported concentrations are the best estimates to date for minimum cluster concentrations in a boreal forest environment.
The ambient and laboratory molecular and ion clusters were investigated. Here we present data on the ambient concentrations of both charged and uncharged molecular clusters as well as the performance of a pulse height condensation particle counter (PH-CPC) and an expansion condensation particle counter (E-CPC). The ambient molecular cluster concentrations were measured using both instruments, and they were deployed in conjunction with ion spectrometers and other aerosol instruments in Hyytiälä, Finland at the SMEAR II station during 1 March to 30 June 2007. The observed cluster concentrations varied and were from ca. 1000 to 100 000 cm−3. Both instruments showed similar concentrations. The average size of detected clusters was approximately 1.8 nm. As the atmospheric measurements at sub 2-nm particles and molecular clusters are a challenging task, and we were most likely unable to detect the smallest clusters, the reported concentrations are our best estimates for minimum cluster concentrations in boreal forest environment.