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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.
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.). ...
In vorliegender Studie wurde lebend und tot gesammeltes Schalenmaterial der Europäischen Flussperlmuschel Margaritifera margaritifera verschiedener Lokalitäten in Schweden, Finnland und Deutschland (bzw. Frankreich) sklerochronologisch und isotopengeochemisch untersucht. Sauerstoffisotopen-Zeitreihen, trendbereinigte und standardisierte stabile Kohlenstoffisotopen-Zeitreihen (SSCI) sowie jährliche Zuwachsraten (SGI-Zeitreihen) jeder der acht Populationen sind zu Compound-Chronologien zusammengefasst und auf Zusammenhänge mit Temperatur, Sonnenflecken-Zyklen und Niederschlag untersucht sowie auf Korrelationen mit verschiedenen Klimaindizes (z.B. dem Dipol der Meeres-Oberflächenwasser Temperatur-Anomalien im Nordatlantik, NADP-SST, und der Nordatlantischen Oszillation, NAO) getestet worden. Im Vergleich ergaben sich für die geglätteten Zeitreihen (25-Jahresfilter) Korrelationskoeffizienten von r = 0,57 (SGI Master-Chronologie und NAO) bzw. r = 0,59 (Master-Chronologie) und NADP-SST. Obwohl weder Isotopendaten noch Zuwachschronologien der Muscheln auf hochfrequenten Signalen hohe Korrelationen mit instrumentellen Messdaten aufweisen, sind dekadische Klimaoszillationen deutlich repräsentiert. Mit zunehmendem Lebensalter nimmt der Schalenzuwachs exponentiell ab. Gleichzeitig nähern sich die d13C-Werte der Schale dem d13CDIC-Wert des Wassers, der bei den hier untersuchten Lokalitäten zwischen -9,3 ‰ und -12,7 ‰ lag. Erst im hohen Lebensalter findet also die Schalenbildung nahezu im kohlenstoffisotopischen Gleichgewicht mit dem umgebenden Medium statt. In der Jugend der Tiere hingegen wirken sich lokalitätsspezifische Trends aus. Extrinsische Faktoren führen zu drei Mustern: 1) Trends hin zu stärker negativen d13C-Werten (um etwa -4,5 ‰) in den Bächen Nuortejaurbäcken (NJB) und Grundträsktjärnbäcken (GTB), 2) Trends hin zu weniger stark negativen d13C-Werten (um etwa +4,5 ‰) in den großen Flüssen (GJ: Görjeån, NWS: Tarn/Frankreich) und 3) Schwankungen um etwa ±1,5 ‰ um einen Mittelwert (RG: Regnitz). Der Einfluss auf die d13C-Trends könnte möglicherweise in Veränderungen der Bioproduktivität begründet sein, da sich diese unmittelbar auf den DIC-Pool des umgebenden Milieus und des Habitats auswirkt. In den Sauerstoffisotopen spiegelte sich die geographische Herkunft des untersuchten Materials wider. Die Chronologien der am nördlichsten gelegenen Populationen wiesen d18OMittelwerte von -11,5 ‰ (GJ), bzw. -9,5 ‰ (NJB, GTB) auf, die RG-Chronologie von -7,9 ‰ und die Zeitreihe der NWS von -5,3 ‰. Im Gegensatz zu anderen Arbeiten zeigten die untersuchten Individuen jedoch keinen statistischen Zusammenhang mit annuellen Temperaturdaten. Als beeinflussende Faktoren kommen die Schneeschmelze und die isotopengeochemische Ausprägung des Habitats (See, Fluss, Bach) in Frage. Eine sehr hohe Korrelation von r = -0,74 (25-Jahresfilter) wurde zwischen der Görjeån-Chronologie (d18OAragonit) und Niederschlagsraten für das in der Nähe des Flusses gelegene Jokkmokk festgestellt.
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.
The main objective of the study presented in this paper was to develop an evaluation scheme which is suitable for spatially explicit groundwater vulnerability assessment according to the Water Framework Directive (WFD). Study area was the Hase river catchment, an area of about 3 000 km2 in north-west Germany which is dominated by livestock farming, in particular pig and poultry production. For the Hase river catchment, the first inventory of the WFD led to the conclusion that 98% of the catchment area is "unclear/unlikely" to reach a good groundwater status due to diffuse nitrogen emissions from agriculture. The groundwater vulnerability assessment was embedded in the PartizipA project ("Participative modelling, Actor and Ecosystem Analysis in Regions with Intensive Agriculture", www.partizipa.net), within which a so-called actors´ platform was established in the study area. The objective of the participatory process was to investigate the effects of the WFD on agriculture as well as to discuss groundwater protection measures which are suitable for an integration in the programme of measures. The study was conducted according to the vulnerability assessment concept of the Intergovernmental Panel on Climate Change, considering sensitivity, exposure and adaptive capacity. Sensitivity was computed using the DRASTIC index of natural groundwater pollution potential. Exposure (for a reference scenario) was computed using the STOFFBILANZ nutrient model. Several regional studies were analysed to evaluate the adaptive capacity. From these studies it was concluded that the adaptive capacity in the Hase river catchment is very low due to the economic importance of the agricultural sector which will be significantly affected by groundwater protection measures. As a consequence, the adaptive capacity was not considered any more in the vulnerability assessment. A groundwater vulnerability evaluation scheme is presented which enjoys the advantage that both exposure and sensitivity can be operationalized in a spatially resolved manner (500×500 m grid) by the two models mentioned above. The evaluation scheme was applied in the Hase river catchment. 21% of the catchment was classified as highly vulnerable, another 73% as medium vulnerable. Only 6% of the Hase river catchment has low vulnerability. Grid cells of the high vulnerability class are considered as priority areas for groundwater protection measures in the programme of measures of the WFD. Measures will be particularly effective in the north-eastern part of the catchment where groundwater vulnerability is mainly due to high nitrogen emissions.
The present study was elaborated within the scope of the INTAFERE (Integrated Analysis of Mobile Organic Foreign Substances in Rivers) project which investigates the occurrence of xenobiotics in small freshwater streams with particular consideration of social impact factors. The aim of this study is to investigate the seasonal and spatial variance of organic micropollutants in small fresh water streams and to identify possible sources and sinks. Therefore four small freshwater river systems in Hesse, Germany, have been investigated with respect to common organic pollutants such as: the organophosphates tri-n-butyl phosphate (TBP), tris(2-butoxyethyl)phosphate (TBEP), tris(2-chloroethyl)phosphate (TCEP), tris(1-chloro-2-propyl)phosphate (TCPP), and tris(1,3-dichloro-2-propyl)phosphate (TDCPP), the synthetic musk fragrances 1,3,4,6,7,8-hexahydro-4,6,6,7,8,8-hexa-methylcyclopenta-[g]-2-benzopyran (HHCB) and 7-acetyl-1,1,3,4,4,6-hexamethyl-1,2,3,4-tetrahydronaphthalene (AHTN), the endocrine disruptors bisphenol A (BPA), 4-tert-octylphenol (OP) and the technical isomer mixture of 4-nonylphenol (NP), the herbicide terbutryn [2-(t-butylamino)-4-(ethylamino)-6-(methylthio)-s-triazine] as well as the insect repellent N,N-diethyl-m-toluamide (DEET). Water samples were collected in the time span from September 2003 to September 2006 at 26 sampling locations. The samples were extracted with solid phase extraction (SPE) and analyzed by coupled gas chromatography-mass spectrometry (GC-MS). For quantification the internal standard method was used. The results of the study showed an ubiquitous occurrence of organic pollutants in the fresh water streams of the study area. The organophosphates have been detected in 90 % of the water samples with mean concentrations of 502 ng/l (TCPP), 276 ng/l (TBP), 183 ng/l (TBEP), 118 ng/l (TCEP) and 117 ng/l (TDCPP). Sewage treatment plant (STP) effluents were identified as the dominating source for the chlorinated organophosphates as well as for the synthetic musk fragrances and the insect repellent DEET in the river systems. Consequently the highest concentrations were observed in the Schwarzbach system characterized by the highest proportion of waste water compared to the other river systems. Mean concentration levels of the synthetic musk fragrances HHCB and ATHN were 141 ng/l and 46 ng/l, respectively and 124 ng/l in case of DEET. The synthetic musk fragrances showed a clear seasonal trend with significantly lower concentrations in summer times compared to winter times, which is ascribed to stronger photodegradation and volatization during summer times. In contrast, mean DEET concentrations and loads were significantly higher in summer than in autumn, winter and spring, in parallel with the main insect season. The concentrations of the endocrine disruptors BPA, NP and OP in the river water samples ranged from <20 ng/l to 1927 ng/l, <10 ng/l to 770 ng/l, and <10 ng/l to 420 ng/l, respectively. Whereas OP was present in about 2/3 of the samples, NP and BPA could only be detected in 56% and 13% of the water samples, respectively. BPA levels exceeded in two samples the predicted no-effect concentration (PNEC) for water organisms. In case of NP, highest concentrations and loads were found in September 2003 and decreased significantly since then. In contrast, concentrations and loads of OP which serves in a similar application field remained nearly constant during the sampling period. The decrease of NP can be attributed to the implementation of the European Directive 2003/53/EG, which restricts the use of nonylphenols and nonylphenol ethoxylates since January 2005. However, at the end of the sampling period in September 2006, NP could still be detected at mean concentrations of 18 ng/l in the river waters of the sampling area. Furthermore, absence of NP in several samples from associated STP effluents indicate that the STPs cannot be the only sources for NP found in the river water. The herbicide terbutryn was present in the rivers during the whole sampling period from September 2003 to September 2006 despite a ban on its use as a herbicide from January 2004 on. Terbutryn levels ranged from < 4 ng/l to 5600 ng/l, showing a clear spatial pattern with high terbutryn concentrations in the Weschnitz and Modau river systems and significantly lower terbutryn levels in Schwarzbach and Winkelbach. Results from the analysis of two STP effluents discharging into the Weschnitz and the Modau, respectively, indicate that terbutryn enters the rivers from this source. Furthermore, terbutryn concentrations and loads showed a clear seasonal trend with significantly higher levels in summer and autumn. Obviously, the ban on agricultural use of terbutryn at the end of 2003 had no discernable influence on terbutryn concentration in the rivers because there was no trend of decreasing.
A data set of annual values of area equipped for irrigation for all 236 countries in the world during the time period 1900 - 2003 was generated. The basis for this data product was information available through various online data bases and from other published materials. The complete time series were then constructed around the reported data applying six statistical methods. The methods are discussed in terms of reliability and data uncertainties. The total area equipped for irrigation in the world in 1900 was 53.2 million hectares. Irrigation was mainly practiced in all the arid regions of the globe and in paddy rice areas of South and East Asia. In some temperate countries in Western Europe irrigation was practiced widely on pastures and meadows. The time series suggest a modest rate of increase of irrigated areas in the first half of the 20th century followed by a more dynamic development in the second half. The turn of the century is characterized by an overall consolidating trend resulting at a total of 285.8 million hectares in 2003. The major contributing countries have changed little throughout the century. This data product is regarded as a preliminary result toward an ongoing effort to develop a detailed data set and map of areas equipped for irrigation in the world over the 20th century using sub-national statistics and historical irrigation maps.