Stability of preconditioned finite volume schemes at low Mach numbers

In [4], Guillard and Viozat propose a finite volume method for the simulation of inviscid steady as well as unsteady flows at low Mach numbers, based on a preconditioning technique. The scheme satisfies the results of a single scale asymptotic analysis in a discrete sense and comprises the advantage that this can be derived by a slight modification of the dissipation term within the numerical flux function. Unfortunately, it can be observed by numerical experiments that the preconditioned approach combined with an explicit time integration scheme turns out to be unstable if the time step Dt does not satisfy the requirement to be O(M2) as the Mach number M tends to zero, whereas the corresponding standard method remains stable up to Dt=O(M), M to 0, which results from the well-known CFL-condition. We present a comprehensive mathematical substantiation of this numerical phenomenon by means of a von Neumann stability analysis, which reveals that in contrast to the standard approach, the dissipation matrix of the preconditioned numerical flux function possesses an eigenvalue growing like M-2 as M tends to zero, thus causing the diminishment of the stability region of the explicit scheme. Thereby, we present statements for both the standard preconditioner used by Guillard and Viozat [4] and the more general one due to Turkel [21]. The theoretical results are after wards confirmed by numerical experiments.

Composition and stability of organic matter fractions in soils under different land use regimes

Soil organic matter (SOM) vitally impacts all soil functions and plays a key role in the global carbon (C) cycle. More than 70% of the terrestric C stocks that participate in the active C cycle are stored in the soil. Therefore, quantitative knowledge of the rates of C incorporation into SOM fractions of different residence time is crucial to understand and predict the sequestration and stabilization of soil organic carbon (SOC). Consequently, there is a need of fractionation procedures that are capable of isolating functionally SOM fractions, i.e. fractions that are defined by their stability. The literature generally refers to three main mechanisms of SOM stabilization: protection of SOM from decomposition by (i) its structural composition, i.e. recalcitrance, (ii) spatial inaccessibility and/or (iii) interaction with soil minerals and metal ions. One of the difficulties in developing fractionation procedures for the isolation of functional SOM fractions is the marked heterogeneity of the soil environment with its various stabilization mechanisms – often several mechanisms operating simultaneously – in soils and soil horizons of different texture and mineralogy. The overall objective of the present thesis was to evaluate present fractionation techniques and to get a better understanding of the factors of SOM sequestration and stabilization. The first part of this study is attended to the structural composition of SOM. Using 13C cross-polarization magic-angle spinning (CPMAS) nuclear magnetic resonance (NMR) spectroscopy, (i) the effect of land use on SOM composition was investigated and (ii) examined whether SOM composition contributes to the different stability of SOM in density and aggregate fractions. The second part of the present work deals with the mineral-associated SOM fraction. The aim was (iii) to evaluate the suitability of chemical fractionation procedures used in the literature for the isolation of stable SOM pools (stepwise hydrolysis, treatments using oxidizing agents like Na2S2O8, H2O2, and NaOCl as well as demineralization of the residue obtained by the NaOCl treatment using HF (NaOCl+HF)) by pool sizes, 13C and 14C data. Further, (iv) the isolated SOM fractions were compared to the inert organic matter (IOM) pool obtained for the investigated soils using the Rothamsted Carbon Model and isotope data in order to see whether the tested chemical fractionation methods produce SOM fractions capable to represent this pool. Besides chemical fractionation, (v) the suitability of thermal oxidation at different temperatures for obtaining stable SOC pools was evaluated. Finally, (vi) the short-term aggregate dynamics and the factors that impact macroaggregate formation and C stabilization were investigated by means of an incubation study using treatments with and without application of 15N labeled maize straw of different degradability (leaves and coarse roots). All treatments were conducted with and without the addition of fungicide. Two study sites with different soil properties and land managements were chosen for these investigations. The first one, located at Rotthalmünster, is a Stagnic Luvisol (silty loam) under different land use regimes. The Ah horizons of a spruce forest and continuous grassland and the Ap and E horizons of two plots with arable crops (continuous maize and wheat cropping) were examined. The soil of the second study site, located at Halle, is a Haplic Phaeozem (loamy sand) where the Ap horizons of two plots with arable crops (continuous maize and rye cropping) were investigated. Both study sites had a C3-/C4-vegetational change on the maize plot for the purpose of tracing the incorporation of the younger, maize-derived C into different SOM fractions and the calculation of apparent C turnover times of these. The Halle site is located near a train station and industrial areas, which caused a contamination with high amounts of fossil C. The investigation of aggregate and density fractions by 13C CPMAS NMR spectroscopy revealed that density fractionation isolated SOM fractions of different composition. The consumption of a considerable part (10–20%) of the easily available O-alkyl-C and the selective preservation of the more recalcitrant alkyl-C when passing from litter to the different particulate organic matter (POM) fractions suggest that density fractionation was able to isolate SOM fractions with different degrees of decomposition. The spectra of the aggregate fractions resembled those of the mineral-associated SOM fraction obtained by density fractionation and no considerable differences were observed between aggregate size classes. Comparison of plant litter, density and aggregate size fractions from soil under different land use showed that the type of land use markedly influenced the composition of SOM. While SOM of the acid forest soil was characterized by a large content (> 50%) of POM, which contained high amounts of spruce-litter derived alkyl-C, the organic matter in the biologically more active grassland and arable soils was dominated by mineral-associated SOM (> 95%). This SOM fraction comprised greater proportions of aryl- and carbonyl-C and is considered to contain a higher amount of microbially-derived organic substances. Land use can alter both, structure and stability of SOM fractions. All applied chemical treatments induced considerable SOC losses (> 70–95% of mineral-associated SOM) in the investigated soils. The proportion of residual C after chemical fractionation was largest in the arable Ap and E horizons and increased with decreasing C content in the initial SOC after stepwise hydrolysis as well as after the oxidative treatments with H2O2 and Na2S2O8. This can be expected for a functional stable pool of SOM, because it is assumed that the more easily available part of SOC is consumed first if C inputs decrease. All chemical treatments led to a preferential loss of the younger, maize-derived SOC, but this was most pronounced after the treatments with Na2S2O8 and H2O2. After all chemical fractionations, the mean 14C ages of SOC were higher than in the mineral-associated SOM fraction for both study sites and increased in the order: NaOCl < NaOCl+HF ≤ stepwise hydrolysis << H2O2 ≈ Na2S2O8. The results suggest that all treatments were capable of isolating a more stable SOM fraction, but the treatments with H2O2 and Na2S2O8 were the most efficient ones. However, none of the chemical fractionation methods was able to fit the IOM pool calculated using the Rothamsted Carbon Model and isotope data. In the evaluation of thermal oxidation for obtaining stable C fractions, SOC losses increased with temperature from 24–48% (200°C) to 100% (500°C). In the Halle maize Ap horizon, losses of the young, maize-derived C were considerably higher than losses of the older C3-derived C, leading to an increase in the apparent C turnover time from 220 years in mineral-associated SOC to 1158 years after thermal oxidation at 300°C. Most likely, the preferential loss of maize-derived C in the Halle soil was caused by the presence of the high amounts of fossil C mentioned above, which make up a relatively large thermally stable C3-C pool in this soil. This agrees with lower overall SOC losses for the Halle Ap horizon compared to the Rotthalmünster Ap horizon. In the Rotthalmünster soil only slightly more maize-derived than C3-derived SOC was removed by thermal oxidation. Apparent C turnover times increased slightly from 58 years in mineral-associated SOC to 77 years after thermal oxidation at 300°C in the Rotthalmünster Ap and from 151 to 247 years in the Rotthalmünster E horizon. This led to the conclusion that thermal oxidation of SOM was not capable of isolating SOM fractions of considerably higher stability. The incubation experiment showed that macroaggregates develop rapidly after the addition of easily available plant residues. Within the first four weeks of incubation, the maximum aggregation was reached in all treatments without addition of fungicide. The formation of water-stable macroaggregates was related to the size of the microbial biomass pool and its activity. Furthermore, fungi were found to be crucial for the development of soil macroaggregates as the formation of water-stable macroaggregates was significantly delayed in the fungicide treated soils. The C concentration in the obtained aggregate fractions decreased with decreasing aggregate size class, which is in line with the aggregate hierarchy postulated by several authors for soils with SOM as the major binding agent. Macroaggregation involved incorporation of large amounts maize-derived organic matter, but macroaggregates did not play the most important role in the stabilization of maize-derived SOM, because of their relatively low amount (less than 10% of the soil mass). Furthermore, the maize-derived organic matter was quickly incorporated into all aggregate size classes. The microaggregate fraction stored the largest quantities of maize-derived C and N – up to 70% of the residual maize-C and -N were stored in this fraction.

Relativistic LCAO with Minimax Principle and New Balanced Basis Sets

Relativistic density functional theory is widely applied in molecular calculations with heavy atoms, where relativistic and correlation effects are on the same footing. Variational stability of the Dirac Hamiltonian is a very important field of research from the beginning of relativistic molecular calculations on, among efforts for accuracy, efficiency, and density functional formulation, etc. Approximations of one- or two-component methods and searching for suitable basis sets are two major means for good projection power against the negative continuum. The minimax two-component spinor linear combination of atomic orbitals (LCAO) is applied in the present work for both light and super-heavy one-electron systems, providing good approximations in the whole energy spectrum, being close to the benchmark minimax finite element method (FEM) values and without spurious and contaminated states, in contrast to the presence of these artifacts in the traditional four-component spinor LCAO. The variational stability assures that minimax LCAO is bounded from below. New balanced basis sets, kinetic and potential defect balanced (TVDB), following the minimax idea, are applied with the Dirac Hamiltonian. Its performance in the same super-heavy one-electron quasi-molecules shows also very good projection capability against variational collapse, as the minimax LCAO is taken as the best projection to compare with. The TVDB method has twice as many basis coefficients as four-component spinor LCAO, which becomes now linear and overcomes the disadvantage of great time-consumption in the minimax method. The calculation with both the TVDB method and the traditional LCAO method for the dimers with elements in group 11 of the periodic table investigates their difference. New bigger basis sets are constructed than in previous research, achieving high accuracy within the functionals involved. Their difference in total energy is much smaller than the basis incompleteness error, showing that the traditional four-spinor LCAO keeps enough projection power from the numerical atomic orbitals and is suitable in research on relativistic quantum chemistry. In scattering investigations for the same comparison purpose, the failure of the traditional LCAO method of providing a stable spectrum with increasing size of basis sets is contrasted to the TVDB method, which contains no spurious states already without pre-orthogonalization of basis sets. Keeping the same conditions including the accuracy of matrix elements shows that the variational instability prevails over the linear dependence of the basis sets. The success of the TVDB method manifests its capability not only in relativistic quantum chemistry but also for scattering and under the influence of strong external electronic and magnetic fields. The good accuracy in total energy with large basis sets and the good projection property encourage wider research on different molecules, with better functionals, and on small effects.

Effects of fertilizer type and rate on partitioning of soil organic matter into pools of different stability

Type and rate of fertilizers influence the level of soil organic carbon (Corg) and total nitrogen (Nt) markedly, but the effect on C and N partitioning into different pools is open to question. The objectives of the present work were to: (i) quantify the impact of fertilizer type and rate on labile, intermediate and passive C and N pools by using a combination of biological, chemical and mathematical methods; (ii) explain previously reported differences in the soil organic matter (SOM) levels between soils receiving farmyard manure with or without biodynamic preparations by using Corg time series and information on SOM partitioning; and (iii) quantify the long-term and short-term dynamics of SOM in density fractions and microbial biomass as affected by fertilizer type and rate and determine the incorporation of crop residues into labile SOM fractions. Samples were taken from a sandy Cambisol from the long-term fertilization trial in Darmstadt, Germany, founded in 1980. The nine treatments (four field replicates) were: straw incorporation plus application of mineral fertilizer (MSI) and application of rotted farmyard manure with (DYN) or without (FYM) addition of biodynamic preparations, each at high (140 – 150 kg N ha-1 year-1; MSIH, DYNH, FYMH), medium (100 kg N ha-1 year-1; MSIM, DYNM, FYMM) and low (50 – 60 kg N ha-1 year-1; MSIL, DYNL, FYML) rates. The main findings were: (i) The stocks of Corg (t ha-1) were affected by fertilizer type and rate and increased in the order MSIL (23.6), MSIM (23.7), MSIH (24.2) < FYML (25.3) < FYMM (28.1), FYMH (28.1). Stocks of Nt were affected in the same way (C/N ratio: 11). Storage of C and N in the modelled labile pools (turnover times: 462 and 153 days for C and N, respectively) were not influenced by the type of fertilizer (FYM and MSI) but depended significantly (p ≤ 0.05) on the application rate and ranged from 1.8 to 3.2 t C ha 1 (7 – 13% of Corg) and from 90 to 140 kg N ha-1 (4-5% of Nt). In the calculated intermediate pool (C/N ratio 7), stocks of C were markedly higher in FYM treatments (15-18 t ha-1) compared to MSI treatments (12-14 t ha-1). This showed that differences in SOM stocks in the sandy Cambisol induced by fertilizer rate may be short-lived in case of changing management, but differences induced by fertilizer type may persist for decades. (ii) Crop yields, estimated C inputs (1.5 t ha-1 year-1) with crop residue, microbial bio¬mass C (Cmic, 118 – 150 mg kg-1), microbial biomass N (17 – 20 mg kg-1) and labile C and N pools did not differ significantly between FYM and DYN treatments. However, labile C increased linearly with application rate (R2 = 0.53) from 7 to 11% of Corg. This also applied for labile N (3.5 to 4.9% of Nt). The higher contents of Corg in DYN treatments existed since 1982, when the first sampling was conducted for all individual treatments. Contents of Corg between DYN and FYM treatments con-verged slightly since then. Furthermore, at least 30% of the difference in Corg was located in the passive pool where a treatment effect could be excluded. Therefore, the reported differences in Corg contents existed most likely since the beginning of the experiment and, as a single factor of biodynamic agriculture, application of bio-dynamic preparations had no effect on SOM stocks. (iii) Stocks of SOM, light fraction organic C (LFOC, ρ ≤ 2.0 g cm-3), light fraction organic N and Cmic decreased in the order FYMH > FYML > MSIH, MSIL for all sampling dates in 2008 (March, May, September, December). However, statistical significance of treatment effects differed between the dates, probably due to dif-ferences in the spatial variation throughout the year. The high proportion of LFOC on total Corg stocks (45 – 55%) highlighted the importance of selective preservation of OM as a stabilization mechanism in this sandy Cambisol. The apparent turnover time of LFOC was between 21 and 32 years, which agreed very well with studies with substantially longer vegetation change compared to our study. Overall, both approaches; (I) the combination of incubation, chemical fractionation and simple modelling and (II) the density fractionation; provided complementary information on the partitioning of SOM into pools of different stability. The density fractionation showed that differences in Corg stocks between FYM and MSI treatments were mainly located in the light fraction, i.e. induced by higher recalcitrance of the organic input in the FYM treatments. Moreover, the use of the combination of biological, chemical and mathematical methods indicated that effects of fertilizer rate on total Corg and Nt stocks may be short-lived, but that the effect of fertilizer type may persist for longer time spans in the sandy Cambisol.

Effects of tillage intensity on soil C, N, and P pools with different stability

Es ist bekannt, dass die Umsatzdynamik der organischen Substanz von der Bodenbearbeitungsintensität abhängt. Bis jetzt sind nur wenige Daten zum Einfluss der Bearbeitungsintensität und des Zwischenfruchtanbaus auf C-, N-, und P-Dynamik im Ober- (0-5 cm Tiefe) und Unterboden (5-25 cm Tiefe) von Lössböden verfügbar. Hauptziele dieser Arbeit waren die (i) Quantifizierung des Einflusses von verschiedenen langzeitig durchgeführten Bearbeitungssystemen auf labile, intermediäre, und passive C- und N-Pools; (ii) Quantifizierung des Einflusses dieser Systeme auf P-Fraktionen mit unterschiedlicher Verfügbarkeit für die Pflanzenaufnahme; (iii) Quantifizierung des Einflusses des Zwischenfruchtanbaus in Verbindung mit einer unterschiedlichen Einarbeitungstiefe der der Zwischenfrüchte auf mineralisierbares C und N. Die Ergebnisse des 1. und 2. Teilexperiments basieren auf Untersuchungen von 4 Langzeitfeldexperimenten (LFE) in Ost- und Süddeutschland, die zwischen 1990 und 1997 durch das Institut für Zuckerrübenforschung angelegt wurden. Jedes LFE umfasst 3 Bearbeitungssysteme: konventionelle Bearbeitung (CT), reduzierte Bearbeitung (RT) und Direktsaat (NT). Die Ergebnisse des 3. Teilexperiments basieren auf einem Inkubationsexperiment. Entsprechend den Hauptfragestellungen wurden folgende Untersuchungsergebnisse beschrieben: (i) Im Oberboden von NT wurden höhere labile C-Vorräte gefunden (C: 1.76 t ha-1, N: 166 kg ha-1), verglichen mit CT (C: 0.44 t ha-1, N: 52 kg ha-1). Im Gegensatz dazu waren die labile- C-Vorräte höher im Unterboden von CT mit 2.68 t ha-1 verglichen zu NT mit 2 t ha-1 und RT mit 1.87 t ha-1. Die intermediären C-Vorräte betrugen 73-85% der gesamten organischen C-Vorräte, intermediäre N-Vorräte betrugen 70-95% des Gesamt-N im Ober- und Unterboden und waren vielfach größer als die labilen und passiven C- und N-Vorräte. Nur im Oberboden konnte ein Effekt der Bearbeitungsintensität auf die intermediären N-Pools mit höheren Vorräten unter NT als CT festgestellt werden. Die passiven C- und N-Pools waren eng mit den mineralischen Bodeneigenschaften verbunden und unabhängig vom Bearbeitungssystem. Insgesamt hat sich gezeigt, dass 14 bis 22 Jahre durchgängige Direktsaatverfahren nur im Oberboden zu höheren labilen C- und N-Vorräten führen, verglichen zu konventionellen Systemen. Dies lässt eine tiefenabhängige Stärke der Dynamik der organischen Bodensubstanz vermuten. (ii) Die Konzentration des Gesamt-P (Pt) im Oberboden war höher in NT (792 mg kg-1) und ~15% höher als die Pt-Konzentration in CT (691 mg kg 1). Die Abnahme der Pt-Konzentration mit zunehmender Bodentiefe war höher in NT als in CT. Dies gilt auch für die einzelnen P-Fraktionen, ausgenommen der stabilsten P-Fraktion (residual-P). Generell hatte das Bearbeitungssystem nur einen kleinen Einfluss auf die P-Konzentration mit höheren Pt-Konzentrationen in Böden unter NT als CT. Dies resultiert vermutlich aus der flacheren Einarbeitung der Pflanzenreste als in CT. (iii) Im Zwischenfruchtexperiment war der Biomassezuwachs von Senf am höchsten und nimmt in der Reihenfolge ab (oberirdischer Ertrag in t / ha): Senf (7.0 t ha-1) > Phacelia (5.7 t ha-1) > Ölrettich (4.4 t ha-1). Damit war potentiell mineralisierbares C und N am höchsten in Böden mit Senfbewuchs. Kumulative CO2- und N2O-Emissionen während der Inkubation unterschieden sich nicht signifikant zwischen den Zwischenfruchtvarianten und waren unabhängig von der Verteilung der Pflanzenreste im Boden. Die kumulativen ausgewaschenen mineralisierten N (Nmin)-Vorräte waren in den brachliegenden Böden am höchsten. Die Nmin-Vorräte waren 51-72% niedriger in den Varianten mit Zwischenfrucht und Einarbeitung verglichen zur Brache. In den Varianten ohne Einarbeitung waren die Nmin-Vorräte 36-55% niedriger verglichen zur Brache. Dies weißt auf einen deutlichen Beitrag von Zwischenfrüchten zur Reduzierung von Nitrat-Auswaschung zwischen Winter und Frühjahr hin. Insgesamt führte reduzierte Bearbeitung zu einer Sequestrierung von C und N im Boden und der Zwischenfruchtanbau führte zu reduzierten N-Verlusten. Die P-Verfügbarkeit war höher unter Direktsaat verglichen zur konventionellen Bearbeitung. Diese Ergebnisse resultieren aus den höheren Konzentrationen der OS in den reduzierten, als in den konventionellen Systemen. Die Ergebnisse zeigen deutlich das Potential von reduzierter Bearbeitung zur Sequestrierung von intermediärem C und N zur Reduzierung von klimarelevanten Treibhausgasen. Gleichzeitig steigen die Konzentrationen an pflanzenverfügaren P-Gehalten. Zwischenfrüchte führen auch zu einem Anstieg der C- und N-Vorräte im Boden, offensichtlich unabhängig von der Zwischenfruchtart.

Optical amplification and stability of spiroquaterphenyl compounds and blends

In this contribution, we present a systematic investigation on a series of spiroquaterphenyl compounds optimised for solid state lasing in the near ultraviolet (UV). Amplified spontaneous emission (ASE) thresholds in the order of 1 μJ/cm2 are obtained in neat (undiluted) films and blends, with emission peaks at 390 1 nm for unsubstituted and meta-substituted quaterphenyls and 400 4 nm for para-ether substituted quaterphenyls. Mixing with a transparent matrix retains a low threshold, shifts the emission to lower wavelengths and allows a better access to modes having their intensity maximum deeper in the film. Chemical design and blending allow an independent tuning of optical and processing properties such as the glass transition.

Adsorption kinetic investigations of phthalocyanine derivatives self assembled monolayers (SAMs) on gold: Temperature influence on the SAM formation process and quality

The ordered nano-structured surfaces, like self-assembled monolayers (SAMs) are of a great scientific interest, due to the low cost, simplicity, and versatility of this method. SAMs found numerous of applications in molecular electronics, biochemistry and optical devices. Phthalocyanine (Pc) complexes are of particular interest for the SAM preparation. These molecules exhibit fascinating physical properties and are chemically and thermally stable. Moreover their complex structure is advantageous for the fabrication of switchable surfaces. In this work the adsorption process of Pcs derivatives, namely, subphthalocyanines (SubPcB) and terbium (2TbPc) sandwich complexes on gold has been investigated. The influence of the molecular concentration, chain length of peripheral groups, and temperature on the film formation process has been examined using a number of techniques. The SAMs formation process has been followed in situ and in real time by means of second harmonic generation (SHG) and surface plasmon resonance (SPR) spectroscopy. To investigate the quality of the SAMs prepared at different temperatures atomic force microscopy (AFM) and X-Ray photoelectron spectroscopy (XPS)measurements were performed. Valuable information about SubPcB and 2TbPc adsorbtion process has been obtained in the frame of this work. The kinetic data, obtained with SHG and SPR, shows the best conformance with the first order Langmuir kinetic model. Comparing SHG and SPR results, it has been found, that the film formation occurs faster than the formation of chemical bonds. Such, the maximum amount of molecules on the surface is reached after 6 min for SubPcB and 30 min for 2TbPc. However, at this time the amount of formed chemicals bonds is only 10% and 40% for SubPcB and 2TbPc, respectively. The most intriguing result, among others, was obtained at T = 2 °C, where the formation of the less dense SAMs have been detected with SHG.However, analyzing XPS and AFM data, it has been revealed, that there is the same amount of molecules on the surface at both temperature T = 2 °C, and T = 21 °C, but the amount of formed chemicals bond is different. At T = 2 °C molecules form aggregates, therefore many of available anchor groups stay unattached.