Weak-noise solution of Fokker–Planck equations with n (>2) variables: A simpler evaluation near equilibrium points

A recent approach to the quasipotential of drift–diffusion models is extended to the case of n>2$n>2$ variables. The quasipotential determines the stationary probability density at weak noise, for some models even with each noise. At equilibrium points, the symmetric n-by-n matrix of its second derivatives is determined by a quadratic (Riccati) equation, and this is now replaced by a linear equation for an antisymmetric matrix of the same size. The resulting density function is unique and smooth near equilibrium points, including when the next term in the noise strength is taken into account.     

Structural investigation of high-tc superconductors under high pressure

Abstract

The results of X-ray investigations of Tl₂Ba₂Ca₂Cu₃O₁₀ show a preferential c-axis decrease under high pressure, leading to a bulk modulus of B = 1370 kbar at 300 K. The results are compared to previous investigations of La₂CuO₄, La_1.8Sr_0.2CuO₄ and Pr₂CuO₄, that show a similar linear compressibility in a- and b- axis direction. The linear compressibility in c-axis direction is dominated by the degeneration of the Cu-O octohedra and by the compressibility of intercalated layers.     

The use of stable isotopes in ecosystem research. First results of a field study with 15N

Terrestrial ecosystems, e.g. forest ecosystems, are characterized by a complex and sensitive network of biotic and abiotic factors and their interactions. By using stable isotopes (e.g. labelled nitrogen compounds), very small addition rates of highly enriched compounds can be applied, which do not change or disturb the investigated system, but provide information about single processes, their interactions and especially about their dynamics.

First results of a field study in the Fichtelgebirge, Northeast-Bavaria, Germany, are presented. The distribution of labelled nitrogen (as ¹⁵N-NH₄ ⁺ and ¹⁵N[sbnd]NO₃ ^?) within a spruce ecosystem (Picea abies (L.) Karst. in competition with understory vegetation of Vaccinium myrtillus, Calluna vulgaris and Deschampsia flexuosa) showed maximum ¹⁵N concentrations in tissues of the understory vegetation. During the first six weeks after the ¹⁵N application, the nitrogen uptake of all investigated species was higher after the ¹⁵N[sbnd]NO₃ ^? treatment than after the ¹⁵N[sbnd]NH₄ ⁺ treatment.     

Nitrogen Isotope Ratios in Different Compartments of a Mixed Stand of Spruce,Larch and Beech Trees and of Understorey Vegetation Including Fungi

Abstract

Natural nitrogen isotope ratios were measured in different compartments (needles or leaves and twigs of different age classes and crown positions, roots and soil of different horizons) of spruce (Picea abies), larch (Larix decidua) and beech (Fagus sylvatica) trees in an 11-year-old mixed stand in the Fichtelgebirge, NE Bavaria, Germany. In addition, samples of understorey vegetation (mainly ericaceous shrubs and grass) and of ectomycorrhizal and saprophytic fungi were analyzed. The δ¹⁵N values found for all samples ranged between ?7.5 and + 4.5‰. No significant differences were found for the nitrogen isotope ratios of the three tree species despite of their evergreen versus deciduous foliage and despite of their different rooting depth. Ericaceous shrubs had the most negative and fungi and soil from the mineral horizon the most positive δ¹⁵N values. Positive δ¹⁵N values of the fungi indicate their ability to utilize organic soil nitrogen, but the data do not unequivocally show that plants forming mycorrhizas profit from this organic nitrogen source.     

Chromatographic approaches for determination of low-molecular mass aldehydes in bio-oil

HPLC–UV and GC/MS determination of aldehydes in bio-oil were evaluated. HPLC–UV preceded by derivatization with 2,4-dinitrophenylhydrazine allows separation and detection of bio-oil aldehydes, but the derivatization affected the bio-oil stability reducing their quantitative applicability. GC/MS determination of aldehydes was reached by derivatization with o-(2,3,4,5,6-pentafluorobenzyl) hydroxylamine hydrochloride. Two approaches for this reaction were evaluated. The first: “in solution derivatization and head space extraction” and the second: “on fiber derivatization SPME”, the latter through an automatic procedure. Both sample treatments allows the quantification of most important aliphatic aldehydes in bio-oil, being the SPME approach more efficient. The aldehyde concentrations in bio-oil were ～2% formaldehyde, ～0.1% acetaldehyde and ～0.05% propionaldehyde.     

Mesopores in USY Zeolites II

Microporous zeolites Na‐Y and K‐Y were converted into the NaNH₄‐Y and KNH₄‐Y modifications by ion exchange being active in dealumination. Removal of framework aluminium and silicon is accompanied by formation of secondary mesopores. Internal mesopores are formed in the centre of zeolite crystals and external pores at their surface. Formation of mesopores changes the sorption behaviour.Residual alkali metal cations as Na⁺ or K⁺ stabilise, however, the framework ≡Si‐O‐Al≡ bonds. Because of inhomogeneous distribution of sodium ions, in NaNH₄‐Y less internal but more external mesopores are formed. Potassium ions of KNH₄‐Y are more homogeneous distributed over the framework why a more balanced formation of secondary pores takes place.