Analytical solutions for non-linear conversion of a porous solid particle in a gas–I. Isothermal conversion

Analytical description are presented for non-linear heterogeneous conversion of a porous solid particle reacting with a surrounding gas. Account has been taken of a reaction rate of general order with respect to gas concentration, intrinsic reaction surface area and pore diffusion, which change with solid conversion and external film transport. Results include expressions for the concentration distributions of the solid and gaseous reactant, the propagation velocity of the conversion zone inside the particle, the conversion time and the conversion rate. The complete analytical description of the non-linear conversion process is based on a combination of two asymptotic solutions. The asymptotic solutions are derived in closed form from the governing non-linear coupled partial differential equations pertaining to conservation of mass of solid and gaseous reactant, considering the limiting cases of a small and large Thiele modulus, respectively. For a small Thiele modulus, the solutions correspond to conversion dominated by reaction kinetics. For a large Thiele modulus, conversion is strongly influenced by internal and external transport processes and takes place in a narrow zone near the outer surface of the particle: solutions are derived by employing boundary layer theory. In Part II of this paper the analytical solutions are extended to non-isothermal conversion and are compared with results of numerical simulations

Analytical solutions for non-linear conversion of a porous solid particle in a gas–II. Non-isothermal conversion and numerical verification

In Part I, analytical solutions were given for the non-linear isothermal heterogeneous conversion of a porous solid particle. Account was taken of a reaction rate of general order with respect to the gas reactant, intrinsic reaction surface area and effective pore diffusion, which change with solid conversion and external film transport. In this part, the analytical solutions are extended to non-isothermal conversion. Analytical solutions for the particle overshoot temperature due to heat of reaction are derived from the governing differential equation pertaining to conservation of energy, considering the limiting cases of small and large Thiele moduli. The solutions are used to assess the effect of interaction between chemical reaction rate and particle overshoot temperature on particle conversion. The analytical solutions are shown to compare favourably with numerical simulation results

Fuzzy Transfer Pricing World: On the Analysis of Transfer Pricing with Fuzzy Logic Techniques

The arm’s length analysis of international transfer prices of multinational firms lacks sound methodological approach of the so-called function and risk analysis. In practice, such analyses are descriptive. Derived from Zadeh’s mathematical theory of fuzzy sets, this paper investigates a quantitative approach to identify the function and risk pattern of related parties of multinational companies. We illustrate our fuzzy logic approach with a simple case.

Exciton Relaxation Cascade in Two-dimensional Transition-metal dichalcogenides

Monolayers of transition-metal dichalcogenides (TMDs) are characterized by an extraordinarily strong Coulomb interaction giving rise to tightly bound excitons with binding energies of hundreds of meV. Excitons dominate the optical response as well as the ultrafast dynamics in TMDs. As a result, a microscopic understanding of exciton dynamics is the key for technological application of these materials. In spite of this immense importance, elementary processes guiding the formation and relaxation of excitons after optical excitation of an electron-hole plasma has remained unexplored to a large extent. Here, we provide a fully quantum mechanical description of momentum- and energy-resolved exciton dynamics in monolayer molybdenum diselenide (MoSe$_2$) including optical excitation, formation of excitons, radiative recombination as well as phonon-induced cascade-like relaxation down to the excitonic ground state. Based on the gained insights, we reveal experimentally measurable features in pump-probe spectra providing evidence for the exciton relaxation cascade

Tidal disruptions in circumbinary disks. II: Observational signatures in the reverberation spectra

Supermassive Binary Black Holes (SMBBHs) with sub-pc separations form in the course of galaxy mergers, if both galaxies harbour massive black holes. Clear observational evidence for them however still eludes us. We propose a novel method of identifying these systems by means of reverberation mapping their circumbinary disk after a tidal disruption event has ionized it. The tidal disruption of a star at the secondary leads to strong asymmetries in the disk response. We model the shape of the velocity--delay maps for various toy disk models and more realistic gas distributions obtained by SPH simulations. The emissivity of the ionized disk is calculated with {\em Cloudy}. We find peculiar asymmetries in the maps for off center ionizing sources that may help us constrain geometrical parameters of a circumbinary disk such as semi-major axis and orbital phase of the secondary, as well as help strengthen the observational evidence for sub-parsec SMBBHs as such.Comment: 10 pages, 5 figures. Accepted for publication in Ap

Spatio-temporal dynamics in graphene

Temporally and spectrally resolved dynamics of optically excited carriers in graphene has been intensively studied theoretically and experimentally, whereas carrier diffusion in space has attracted much less attention. Understanding the spatio-temporal carrier dynamics is of key importance for optoelectronic applications, where carrier transport phenomena play an important role. In this work, we provide a microscopic access to the time-, momentum-, and space-resolved dynamics of carriers in graphene. We determine the diffusion coefficient to be $D \approx 360$cm$^{2}$/s and reveal the impact of carrier-phonon and carrier-carrier scattering on the diffusion process. In particular, we show that phonon-induced scattering across the Dirac cone gives rise to back-diffusion counteracting the spatial broadening of the carrier distribution

Changes in forest acreage between 1800 and 2000 in the Upper Bavarian Fünfseenland and their dependence on site conditions

Quantitative Veränderungen der Waldfläche im Laufe der letzten beiden Jahrhunderte für bestimmte Gebiete gehen aus zahlreichen Arbeiten zur Kulturlandschaftsanalyse hervor, die auf der Grundlage von geographischen Informationssystemen (GIS) durchgeführt wurden. Diese Untersuchungen beschäftigen sich in der Regel mit Flächenverschiebungen zwischen einzelnen Kulturarten und berücksichtigen standortskundliche Faktoren meist nicht oder nur indirekt. BENDER (2002, S.20 ff) beispielsweise verwendet pflanzensoziologische Aufnahmen im Gelände, um den Standort in seine Untersuchung mit einzubeziehen. Im Auftrag des Bundesamtes für Naturschutz wurde von GLASER (2004) eine deutschlandweite Erhebung historisch alter Waldstandorte durchgeführt, die sich mit der Analyse von Fläche und Baumartenzusammensetzung historisch alter und neuer Wälder beschäftigt. Daten zu Waldflächenverlusten, die für eine Bewertung der Waldflächenentwicklung unerlässlich sind, gehen daraus nicht direkt hervor. Daneben war es Ziel der Untersuchung von GLASER (2004), einen Datenbestand für weitergehende Fragestellungen aufzubauen. Das in dieser Untersuchung aufgebaute GIS ist bis zu einem Maßstab von 1:100.000 einsetzbar. Die Verwendbarkeit beschränkt sich daher auf großflächige, übersichtsartige Auswertungen (GLASER 2004, S. 123). UEBERFUHR & MIETKE (2003) haben für den Freistaat Sachsen eine Waldflächenbilanz von 1800 bis 2000 mit dem Zielmaßstab 1:50.000 erstellt. Ökologische Aspekte wurden dabei durch die Gliederung der Ergebnisse nach Wuchsbezirken berücksichtigt. Auf dieser Grundlage können jedoch keine qualitativen Aussagen über konkrete Waldflächen getroffen werden. Eine GIS-basierte Untersuchung der Standortsabhängigkeit der Waldflächenentwicklung liegt daher nahe, wurde aber bislang nur selten mit quantitativen Methoden in Angriff genommen (JANSEN 2005). Die kombinierte Nutzung historischer und aktueller Karten der Waldbedeckung mit bodenkundlichen Standortskarten vergleichbaren Maßstabs ist deshalb ein vielversprechender Ansatz. Ziel der vorliegenden Arbeit ist es daher, am Beispiel des oberbayerischen Fünfseenlandes darzustellen, in wieweit die Standortseigenschaften die Waldflächenentwicklung der letzten 200 Jahre beeinflusst haben. Die Analyse gründet sich auf ein speziell für diesen Zweck erstelltes GIS. Als Datengrundlage dienen alte Flurkarten zur Rekonstruktion der Waldfläche von 1800, der aktuelle Stand der Waldfläche des Digitalen Basis-Landschaftsmodells und vektorisierte Bodenkarten im Maßstab 1:25.000. Das GIS ist bis zu einem Maßstab von 1:25.000 einsetzbar und liefert dadurch sehr detaillierte Informationen über die Beziehung zwischen Standort und Waldflächenentwicklung.This paper quantifies changes in forest-acreage since the 19th century on the basis of historical cadastral maps and investigates the role of site conditions within the complex of circumstances influencing that development. As a study-area, the Fünfseenland, Upper Bavaria, a popular recreation-area with valuable ecological landscape-structures situated close to the city of Munich, was chosen. The study contributes to the rational appreciation of conflicting economical and ecological values. A geographical information system satisfying high standards of accuracy was set up for this purpose. Intersection of historical and present-day woodland cover yielded the land cover categories afforested woodland, cleared woodland, permanent woodland and permanent open land. Effects of site-conditions on the development of forest-acreage were quantified by a preference index measuring the difference between the percentage of a soil-types area in one of the land cover categories and the percentage of its total acreage in the whole study area. Since 1800, there has been a very small net increase of forest acreage for the total study area, from 38.1 % in 1800 to 38.3 % today. However, substantial displacements of wooded area are hidden in that figure: On 7.9 % of the woodlands were cleared since 1800, and afforestation took place on 8.2 % of the study area. Large forest areas were cleared in the north-eastern parts, situated closest to Munich, whereas large areas of new forest were created by afforestation in former clearings and at the edges of old forests in the western and southwestern part of the study area. Only a certain part of those displacements can be explained by soilproperties. Since 1800 the major reason for afforestation was the abandonment of small agricultural businesses and pastures in public ownership. Abandoned acreages were often acquired by tycoons or aristocrats and afforested without consideration of soil-properties. As a consequence, the proportion of afforestations, which can be explained by soil-properties, is only 5.4 %. On the other hand 43.0 % of woodland clearings, can be explained by soil-properties, which appears to be more substantial. However, large parts of these soil-related clearings took place in the north-east of the study area (inlay map 3), where the statistical effect of soils is confounded with probable socio-economical effects of the expanding city of Munich. The GIS designed in this study, allows locating old forests and new forests with certain site conditions easily and accurately. It can be used as a base for future studies, inquiring the structure of plant and animal communities of old versus new forests and defining corresponding indicator species. The GIS offers the high precision needed for such studies, including every forested area larger than 0.1 hectare. The GIS offers practical uses for land-use administrations: The department of agriculture and forestry can use it for supporting decisions of clearing or afforestation. The departments of nature conservation and landscape planning can locate sensitive forest habitats. Thus, the influence of management on landscape-structure can be quantified and negative effects on the natural environment can be minimised