Exact solution at integrable coupling of a model for the Josephson effect between small metallic grains

A model is introduced for two reduced BCS systems which are coupled through the transfer of Cooper pairs between the systems. The model may thus be used in the analysis of the Josephson effect arising from pair tunneling between two strongly coupled small metallic grains. At a particular coupling strength the model is integrable and explicit results are derived for the energy spectrum, conserved operators, integrals of motion, and wave function scalar products. It is also shown that form factors can be obtained for the calculation of correlation functions. Furthermore, a connection with perturbed conformal field theory is made.

Integrable coupling in a model for Josephson tunneling between non-identical BCS systems

We extend a recent construction for an integrable model describing Josephson tunneling between identical BCS systems to the case where the BCS systems have different single particle energy levels. The exact solution of this generalized model is obtained through the Bethe ansatz.

A crop-land allocation model: A case study in La Rioja, Spain

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Estimation of electronic coupling in π -stacked donor-bridge-acceptor systems: correction of the two-state model

Comparison of donor-acceptor electronic couplings calculated within two-state and three-state models suggests that the two-state treatment can provide unreliable estimates of Vda because of neglecting the multistate effects. We show that in most cases accurate values of the electronic coupling in a π stack, where donor and acceptor are separated by a bridging unit, can be obtained as Ṽ da = (E2 - E1) μ12 Rda + (2 E3 - E1 - E2) 2 μ13 μ23 Rda2, where E1, E2, and E3 are adiabatic energies of the ground, charge-transfer, and bridge states, respectively, μij is the transition dipole moments between the states i and j, and Rda is the distance between the planes of donor and acceptor. In this expression based on the generalized Mulliken-Hush approach, the first term corresponds to the coupling derived within a two-state model, whereas the second term is the superexchange correction accounting for the bridge effect. The formula is extended to bridges consisting of several subunits. The influence of the donor-acceptor energy mismatch on the excess charge distribution, adiabatic dipole and transition moments, and electronic couplings is examined. A diagnostic is developed to determine whether the two-state approach can be applied. Based on numerical results, we showed that the superexchange correction considerably improves estimates of the donor-acceptor coupling derived within a two-state approach. In most cases when the two-state scheme fails, the formula gives reliable results which are in good agreement (within 5%) with the data of the three-state generalized Mulliken-Hush model

Studies on rainfall variability and the influence of orography and land use on the climate of Peninsular India

The present study helped to understand the trend in rainfall patterns at smaller spatial scales and the large regional differences in the variability of rainfall. The effect of land use and orography on the diurnal variability is also understood. But a better understanding on the long term variation in rainfall is possible by using a longer dataset,which may provide insight into the rainfall variation over country during the past century. The basic mechanism behind the interannual rainfall variability would be possible with numerical studies using coupled Ocean-Atmosphere models. The regional difference in the active-break conditions points to the significance of regional studies than considering India as a single unit. The underlying dynamics of diurnal variability need to be studied by making use of a high resolution model as the present study could not simulate the local onshore circulation. Also the land use modification in this study, selected a region, which is surrounded by crop land. This implies the high possibility for the conversion of the remaining region to agricultural land. Therefore the study is useful than considering idealized conditions, but the adverse effect of irrigated crop is more than non-irrigated crop. Therefore, such studies would help to understand the climate changes occurred in the recent period. The large accumulation of rainfall between 300-600 m height of western Ghats has been found but the reason behind this need to be studied, which is possible by utilizing datasets that would better represent the orography and landuse over the region in high resolution model. Similarly a detailed analysis is needed to clearly identify the causative relations of the predictors identified with the predictant and the physical reasons behind them. New approaches that include nonlinear relationships and dynamical variables from model simulations can be included in the existing statistical models to improve the skill of the models. Also the statistical models for the forecasts of monsoon have to be continually updated.

Räumliche Modellierung der Dynamik von Landnutzung in Hessen und ihrer Wirkung auf die biologische Kohlenstoffspeicherung - Entwicklung eines GIS-basierten Modellsystems

Die gegenwärtige Entwicklung der internationalen Klimapolitik verlangt von Deutschland eine Reduktion seiner Treibhausgasemissionen. Wichtigstes Treibhausgas ist Kohlendioxid, das durch die Verbrennung fossiler Energieträger in die Atmosphäre freigesetzt wird. Die Reduktionsziele können prinzipiell durch eine Verminderung der Emissionen sowie durch die Schaffung von Kohlenstoffsenken erreicht werden. Senken beschreiben dabei die biologische Speicherung von Kohlenstoff in Böden und Wäldern. Eine wichtige Einflussgröße auf diese Prozesse stellt die räumliche Dynamik der Landnutzung einer Region dar. In dieser Arbeit wird das Modellsystem HILLS entwickelt und zur Simulation dieser komplexen Wirkbeziehungen im Bundesland Hessen genutzt. Ziel ist es, mit HILLS über eine Analyse des aktuellen Zustands hinaus auch Szenarien über Wege der zukünftigen regionalen Entwicklung von Landnutzung und ihrer Wirkung auf den Kohlenstoffhaushalt bis 2020 zu untersuchen. Für die Abbildung der räumlichen und zeitlichen Dynamik von Landnutzung in Hessen wird das Modell LUCHesse entwickelt. Seine Aufgabe ist die Simulation der relevanten Prozesse auf einem 1 km2 Raster, wobei die Raten der Änderung exogen als Flächentrends auf Ebene der hessischen Landkreise vorgegeben werden. LUCHesse besteht aus Teilmodellen für die Prozesse: (A) Ausbreitung von Siedlungs- und Gewerbefläche, (B) Strukturwandel im Agrarsektor sowie (C) Neuanlage von Waldflächen (Aufforstung). Jedes Teilmodell umfasst Methoden zur Bewertung der Standorteignung der Rasterzellen für unterschiedliche Landnutzungsklassen und zur Zuordnung der Trendvorgaben zu solchen Rasterzellen, die jeweils am besten für eine Landnutzungsklasse geeignet sind. Eine Validierung der Teilmodelle erfolgt anhand von statistischen Daten für den Zeitraum von 1990 bis 2000. Als Ergebnis eines Simulationslaufs werden für diskrete Zeitschritte digitale Karten der Landnutzugsverteilung in Hessen erzeugt. Zur Simulation der Kohlenstoffspeicherung wird eine modifizierte Version des Ökosystemmodells Century entwickelt (GIS-Century). Sie erlaubt einen gesteuerten Simulationslauf in Jahresschritten und unterstützt die Integration des Modells als Komponente in das HILLS Modellsystem. Es werden verschiedene Anwendungsschemata für GIS-Century entwickelt, mit denen die Wirkung der Stilllegung von Ackerflächen, der Aufforstung sowie der Bewirtschaftung bereits bestehender Wälder auf die Kohlenstoffspeicherung untersucht werden kann. Eine Validierung des Modells und der Anwendungsschemata erfolgt anhand von Feld- und Literaturdaten. HILLS implementiert eine sequentielle Kopplung von LUCHesse mit GIS-Century. Die räumliche Kopplung geschieht dabei auf dem 1 km2 Raster, die zeitliche Kopplung über die Einführung eines Landnutzungsvektors, der die Beschreibung der Landnutzungsänderung einer Rasterzelle während des Simulationszeitraums enthält. Außerdem integriert HILLS beide Modelle über ein dienste- und datenbankorientiertes Konzept in ein Geografisches Informationssystem (GIS). Auf diesem Wege können die GIS-Funktionen zur räumlichen Datenhaltung und Datenverarbeitung genutzt werden. Als Anwendung des Modellsystems wird ein Referenzszenario für Hessen mit dem Zeithorizont 2020 berechnet. Das Szenario setzt im Agrarsektor eine Umsetzung der AGENDA 2000 Politik voraus, die in großem Maße zu Stilllegung von Ackerflächen führt, während für den Bereich Siedlung und Gewerbe sowie Aufforstung die aktuellen Trends der Flächenausdehnung fortgeschrieben werden. Mit HILLS ist es nun möglich, die Wirkung dieser Landnutzungsänderungen auf die biologische Kohlenstoffspeicherung zu quantifizieren. Während die Ausdehnung von Siedlungsflächen als Kohlenstoffquelle identifiziert werden kann (37 kt C/a), findet sich die wichtigste Senke in der Bewirtschaftung bestehender Waldflächen (794 kt C/a). Weiterhin führen die Stilllegung von Ackerfläche (26 kt C/a) sowie Aufforstung (29 kt C/a) zu einer zusätzlichen Speicherung von Kohlenstoff. Für die Kohlenstoffspeicherung in Böden zeigen die Simulationsexperimente sehr klar, dass diese Senke nur von beschränkter Dauer ist.

A Modeling Analysis of Changing Global Land Use as affected by Changing Demands for Wood Products

The 21st century has brought new challenges for forest management at a time when globalization in world trade is increasing and global climate change is becoming increasingly apparent. In addition to various goods and services like food, feed, timber or biofuels being provided to humans, forest ecosystems are a large store of terrestrial carbon and account for a major part of the carbon exchange between the atmosphere and the land surface. Depending on the stage of the ecosystems and/or management regimes, forests can be either sinks, or sources of carbon. At the global scale, rapid economic development and a growing world population have raised much concern over the use of natural resources, especially forest resources. The challenging question is how can the global demands for forest commodities be satisfied in an increasingly globalised economy, and where could they potentially be produced? For this purpose, wood demand estimates need to be integrated in a framework, which is able to adequately handle the competition for land between major land-use options such as residential land or agricultural land. This thesis is organised in accordance with the requirements to integrate the simulation of forest changes based on wood extraction in an existing framework for global land-use modelling called LandSHIFT. Accordingly, the following neuralgic points for research have been identified: (1) a review of existing global-scale economic forest sector models (2) simulation of global wood production under selected scenarios (3) simulation of global vegetation carbon yields and (4) the implementation of a land-use allocation procedure to simulate the impact of wood extraction on forest land-cover. Modelling the spatial dynamics of forests on the global scale requires two important inputs: (1) simulated long-term wood demand data to determine future roundwood harvests in each country and (2) the changes in the spatial distribution of woody biomass stocks to determine how much of the resource is available to satisfy the simulated wood demands. First, three global timber market models are reviewed and compared in order to select a suitable economic model to generate wood demand scenario data for the forest sector in LandSHIFT. The comparison indicates that the ‘Global Forest Products Model’ (GFPM) is most suitable for obtaining projections on future roundwood harvests for further study with the LandSHIFT forest sector. Accordingly, the GFPM is adapted and applied to simulate wood demands for the global forestry sector conditional on selected scenarios from the Millennium Ecosystem Assessment and the Global Environmental Outlook until 2050. Secondly, the Lund-Potsdam-Jena (LPJ) dynamic global vegetation model is utilized to simulate the change in potential vegetation carbon stocks for the forested locations in LandSHIFT. The LPJ data is used in collaboration with spatially explicit forest inventory data on aboveground biomass to allocate the demands for raw forest products and identify locations of deforestation. Using the previous results as an input, a methodology to simulate the spatial dynamics of forests based on wood extraction is developed within the LandSHIFT framework. The land-use allocation procedure specified in the module translates the country level demands for forest products into woody biomass requirements for forest areas, and allocates these on a five arc minute grid. In a first version, the model assumes only actual conditions through the entire study period and does not explicitly address forest age structure. Although the module is in a very preliminary stage of development, it already captures the effects of important drivers of land-use change like cropland and urban expansion. As a first plausibility test, the module performance is tested under three forest management scenarios. The module succeeds in responding to changing inputs in an expected and consistent manner. The entire methodology is applied in an exemplary scenario analysis for India. A couple of future research priorities need to be addressed, particularly the incorporation of plantation establishments; issue of age structure dynamics; as well as the implementation of a new technology change factor in the GFPM which can allow the specification of substituting raw wood products (especially fuelwood) by other non-wood products.

Estimation of electronic coupling in π -stacked donor-bridge-acceptor systems: correction of the two-state model

Comparison of donor-acceptor electronic couplings calculated within two-state and three-state models suggests that the two-state treatment can provide unreliable estimates of Vda because of neglecting the multistate effects. We show that in most cases accurate values of the electronic coupling in a π stack, where donor and acceptor are separated by a bridging unit, can be obtained as Ṽ da = (E2 - E1) μ12 Rda + (2 E3 - E1 - E2) 2 μ13 μ23 Rda2, where E1, E2, and E3 are adiabatic energies of the ground, charge-transfer, and bridge states, respectively, μij is the transition dipole moments between the states i and j, and Rda is the distance between the planes of donor and acceptor. In this expression based on the generalized Mulliken-Hush approach, the first term corresponds to the coupling derived within a two-state model, whereas the second term is the superexchange correction accounting for the bridge effect. The formula is extended to bridges consisting of several subunits. The influence of the donor-acceptor energy mismatch on the excess charge distribution, adiabatic dipole and transition moments, and electronic couplings is examined. A diagnostic is developed to determine whether the two-state approach can be applied. Based on numerical results, we showed that the superexchange correction considerably improves estimates of the donor-acceptor coupling derived within a two-state approach. In most cases when the two-state scheme fails, the formula gives reliable results which are in good agreement (within 5%) with the data of the three-state generalized Mulliken-Hush model

Solar influences on dynamical coupling between the stratosphere and troposphere

We use a simplified atmospheric general circulation model (AGCM) to investigate the response of the lower atmosphere to thermal perturbations in the lower stratosphere. The results show that generic heating of the lower stratosphere tends to weaken the sub-tropical jets and the tropospheric mean meridional circulations. The positions of the jets, and the extent of the Hadley cells, respond to the distribution of the stratospheric heating, with low latitude heating displacing them poleward, and uniform heating displacing them equatorward. The patterns of response to the low latitude heating are similar to those found to be associated with solar variability in previous observational data analysis, and to the effects of varying solar UV radiation in sophisticated AGCMs. In order to investigate the chain of causality involved in converting the stratospheric thermal forcing to a tropospheric climate signal we conduct an experiment which uses an ensemble of model spin-ups to analyse the time development of the response to an applied stratospheric perturbation. We find that the initial effect of the change in static stability at the tropopause is to reduce the eddy momentum flux convergence in this region. This is followed by a vertical transfer of the momentum forcing anomaly by an anomalous mean circulation to the surface, where it is partly balanced by surface stress anomalies. The unbalanced part drives the evolution of the vertically integrated zonal flow. We conclude that solar heating of the stratosphere may produce changes in the circulation of the troposphere even without any direct forcing below the tropopause. We suggest that the impact of the stratospheric changes on wave propagation is key to the mechanisms involved.

Land/sea warming ratio in response to climate change: IPCC AR4 model results and comparison with observations

Climate model simulations consistently show that in response to greenhouse gas forcing surface temperatures over land increase more rapidly than over sea. The enhanced warming over land is not simply a transient effect, since it is also present in equilibrium conditions. We examine 20 models from the IPCC AR4 database. The global land/sea warming ratio varies in the range 1.36–1.84, independent of global mean temperature change. In the presence of increasing radiative forcing, the warming ratio for a single model is fairly constant in time, implying that the land/sea temperature difference increases with time. The warming ratio varies with latitude, with a minimum in equatorial latitudes, and maxima in the subtropics. A simple explanation for these findings is provided, and comparisons are made with observations. For the low-latitude (40°S–40°N) mean, the models suggest a warming ratio of 1.51 ± 0.13, while recent observations suggest a ratio of 1.54 ± 0.09.

A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations

Simulations of the global atmosphere for weather and climate forecasting require fast and accurate solutions and so operational models use high-order finite differences on regular structured grids. This precludes the use of local refinement; techniques allowing local refinement are either expensive (eg. high-order finite element techniques) or have reduced accuracy at changes in resolution (eg. unstructured finite-volume with linear differencing). We present solutions of the shallow-water equations for westerly flow over a mid-latitude mountain from a finite-volume model written using OpenFOAM. A second/third-order accurate differencing scheme is applied on arbitrarily unstructured meshes made up of various shapes and refinement patterns. The results are as accurate as equivalent resolution spectral methods. Using lower order differencing reduces accuracy at a refinement pattern which allows errors from refinement of the mountain to accumulate and reduces the global accuracy over a 15 day simulation. We have therefore introduced a scheme which fits a 2D cubic polynomial approximately on a stencil around each cell. Using this scheme means that refinement of the mountain improves the accuracy after a 15 day simulation. This is a more severe test of local mesh refinement for global simulations than has been presented but a realistic test if these techniques are to be used operationally. These efficient, high-order schemes may make it possible for local mesh refinement to be used by weather and climate forecast models.

Storm track sensitivity to sea surface temperature resolution in a regional atmosphere model

A high resolution regional atmosphere model is used to investigate the sensitivity of the North Atlantic storm track to the spatial and temporal resolution of the sea surface temperature (SST) data used as a lower boundary condition. The model is run over an unusually large domain covering all of the North Atlantic and Europe, and is shown to produce a very good simulation of the observed storm track structure. The model is forced at the lateral boundaries with 15–20 years of data from the ERA-40 reanalysis, and at the lower boundary by SST data of differing resolution. The impacts of increasing spatial and temporal resolution are assessed separately, and in both cases increasing the resolution leads to subtle, but significant changes in the storm track. In some, but not all cases these changes act to reduce the small storm track biases seen in the model when it is forced with low-resolution SSTs. In addition there are several clear mesoscale responses to increased spatial SST resolution, with surface heat fluxes and convective precipitation increasing by 10–20% along the Gulf Stream SST gradient.