@phdthesis{Sposini2020,
  author    = {Sposini, Vittoria},
  title     = {The random diffusivity approach for diffusion in heterogeneous systems},
  doi       = {10.25932/publishup-48780},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-487808},
  school      = {Universit{\"a}t Potsdam},
  year      = {2020},
  abstract  = {The two hallmark features of Brownian motion are the linear growth < x2(t)> = 2Ddt of the mean squared displacement (MSD) with diffusion coefficient D in d spatial dimensions, and the Gaussian distribution of displacements. With the increasing complexity of the studied systems deviations from these two central properties have been unveiled over the years. Recently, a large variety of systems have been reported in which the MSD exhibits the linear growth in time of Brownian (Fickian) transport, however, the distribution of displacements is pronouncedly non-Gaussian (Brownian yet non-Gaussian, BNG). A similar behaviour is also observed for viscoelastic-type motion where an anomalous trend of the MSD, i.e., <x2(t)> ~ ta, is combined with a priori unexpected non-Gaussian distributions (anomalous yet non-Gaussian, ANG). This kind of behaviour observed in BNG and ANG diffusions has been related to the presence of heterogeneities in the systems and a common approach has been established to address it, that is, the random diffusivity approach. This dissertation explores extensively the field of random diffusivity models. Starting from a chronological description of all the main approaches used as an attempt of describing BNG and ANG diffusion, different mathematical methodologies are defined for the resolution and study of these models. The processes that are reported in this work can be classified in three subcategories, i) randomly-scaled Gaussian processes, ii) superstatistical models and iii) diffusing diffusivity models, all belonging to the more general class of random diffusivity models. Eventually, the study focuses more on BNG diffusion, which is by now well-established and relatively well-understood. Nevertheless, many examples are discussed for the description of ANG diffusion, in order to highlight the possible scenarios which are known so far for the study of this class of processes. The second part of the dissertation deals with the statistical analysis of random diffusivity processes. A general description based on the concept of moment-generating function is initially provided to obtain standard statistical properties of the models. Then, the discussion moves to the study of the power spectral analysis and the first passage statistics for some particular random diffusivity models. A comparison between the results coming from the random diffusivity approach and the ones for standard Brownian motion is discussed. In this way, a deeper physical understanding of the systems described by random diffusivity models is also outlined. To conclude, a discussion based on the possible origins of the heterogeneity is sketched, with the main goal of inferring which kind of systems can actually be described by the random diffusivity approach.},
  language  = {en}
}
@phdthesis{Graeff2011,
  author    = {Gr{\"a}ff, Thomas},
  title     = {Soil moisture dynamics and soil moisture controlled runoff processes at different spatial scales : from observation to modelling},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-54470},
  school      = {Universit{\"a}t Potsdam},
  year      = {2011},
  abstract  = {Soil moisture is a key state variable that controls runoff formation, infiltration and partitioning of radiation into latent and sensible heat. However, the experimental characterisation of near surface soil moisture patterns and their controls on runoff formation remains a challenge. This subject was one aspect of the BMBF-funded OPAQUE project (operational discharge and flooding predictions in head catchments). As part of that project the focus of this dissertation is on: (1) testing the methodology and feasibility of the Spatial TDR technology in producing soil moisture profiles along TDR probes, including an inversion technique of the recorded signal in heterogeneous field soils, (2) the analysis of spatial variability and temporal dynamics of soil moisture at the field scale including field experiments and hydrological modelling, (3) the application of models of different complexity for understanding soil moisture dynamics and its importance for runoff generation as well as for improving the prediction of runoff volumes. To fulfil objective 1, several laboratory experiments were conducted to understand the influence of probe rod geometry and heterogeneities in the sampling volume under different wetness conditions. This includes a detailed analysis on how these error sources affect retrieval of soil moisture profiles in soils. Concerning objective 2 a sampling strategy of two TDR clusters installed in the head water of the Wilde Weißeritz catchment (Eastern Ore Mountains, Germany) was used to investigate how well "the catchment state" can be characterised by means of distributed soil moisture data observed at the field scale. A grassland site and a forested site both located on gentle slopes were instrumented with two Spatial TDR clusters that consist of up to 39 TDR probes. Process understanding was gained by modelling the interaction of evapotranspiration and soil moisture with the hydrological process model CATFLOW. A field scale irrigation experiment was carried out to investigate near subsurface processes at the hillslope scale. The interactions of soil moisture and runoff formation were analysed using discharge data from three nested catchments: the Becherbach with a size of 2 km², the Rehefeld catchment (17 km²) and the superordinate Ammelsdorf catchment (49 km²). Statistical analyses including observations of pre-event runoff, soil moisture and different rainfall characteristics were employed to predict stream flow volume. On the different scales a strong correlation between the average soil moisture and the runoff coefficients of rainfall-runoff events could be found, which almost explains equivalent variability as the pre-event runoff. Furthermore, there was a strong correlation between surface soil moisture and subsurface wetness with a hysteretic behaviour between runoff soil moisture. To fulfil objective 3 these findings were used in a generalised linear model (GLM) analysis which combines state variables describing the catchments antecedent wetness and variables describing the meteorological forcing in order to predict event runoff coefficients. GLM results were compared to simulations with the catchment model WaSiM ETH. Hereby were the model results of the GLMs always better than the simulations with WaSiM ETH. The GLM analysis indicated that the proposed sampling strategy of clustering TDR probes in typical functional units is a promising technique to explore soil moisture controls on runoff generation and can be an important link between the scales. Long term monitoring of such sites could yield valuable information for flood warning and forecasting by identifying critical soil moisture conditions for the former and providing a better representation of the initial moisture conditions for the latter.},
  language  = {en}
}
@phdthesis{Naumann2008,
  author    = {Naumann, Siglinde},
  title     = {Heterogenit{\"a}t und Bildungsprozesse in b{\"u}rgerschaftlichen Initiativen : eine empirische Studie zur Transformation konjunktiver Orientierungen},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-19784},
  school      = {Universit{\"a}t Potsdam},
  year      = {2008},
  abstract  = {In dieser qualitativ rekonstruktiven Studie wird an Hand der empirischen Rekonstruktion von Gruppendiskussionen der Fragestellung nachgegangen, welchen handlungsleitenden Orientierungen die Mitglieder der untersuchten Initiativen im Umgang mit ihrer Heterogenit{\"a}t folgen und wie diese Orientierungen mit Lern- beziehungsweise Bildungsprozessen korrespondieren. Diese Fragestellung ist mit unterschiedlichen theoretischen Kontexten verwoben. Zum Einen geht es hier um Heterogenit{\"a}t und Pluralit{\"a}t. Der Umgang mit Heterogenit{\"a}t und Pluralit{\"a}t gilt als eine zentrale Herausforderung in modernen stark ausdifferenzierten und hochkomplexen Gesellschaften, die mit fluiden mikro- und makrogesellschaftlichen Strukturen (vgl. Sch{\"a}ffter 1998) und vielf{\"a}ltigsten Formen kultureller Pluralit{\"a}t (vgl. Nohl 2006) einhergehen. Ein Reflexionsangebot f{\"u}r die erziehungswissenschaftliche Diskussion bietet die Denkfigur der egalit{\"a}ren Differenz. (Vgl. Prengel Ein Reflexionsangebot f{\"u}r die erziehungswissenschaftliche Diskussion bietet die Denkfigur der egalit{\"a}ren Differenz. Zum Anderen ist eine rekonstruktive Untersuchung b{\"u}rgerschaftlicher Initiativen nicht ohne Bezug zu ihrem zivilgesellschaftlichen Kontext zu denken. So sei hier stellvertretend f{\"u}r andere zeitdiagnostische {\"U}berlegungen auf Giddens Position (vgl. Giddens 1996) verwiesen, der die gesellschaftlichen Ver{\"a}nderungen in der reflexiven Moderne mit weitreichenden Prozessen des sozialen Wandels verbunden sieht. In dieser Studie wird im Anschluss an die strukturale Bildungstheorie von Marotzki (vgl. Marotzki 1990) zwischen Lern- und Bildungsprozessen unterschieden. Vor dem Hintergrund der Theorie Mannheims zu konjunktiven existentiellen Erfahrungen und der damit einhergehenden Seinsverbundenheit des Wissens (vgl. Mannheim 1980) werden diese Prozesse im Anschluss an Sch{\"a}ffers qualitative Studie zu generationenfundierten Bildungsprozessen (vgl. Sch{\"a}ffer 2003) als kollektiv fundierte Prozesse verstanden. Das von Karl Mannheim entwickelte Konzept des „konjunktiven Erfahrungsraums" (vgl. Mannheim 1980) wird im Anschluss an andere Studien der qualitativen Bildungsforschung (vgl. Sch{\"a}ffer 2003, Nohl 2006) f{\"u}r die Rekonstruktion von Bildungsprozessen genutzt, die auf der Transformation konjunktiver Erfahrungen beruhen. In der vorliegenden Studie werden die in den untersuchten Initiativen relevanten habituellen Muster des Umgangs mit Heterogenit{\"a}t rekonstruiert und ihre Bedeutung f{\"u}r Lern- und Bildungsprozesse zu erhellt. B{\"u}rgerschaftliche Initiativen werden als lebensweltliche Lernorte in den Blick genommen, mit der Auswertung nach der dokumentarischen Methode wird ein Verst{\"a}ndnis zu Grunde gelegt, dass auf die Verwobenheit gesellschaftlicher Strukturen mit dem Erleben der Akteure und damit den Prozessen der sozialen Genese von Interaktion und Identit{\"a}t verweist. (Vgl. Bohnsack 2003, Kubisch 2008)},
  language  = {de}
}