Models of the Distribution of Persistent Organic Pollutants in the Marine Environment

Persistent organic pollutants (POPs) is a group of chemicals that are toxic, undergo long-range transport and accumulate in biota. Due to their persistency the distribution and recirculation in the environment often continues for a long period of time. Thereby they appear virtually everywhere within the biosphere, and poses a toxic stress to living organisms. In this thesis, attempts are made to contribute to the understanding of factors that influence the distribution of POPs with focus on processes in the marine environment. The bioavailability and the spatial distribution are central topics for the environmental risk management of POPs. In order to study these topics, various field studies were undertaken. To determine the bioavailable fraction of polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs), polychlorinated naphthalenes (PCNs), and polychlorinated biphenyls (PCBs) the aqueous dissolved phase were sampled and analysed. In the same samples, we also measured how much of these POPs were associated with suspended particles. Different models, which predicted the phase distribution of these POPs, were then evaluated. It was found that important water characteristics, which influenced the solid-water phase distribution of POPs, were particulate organic matter (POM), particulate soot (PSC), and dissolved organic matter (DOM). The bioavailable dissolved POP-phase in the water was lower when these sorbing phases were present. Furthermore, sediments were sampled and the spatial distribution of the POPs was examined. The results showed that the concentration of PCDD/Fs, and PCNs were better described using PSC- than using POM-content of the sediment. In parallel with these field studies, we synthesized knowledge of the processes affecting the distribution of POPs in a multimedia mass balance model. This model predicted concentrations of PCDD/Fs throughout our study area, the Grenlandsfjords in Norway, within factors of ten. This makes the model capable to validate the effect of suitable remedial actions in order to decrease the exposure of these POPs to biota in the Grenlandsfjords which was the aim of the project. Also, to evaluate the influence of eutrophication on the marine occurrence PCB data from the US Musselwatch and Benthic Surveillance Programs are examined in this thesis. The dry weight based concentrations of PCB in bivalves were found to correlate positively to the organic matter content of nearby sediments, and organic matter based concentrations of PCB in sediments were negatively correlated to the organic matter content of the sediment.

Topics in geometry, analysis and inverse problems

The thesis consists of three independent parts. Part I: Polynomial amoebas We study the amoeba of a polynomial, as de ned by Gelfand, Kapranov and Zelevinsky. A central role in the treatment is played by a certain convex function which is linear in each complement component of the amoeba, which we call the Ronkin function. This function is used in two di erent ways. First, we use it to construct a polyhedral complex, which we call a spine, approximating the amoeba. Second, the Monge-Ampere measure of the Ronkin function has interesting properties which we explore. This measure can be used to derive an upper bound on the area of an amoeba in two dimensions. We also obtain results on the number of complement components of an amoeba, and consider possible extensions of the theory to varieties of codimension higher than 1. Part II: Differential equations in the complex plane We consider polynomials in one complex variable arising as eigenfunctions of certain differential operators, and obtain results on the distribution of their zeros. We show that in the limit when the degree of the polynomial approaches innity, its zeros are distributed according to a certain probability measure. This measure has its support on the union of nitely many curve segments, and can be characterized by a simple condition on its Cauchy transform. Part III: Radon transforms and tomography This part is concerned with different weighted Radon transforms in two dimensions, in particular the problem of inverting such transforms. We obtain stability results of this inverse problem for rather general classes of weights, including weights of attenuation type with data acquisition limited to a 180 degrees range of angles. We also derive an inversion formula for the exponential Radon transform, with the same restriction on the angle.