Exchange of nitrogen dioxide (NO 2) between plants and the atmosphere under laboratory and field conditions

Nitrogen is an essential nutrient. It is for human, animal and plants a constituent element of proteins and nucleic acids. Although the majority of the Earth’s atmosphere consists of elemental nitrogen (N2, 78 %) only a few microorganisms can use it directly. To be useful for higher plants and animals elemental nitrogen must be converted to a reactive oxidized form. This conversion happens within the nitrogen cycle by free-living microorganisms, symbiotic living Rhizobium bacteria or by lightning. Humans are able to synthesize reactive nitrogen through the Haber-Bosch process since the beginning of the 20th century. As a result food security of the world population could be improved noticeably. On the other side the increased nitrogen input results in acidification and eutrophication of ecosystems and in loss of biodiversity. Negative health effects arose for humans such as fine particulate matter and summer smog. Furthermore, reactive nitrogen plays a decisive role at atmospheric chemistry and global cycles of pollutants and nutritive substances.rnNitrogen monoxide (NO) and nitrogen dioxide (NO2) belong to the reactive trace gases and are grouped under the generic term NOx. They are important components of atmospheric oxidative processes and influence the lifetime of various less reactive greenhouse gases. NO and NO2 are generated amongst others at combustion process by oxidation of atmospheric nitrogen as well as by biological processes within soil. In atmosphere NO is converted very quickly into NO2. NO2 is than oxidized to nitrate (NO3-) and to nitric acid (HNO3), which bounds to aerosol particles. The bounded nitrate is finally washed out from atmosphere by dry and wet deposition. Catalytic reactions of NOx are an important part of atmospheric chemistry forming or decomposing tropospheric ozone (O3). In atmosphere NO, NO2 and O3 are in photosta¬tionary equilibrium, therefore it is referred as NO-NO2-O3 triad. At regions with elevated NO concentrations reactions with air pollutions can form NO2, altering equilibrium of ozone formation.rnThe essential nutrient nitrogen is taken up by plants mainly by dissolved NO3- entering the roots. Atmospheric nitrogen is oxidized to NO3- within soil via bacteria by nitrogen fixation or ammonium formation and nitrification. Additionally atmospheric NO2 uptake occurs directly by stomata. Inside the apoplast NO2 is disproportionated to nitrate and nitrite (NO2-), which can enter the plant metabolic processes. The enzymes nitrate and nitrite reductase convert nitrate and nitrite to ammonium (NH4+). NO2 gas exchange is controlled by pressure gradients inside the leaves, the stomatal aperture and leaf resistances. Plant stomatal regulation is affected by climate factors like light intensity, temperature and water vapor pressure deficit. rnThis thesis wants to contribute to the comprehension of the effects of vegetation in the atmospheric NO2 cycle and to discuss the NO2 compensation point concentration (mcomp,NO2). Therefore, NO2 exchange between the atmosphere and spruce (Picea abies) on leaf level was detected by a dynamic plant chamber system under labo¬ratory and field conditions. Measurements took place during the EGER project (June-July 2008). Additionally NO2 data collected during the ECHO project (July 2003) on oak (Quercus robur) were analyzed. The used measuring system allowed simultaneously determina¬tion of NO, NO2, O3, CO2 and H2O exchange rates. Calculations of NO, NO2 and O3 fluxes based on generally small differences (∆mi) measured between inlet and outlet of the chamber. Consequently a high accuracy and specificity of the analyzer is necessary. To achieve these requirements a highly specific NO/NO2 analyzer was used and the whole measurement system was optimized to an enduring measurement precision.rnData analysis resulted in a significant mcomp,NO2 only if statistical significance of ∆mi was detected. Consequently, significance of ∆mi was used as a data quality criterion. Photo-chemical reactions of the NO-NO2-O3 triad in the dynamic plant chamber’s volume must be considered for the determination of NO, NO2, O3 exchange rates, other¬wise deposition velocity (vdep,NO2) and mcomp,NO2 will be overestimated. No significant mcomp,NO2 for spruce could be determined under laboratory conditions, but under field conditions mcomp,NO2 could be identified between 0.17 and 0.65 ppb and vdep,NO2 between 0.07 and 0.42 mm s-1. Analyzing field data of oak, no NO2 compensation point concentration could be determined, vdep,NO2 ranged between 0.6 and 2.71 mm s-1. There is increasing indication that forests are mainly a sink for NO2 and potential NO2 emissions are low. Only when assuming high NO soil emissions, more NO2 can be formed by reaction with O3 than plants are able to take up. Under these circumstance forests can be a source for NO2.

Periodicities in the Hodgkin-Huxley model and versions of this model with stochastic input

A field of computational neuroscience develops mathematical models to describe neuronal systems. The aim is to better understand the nervous system. Historically, the integrate-and-fire model, developed by Lapique in 1907, was the first model describing a neuron. In 1952 Hodgkin and Huxley [8] described the so called Hodgkin-Huxley model in the article “A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve”. The Hodgkin-Huxley model is one of the most successful and widely-used biological neuron models. Based on experimental data from the squid giant axon, Hodgkin and Huxley developed their mathematical model as a four-dimensional system of first-order ordinary differential equations. One of these equations characterizes the membrane potential as a process in time, whereas the other three equations depict the opening and closing state of sodium and potassium ion channels. The membrane potential is proportional to the sum of ionic current flowing across the membrane and an externally applied current. For various types of external input the membrane potential behaves differently. This thesis considers the following three types of input: (i) Rinzel and Miller [15] calculated an interval of amplitudes for a constant applied current, where the membrane potential is repetitively spiking; (ii) Aihara, Matsumoto and Ikegaya [1] said that dependent on the amplitude and the frequency of a periodic applied current the membrane potential responds periodically; (iii) Izhikevich [12] stated that brief pulses of positive and negative current with different amplitudes and frequencies can lead to a periodic response of the membrane potential. In chapter 1 the Hodgkin-Huxley model is introduced according to Izhikevich [12]. Besides the definition of the model, several biological and physiological notes are made, and further concepts are described by examples. Moreover, the numerical methods to solve the equations of the Hodgkin-Huxley model are presented which were used for the computer simulations in chapter 2 and chapter 3. In chapter 2 the statements for the three different inputs (i), (ii) and (iii) will be verified, and periodic behavior for the inputs (ii) and (iii) will be investigated. In chapter 3 the inputs are embedded in an Ornstein-Uhlenbeck process to see the influence of noise on the results of chapter 2.

Spectral theory of differential operators on finite metric graphs and on bounded domains

Die vorliegende Arbeit widmet sich der Spektraltheorie von Differentialoperatoren auf metrischen Graphen und von indefiniten Differentialoperatoren auf beschränkten Gebieten. Sie besteht aus zwei Teilen. Im Ersten werden endliche, nicht notwendigerweise kompakte, metrische Graphen und die Hilberträume von quadratintegrierbaren Funktionen auf diesen betrachtet. Alle quasi-m-akkretiven Laplaceoperatoren auf solchen Graphen werden charakterisiert, und Abschätzungen an die negativen Eigenwerte selbstadjungierter Laplaceoperatoren werden hergeleitet. Weiterhin wird die Wohlgestelltheit eines gemischten Diffusions- und Transportproblems auf kompakten Graphen durch die Anwendung von Halbgruppenmethoden untersucht. Eine Verallgemeinerung des indefiniten Operators $-tfrac{d}{dx}sgn(x)tfrac{d}{dx}$ von Intervallen auf metrische Graphen wird eingeführt. Die Spektral- und Streutheorie der selbstadjungierten Realisierungen wird detailliert besprochen. Im zweiten Teil der Arbeit werden Operatoren untersucht, die mit indefiniten Formen der Art $langlegrad v, A(cdot)grad urangle$ mit $u,vin H_0^1(Omega)subset L^2(Omega)$ und $OmegasubsetR^d$ beschränkt, assoziiert sind. Das Eigenwertverhalten entspricht in Dimension $d=1$ einer verallgemeinerten Weylschen Asymptotik und für $dgeq 2$ werden Abschätzungen an die Eigenwerte bewiesen. Die Frage, wann indefinite Formmethoden für Dimensionen $dgeq 2$ anwendbar sind, bleibt offen und wird diskutiert.