Mutually catalytic branching at infinite rate

The purpose of this doctoral thesis is to prove existence for a mutually catalytic random walk with infinite branching rate on countably many sites. The process is defined as a weak limit of an approximating family of processes. An approximating process is constructed by adding jumps to a deterministic migration on an equidistant time grid. As law of jumps we need to choose the invariant probability measure of the mutually catalytic random walk with a finite branching rate in the recurrent regime. This model was introduced by Dawson and Perkins (1998) and this thesis relies heavily on their work. Due to the properties of this invariant distribution, which is in fact the exit distribution of planar Brownian motion from the first quadrant, it is possible to establish a martingale problem for the weak limit of any convergent sequence of approximating processes. We can prove a duality relation for the solution to the mentioned martingale problem, which goes back to Mytnik (1996) in the case of finite rate branching, and this duality gives rise to weak uniqueness for the solution to the martingale problem. Using standard arguments we can show that this solution is in fact a Feller process and it has the strong Markov property. For the case of only one site we prove that the model we have constructed is the limit of finite rate mutually catalytic branching processes as the branching rate approaches infinity. Therefore, it seems naturalto refer to the above model as an infinite rate branching process. However, a result for convergence on infinitely many sites remains open.

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.

Light-sensitive polymeric nanoparticles based on photo-cleavable chromophores

Der Fokus dieser Arbeit liegt in dem Design, der Synthese und der Charakterisierung neuartiger photosensitiver Mikrogele und Nanopartikel als potentielle Materialien für Beladungs- und Freisetzungsanwendungen. Zur Realisierung dieses Konzepts wurden verschiedene Ansätze untersucht.Es wurden neuartige niedermolekulare lichtspaltbare Vernetzermoleküle auf der Basis von o-Nitrobenzylderivaten synthetisiert, charakterisiert und zur Herstellung von photosensitiven PMMA und PHEMA Mikrogelen verwendet. Diese sind unter Bestrahlung in organischen Lösungsmitteln quellbar und zersetzbar. Durch die Einführung anionischer MAA Gruppen in solche PHEMA Mikrogele wurde dieses Konzept auf doppelt stimuliresponsive p(HEMA-co-MAA) Mikrogele erweitert. Hierbei wurde ein pH-abhängiges Quellbarkeitsprofil mit der lichtinduzierten Netzwerkspaltung in wässrigen Medien kombiniert. Diese duale Sensitivität zu zwei zueinander orthogonalen Reizen stellt ein vielversprechendes Konzept zur Kombination einer pH-abhängigen Beladung mit einer lichtinduzierten Freisetzung von funktionellen Substanzen dar. Desweiteren wurden PAAm Mikrogele entwickelt, welche sowohl eine Sensitivität gegenüber Enzymen als auch Licht aufweisen. Dieses Verhalten wurde durch die Verwendung von (meth-)acrylatfunktionalisierten Dextranen als polymere Vernetzungsmoleküle erreicht. Das entsprechende stimuliresponsive Profil basiert auf der enzymatischen Zersetzbarkeit der Polysaccharid-Hauptkette und der Anbindung der polymerisierbaren Vinyleinheiten an diese über photospaltbare Gruppen. Die gute Wasserlöslichkeit der Vernetzermoleküle stellt einen vielversprechenden Ansatz zur Beladung solcher Mikrogele mit funktionellen hydrophilen Substanzen bereits während der Partikelsynthese dar. Ein weiteres Konzept zur Beladung von Mikrogelen basiert auf der Verwendung von photolabilen Wirkstoff-Mikrogel Konjugaten. In einem ersten Schritt zur Realisierung solch eines Ansatzes wurde ein neuartiges Monomer entwickelt. Hierbei wurde Doxorubicin über eine lichtspaltbare Gruppe an eine polymerisierbare Methacrylatgruppe angebunden. Für die Freisetzung hydrophober Substanzen in wässrigen Medien wurden polymere Photolack-Nanopartikel entwickelt, welche sich unter Bestrahlung in Wasser zersetzen. Die lichtinduzierte Änderung der Hydrophobizität des Polymers ermöglichte die Freisetzung von Nilrot durch das Auflösen der partikulären Struktur. Ein interessanter Ansatz zur Verhinderung einer unkontrollierten Freisetzung funktioneller Substanzen aus Mikrogelen ist die Einführung einer stimuliresponsiven Schale. In diesem Kontext wurden Untersuchungen zur Bildung von nicht-stimulisensitiven Schalen um vorgefertigte Mikrogelkerne und zur Synthese von Hydrogelkernen in vorgefertigten polymeren Schalen (Nanokapseln) durchgeführt.

Photo- und Elektropionproduktion in chiraler effektiver Feldtheorie

In der vorliegenden Arbeit werden Photopionproduktion (PPP) und Elektropionproduktion (EPP) im Rahmen der manifest lorentzinvarianten baryonischen chiralen Störungstheorie untersucht. Dabei werden zwei verschiedene Ansätze verfolgt. Zum einen wird eine Rechnung auf Einschleifenniveau bis zur chiralen Ordnung O(q^4) mit Pionen und Nukleonen als Freiheitsgrade durchgeführt, um die Energieabhängigkeit der Reaktionen über einen möglichst großen Bereich zu beschreiben. Um die Abhängigkeit von der Photonvirtualität in der EPP zu verbessern, werden zum anderen in einer zweiten Rechnung Vektormesonen in die Theorie einbezogen. Diese Rechnung wird bis zur chiralen Ordnung O(q^3) auf Einschleifenniveau durchgeführt. rnrnVon den vier physikalischen Prozessen in PPP und EPP sind nur drei experimentell zugänglich. Untersucht werden diese Reaktionen an mehreren verschiedenen Anlagen, z.B. in Mainz, Bonn oder Saskatoon. Die dort gewonnenen Daten werden hier verwendet, um die Grenzen der chiralen Störungstheorie auszuloten. rnrnDiese Arbeit stellt die erste, vollständige, manifest lorentzinvariante Rechnung in O(q^4) für PPP und EPP, und die erste jemals durchgeführte Rechnung mit Vektormesonen als Freiheitsgrade für diesen Prozess, dar. Neben der Berechnung der physikalischen Observablen wird auch eine Partialwellenzerlegung durchgeführt und die wichtigsten Multipole untersucht. Diese lassen sich aus den gewonnenen Amplituden extrahieren und bieten eine gute Möglichkeit das Nukleon und Resonanzen zu untersuchen. rnrnUm das Matrixelement für die Prozesse berechnen zu können, wurden verschiedene Routinen für das Computeralgebrasystem Mathematica entwickelt, da die Anzahl der zu bestimmenden Diagramme sehr groß ist. Für die Multipolzerlegung werden zwei verschiedene Programme verwendet. Zum einen das bereits existierende Programm XMAID, welches für diese Arbeit entsprechend modifiziert wurde. Zum anderen wurden vergleichbare Routinen für Mathematica entwickelt. Am Ende der Analysen werden die verschiedenen Rechnungen bezüglich ihrer Anwendbarkeit auf PPP und EPP verglichen.

Photo-induced reversible assembly of colloidal polymer nanoparticles

Polymer nanoparticles functionalized on the surface with photo-responsive labels were synthesized. In a first synthetic step, polystyrene was copolymerized with the cross-linker divinylbenzene and poly(ethylene glycol) acrylate in a miniemulsion, to produce nano-sized spheres (~ 60 nm radius) with terminal hydroxyl groups, which were functionalized in a subsequent synthetic step with photo-responsive labels. For this purpose, two photo-active molecular structures were separately used: anthracene, which is well known to form covalently bonded dimers upon photo-excitation; and pyrene, which only forms short lived excited state dimers (excimers). Acid derivatives of these labels (9-anthracene carboxylic acid and 1-pyrene butyric acid) were bonded to the hydroxyl terminal groups of the nanoparticles through an esterification reaction, via the intermediate formation of the corresponding acid chloride.rnThe obtained labeled nanoparticles appeared to be highly hydrophobic structures. They formed lyophobic suspensions in water, which after analysis by dynamic light scattering (DLS) and ultramicroscopic particle tracking, appeared to equilibrate as a collection of singly dispersed nanoparticles, together with a few nanoparticle aggregates. The relative amount of aggregates decreased with increasing amounts of the surfactant sodium dodecyl sulfate (SDS), thus confirming that aggregation is an equilibrated state resulting from lyophobicity. The formation of such aggregates was corroborated using scanning electron microscopy (SEM). The photo-irradiation of the lyophobic aqueous suspensions of anthracene labeled nanoparticles (An-NP) resulted in the formation of higher aggregates, as evidenced by DLS and ultramicroscopy. The obtained state of aggregation could be reverted by sonication. The possibility to re-aggregate the system in subsequent photo-excitation and sonication cycles was established. Likewise, the photo-irradiation of lyophobic aqueous suspensions of pyrene-labeled nanoparticles (Py-NP) resulted in the formation of higher aggregates, as evidenced by DLS and ultramicroscopy. These appeared to remain aggregated due to hydrophobic interactions. This system could also be re-dispersed by sonication and re-aggregated in subsequent cycles of photo-excitation and sonication.