The effect of elastic modulus and equilibrium vapor adsorption on capillary forces

Die Kapillarkraft entsteht durch die Bildung eines Meniskus zwischen zwei Festkörpen. In dieser Doktorarbeit wurden die Auswirkungen von elastischer Verformung und Flϋssigkeitadsorption auf die Kapillarkraft sowohl theoretisch als auch experimentell untersucht. Unter Verwendung eines Rasterkraftmikroskops wurde die Kapillarkraft zwischen eines Siliziumoxid Kolloids von 2 µm Radius und eine weiche Oberfläche wie n.a. Polydimethylsiloxan oder Polyisopren, unter normalen Umgebungsbedingungen sowie in variierende Ethanoldampfdrϋcken gemessen. Diese Ergebnisse wurden mit den Kapillarkräften verglichen, die auf einem harten Substrat (Silizium-Wafer) unter denselben Bedingungen gemessen wurden. Wir beobachteten eine monotone Abnahme der Kapillarkraft mit zunehmendem Ethanoldampfdruck (P) fϋr P/Psat > 0,2, wobei Psat der Sättigungsdampfdruck ist.rnUm die experimentellen Ergebnisse zu erklären, wurde ein zuvor entwickeltes analytisches Modell (Soft Matter 2010, 6, 3930) erweitert, um die Ethanoladsorption zu berϋcksichtigen. Dieses neue analytische Modell zeigte zwei verschiedene Abhängigkeiten der Kapillarkraft von P/Psat auf harten und weichen Oberflächen. Fϋr die harte Oberfläche des Siliziumwafers wird die Abhängigkeit der Kapillarkraft vom Dampfdruck vom Verhältnis der Dicke der adsorbierten Ethanolschicht zum Meniskusradius bestimmt. Auf weichen Polymeroberflächen hingegen hängt die Kapillarkraft von der Oberflächenverformung und des Laplace-Drucks innerhalb des Meniskus ab. Eine Abnahme der Kapillarkraft mit zunehmendem Ethanoldampfdruck hat demnach eine Abnahme des Laplace-Drucks mit zunehmendem Meniskusradius zur folge. rnDie analytischen Berechnungen, fϋr die eine Hertzsche Kontakt-deformation angenommen wurde, wurden mit Finit Element Methode Simulationen verglichen, welche die reale Deformation des elastischen Substrats in der Nähe des Meniskuses explizit berϋcksichtigen. Diese zusätzliche nach oben gerichtete oberflächenverformung im Bereich des Meniskus fϋhrt zu einer weiteren Erhöhung der Kapillarkraft, insbesondere fϋr weiche Oberflächen mit Elastizitätsmodulen < 100 MPa.rn

Systematic studies of the interaction between amyloid beta-protein and lipids

The amyloid peptide (Aß), a normal constituent of neuronal and non-neuronal cells, has been shown to be a major component of the extracellular plaque of Alzheimer’s disease (AD). The interaction of Aß peptides with the lipid matrix of neuronal cell membranes plays an important role in the pathogenesis of AD. In this study, we have developed peptide-tethered artificial lipid membranes by the Langmuir-Blodgett and Langmuir-Schaefer methods. Anti-Aß40-mAb labeled with a fluorophore was used to probe the Aß40 binding to the model membrane system. Systematic studies on the antibody or Aß-membrane interactions were carried out in our model systems by Surface Plasmon Field-Enhanced Fluorescence Spectroscopy (SPFS). Aß adsorption is critically determined by the lipid composition of the membranes. Aß specifically binds with membranes of sphingomyelin, and this preferential adsorption was markedly amplified by the addition of sterols (cholesterol or 25-OH-Chol). Fluorescence microscopy indicated that 25-OH-Chol could also form micro-domains with sphingomyelin as cholesterol does at the conditions used for the built-up of the model membranes. Our findings suggest that micro-domains composed of sphingomyelin and the sterols could be the binding sites of Aß and the role of sphingomyelin in AD should receive much more attention. The artificial membranes provide a novel platform for the study on AD, and SPFS is a potential tool for detecting Aß-membrane interaction. Numerous investigations indicate that the ability of Aß to form fibrils is considerably dependent upon the levels of ß-sheet structure adopted by Aß. Membrane-mediated conformational transition of Aß has been demonstrated. In this study, we focus on the interaction of Aß and the membranes composed of POPC/SM/25-OH-Chol (2:1:1). The artificial membrane system was established by the methods as described above. Immunoassy based on a pair of monoclonal antibodies (mAbs) against different epitopes was employed to detect the orientation of the Aß at the model membranes. Kinetics of antibody-Aß binding was determined by surface plasmon field-enhanced fluorescence spectroscopy (SPFS). The attempt has also been made to probe the change in the conformation of Aß using SPFS combined with immunoassay. Melatonin was employed to induce the conformational change of Aß. The orientation and the conformational change of Aß are evaluated by analysing kinetic/affinity parameters. This work provides novel insight into the investigation on the structure of Aß at the membrane surface.

Psychosoziale Belastung bei Herztransplantationskandidaten

Fragestellung: In der vorliegenden Untersuchung wurde geprüft, ob sich neu gelistete Herztransplantationskandidaten mit ischämischer Herzinsuffizienz (IKMP) und dilatativer Kardiomyopathie (DKMP) nach Kontrolle von Krankheitsschwere und Geschlecht in psychosozialen Variablen unterscheiden. Zudem wurde untersucht, ob psychosoziale Risikofaktoren für IKMP-Patienten stärker mit der 1-Jahres-Mortalität auf der Warteliste assoziiert sind als für DKMP-Patienten. Methode: Im Rahmen der multizentrischen, prospektiv angelegten Studie „Warten auf ein neues Herz“ bearbeiteten 160 DKMP- (16 % Frauen) und 122 IKMP-Patienten (13 % Frauen) kurz nach Aufnahme auf die Warteliste einen Fragebogen, der subjektiven Gesundheitszustand, Angst, Depressivität, soziale Unterstützung, Netzwerkgröße, Ärger, Ärgerausdruck und wartezeitspezifische Belastungen erfasste. Medizinische Daten zum Zeitpunkt der Listung und Veränderungen im Wartelistenstatus im 1-Jahres-Follow-Up wurden von Eurotransplant bereitgestellt. Ergebnisse: IKMP-Patienten waren im Vergleich mit DKMP-Patienten älter, häufiger ehemalige Raucher, hatten häufiger vorherige Herzoperationen erlebt, litten seltener unter einer Erregungsleitungsstörung, wurden seltener mit Aldosteronantagonisten sowie häufiger mit Katecholaminen behandelt. Nach Kontrolle dieser Variablen und unter Einbezug des Geschlechts berichteten nur Männer mit IKMP höhere Angstwerte und mehr Anger-In als Männer mit DKMP. Ein höheres Mortalitätsrisiko für IKMP-Patienten ein Jahr nach Aufnahme auf die Warteliste konnte nicht belegt werden. Auch zeigte sich keine Interaktion zwischen psychosozialer Belastung und Grunderkrankung hinsichtlich der Mortalität. Niedrige emotionale Unterstützung ging unabhängig von der Grunderkrankung mit einem dreifach erhöhten Mortalitätsrisiko einher. Fazit: Männer mit IKMP sind stärker durch negative Emotionen belastet als Männer mit DKMP. Eine weitere Risikogruppe stellen Personen mit niedriger emotionaler Unterstützung dar. Psychosoziale Risikofaktoren sollten daher bereits bei Aufnahme auf die Warteliste erfasst und Betreuungsangebote gezielt auf diese beiden Gruppen abgestimmt werden.

The life histories of the two tropical warblers Sylvia boehmi and Sylvia lugens

Ziel der Arbeit war die Quantifizierung einer Reihe von Lebenszyklusmerkmalen der beiden tropischen Grasmückenarten Sylvia boehmi und S. lugens (Aves: Sylviidae; frühere Gattung Parisoma). 13 Brutpaare beider Arten wurden von 2000 bis 2002 in Kenia beobachtet. Die Daten wurden mit multivariater Statistik und multistate mark-recapture Modellen ausgewertet. Die Lebenszyklusmerkmale der beiden untersuchten Sylvia Arten sind im Vergleich zu den temperaten Sylvia-Arten gekennzeichnet durch kleine Gelege von zwei Eiern, lange Inkubationsperioden (S. boehmi (b.) 15.0 Tage, S. lugens (l.) 14.5 Tage), lange Nestlingsperioden (b. 12.9 Tage, l. 16.0 Tage), und niedrige Nesterfolgsraten (b. 19.4%, l. 33.2%). Der Zeitraum vom Ausfliegen der Jungen bis zu ihrer Unabhängigkeit war mit 58.5 Tagen bei S. boehmi und 37.5 Tagen bei S. lugens vergleichsweise lang und die Überlebensrate der flüggen Jungen in dieser Zeit war relativ hoch (b. 69.2%, l. 55.4%). Die jährliche Überlebensrate der brütenden adulten Tiere betrug bei S. boehmi 71.2% und bei S. lugens 57.2%. Die Saisonalität des Habitats, bedingt durch Regen- und Trockenzeiten, hatte keinen Einfluss auf die monatliche Überlebensrate im Laufe eines Jahres. Trotz hoher Nestprädationsraten gab es keinen klaren Zusammenhang zwischen Prädation und Fütterungsrate, Nestbewachung oder Neststandort.

Assembly and characterization of supramolecular architectures for biosensor applications

The research has included the efforts in designing, assembling and structurally and functionally characterizing supramolecular biofunctional architectures for optical biosensing applications. In the first part of the study, a class of interfaces based on the biotin-NeutrAvidin binding matrix for the quantitative control of enzyme surface coverage and activity was developed. Genetically modified ß-lactamase was chosen as a model enzyme and attached to five different types of NeutrAvidin-functionalized chip surfaces through a biotinylated spacer. All matrices are suitable for achieving a controlled enzyme surface density. Data obtained by SPR are in excellent agreement with those derived from optical waveguide measurements. Among the various protein-binding strategies investigated in this study, it was found that stiffness and order between alkanethiol-based SAMs and PEGylated surfaces are very important. Matrix D based on a Nb2O5 coating showed a satisfactory regeneration possibility. The surface-immobilized enzymes were found to be stable and sufficiently active enough for a catalytic activity assay. Many factors, such as the steric crowding effect of surface-attached enzymes, the electrostatic interaction between the negatively charged substrate (Nitrocefin) and the polycationic PLL-g-PEG/PEG-Biotin polymer, mass transport effect, and enzyme orientation, are shown to influence the kinetic parameters of catalytic analysis. Furthermore, a home-built Surface Plasmon Resonance Spectrometer of SPR and a commercial miniature Fiber Optic Absorbance Spectrometer (FOAS), served as a combination set-up for affinity and catalytic biosensor, respectively. The parallel measurements offer the opportunity of on-line activity detection of surface attached enzymes. The immobilized enzyme does not have to be in contact with the catalytic biosensor. The SPR chip can easily be cleaned and used for recycling. Additionally, with regard to the application of FOAS, the integrated SPR technique allows for the quantitative control of the surface density of the enzyme, which is highly relevant for the enzymatic activity. Finally, the miniaturized portable FOAS devices can easily be combined as an add-on device with many other in situ interfacial detection techniques, such as optical waveguide lightmode spectroscopy (OWLS), the quartz crystal microbalance (QCM) measurements, or impedance spectroscopy (IS). Surface plasmon field-enhanced fluorescence spectroscopy (SPFS) allows for an absolute determination of intrinsic rate constants describing the true parameters that control interfacial hybridization. Thus it also allows for a study of the difference of the surface coupling influences between OMCVD gold particles and planar metal films presented in the second part. The multilayer growth process was found to proceed similarly to the way it occurs on planar metal substrates. In contrast to planar bulk metal surfaces, metal colloids exhibit a narrow UV-vis absorption band. This absorption band is observed if the incident photon frequency is resonant with the collective oscillation of the conduction electrons and is known as the localized surface plasmon resonance (LSPR). LSPR excitation results in extremely large molar extinction coefficients, which are due to a combination of both absorption and scattering. When considering metal-enhanced fluorescence we expect the absorption to cause quenching and the scattering to cause enhancement. Our further study will focus on the developing of a detection platform with larger gold particles, which will display a dominant scattering component and enhance the fluorescence signal. Furthermore, the results of sequence-specific detection of DNA hybridization based on OMCVD gold particles provide an excellent application potential for this kind of cheap, simple, and mild preparation protocol applied in this gold fabrication method. In the final chapter, SPFS was used for the in-depth characterizations of the conformational changes of commercial carboxymethyl dextran (CMD) substrate induced by pH and ionic strength variations were studied using surface plasmon resonance spectroscopy. The pH response of CMD is due to the changes in the electrostatics of the system between its protonated and deprotonated forms, while the ionic strength response is attributed from the charge screening effect of the cations that shield the charge of the carboxyl groups and prevent an efficient electrostatic repulsion. Additional studies were performed using SPFS with the aim of fluorophore labeling the carboxymethyl groups. CMD matrices showed typical pH and ionic strength responses, such as high pH and low ionic strength swelling. Furthermore, the effects of the surface charge and the crosslink density of the CMD matrix on the extent of stimuli responses were investigated. The swelling/collapse ratio decreased with decreasing surface concentration of the carboxyl groups and increasing crosslink density. The study of the CMD responses to external and internal variables will provide valuable background information for practical applications.

Synthesis and characterization of polyelectrolyte brushes

On the pathway to synthesizing synthetic model systems for human cartilage, macroinitiators for the ATRP of styrene sulfonate esters with different chain lengths and initiation site densities from 10 % to 100 % were synthesized. Polymer brushes from styrene sulfonate ethyl ester and styrene sulfonate dodecyl ester with varying grafting density, backbone length and side chain length were synthesized and characterized by 1H-NMR, AUC, AFM, TEM, and in the case of the ethyl esters, GPC-MALLS. Polyelectrolyte brushes from styrene sulfonate were synthesized from the corresponding esters. These brushes were characterized in solution (GPC-MALLS, static and dynamic light scattering, SANS, 1H-NMR) and on solid interfaces (AFM and TEM). It was shown that these brushes may form extended aggregates in solution. The aggregation behavior and the size and shape of the aggregates depend on the side chain length and the degree of saponification. For samples with identical backbone and side chain length, but varying degrees of ester hydrolysis, marked differences in the aggregation behavior were observed. A functionalized ATRP macroinitiator with a positively charged head group was synthesized and employed for the synthesis of a functionalized polyelectrolyte brush. These brushes were found to form complexes with negatively charged latex particles and are thus suitable as proteoglycan models in the proteoglycan-hyaluronic acid complex.

Measurement of volatile organic compounds and total OH reactivity in the atmosphere

Volatile organic compounds play a critical role in ozone formation and drive the chemistry of the atmosphere, together with OH radicals. The simplest volatile organic compound methane is a climatologically important greenhouse gas, and plays a key role in regulating water vapour in the stratosphere and hydroxyl radicals in the troposphere. The OH radical is the most important atmospheric oxidant and knowledge of the atmospheric OH sink, together with the OH source and ambient OH concentrations is essential for understanding the oxidative capacity of the atmosphere. Oceanic emission and / or uptake of methanol, acetone, acetaldehyde, isoprene and dimethyl sulphide (DMS) was characterized as a function of photosynthetically active radiation (PAR) and a suite of biological parameters, in a mesocosm experiment conducted in the Norwegian fjord. High frequency (ca. 1 minute-1) methane measurements were performed using a gas chromatograph - flame ionization detector (GC-FID) in the boreal forests of Finland and the tropical forests of Suriname. A new on-line method (Comparative Reactivity Method - CRM) was developed to directly measure the total OH reactivity (sink) of ambient air. It was observed that under conditions of high biological activity and a PAR of ~ 450 μmol photons m-2 s-1, the ocean acted as a net source of acetone. However, if either of these criteria was not fulfilled then the ocean acted as a net sink of acetone. This new insight into the biogeochemical cycling of acetone at the ocean-air interface has helped to resolve discrepancies from earlier works such as Jacob et al. (2002) who reported the ocean to be a net acetone source (27 Tg yr-1) and Marandino et al. (2005) who reported the ocean to be a net sink of acetone (- 48 Tg yr-1). The ocean acted as net source of isoprene, DMS and acetaldehyde but net sink of methanol. Based on these findings, it is recommended that compound specific PAR and biological dependency be used for estimating the influence of the global ocean on atmospheric VOC budgets. Methane was observed to accumulate within the nocturnal boundary layer, clearly indicating emissions from the forest ecosystems. There was a remarkable similarity in the time series of the boreal and tropical forest ecosystem. The average of the median mixing ratios during a typical diel cycle were 1.83 μmol mol-1 and 1.74 μmol mol-1 for the boreal forest ecosystem and tropical forest ecosystem respectively. A flux value of (3.62 ± 0.87) x 1011 molecules cm-2 s-1 (or 45.5 ± 11 Tg CH4 yr-1 for global boreal forest area) was derived, which highlights the importance of the boreal forest ecosystem for the global budget of methane (~ 600 Tg yr-1). The newly developed CRM technique has a dynamic range of ~ 4 s-1 to 300 s-1 and accuracy of ± 25 %. The system has been tested and calibrated with several single and mixed hydrocarbon standards showing excellent linearity and accountability with the reactivity of the standards. Field tests at an urban and forest site illustrate the promise of the new method. The results from this study have improved current understanding about VOC emissions and uptake from ocean and forest ecosystems. Moreover, a new technique for directly measuring the total OH reactivity of ambient air has been developed and validated, which will be a valuable addition to the existing suite of atmospheric measurement techniques.

Copper and zinc stable isotope ratios as tracers of biogeochemical processes, sources and transport of Cu and Zn in soils

Copper and Zn are essential micronutrients for plants, animals, and humans; however, they may also be pollutants if they occur at high concentrations in soil. Therefore, knowledge of Cu and Zn cycling in soils is required both for guaranteeing proper nutrition and to control possible risks arising from pollution.rnThe overall objective of my study was to test if Cu and Zn stable isotope ratios can be used to investigate into the biogeochemistry, source and transport of these metals in soils. The use of stable isotope ratios might be especially suitable to trace long-term processes occurring during soil genesis and transport of pollutants through the soil. In detail, I aimed to answer the questions, whether (1) Cu stable isotopes are fractionated during complexation with humic acid, (2) 65Cu values can be a tracer for soil genetic processes in redoximorphic soils (3) 65Cu values can help to understand soil genetic processes under oxic weathering conditions, and (4) 65Cu and 66Zn values can act as tracers of sources and transport of Cu and Zn in polluted soils.rnTo answer these questions, I ran adsorption experiments at different pH values in the laboratory and modelled Cu adsorption to humic acid. Furthermore, eight soils were sampled representing different redox and weathering regimes of which two were influenced by stagnic water, two by groundwater, two by oxic weathering (Cambisols), and two by podzolation. In all horizons of these soils, I determined selected basic soil properties, partitioned Cu into seven operationally defined fractions and determined Cu concentrations and Cu isotope ratios (65Cu values). Finally, three additional soils were sampled along a deposition gradient at different distances to a Cu smelter in Slovakia and analyzed together with bedrock and waste material from the smelter for selected basic soil properties, Cu and Zn concentrations and 65Cu and 66Zn values.rnMy results demonstrated that (1) Copper was fractionated during adsorption on humic acid resulting in an isotope fractionation between the immobilized humic acid and the solution (65CuIHA-solution) of 0.26 ± 0.11‰ (2SD) and that the extent of fractionation was independent of pH and involved functional groups of the humic acid. (2) Soil genesis and plant cycling causes measurable Cu isotope fractionation in hydromorphic soils. The results suggested that an increasing number of redox cycles depleted 63Cu with increasing depth resulting in heavier 65Cu values. (3) Organic horizons usually had isotopically lighter Cu than mineral soils presumably because of the preferred uptake and recycling of 63Cu by plants. (4) In a strongly developed Podzol, eluviation zones had lighter and illuviation zones heavier 65Cu values because of the higher stability of organo-65Cu complexes compared to organo-63Cu complexes. In the Cambisols and a little developed Podzol, oxic weathering caused increasingly lighter 65Cu values with increasing depth, resulting in the opposite depth trend as in redoximorphic soils, because of the preferential vertical transport of 63Cu. (5) The 66Zn values were fractionated during the smelting process and isotopically light Zn was emitted allowing source identification of Zn pollution while 65Cu values were unaffected by the smelting and Cu emissions isotopically indistinguishable from soil. The 65Cu values in polluted soils became lighter down to a depth of 0.4 m indicating isotope fractionation during transport and a transport depth of 0.4 m in 60 years. 66Zn values had an opposite depth trend becoming heavier with depth because of fractionation by plant cycling, speciation changes, and mixing of native and smelter-derived Zn. rnCopper showed measurable isotope fractionation of approximately 1‰ in unpolluted soils, allowing to draw conclusions on plant cycling, transport, and redox processes occurring during soil genesis and 65Cu and 66Zn values in contaminated soils allow for conclusions on sources (in my study only possible for Zn), biogeochemical behavior, and depth of dislocation of Cu and Zn pollution in soil. I conclude that stable Cu and Zn isotope ratios are a suitable novel tool to trace long-term processes in soils which are difficult to assess otherwise.rn

Adsorption of macromolecules on interfaces studied by isothermal titration calorimetry

The mixing of nanoparticles with polymers to form composite materials has been applied for decades. They combine the advantages of polymers (e.g., elasticity, transparency, or dielectric properties) and inorganic nanoparticles (e.g., specific absorption of light, magneto resistance effects, chemical activity, and catalysis etc.). Nanocomposites exhibit several new characters that single-phase materials do not have. Filling the polymeric matrix with an inorganic material requires its homogeneous distribution in order to achieve the highest possible synergetic effect. To fulfill this requirement, the incompatibility between the filler and the matrix, originating from their opposite polarity, has to be resolved. A very important parameter here is the strength and irreversibility of the adsorption of the surface active compound on the inorganic material. In this work the Isothermal titration calorimetry (ITC) was applied as a method to quantify and investigate the adsorption process and binding efficiencies in organic-inorganic–hybrid-systems by determining the thermodynamic parameters (ΔH, ΔS, ΔG, KB as well as the stoichiometry n). These values provide quantification and detailed understanding of the adsorption process of surface active molecules onto inorganic particles. In this way, a direct correlation between the adsorption strength and structure of the surface active compounds can be achieved. Above all, knowledge of the adsorption mechanism in combination with the structure should facilitate a more rational design into the mainly empirically based production and optimization of nanocomposites.

Investigations into the effect of nucleoside modifications on the physicochemical properties and biological function of DNA and RNA

This thesis explores the effect of chemical nucleoside modification on the physicochemical and biological properties of nucleic acids. Positional alteration on the Watson-Crick edge of purines and pyrimidines, the “C-H” edge of pyrimidines, as well as both the Hoogsteen and sugar edges of purines were attempted by means of copper catalyzed azide-alkyne cycloaddition. For this purpose, nucleic acid building blocks carrying terminal alkynes were synthesized and introduced into oligonucleotides by solid-phase oligonucleotide chemistry. rnOf particular interest was the effect of nucleoside modification on hydrogen bond formation with complementary nucleosides. The attachment of propargyl functionalities onto the N2 of guanosine and the N4 of 5-methylcytosine, respectively, followed by incorporation of the modified analogs into oligonucleotides, was successfully achieved. Temperature dependent UV-absorption melting measurements with duplexes formed between modified oligonucleotides and a variety of complementary strands resulted in melting temperatures for the respective duplexes. As a result, the effect that both the nature and the site of nucleoside modification have on base pairing properties could thus be assisted. rnTo further explore the enzymatic recognition of chemically modified nucleosides, the oligonucleotide containing the N2-modified guanosine derivative on the 5’-end, which was clicked to a fluorescent dye, was subjected to knockdown analyses of the eGFP reporter gene in the presence of increasing concentrations of siRNA duplexes. From these dose-dependent experiments, a clear effect of 5’-labeling on the knockdown efficiency could be seen. In contrast, 3’-labeling was found to be relatively insignificant.rn

Dynamic distance analysis : new geometric data structures and algorithms for the real-time calculation of tolerance violating regions in the digital mockup process

In vielen Industriezweigen, zum Beispiel in der Automobilindustrie, werden Digitale Versuchsmodelle (Digital MockUps) eingesetzt, um die Konstruktion und die Funktion eines Produkts am virtuellen Prototypen zu überprüfen. Ein Anwendungsfall ist dabei die Überprüfung von Sicherheitsabständen einzelner Bauteile, die sogenannte Abstandsanalyse. Ingenieure ermitteln dabei für bestimmte Bauteile, ob diese in ihrer Ruhelage sowie während einer Bewegung einen vorgegeben Sicherheitsabstand zu den umgebenden Bauteilen einhalten. Unterschreiten Bauteile den Sicherheitsabstand, so muss deren Form oder Lage verändert werden. Dazu ist es wichtig, die Bereiche der Bauteile, welche den Sicherhabstand verletzen, genau zu kennen. rnrnIn dieser Arbeit präsentieren wir eine Lösung zur Echtzeitberechnung aller den Sicherheitsabstand unterschreitenden Bereiche zwischen zwei geometrischen Objekten. Die Objekte sind dabei jeweils als Menge von Primitiven (z.B. Dreiecken) gegeben. Für jeden Zeitpunkt, in dem eine Transformation auf eines der Objekte angewendet wird, berechnen wir die Menge aller den Sicherheitsabstand unterschreitenden Primitive und bezeichnen diese als die Menge aller toleranzverletzenden Primitive. Wir präsentieren in dieser Arbeit eine ganzheitliche Lösung, welche sich in die folgenden drei großen Themengebiete unterteilen lässt.rnrnIm ersten Teil dieser Arbeit untersuchen wir Algorithmen, die für zwei Dreiecke überprüfen, ob diese toleranzverletzend sind. Hierfür präsentieren wir verschiedene Ansätze für Dreiecks-Dreiecks Toleranztests und zeigen, dass spezielle Toleranztests deutlich performanter sind als bisher verwendete Abstandsberechnungen. Im Fokus unserer Arbeit steht dabei die Entwicklung eines neuartigen Toleranztests, welcher im Dualraum arbeitet. In all unseren Benchmarks zur Berechnung aller toleranzverletzenden Primitive beweist sich unser Ansatz im dualen Raum immer als der Performanteste.rnrnDer zweite Teil dieser Arbeit befasst sich mit Datenstrukturen und Algorithmen zur Echtzeitberechnung aller toleranzverletzenden Primitive zwischen zwei geometrischen Objekten. Wir entwickeln eine kombinierte Datenstruktur, die sich aus einer flachen hierarchischen Datenstruktur und mehreren Uniform Grids zusammensetzt. Um effiziente Laufzeiten zu gewährleisten ist es vor allem wichtig, den geforderten Sicherheitsabstand sinnvoll im Design der Datenstrukturen und der Anfragealgorithmen zu beachten. Wir präsentieren hierzu Lösungen, die die Menge der zu testenden Paare von Primitiven schnell bestimmen. Darüber hinaus entwickeln wir Strategien, wie Primitive als toleranzverletzend erkannt werden können, ohne einen aufwändigen Primitiv-Primitiv Toleranztest zu berechnen. In unseren Benchmarks zeigen wir, dass wir mit unseren Lösungen in der Lage sind, in Echtzeit alle toleranzverletzenden Primitive zwischen zwei komplexen geometrischen Objekten, bestehend aus jeweils vielen hunderttausend Primitiven, zu berechnen. rnrnIm dritten Teil präsentieren wir eine neuartige, speicheroptimierte Datenstruktur zur Verwaltung der Zellinhalte der zuvor verwendeten Uniform Grids. Wir bezeichnen diese Datenstruktur als Shrubs. Bisherige Ansätze zur Speicheroptimierung von Uniform Grids beziehen sich vor allem auf Hashing Methoden. Diese reduzieren aber nicht den Speicherverbrauch der Zellinhalte. In unserem Anwendungsfall haben benachbarte Zellen oft ähnliche Inhalte. Unser Ansatz ist in der Lage, den Speicherbedarf der Zellinhalte eines Uniform Grids, basierend auf den redundanten Zellinhalten, verlustlos auf ein fünftel der bisherigen Größe zu komprimieren und zur Laufzeit zu dekomprimieren.rnrnAbschießend zeigen wir, wie unsere Lösung zur Berechnung aller toleranzverletzenden Primitive Anwendung in der Praxis finden kann. Neben der reinen Abstandsanalyse zeigen wir Anwendungen für verschiedene Problemstellungen der Pfadplanung.