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Adherent cells constantly collect information about the mechanical properties of their extracellular environment by actively pulling on it through cell-matrix contacts, which act as mechanosensors. In recent years, the sophisticated use of elastic substrates has shown that cells respond very sensitively to changes in effective stiffness in their environment, which results in a reorganization of the cytoskeleton in response to mechanical input. We develop a theoretical model to predict cellular self-organization in soft materials on a coarse grained level. Although cell organization in principle results from complex regulatory events inside the cell, the typical response to mechanical input seems to be a simple preference for large effective stiffness, possibly because force is more efficiently generated in a stiffer environment. The term effective stiffness comprises effects of both rigidity and prestrain in the environment. This observation can be turned into an optimization principle in elasticity theory. By specifying the cellular probing force pattern and by modeling the environment as a linear elastic medium, one can predict preferred cell orientation and position. Various examples for cell organization, which are of large practical interest, are considered theoretically: cells in external strain fields and cells close to boundaries or interfaces for different sample geometries and boundary conditions. For this purpose the elastic equations are solved exactly for an infinite space, an elastic half space and the elastic sphere. The predictions of the model are in excellent agreement with experiments for fibroblast cells, both on elastic substrates and in hydrogels. Mechanically active cells like fibroblasts could also interact elastically with each other. We calculate the optimal structures on elastic substrates as a function of material properties, cell density and the geometry of cell positioning, respectively, that allows each cell to maximize the effective stiffness in its environment due to the traction of all the other cells. Finally, we apply Monte Carlo simulations to study the effect of noise on cellular structure formation. The model not only contributes to a better understanding of many physiological situations. In the future it could also be used for biomedical applications to optimize protocols for artificial tissues with respect to sample geometry, boundary condition, material properties or cell density.
This work deals with the connection between two basic phenomena in Nonlinear Dynamics: synchronization of chaotic systems and recurrences in phase space. Synchronization takes place when two or more systems adapt (synchronize) some characteristic of their respective motions, due to an interaction between the systems or to a common external forcing. The appearence of synchronized dynamics in chaotic systems is rather universal but not trivial. In some sense, the possibility that two chaotic systems synchronize is counterintuitive: chaotic systems are characterized by the sensitivity ti different initial conditions. Hence, two identical chaotic systems starting at two slightly different initial conditions evolve in a different manner, and after a certain time, they become uncorrelated. Therefore, at a first glance, it does not seem to be plausible that two chaotic systems are able to synchronize. But as we will see later, synchronization of chaotic systems has been demonstrated. On one hand it is important to investigate the conditions under which synchronization of chaotic systems occurs, and on the other hand, to develop tests for the detection of synchronization. In this work, I have concentrated on the second task for the cases of phase synchronization (PS) and generalized synchronization (GS). Several measures have been proposed so far for the detection of PS and GS. However, difficulties arise with the detection of synchronization in systems subjected to rather large amounts of noise and/or instationarities, which are common when analyzing experimental data. The new measures proposed in the course of this thesis are rather robust with respect to these effects. They hence allow to be applied to data, which have evaded synchronization analysis so far. The proposed tests for synchronization in this work are based on the fundamental property of recurrences in phase space.
Paleomagnetic dating of climatic events in Late Quaternary sediments of Lake Baikal (Siberia)
(2004)
Lake Baikal provides an excellent climatic archive for Central Eurasia as global climatic variations are continuously depicted in its sediments. We performed continuous rock magnetic and paleomagnetic analyses on hemipelagic sequences retrieved from 4 underwater highs reaching back 300 ka. The rock magnetic study combined with TEM, XRD, XRF and geochemical analyses evidenced that a magnetite of detrital origin dominates the magnetic signal in glacial sediments whereas interglacial sediments are affected by early diagenesis. HIRM roughly quantifies the hematite and goethite contributions and remains the best proxy for estimating the detrital input in Lake Baikal. Relative paleointensity records of the earth′s magnetic field show a reproducible pattern, which allows for correlation with well-dated reference curves and thus provides an alternative age model for Lake Baikal sediments. Using the paleomagnetic age model we observed that cooling in the Lake Baikal region and cooling of the sea surface water in the North Atlantic, as recorded in planktonic foraminifera δ18 O, are coeval. On the other hand, benthic δ18 O curves record mainly the global ice volume change, which occurs later than the sea surface temperature change. This proves that a dating bias results from an age model based on the correlation of Lake Baikal sedimentary records with benthic δ18 O curves. The compilation of paleomagnetic curves provides a new relative paleointensity curve, “Baikal 200”. With a laser-assisted grain size analysis of the detrital input, three facies types, reflecting different sedimentary dynamics can be distinguished. (1) Glacial periods are characterised by a high clay content mostly due to wind activity and by occurrence of a coarse fraction (sand) transported over the ice by local winds. This fraction gives evidence for aridity in the hinterland. (2) At glacial/interglacial transitions, the quantity of silt increases as the moisture increases, reflecting increased sedimentary dynamics. Wind transport and snow trapping are the dominant process bringing silt to a hemipelagic site (3) During the climatic optimum of the Eemian, the silt size and quantity are minimal due to blanketing of the detrital sources by the vegetal cover.
Understanding stars, their magnetic activity phenomena and the underlying dynamo action is the foundation for understanding 'life, the universe and everything' - as stellar magnetic fields play a fundamental role for star and planet formation and for the terrestrial atmosphere and climate. Starspots are the fingerprints of magnetic field lines and thereby the most important sign of activity in a star's photosphere. However, they cannot be observed directly, as it is not (yet) possible to spacially resolve the surfaces of even the nearest neighbouring stars. Therefore, an indirect approach called 'Doppler imaging' is applied, which allows to reconstruct the surface spot distribution on rapidly rotating, active stars. In this work, data from 11 years of continuous spectroscopic observations of the active binary star EI Eridani are reduced and analysed. 34 Doppler maps are obtained and the problem of how to parameterise the information content of Doppler maps is discussed. Three approaches for parameter extraction are introduced and applied to all maps: average temperature, separated for several latitude bands; fractional spottedness; and, for the analysis of structural temperature distribution, longitudinal and latitudinal spot-occurrence functions. The resulting values do not show a distinct correlation with the proposed activity cycle as seen from photometric long-term observations, thereby suggesting that the photometric activity cycle is not accompanied by a spot cycle as seen on the Sun. The general morphology of the spot pattern on EI Eri remains persistent for the whole period of 11 years. In addition, a detailed parameter study is performed. Improved orbital parameters suggest that EI Eri might be complemented by a third star in a wide orbit of about 19 years. Preliminary differential rotation measurements are carried out, indicating an anti-solar orientation.
In this thesis, dynamical structures and manifolds in closed chaotic flows will be investigated. The knowledge about the dynamical structures (and manifolds) of a system is of importance, since they provide us first information about the dynamics of the system - means, with their help we are able to characterize the flow and maybe even to forecast it`s dynamics. The visualization of such structures in closed chaotic flows is a difficult and often long-lasting process. Here, the so-called 'Leaking-method' will be introduced, in examples of simple mathematical maps as the baker- or sine-map, with which we are able to visualize subsets of the manifolds of the system`s chaotic saddle. Comparisons between the visualized manifolds and structures traced out by chemical or biological reactions superimposed on the same flow will be done in the example of a kinematic model of the Gulf Stream. It will be shown that with the help of the leaking method dynamical structures can be also visualized in environmental systems. In the example of a realistic model of the Mediterranean Sea, the leaking method will be extended to the 'exchange-method'. The exchange method allows us to characterize transport between two regions, to visualize transport routes and their exchange sets and to calculate the exchange times. Exchange times and sets will be shown and calculated for a northern and southern region in the western basin of the Mediterranean Sea. Furthermore, mixing properties in the Earth mantle will be characterized and geometrical properties of manifolds in a 3dimensional mathematical model (ABC map) will be investigated.
In this work different approaches are undertaken to improve the understanding of the sucrose-to-starch pathway in developing potato tubers. At first an inducible gene expression system from fungal origin is optimised for the use of studying metabolism in the potato tuber. It is found that the alc system from Aspergillus nidulans responds more rapidly to acetaldehyde than ethanol, and that acetaldehyde has less side-effects on metabolism. The optimal induction conditions then are used to study the effects of temporally controlled cytosolic expression of a yeast invertase on metabolism of potato tubers. The observed differences between induced and constitutive expression of the invertase lead to the conclusion that glycolysis is induced after an ATP demand has been created by an increase in sucrose cycling. Furthermore, the data suggest that in the potato tuber maltose is a product of glucose condensation rather than starch degradation. In the second part of the work it is shown that the expression of a yeast invertase in the vacuole of potato tubers has similar effects on metabolism than the expression of the same enzyme in the apoplast. These observations give further evidence to the presence of a mechanism by which sucrose is taken up via endocytosis to the vacuole rather than via transporters directly to the cytosol. Finally, a kinetic in silico model of sucrose breakdown is presented that is able to simulate this part of potato tuber metabolism on a quantitative level. Furthermore, it can predict the metabolic effects of the introduction of a yeast invertase in the cytosol of potato tubers with an astonishing precision. In summary, these data prove that inducible gene expression and kinetic computer models of metabolic pathways are useful tools to greatly improve the understanding of plant metabolism.
Polymer optical fibers (POFs) are a rather new tool for high-speed data transfer by modulated light. They allow the transport of high amounts of data over distances up to about 100 m without be influenced by external electromagnetic fields. Due to organic chemical nature of POFs, they are sensitive to the climate of their environment and therefore the optical fiber properties are as well. Hence, the optical stability is a key issue for long-term applications of POFs. The causes for a loss of optical transmission due to climatic exposures (aging/degradation) are researched by means of chemical analytical tools such as chemiluminescence (CL) and Fourier transform infrared (FTIR) spectroscopy for five different (with respect to manufacturers) step-index multimode PMMA based POFs and for seven different climatic conditions. Three of the five POF samples are studied more in detail to realize the effects of individual parameters and for forecasting longterm optical stability by short-term exposure tests. At first, the unexposed POF components (core, cladding, and bare POF as combination of core and cladding) are characterized with respect to important physical and chemical properties. The glass transition temperature Tg, and the melting temperature Tm are in the region of 120 °C to 140 °C, the molecular weight (Mw) of cores is in the order of 105 g mol-1. POFs are found to have different chemical compositions of their claddings as could be detected by FTIR, but identical compositions of their cores. Two of the POFs are exposed as cables (core, cladding and jacket) for about 3300 hours to the climate 92 °C / 95 % relative humidity (RH) resulting in a different transmission decrease. Investigating the related unexposed and exposed bare POFs for degradation using CL, FTIR, thermogravimetry (TG), UV/visible transmittance and gel permeation chromatography (GPC) suggest that claddings of POFs are more affected than cores. Probably the observed loss of transmission is mainly due to increased light absorption and imperfections at the core-cladding boundary caused by a large degradation of claddings. Hence, it is highly possible that the optical transmission stability of POFs is governed mainly by the thermo-oxidative stability of the cladding and minor of the core. Three bare POFs (core and cladding only) are exposed for different duration of exposure time (30 hours to 4500 hours) to 92 °C / 95 %RH, 92 °C / 50 %RH, 50 °C / 95 %RH, 90 °C / low humidity, 100 °C / low humidity, 110 °C / low humidity and 120 °C / low humidity. In these climates their transmission variations are found to be different from each other, too. The outcomes strongly inform that under high temperature and high humid climates physical changes such as volume expansion, are the main sources for the loss of optical transmission. Also, the optical transmission stability of POFs is found to be dependent on chemical compositions of claddings. Under high temperature and low humid conditions, a loss of transmission at the early stages of the exposure is mainly caused by physical changes, presumable by corecladding interface imperfections. For the later stages of exposures it is proposed to an additional increase of light absorption by core and cladding owes to degradation. Optical simulation results obtained parallel by Mr. L. Jankowski (a PhD student of BAM) are found to confirm these results. For bare POFs, too, the optical stability of POFs seems to depend on their thermo-oxidative stability. Some short-term exposure tests are conducted to realize influences of individual climatic parameters on the transmission property of POFs. It is found that at stationary high temperature and variable humidity conditions POFs display to a certain amount a reversible transmission loss due to physically absorbed water. But in the case of varying temperature and constant high humidity such reversibility is hardly noticeable. However, at room temperature and varying humidity, POFs display fully reversible transmission loss. The whole research described above has to be regarded as a starting point for further investigations. The restricted distribution of fundamental POF data by the manufacturers and the time consuming aging by climatic exposures restrict the results more or less to the samples, investigated here. Significant general statements require for example additional information concerning the variation of POF properties due to production. Nevertheless the tests, described here, have the capability for approximating and forecasting the long-term optical transmission stability of POFs. -------------- Auch im Druck erschienen: Appajaiah, Anilkumar: Climatic stability of polymer optical fibers (POF) / Anilkumar Appajaiah. - Bremerhaven : Wirtschaftsverl. NW, Verl. für neue Wiss., 2005. - Getr. Zählung [ca. 175 S.]. : Ill., graph. Darst. - (BAM-Dissertationsreihe ; 9) ISBN 3-86509-302-7
This thesis discusses theoretical and practical aspects of modelling of light propagation in non-aged and aged step-index polymer optical fibres (POFs). Special attention has been paid in describing optical characteristics of non-ideal fibres, scattering and attenuation, and in combining application-oriented and theoretical approaches. The precedence has been given to practical issues, but much effort has been also spent on the theoretical analysis of basic mechanisms governing light propagation in cylindrical waveguides.As a result a practically usable general POF model based on the raytracing approach has been developed and implemented. A systematic numerical optimisation of its parameters has been performed to obtain the best fit between simulated and measured optical characteristics of numerous non-aged and aged fibre samples. The model was verified by providing good agreement, especially for the non-aged fibres. The relations found between aging time and optimal values of model parameters contribute to a better understanding of the aging mechanisms of POFs.
Modelling and simulation of light propagation in non-aged and aged step-index polymer optical fibres
(2004)
This thesis discusses theoretical and practical aspects of modelling of light propagation in non-aged and aged step-index polymer optical fibres (POFs). Special attention has been paid in describing optical characteristics of non-ideal fibres, scattering and attenuation, and in combining application-oriented and theoretical approaches. The precedence has been given to practical issues, but much effort has been also spent on the theoretical analysis of basic mechanisms governing light propagation in cylindrical waveguides. As a result a practically usable general POF model based on the raytracing approach has been developed and implemented. A systematic numerical optimisation of its parameters has been performed to obtain the best fit between simulated and measured optical characteristics of numerous non-aged and aged fibre samples. The model was verified by providing good agreement, especially for the non-aged fibres. The relations found between aging time and optimal values of model parameters contribute to a better understanding of the aging mechanisms of POFs.
Recurrence plots, a rather promising tool of data analysis, have been introduced by Eckman et al. in 1987. They visualise recurrences in phase space and give an overview about the system's dynamics. Two features have made the method rather popular. Firstly they are rather simple to compute and secondly they are putatively easy to interpret. However, the straightforward interpretation of recurrence plots for some systems yields rather surprising results. For example indications of low dimensional chaos have been reported for stock marked data, based on recurrence plots. In this work we exploit recurrences or ``naturally occurring analogues'' as they were termed by E. Lorenz, to obtain three key results. One of which is that the most striking structures which are found in recurrence plots are hinged to the correlation entropy and the correlation dimension of the underlying system. Even though an eventual embedding changes the structures in recurrence plots considerably these dynamical invariants can be estimated independently of the special parameters used for the computation. The second key result is that the attractor can be reconstructed from the recurrence plot. This means that it contains all topological information of the system under question in the limit of long time series. The graphical representation of the recurrences can also help to develop new algorithms and exploit specific structures. This feature has helped to obtain the third key result of this study. Based on recurrences to points which have the same ``recurrence structure'', it is possible to generate surrogates of the system which capture all relevant dynamical characteristics, such as entropies, dimensions and characteristic frequencies of the system. These so generated surrogates are shadowed by a trajectory of the system which starts at different initial conditions than the time series in question. They can be used then to test for complex synchronisation.