@misc{Dietrich2008,
  type      = {Master Thesis},
  author    = {Dietrich, Jan Philipp},
  title     = {Phase Space Reconstruction using the frequency domain : a generalization of actual methods},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-50738},
  school      = {Universit{\"a}t Potsdam},
  year      = {2008},
  abstract  = {Phase Space Reconstruction is a method that allows to reconstruct the phase space of a system using only an one dimensional time series as input. It can be used for calculating Lyapunov-exponents and detecting chaos. It helps to understand complex dynamics and their behavior. And it can reproduce datasets which were not measured. There are many different methods which produce correct reconstructions such as time-delay, Hilbert-transformation, derivation and integration. The most used one is time-delay but all methods have special properties which are useful in different situations. Hence, every reconstruction method has some situations where it is the best choice. Looking at all these different methods the questions are: Why can all these different looking methods be used for the same purpose? Is there any connection between all these functions? The answer is found in the frequency domain : Performing a Fourier transformation all these methods getting a similar shape: Every presented reconstruction method can be described as a multiplication in the frequency domain with a frequency-depending reconstruction function. This structure is also known as a filter. From this point of view every reconstructed dimension can be seen as a filtered version of the measured time series. It contains the original data but applies just a new focus: Some parts are amplified and other parts are reduced. Furthermore I show, that not every function can be used for reconstruction. In the thesis three characteristics are identified, which are mandatory for the reconstruction function. Under consideration of these restrictions one gets a whole bunch of new reconstruction functions. So it is possible to reduce noise within the reconstruction process itself or to use some advantages of already known reconstructions methods while suppressing unwanted characteristics of it.},
  language  = {en}
}
@misc{Flassig2008,
  type      = {Master Thesis},
  author    = {Flassig, Robert Johann},
  title     = {Dusty ringlets in Saturn's ring system},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-27046},
  school      = {Universit{\"a}t Potsdam},
  year      = {2008},
  abstract  = {Recently, several faint ringlets in the Saturnian ring system were found to maintain a peculiar orientation relative to Sun. The Encke gap ringlets as well as the ringlet in the outer rift of the Cassini division were found to have distinct spatial displacements of several tens of kilometers away from Saturn towards Sun, referred to as heliotropicity (Hedman et al., 2007). This is quite exceptional, since dynamically one would expect eccentric features in the Saturnian rings to precess around Saturn over periods of months. In our study we address this exceptional behavior by investigating the dynamics of circumplanetary dust particles with sizes in the range of 1-100 µm. These small particles are perturbed by non-gravitational forces, in particular, solar radiation pres- sure, Lorentz force, and planetary oblateness, on time-scales of the order of days. The combined influences of these forces cause periodical evolutions of grains' orbital ec- centricities as well as precession of their pericenters, which can be shown by secular perturbation theory. We show that this interaction results in a stationary eccentric ringlet, oriented with its apocenter towards the Sun, which is consistent with obser- vational findings. By applying this heliotropic dynamics to the central Encke gap ringlet, we can give a limit for the expected smallest grain size in the ringlet of about 8.7 microns, and constrain the minimal lifetime to lie in the order of months. Furthermore, our model matches fairly well the observed ringlet eccentricity in the Encke gap, which supports recent estimates on the size distribution of the ringlet material (Hedman et al., 2007). The ringlet-width however, that results from our modeling based on heliotropic dynamics, slightly overestimates the observed confined ringlet-width by a factor of 3 to 10, depending on the width-measure being used. This is indicative for mechanisms, not included in the heliotropic model, which potentially confine the ringlet to its observed width, including shepherding and scattering by embedded moonlets in the ringlet region. Based on these results, early investigations (Cuzzi et al., 1984, Spahn and Wiebicke, 1989, Spahn and Sponholz, 1989), and recent work that has been published on the F ring (Murray et al., 2008) - to which the Encke gap ringlets are found to share similar morphological structures - we model the maintenance of the central ringlet by embedded moonlets. These moonlets, believed to have sizes of hundreds of meters across, release material into space, which is eroded by micrometeoroid bombardment (Divine, 1993). We further argue that Pan - one of Saturn's moons, which shares its orbit with the central ringlet of the Encke gap - is a rather weak source of ringlet material that efficiently confines the ringlet sources (moonlets) to move on horseshoe-like orbits. Moreover, we suppose that most of the narrow heliotropic ringlets are fed by a moonlet population, which is held together by the largest member to move on horseshoe-like orbits. Modeling the equilibrium between particle source and sinks with a primitive balance equation based on photometric observations (Porco et al., 2005), we find the minimal effective source mass of the order of 3 · 10-2MPan, which is needed to keep the central ringlet from disappearing.},
  language  = {en}
}