Immortal homogeneous Ricci flows

We show that for an immortal homogeneous Ricci flow solution any sequence of parabolic blow-downs subconverges to a homogeneous expanding Ricci soliton. This is established by constructing a new Lyapunov function based on curvature estimates which come from real geometric invariant theory.Comment: Final version, to appear in Invent. Mat

Atmospheric water supply to the Atacama Desert from newly developed satellite remote sensing techniques and reanalysis

Many facets of atmospheric water supply to the Atacama Desert are poorly understood. However, in-depth knowledge regarding water availability, moisture sources and the underlying mechanisms is required to investigate biological and geological processes and to identify potential mutual relationships. This thesis provides a comprehensive meteorological perspective on the atmospheric water supply to the Atacama Desert within the context of the recent climate. Spatial and temporal variability of moisture as well as their controlling mechanisms depend on the type of water supply, i.e. clouds, water vapor, fog or precipitation. To investigate the influence of the persistent stratocumulus cloud deck above the southeast Pacific on the desert region, a new cloud base height retrieval method is introduced. It allows to estimate the vertical position of these clouds, which can help to identify regions within the coastal desert that are potentially influenced by these clouds. A first application of this new method revealed a strong relation between stratocumulus properties and the isotopic composition of coastal Tillandsia populations. The proximity of the Atacama Desert to main acting zones of the El Niño-Southern Oscillation (ENSO) phenomenon and of the Pacific Decadal Oscillation (PDO) together with results from previous studies suggest that modes of climate variability have strong influence on the moisture supply to this region. As oscillating extreme phases of these climate modes have recurring periods on the order of a few years to decades, a long data record is needed to study their impact. Therefore, spatio-temporal variability of integrated water vapor (IWV) provided by a century-spanning reanalysis data set is studied in relation to ENSO and PDO. It is shown that the reanalysis represents IWV in a suitable manner to study its long-term variability. On a decadal time scale, the PDO revealed a stronger coupling to IWV compared to ENSO. According to a seasonal analysis, identified relationships between ENSO and IWV are in line with findings reported for precipitation in the northeastern Atacama. This suggests that IWV has the potential to serve as a proxy for precipitation. The ENSO signal is opposite for summer and winter season. The negative phase (La Niña) favors wetter summers and drier winters, whereas the positive phase (El Niño) is associated with drier summers and wetter winters. Besides, it is shown that enhanced IWV under La Niña conditions is not constrained to the northeastern part of the Atacama Desert but can reach even offshore regions near the west coast. This effect can be typically observed in the summer season. Thus, the moisture can be supplied to the Atacama Desert from easterly or westerly sources depending on season and ENSO phase with regionally varying impacts. Water vapor is a key variable which controls fog formation. While a few studies demonstrate the impact of fog on the coastal desert based on in-situ measurements as well as spatially and temporally limited satellited-based observations, this thesis introduces a novel satellite-based fog detection method which allows a region-wide assessment. An application of the algorithm for a 3-year period shows the spatial distribution of fog frequencies across the Atacama Desert. Aside from the coastal maximum, high fog frequencies are also revealed for isolated locations farther inland, which often coincide with salt flats within the central valley. The mechanisms driving fog formation within these inland regions remain unclear. The novel fog detection method creates the opportunity to further investigate this issue in future research. Aside from westerly moisture sources associated with the Pacific Ocean and episodic easterly inflow from the continental interior, a third scenario is identified in this thesis. By investigating the role of atmospheric rivers for the Atacama Desert, it is revealed that moisture can be transported from the Amazon Basin across the Andes and the southeast Pacific towards the Atacama Desert. Furthermore, fractional precipitation rates of more than 50 % for various regions within the Atacama Desert demonstrate the importance of atmospheric rivers for this hyperarid environment

A Reliable Low-area Low-power PUF-based Key Generator

This paper reports the implementation of a lowarea low-power 128-bit PUF-based key generation module which exploits a novel Two-Stage IDentification (TSID) cell showing a higher noise immunity then a standard SRAM cell. In addition, the pre-selection technique introduced in [1] is applied. This results in a stable PUF response in spite of process and environmental variations thus requiring a low cost error correction algorithm in order to generate a reliable key. The adopted PUF cell array includes 1056 cells and shows a power consumption per bit of 4:2 W at 100MHz with an area per bit of 2:4 m2. In order to evaluate reliability and unpredictability of the generated key, extensive tests have been performed both on the raw PUF data and on the final key. The raw PUF data after pre-selection show a worst case intra-chip Hamming distance below 0:7%. After a total of more than 5 109 key reconstructions, no single fail has been detected

Non-compact Einstein manifolds with unimodular isometry group

We show that a negative Einstein manifold admitting a proper isometric action of a connected unimodular Lie group with compact, possibly singular, orbit space splits isometrically as a product of a symmetric space and a compact negative Einstein manifold. The proof involves the theory of polar actions, Lie-theoretic arguments and maximum principles.Comment: 26 page

Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds

We show that homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds, using that they admit periodic, integrally minimal foliations by homogeneous hypersurfaces. For the geometric flow induced by the orbit-Einstein condition, we construct a Lyapunov function based on curvature estimates which come from real GIT.Comment: 23 page