L2-torsion of hyperbolic manifolds

The L^2-torsion is an invariant defined for compact L^2-acyclic manifolds of determinant class, for example odd dimensional hyperbolic manifolds. It was introduced by John Lott and Varghese Mathai and computed for hyperbolic manifolds in low dimensions. In this paper we show that the L^2-torsion of hyperbolic manifolds of arbitrary odd dimension does not vanish. This was conjectured by J. Lott and W. Lueck. Some concrete values are computed and an estimate of their growth with the dimension is given.Comment: AMS-LaTeX2e, 5 pages, to appear in Manuscripta Mathematic

Sedimentary evidence of the Late Holocene tsunami in the Shetland Islands (UK) at Loch Flugarth, northern Mainland

Tsunami deposits around the North Sea basin are needed to assess the long-term hazard of tsunamis. Here, we present sedimentary evidence of the youngest tsunami on the Shetland Islands from Loch Flugarth, a coastal lake on northern Mainland. Three gravity cores show organic-rich background sedimentation with many sub-centimetre-scale sand layers, reflecting recurring storm overwash and a sediment source limited to the active beach and uppermost subtidal zone. A basal 13-cm-thick sand layer, dated to 426–787 cal. a CE based on 14C, 137Cs and Bayesian age–depth modelling, was found in all cores. High-resolution grain-size analysis identified four normally graded or massive sublayers with inversely graded traction carpets at the base of two sublayers. A thin organic-rich ‘mud’ drape and a ‘mud’ cap cover the two uppermost sublayers, which also contain small rip-up clasts. Grain-size distributions show a difference between the basal sand layer and the coarser and better sorted storm layers above. Multivariate statistical analysis of X-ray fluorescence core scanning data also distinguishes both sand units: Zr, Fe and Ti dominate the thick basal sand, while the thin storm layers are high in K and Si. Enriched Zr and Ti in the basal sand layer, in combination with increased magnetic susceptibility, may be related to higher heavy mineral content reflecting an additional marine sediment source below the storm-wave base that is activated by a tsunami. Based on reinterpretation of chronological data from two different published sites and the chronostratigraphy of the present study, the tsunami seems to date to c. 1400 cal. a BP. Although the source of the tsunami remains unclear, the lack of evidence for this event outside of the Shetland Islands suggests that it had a local source and was smaller than the older Storegga tsunami (8.15 cal. ka BP), which affected most of the North Sea basin.</p

Bifurcations of a three-toms in a twin-stripe semiconductor laser model

Abstract The dynamic behaviour of the strongly coupled twin-stripe semiconductor laser is studied theoretically in dependence on the pumping strength (current injection). With the aid of power spectra, next-maximum maps, and estimates of the attractor dimensions bifurcations from a three-toms to a two-toms and from two-toil to chaotic attractors are identified

A 1500‐year record of North Atlantic storm flooding from lacustrine sediments, Shetland Islands (UK)

Severe storm flooding poses a major hazard to the coasts of north‐western Europe. However, the long‐term recurrence patterns of extreme coastal flooding and their governing factors are poorly understood. Therefore, high‐resolution sedimentary records of past North Atlantic storm flooding are required. This multi‐proxy study reconstructs storm‐induced overwash processes from coastal lake sediments on the Shetland Islands using grain‐size and geochemical data, and the re‐analysis of historical data. The chronostratigraphy is based on Bayesian age–depth modelling using accelerator mass spectrometry 14 C and 137 Cs data. A high XRF‐based Si/Ti ratio and the unimodal grain‐size distribution link the sand layers to the beach and thus storm‐induced overwash events. Periods with more frequent storm flooding occurred 980–1050, 1150–1300, 1450–1550, 1820–1900 and 1950–2000 ce, which is largely consistent with a positive North Atlantic Oscillation mode. The Little Ice Age (1400–1850 ce ) shows a gap of major sand layers suggesting a southward shift of storm tracks and a seasonal variance with more storm floods in spring and autumn. Warmer phases shifted winter storm tracks towards the north‐east Atlantic, indicating a possible trend for future storm‐track changes and increased storm flooding in the northern North Sea region

Investigations of innovative algorithms for quantitative high temperature event (fires, volcano eruptions, etc.) emission analysis applying infrared spectrum and image data fusion

High Temperature Events (HTEs) like vegetation fires, peat/coal seam burning, and active volcanoes emit large quantities of radiative active gases and aerosols into the atmosphere. Quantification of these is required to determine their influence on atmospheric processes. For this purpose a sensor/data fusion technique has been developed to investigate HTEs from space. It combines high spatial, low spectral resolution infrared image and high spectral, low spatial resolution spectrometer data in order to derive parameters such as: HTE type and area, plume gas concentration and temperature, total plume gas contents, etc.. Simulations of the method rendered promising results. Currently there is no dedicated sensor system in space. Application to AIRS/MODIS data of Portugal 2003 fires have confirmed the need for high spectral resolution The superior spectral resolution of IASI encourages to investigate the IASI/AVHRR combination

Sedimentary evidence of the Late Holocene tsunami in the Shetland Islands (UK) at Loch Flugarth, northern Mainland

Tsunami deposits around the North Sea basin are needed to assess the long-term hazard of tsunamis. Here, we present sedimentary evidence of the youngest tsunami on the Shetland Islands from Loch Flugarth, a coastal lake on northern Mainland. Three gravity cores show organic-rich background sedimentation with many sub-centimetre-scale sand layers, reflecting recurring storm overwash and a sediment source limited to the active beach and uppermost subtidal zone. A basal 13-cm-thick sand layer, dated to 426-787 cal. a CE based on 14C, 137Cs and Bayesian age-depth modelling, was found in all cores. High-resolution grain-size analysis identified four normally graded or massive sublayers with inversely graded traction carpets at the base of two sublayers. A thin organic-rich 'mud' drape and a 'mud' cap cover the two uppermost sublayers, which also contain small rip-up clasts. Grain-size distributions show a difference between the basal sand layer and the coarser and better sorted storm layers above. Multivariate statistical analysis of X-ray fluorescence core scanning data also distinguishes both sand units: Zr, Fe and Ti dominate the thick basal sand, while the thin storm layers are high in K and Si. Enriched Zr and Ti in the basal sand layer, in combination with increased magnetic susceptibility, may be related to higher heavy mineral content reflecting an additional marine sediment source below the storm-wave base that is activated by a tsunami. Based on reinterpretation of chronological data from two different published sites and the chronostratigraphy of the present study, the tsunami seems to date to c. 1400 cal. a BP. Although the source of the tsunami remains unclear, the lack of evidence for this event outside of the Shetland Islands suggests that it had a local source and was smaller than the older Storegga tsunami (8.15 cal. ka BP), which affected most of the North Sea basin. Sediment cores from coastal lake Loch Flugarth on northen Mainland, Shetland Islands (UK), contain a thick unit of sand with four stacked subsequences. Grain-size distribution, geochemistry and geophysical characteristics indicate deposition by a tsunami. The age-depth model of the core points to tsunami impact c. 1400 cal. BP and correlation with deposits from two other sites on the Shetland Islands.imag