Automorphisms of free groups with boundaries

The automorphisms of free groups with boundaries form a family of groups A_{n,k} closely related to mapping class groups, with the standard automorphisms of free groups as A_{n,0} and (essentially) the symmetric automorphisms of free groups as A_{0,k}. We construct a contractible space L_{n,k} on which A_{n,k} acts with finite stabilizers and finite quotient space and deduce a range for the virtual cohomological dimension of A_{n,k}. We also give a presentation of the groups and calculate their first homology group.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-25.abs.htm

Assessing the hydrodynamic boundary conditions for risk analyses in coastal areas: a multivariate statistical approach based on Copula functions

This paper presents an advanced approach to statistically analyse storm surge events. In former studies the highest water level during a storm surge event usually was the only parameter that was used for the statistical assessment. This is not always sufficient, especially when statistically analysing storm surge scenarios for event-based risk analyses. Here, Archimedean Copula functions are applied and allow for the consideration of further important parameters in addition to the highest storm surge water levels. First, a bivariate model is presented and used to estimate exceedance probabilities of storm surges (for two tide gauges in the German Bight) by jointly analysing the important storm surge parameters "highest turning point" and "intensity". Second, another dimension is added and a trivariate fully nested Archimedean Copula model is applied to additionally incorporate the significant wave height as an important wave parameter. With the presented methodology, reliable and realistic exceedance probabilities are derived and can be considered (among others) for integrated flood risk analyses contributing to improve the overall results. It is highlighted that the concept of Copulas represents a promising alternative for facing multivariate problems in coastal engineering.<br/

On analysing sea level rise in the German Bight since 1844

In this paper, a methodology to analyse observed sea level rise (SLR) in the German Bight, the shallow south-eastern part of the North Sea, is presented. The paper focuses on the description of the methods used to generate and analyse mean sea level (MSL) time series. Parametric fitting approaches as well as non-parametric data adaptive filters, such as Singular System Analysis (SSA) are applied. For padding non-stationary sea level time series, an advanced approach named Monte-Carlo autoregressive padding (MCAP) is introduced. This approach allows the specification of uncertainties of the behaviour of smoothed time series near the boundaries. As an example, the paper includes the results from analysing the sea level records of the Cuxhaven tide gauge and the Heligoland tide gauge, both located in the south-eastern North Sea. For comparison, the results from analysing a worldwide sea level reconstruction are also presented. The results for the North Sea point to a weak negative acceleration of SLR since 1844 with a strong positive acceleration at the end of the 19th century, to a period of almost no SLR around the 1970s with subsequent positive acceleration and to high recent rates

Statistics of Extreme Still Water Levels - Between Policy and Objectivity

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

Chemical control of bacterial epibiosis on ascidians

Two co-occurring ascidians of the Pacific subtidal, Polyclinum planum and Cystodytes lobatus, were found to exhibit remarkably different numbers of surface bacteria. On average, epibacterial densities on P. planum were 140 times greater than those on C lobatus as measured by plate-counting methods. Organic extracts of both ascidian species were tested for antimicrobial activities and effects on bacterial settlement. Bacterial settlement was measured using a new bioassay described in this paper. The results of the settlement bioassay clearly demonstrate that extracts of the little-colonized C. lobatus deter bacterial settlement while extracts of the heavily colonized P. planum induce settlement relative to the control. In addition to reducing bacterial settlement, extracts of C. lobatus colonies exhibited varying, but generally low, levels of antiraicrobial activity against, on average, one-half of the 36 strains of marine bacteria tested. On an interspecific level, including 11 ascidian species screened in a pilot study, fouling-deterring activities were correlated with epibacterial abundances while antimicrobial activity was not. It is concluded that the chemical control of bacterial settlement, possibly complemented by antimicrobial toxicity, provides an accurate model to explain the dramatically different bacterial abundance on the surfaces of the ascidian species studied. This investigation presents evidence that non-toxic metabolites influence bacterial settlement and, in this way, may function to regulate bacterial epibiosis on the surfaces of some marine invertebrates

Mean sea level variability and influence of the North Atlantic oscillation on long-term trends in the German Bight

Changes in the seasonal cycle of mean sea level (MSL) may affect the heights of storm surges and thereby flood risk in coastal areas. This study investigates the intra- and inter-annual variability of monthly MSL and its link to the North Atlantic Oscillation using records from 13 tide gauges located in the German Bight. The amplitudes of the seasonal MSL cycle are not regionally uniform and vary between 20 and 29 cm. Generally, the amplitudes are smaller at the southwestern stations, increasing as one travels to the northeastern part. The amplitudes, as well as the phase of the seasonal cycle, are characterized by a large inter-annual and inter-decadal variability, but no long-term trend could be detected. Nevertheless, in the last two decades annual maximum peaks more frequently occurred in January and February, whereas beforehand an accumulation was detected for the November and December period. These changes in phase in the various sea level time series are consistent with a shift in the annual cycle, which is, however, not significant. The changes are associated with strongly increasing trends in monthly MSL of the winter season (J–M), which are considerably higher compared to the remaining seasons. For the same season, the MSL and North Atlantic Oscillation (NAO) indices show strong similarities, resulting in statistically significant correlations (r ~ 0.7). Hence, these changes are linked with changing pressure conditions over the North Atlantic, which lead to a strong phase of positive values in the NAO index between the 1960’s and 1990’s