Abstract:
The objective of this study is the production of an Alpine Permafrost Index Map (APIM) covering the entire European Alps. A unified statistical model that is based on Alpine-wide permafrost observations is used for debris and bedrock surfaces across the entire Alps. The explanatory variables of the model are mean annual air temperatures, potential incoming solar radiation and precipitation. Offset terms were applied to make model predictions for topographic and geomorphic conditions that differ from the terrain features used for model fitting. These offsets are based on literature review and involve some degree of subjective choice during model building. The assessment of the APIM is challenging because limited independent test data are available for comparison and these observations represent point information in a spatially highly variable topography. The APIM provides an index that describes the spatial distribution of permafrost and comes together with an interpretation key that helps to assess map uncertainties and to relate map contents to their actual expression in the terrain. The map can be used as a first resource to estimate permafrost conditions at any given location in the European Alps in a variety of contexts such as research and spatial planning. Results show that Switzerland likely is the country with the largest permafrost area in the Alps, followed by Italy, Austria, France and Germany. Slovenia and Liechtenstein may have marginal permafrost areas. In all countries the permafrost area is expected to be larger than the glacier-covered area.

Abstract:
Permafrost distribution modeling in densely populated mountain regions is an important task to support the construction of infrastructure and for the assessment of climate change effects on permafrost and related natural systems. In order to analyze permafrost distribution and evolution on an Alpine-wide scale, one consistent model for the entire domain is needed. We present a statistical permafrost model for the entire Alps based on rock glacier inventories and rock surface temperatures. Starting from an integrated model framework, two different sub-models were developed, one for debris covered areas (debris model) and one for steep rock faces (rock model). For the debris model a generalized linear mixed-effect model (GLMM) was used to predict the probability of a rock glacier being intact as opposed to relict. The model is based on the explanatory variables mean annual air temperature (MAAT), potential incoming solar radiation (PISR) and the mean annual sum of precipitation (PRECIP), and achieves an excellent discrimination (area under the receiver-operating characteristic, AUROC = 0.91). Surprisingly, the probability of a rock glacier being intact is positively associated with increasing PRECIP for given MAAT and PISR conditions. The rock model was calibrated with mean annual rock surface temperatures (MARST) and is based on MAAT and PISR. The linear regression achieves a root mean square error (RMSE) of 1.6 °C. The final model combines the two sub-models and accounts for the different scales used for model calibration. Further steps to transfer this model into a map-based product are outlined.

Abstract:
Estimates of permafrost distribution in mountain regions are important for the assessment of climate change effects on natural and human systems. In order to make permafrost analyses and the establishment of guidelines for e.g. construction or hazard assessment comparable and compatible between regions, one consistent and traceable model for the entire Alpine domain is required. For the calibration of statistical models, the scarcity of suitable and reliable information about the presence or absence of permafrost makes the use of large areas attractive due to the larger data base available. We present a strategy and method for modelling permafrost distribution of entire mountain regions and provide the results of statistical analyses and model calibration for the European Alps. Starting from an integrated model framework, two statistical sub-models are developed, one for debris-covered areas (debris model) and one for steep bedrock (rock model). They are calibrated using rock glacier inventories and rock surface temperatures. To support the later generalization to surface characteristics other than those available for calibration, so-called offset terms have been introduced into the model that allow doing this in a transparent and traceable manner. For the debris model a generalized linear mixed-effect model (GLMM) is used to predict the probability of a rock glacier being intact as opposed to relict. It is based on the explanatory variables mean annual air temperature (MAAT), potential incoming solar radiation (PISR) and the mean annual sum of precipitation (PRECIP), and achieves an excellent discrimination (area under the receiver-operating characteristic, AUROC = 0.91). Surprisingly, the probability of a rock glacier being intact is positively associated with increasing PRECIP for given MAAT and PISR conditions. The rock model is based on a linear regression and was calibrated with mean annual rock surface temperatures (MARST). The explanatory variables are MAAT and PISR. The linear regression achieves a root mean square error (RMSE) of 1.6 °C. The final model combines the two sub-models and accounts for the different scales used for model calibration. The modelling approach provides a theoretical basis for estimating mountain permafrost distribution over larger mountain ranges and can be expanded to more surface types and sub-models than considered, here. The analyses performed with the Alpine data set further provide quantitative insight into larger-area patterns as well as the model coefficients for a later spatial application. The transfer into a

Abstract:
The objective of this study is the production of an Alpine Permafrost Index Map (APIM) covering the entire European Alps. A unified statistical model that is based on Alpine-wide permafrost observations is used for debris and bedrock surfaces across the entire Alps. The explanatory variables of the model are mean annual air temperatures, potential incoming solar radiation and precipitation. Offset terms were applied to make model predictions for topographic and geomorphic conditions that differ from the terrain features used for model fitting. These offsets are based on literature review and involve some degree of subjective choice during model building. The assessment of the APIM is challenging because limited independent test data are available for comparison and these observations represent point information in a spatially highly variable topography. The APIM provides an index that describes the spatial distribution of permafrost and comes together with an interpretation key that helps to assess map uncertainties and to relate map contents to their actual expression in terrain. The map can be used as a first resource to estimate permafrost conditions at any given location in the European Alps in a variety of contexts such as research and spatial planning. Results show that Switzerland likely is the country with the largest permafrost area in the Alps, followed by Italy, Austria, France and Germany. Slovenia and Liechtenstein may have marginal permafrost areas. In all countries the permafrost area is expected to be larger than the glacier-covered area. The permafrost index map with an approximate grid spacing of 30 m is available at the webpage of the Department of Geography, University of Zurich.

Abstract:
The set S_{F}(x_{0};T) of states y reachable from a given state x_{0} at time T under a set-valued dynamic x’(t)∈F(x (t)) and under constraints x(t)∈K where K is a closed set, is also the capture-viability kernel of x_{0} at T in reverse time of the target {x_{0}} while remaining in K. In dimension up to three, Saint-Pierre’s viability algorithm is well-adapted; for higher dimensions, Bonneuil’s viability algorithm is better suited. It is used on a large-dimensional example.

The introduction of an exponential or power law gradient
in the interstellar medium (ISM) allows to produce an asymmetric
evolution of the supernova remnant (SNR) when the framework of the thin layer
approximation is adopted. Unfortunately both the exponential and power law
gradients for the ISM do not have a well defined physical meaning. The physics
conversely is well represented by an isothermal self-gravitating disk of
particles whose velocity is everywhere Maxwellian. We derived a law of motion
in the framework of the thin layer approximation with a control parameter of
the swept mass. The photon’s losses, which are often neglected in the thin layer
approximation, are modeled trough velocity dependence. The developed framework
is applied to SNR 1987A and the three observed rings are simulated.

Abstract:
A first new luminosity function of galaxies can be built starting from a left truncated beta probability density function, which is characterized by four parameters. In the astrophysical conversion, the number of parameters increases by one, due to the addition of the overall density of galaxies. A second new galaxy luminosity function is built starting from a left truncated beta probability for the mass of galaxies once a simple nonlinear relationship between mass and luminosity is assumed; in this case the number of parameters is six because the overall density of galaxies and a parameter that regulates mass and luminosity are added. The two new galaxy luminosity functions with finite boundaries were tested on the Sloan Digital Sky Survey (SDSS) in five different bands; the results produce a “better fit” than the Schechter luminosity function in two of the five bands considered. A modified Schechter luminosity function with four parameters has been also analyzed.

Abstract:
We argued that the standard field scalar potential couldn’t be widely used for getting the adequate galaxies’ curve lines and determining the profiles of dark matter their halo. For discovering the global properties of scalar fields that can describe the observable characteristics of dark matter on the cosmological space and time scales, we propose the simplest form of central symmetric potential celestial-mechanical type, i.e. U(φ) = –μ/φ. It was shown that this potential allows get rather satisfactorily dark matter profiles and rotational curves lines for dwarf galaxies. The good agreement with some previous results, based on the N-body simulation method, was pointed out. A new possibility of dwarf galaxies’ masses estimation was given, also.

Abstract:
We study the classical dynamics of binary stars when there is an interchange of mass between them. Assuming that one of
the stars is more massive than others, the dynamics of the lighter one is analyzed as a function of its time
depending mass variation. Within our approximations and models for mass
transference, we obtain a general result which establishes that if the lightest
star looses mass, its period increases. If the lightest star wins mass, its period decreases.

Abstract:
We present a method for determining the motion of an electron in a hydrogen atom, which starts from a field Lagrangean foundation for non-conservative systems that can exhibit chaotic behavior. As a consequence, the problem of the formation of the atom becomes the problem of finding the possible stable orbital attractors and the associated transition paths through which the electron mechanical energy varies continuously until a stable energy state is reached.