Random vibrations of the baltic drilling platform subjected to wind loads and water waves

This paper presents random vibrations of the Baltic drilling platform subjected to water waves and wind loads. The platform structure is discretized by the finite element method. Linear beam or truss elements can be used. The structure parameters (i.e. mass, damping and stiffness) are assumed as deterministic. Soil is modelled as an elastic half-space that possesses deterministic or random parameters. Soil–structure interaction is idealized as a system of spring–dashpot elements connecting the structure and subsoil. The parameters of these elements can be random or deterministic. The sea surface is described by the one-dimensional wave spectrum that was proposed by Striekalov and Massel²⁴ for inland seas. It is suitable for the Baltic Sea. The wind velocity is described by the well-known Davenport spectrum. The water and wind loads are treated as stationary ergodic processes. Gaussian distributions and zero means of these processes are assumed. In addition to this, waves and wind loads are considered as independent. Such an assumption corresponds to the situation when the storm sea is fully developed. A frequency-domain random-vibration approach is utilized to obtain the dynamic response of the platform. The equations of motion of the problem were solved using modal reduction. The numerical calculations were made with a specially written computer program. From the results obtained, it is concluded that the wind influence on the response of the platform can be neglected. If random parameters are assumed for the subsoil, then the response of the system describes in a more realistic way the dynamic behaviour of the platform. The velocity coupling due to soil and hydrodynamical damping is negligible. This paper is a condensation of the author's Ph.D. thesis presented at the Technical University of Gdańsk in July 1985.     

Unconfined linear flow to a horizontal well

The validity of a previously proposed but untested modification to equations for flow to a horizontal well is assessed using a specially developed finite-difference model. This modification extends confined flow equations to allow the head in the well and the saturated depth at the well to be estimated in unconfined conditions. The study is limited to the case of two-dimensional flow with no flow in the direction parallel to the line of the well. The results show that the modified equations for both a finite unconfined aquifer and, by inference, an infinite unconfined aquifer are adequately accurate for practical application.     

Distribution of compact object mergers around galaxies

Compact object mergers are one of the currently favoured models for the origin of gamma-ray bursts (GRBs). The discovery of optical afterglows and identification of the nearest, presumably host, galaxies allow the analysis of the distribution of burst sites with respect to these galaxies. Using a model of stellar binary evolution we synthesize a population of compact binary systems which merge within the Hubble time. We include the kicks in the supernovae explosions and calculate orbits of these binaries in galactic gravitational potentials. We present the resulting distribution of merger sites and discuss the results in the framework of the observed GRB afterglows.     

Anisotropic Kepler and anisotropic two fixed centres problems

In this paper we show that the anisotropic Kepler problem is dynamically equivalent to a system of two point masses which move in perpendicular lines (or planes) and interact according to Newton’s law of universal gravitation. Moreover, we prove that generalised version of anisotropic Kepler problem as well as anisotropic two centres problem are non-integrable. This was achieved thanks to investigation of differential Galois groups of variational equations along certain particular solutions. Properties of these groups yield very strong necessary integrability conditions.     

Modelling of hydrogeochemical potential of three lake catchments in Polesie region (Eastern Poland)

Total dissolved solids (TDS) in lake and catchment water is a result of geological structure, as well as duration of rock and water contact and human activity. In this paper, a potential dissolved solids (PtDS) in three ??czna–W?odawa Lake catchments was determined using extraction and computer software (GIS and AquaChem). Human pressure on water quality was estimated as a difference of the TDS and a catchment hydrogeochemical potential (TPtDS, total potential dissolved solids). TPtDS coefficient included hydrogeological features of the aquifer, soil cover impact on infiltrated water quality, and sediments susceptibility to denudation. The main advantage of the model is a possibility of its employment for every catchment or other areas (e.g. administrative) on both microscale and mesoscale. The highest TPtDS occurred in the catchment, favoured with underground supply, which was located in the vicinity of the Cretaceous mesoregional unit (Che?m Hills). The lowest value was observed in the catchment built with organogenic sediments and coarse material. A seasonal constancy of TPtDS values proved a stability of the lake‐catchment systems under study. Copyright © 2012 John Wiley & Sons, Ltd.     

Explicit stress integration with error control for the Barcelona Basic Model: Part I: Algorithms formulations

The numerical integration of the stress–strain relationship is an important part of many finite element code used in geotechnical engineering. The integration of elasto-plastic models for unsaturated soils poses additional challenges associated to the presence of suction as an extra constitutive variable with respect to traditional saturated soil models. In this contribution, a range of explicit stress integration schemes are derived with specific reference to the Barcelona Basic Model (BBM), which is one of the best known elasto-plastic constitutive models for unsaturated soils. These schemes, however, do not address possible non-convexity of the loading collapse (LC) curve and neglect yielding on the suction increase (SI) line. The paper describes eight Runge–Kutta methods of various orders with adaptive substepping as well as a novel integration scheme based on Richardson extrapolation. The algorithms presented also incorporate two alternative error control methods to ensure accuracy of the numerical integration. Extensive validation and comparison of different schemes are presented in a companion paper. Although the algorithms presented were coded for the Barcelona Basic Model, they can be easily adapted to other unsaturated elasto-plastic models formulated in terms of two independent stress variables such as net stress and suction.     

EPR and magnetism of the nanostructured natural carbonaceous material shungite

The X-band EPR and magnetic susceptibility in the temperature range 4.2–300 K study of the shungite-I, natural nanostructured material from the deposit of Shunga are reported. Obtained results allow us to assign the EPR signal to conduction electrons, estimate their number, N _P, and evaluate the Pauli paramagnetism contribution to shungite susceptibility. A small occupation (~5%) of the localized nonbonding π states in the zigzag edges of the open-ended graphene-like layers and/or on σ (sp ^2+x ) orbitals in the curved parts of the shungite globules has been also revealed. The observed temperature dependence of the EPR linewidth can be explained by the earlier considered interaction of conduction π electrons with local phonon modes associated with the vibration of peripheral carbon atoms of the open zigzag-type edges and with peripheral carbon atoms cross-linking different nanostructures. The relaxation time T ₂ and diffusion time T _D are found to have comparable values (2.84 × 10⁻⁸ and 1.73 × 10⁻⁸ s at 5.2 K, respectively), and similar dependence on temperature. The magnetic measurements have revealed the suppression of orbital diamagnetism due to small amount of large enough fragments of the graphene layers.     

On the influence of microphysics parametrization on the rainfall rates in numerical models of clouds

Accuracy of formulas for growth by accretion and evaporation of rain in bulk parametrization of these processes for the case of light and moderate precipitation is investigated. It is done by comparison of results from two simple models: with bulk approach and with exact calculations of growth or evaporation of drops in each size bin separately. Growth by accretion is accurately represented in bulk parametrization but rain evaporation is overpredicted. Corrected formula for rain evaporation is suggested.     

On the bulk parameterization of snow and its application to the quantitative studies of precipitation growth

Appropriate formulation of bulk parameterization of snow growth and evaporation based on observational characteristics of snow particles is presented. The parameterization is compared to that of S. A. Rutledge and P. V. Hobbs and to detailed treatment in which snow particles are assumed to grow or evaporate in each size bin separately. On the contrary to bulk parameterization of rain, snow diffusional growth or evaporation is accurately represented in the suggested bulk formulation, but growth by riming is overpredicted. Integrations of water budget equations in a one-dimensional updraft have shown that quantitative results, e.g., precipitation intensity, cloudwater content, supersaturation with respect to ice, depend on the parameterization scheme employed, which suggests that comparisons of field measurements with parameterized model outputs is usually not straightforward.