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  • Author: Andrzej Nowakowski x
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Abstract

We analyze the “fractional continuum limit” and its generalization to n dimensions of a self-similar discrete spring model which we introduced recently [21]. Application of Hamilton’s (variational) principle determines in rigorous manner a self-similar and as consequence non-local Laplacian operator. In the fractional continuum limit the discrete self-similar Laplacian takes the form of the fractional Laplacian $ - ( - \Delta )^{\tfrac{\alpha } {2}} $ with 0 < α < 2. We analyze the fundamental link of fractal vibrational features of the discrete self-similar spring model and the smooth regular ones of the corresponding fractional continuum limit model in n dimensions: We find a characteristic scaling law for the density of normal modes ∼ $\omega ^{\tfrac{{2n}} {\alpha } - 1} $ with a positive exponent $\tfrac{{2n}} {\alpha } - 1 > n - 1 $ being always greater than n−1 characterizing a regular lattice with local interparticle interactions. Furthermore, we study in this setting anomalous diffusion generated by this Laplacian which is the source of Lévi flights in n-dimensions. In the limit of “large scaled times” ∼ t/r α >> 1 we show that all distributions exhibit the same asymptotically algebraic decay ∼ t -n/α → 0 independent from the initial distribution and spatial position. This universal scaling depends only on the ratio n/α of the dimension n of the physical space and the Lévi parameter α.

Abstract

Relations between climatic factors during the winter season (n days with frost <0oC and −10oC; n days with snow cover: >1 cm, >10 cm and >30 cm; maximum snow cover during season [cm]) and mortality in free-living ungulates (red deer Cervus elaphus Linnaeus, 1758, roe deer Capreolus capreolus Linnaeus, 1758 and mouflon Ovis aries musimon Linnaeus, 1758) in the Owl Mountains (Lower Silesia – Poland) in years 1998–2010 were investigated. Significant effects of all analysed climatic factors on ungulates mortality were documented. Correlations (Pearson) between such weather factors as the depth of snow cover and number of days with frost and recorded mortality in total animal populations analysed ranged from r = 0.33 to r = 0.77. The least adapted to local weather conditions was mouflon introduced to this area ca. 100 years ago from more southern parts of Europe. Roe deer species seems to be environmentally plastic, and are doing quite well in severe winters. Tolerance of red deer to the snow cover is much lower at low temperatures due to the fact that this species, during the period of snow cover, has limited access to the plants covered with snow and difficult access to food base.

Abstract

The subject of the research was a catastrophic recorder of the S2-3a system for recording flight parameters, developed at the Air Force Institute of Technology. The article discusses tests of catastrophic recorders’ resilience to factors present at aircraft accidents. The document specifying the requirements for catastrophic recorders of flight parameters includes the defence standard: NO-16-A200, and the European standard: EuroCAE ED-112. According to NO-16-A200 and ED-112 standards, the protective unit should be resistant to: g-forces existing during crash, puncture, compression, fire, underwater pressure and aggressive liquids.

Abstract

The tendency to increase the temperature of gases and the desire to extend the service life forces the use of a protective coating on the blade. The publication presents the technology of applying a heat-resistant protective coating onto the jet engine turbine blade by means of plasma thermal spraying, taking into account the process of aluminizing and heat treatment after aluminizing. The paper presents the results of work on the possibilities of shaping the thickness of the protective coating on the blade by changing the parameters of the spraying process, such as spraying distance, amount of hydrogen, amount of argon and the number of torch passes.

Abstract

Single crystals of lithium-sodium-tetragermanate, a member of the solid solution series Li2−xNaxGe4O9 with x=0.28, pure and slightly doped with Cr3+ ions (0.03 mol.% and 0.1 mol.%), were grown in ambient atmosphere by the Czochralski technique from stoichiometric melt. The crystals with dimensions up to 20 mm in diameter and 50 mm in length were obtained. The crystal structure has been determined by means of X-ray diffraction. Phase analysis and structural refinement of the Li1.72Na0.28Ge4O9 crystals were performed by X-ray powder diffraction using Ni-filtered Cu Kα radiation with a Siemens D5000 diffractometer. The absorption, excitation and photoluminescence spectra of the crystals were measured in the UV-VIS and IR range at low temperatures. EPR investigations were performed using a conventional X-band Bruker ELEXSYS E 500 CW-spectrometer operating at 9.5 GHz with 100 kHz magnetic field modulation. Temperature and angular dependences of the EPR spectra of the crystal samples were recorded in the 3–300 K temperature range.

Abstract

Emys orbicularis is receding from Europe, mainly due to anthropogenic habitat changes. Its parasite, Placobdella costata, is widely distributed within both the former and the present distribution range of the host. Though closely associated with the mud turtle, it may have other hosts (birds, amphibians, reptiles). Its reproductive period coincides with that of its host’s migration to the breeding grounds, thus facilitating dispersal of the parasite. Based on literature data we have analyzed the geographic spread of P. costata and mud turtle to observe the possible overlap of their habitats. Observations on the population of mud turtle and the associated leech species (P. costata) were carried out in eastern Poland — Podlasie Lowland. The studies were conducted in spring and summer in 1986–1993. The leeches were collected from the turtles caught in the water and on land. Observations showed that most leeches were found on turtles inhabiting the lake or moving to a breeding area. The greatest intensity of invasion was observed in June and July and that most leeches were observed in female E. orbicularis characterized by greater length of the carapace and weight, compared with males and juvenile individuals.