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1
Content available remote Scaling properties of rainfall records in some Mexican zones
EN
Since the 1990 decade, it has been suggested that atmospheric processes associated with rainfall could be a self-organized critical (SOC) phenomenon similar, for example, to seismicity. In this sense, the rain events taken as the output of the complex atmospheric system (sun’s radiation, water evaporation, clouds, etc.) are analogous to earthquakes, as the output of a relaxation process of the earth crust. A clue on this possible SOC behavior of rain phenomenon has been the ubiquitous presence of power laws in rain statistics. In the present article, we report the scaling properties of rain precipitation data taken from meteorological stations located at six zones of Mexico. Our results are consistent with those that assert that rainfall is a SOC phenomenon. We also analyze the Hurst exponent, which is appropriate to measure long-term memory of time series.
EN
Geotechnical centrifuge modelling has been a world-wide used technology in physical tests. In this papers a derivation of scaling laws by dimensional analysis for the centrifugal modelling is presented. Basic principles of centrifuge modelling are described. Scaling laws for slow events like consolidation and fast events like dynamic loads are shown. The differences in scale factors for both processes are noticed. The aim of this paper is to introduce geotechnical centrifuge technology to a wider Polish audience.
3
Content available remote Testing a scaling law for the earthquake recurrence time distributions
EN
The earthquake recurrence time distribution in a given space-time window is being studied, using earthquake catalogues from different seismic regions (Southern California, Canada, and Central Asia). The quality of the available catalogues, taking into account the completeness of the magnitude, is examined. Based on the analysis of the catalogues, it was determined that the probability densities of the earthquake recurrence times can be described by a universal gamma distribution, in which the time is normalized with the mean rate of occurrence. The results show a deviation from the gamma distribution at the short interevent times, suggesting the existence of clustering. This holds from worldwide to local scales and for quite different tectonic environments.
EN
As is well-known, the fatigue strength of materials decreases by increasing the specimen size. Such a decrease can be remarkable when very large structures are considered. An overview of experimental findings and theoretical studies on this phenomenon is presented. Then size effect in fatigue is explained by considering the fractal nature of the reacting cross sections of t structures, that is, the renormalized fatigue strength is represented by a force amplitude acting on I a surface with a fractal dimension lower than 2. This dimensional decrement, which depends on a self-similar weakening of the material ligament, owing to the presence of cracks, defects, voids, etc. (microscopic level), tends to progressively disappear by increasing the structure size (macroscopic level), i.e. the effect of the material microstructure on the fatigue behaviour gradually finishes for relatively large structures (multifractality). Accordingly, two scaling laws for fatigue limit are herein proposed, and some experimental results are examined in order to show how to apply the theoretical approach presented.
5
EN
A simple model based only on steric constrictions of chain molecules is used to describe the conformational characteristics of polymer chains endowed with various degrees of rigidity. The effect of rigidity of bond rotations was studied in terms of the model in relation to chain molecule size; a rigidity criterion was thus obtained, based on the width of the interval of rotational angles. Other results suggested the scaling law between the size of the chain and the number of monomers to become modified with the degree of chain rigidity. Examples of scaling behavior are discussed. An additional parameter, helicity, which corresponds with the average rotation angle, is presented as helpful in understanding the structural characteristics of polymer chains.
PL
Do opisu charakterystyk konformacyjnych łańcuchów o różnych stopniach sztywności zastosowano prosty model oparty jedynie na sferycznych ograniczeniach łańcuchów polimerowych. Za pomocą tego modelu scharakteryzowano wpływ sztywności obrotów wiązań w zależności od wymiarów łańcuchów, uzyskując przy tym kryterium sztywności związane z szerokością przedziału kątów rotacji. Stwierdzono, że stopień sztywności łańcucha wpływa na postać prawa skalowania, które wiąże wymiar łańcucha z liczbą jednostek monomerycznych. Przedyskutowano przykłady dotyczące prawa skalowania. Wprowadzono dodatkowy parametr - helikalność - związany ze średnim kątem rotacji, upraszczający opis charakterystyki strukturalnej łańcuchów polimerów.
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