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Exponential Law (exponential + law)
Selected AbstractsThe scaling law in the hole erosion test with a constant pressure dropINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2008Stéphane Bonelli Abstract A process called ,piping', which often occurs in the soil at dams, levees, and dykes, involves the formation and development of a continuous tunnel between upstream and downstream ends. The hole erosion test is commonly used to quantify the critical stress and the rate of piping erosion progression. The aim of this study is to draw up a model for interpreting the results of this test. A characteristic internal erosion time is defined and expressed as a function of the initial hydraulic gradient and the coefficient of surface erosion. It is established here that the product of the coefficient of erosion and the flow velocity is a significant dimensionless number: when this number is small, the kinetics of erosion are low, and the particle concentration does not have any effect on the flow. This finding applies to most of the available test results. Theoretical and experimental evidence is presented showing that the evolution of the pipe radius during erosion with a constant pressure drop obeys a scaling exponential law. Copyright © 2008 John Wiley & Sons, Ltd. [source] Effective reaction rates of a thin catalyst layerMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2010Michael Lenzinger Abstract The catalyst layer in a fuel cell can be described with a system of reaction diffusion eq uations for the oxygen concentration and the protonic overpotential. The Tafel law gives an exponential expression for the reaction rate, and the Tafel slope is a coefficient in this law. We present a rigorous thin layer analysis for two reaction regimes. In the case of thin catalyst layers and bounded potentials, the original Tafel law enters as an effective boundary condition. Instead, in the case of large protonic overpotentials, we derive an exponential law that contains the doubled Tafel slope. Copyright © 2009 John Wiley & Sons, Ltd. [source] Investigation of the ELAIS field by Vega photometry: absolute magnitude-dependent Galactic model parametersMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2006S. Bilir ABSTRACT We estimate the density laws of the Galactic stellar populations as a function of absolute magnitude in a near-polar Galactic field. The density laws are determined by direct fitting to photometric parallaxes from Vega photometry in the ELAIS field (; epoch 2000), both independently for each population and simultaneously for all stellar populations. Stars have been separated into different populations based on their spatial location. The thick disc and halo are fitted best by an exponential. However, the thin disc is fitted best by using a sech2 law for stars at faint absolute magnitudes [10 < M(g,) , 11, 11 < M(g,) , 12 and 12 < M(g,) , 13], and an exponential law for stars at relatively bright absolute magnitudes [5 < M(g,) , 6, 6 < M(g,) , 7, 7 < M(g,) , 8, 8 < M(g,) , 9 and 9 < M(g,) , 10]. The scaleheights for the sech2 density laws are the equivalent exponential scaleheights. Galactic model parameters are dependent on absolute magnitude. The scaleheight for the thin disc decreases monotonically from stars at bright absolute magnitudes [M(g,) = 5] to stars at faint absolute magnitudes [M(g,) = 13] in the range 363,163 pc, except for the minimum H= 211 pc at 9 < M(g,) , 10 where the sech density law fits better. Its local density is flat at bright absolute magnitudes but increases at faint absolute magnitudes. For the thick disc, the scaleheight is flat within the uncertainties. The local space density of the thick disc relative to the local space density for the thin disc is almost flat in the absolute magnitude intervals 5 < M(g,) , 6 and 6 < M(g,) , 7, 7.59 and 7.41 per cent respectively, whereas it decreases down to 3.31 per cent in the absolute magnitude interval 7 < M(g,) , 8. The axial ratio for the halo is ,= 0.60, 0.73 and 0.78 for the absolute magnitude intervals 4 < M(g,) , 5, 5 < M(g,) , 6 and 6 < M(g,) , 7 respectively, and its local space density relative to the local space density for the thin disc is 0.06 and 0.04 per cent for the intervals 5 < M(g,) , 6 and 6 < M(g,) , 7, respectively [the local space density relative to the thin disc could not be derived for the absolute magnitude interval 4 < M(g,) , 5 owing to a lack of the local space density for the thin disc for this interval]. The simultaneous fit of all three stellar populations agrees within uncertainties with the most recent values in the literature. Also, each parameter is close to one of the corresponding parameters estimated for different absolute magnitude intervals in this work, but with one exception: i.e. the scaleheight for the thick disc is relatively small and its error is rather large (H= 760+62,55 pc). [source] Performance of thin-film transistors fabricated by sequential lateral solidification crystallization techniquesPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 12 2008M. A. Exarchos Abstract The performance of Excimer Laser Annealed (ELA) Thin-Film Transistors (TFTs), in terms of drain current behaviour in unstressed as well as in DC stressed devices, is presented. The transistors studied were fabricated under different irradiation schemes of a novel Sequential Lateral Solidification (SLS) process. As far as unstressed transistors concerned, drain current transients relaxed through stretched exponential law. Fitting results disclosed that both gate dielectric polarization and carrier recombination mechanisms occurred through transient relaxation. Deep Level Transient Spectroscopy (DLTS) technique was called forth in order to investi- gate the origin of carrier recombination mechanisms. DC hot carrier stress measurements, under "worst ageing condition" regime, were conducted in order to probe degradation mechanisms and device reliability standards. Crystal domain size significantly affects threshold voltage degradation. The latter increases with decreasing crystal domain size, due to increased concentration of protrusions in the polysilicon film. Transconductance degradation also depends on crystal domain size, attributed mainly to bulk polysilicon trap generation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||