Search results for "Logarithm"
showing 10 items of 182 documents
ADV measurements of velocity distributions in a gravel-bed flume
2003
Velocity measurements carried out by an acoustic doppler velocimeter (ADV) in a rectangular laboratory flume having a gravel bed are presented. The velocity profiles are measured in six verticals of the channel cross-section having an increasing distance (from 4 to 38.5 cm) from the flume wall. The experimental runs are carried out for five different bed arrangements, characterized by different concentrations of coarser elements, and for the two conditions of small- and large-scale roughness. For both hydraulic conditions, the velocity measurements are first used to test the applicability of the Dean profile and of the logarithmic profile corrected by a divergence function proposed in this …
Iterative approach to the exponential representation of the time–displacement operator
2005
An iterative method due to Voslamber is reconsidered. It provides successive approximations for the logarithm of the time–displacement operator in quantum mechanics. The procedure may be interpreted, a posteriori, as an infinite re-summation of terms in the so-called Magnus expansion. A recursive generator for higher terms is obtained. From two illustrative examples, a detailed comparative study is carried out between the results of the iterative method and those of the Magnus expansion.
Fractional-order nonlinear hereditariness of tendons and ligaments of the human knee
2020
In this paper the authors introduce a nonlinear model of fractional-order hereditariness used to capture experimental data obtained on human tendons of the knee. Creep and relaxation data on fibrous tissues have been obtained and fitted with logarithmic relations that correspond to power-laws with nonlinear dependence of the coefficients. The use of a proper nonlinear transform allows one to use Boltzmann superposition in the transformed variables yielding a fractional-order model for the nonlinear material hereditariness. The fundamental relations among the nonlinear creep and relaxation functions have been established, and the results from the equivalence relations have been contrasted wi…
Shift- and scale-invariant recognition of contour objects with logarithmic radial harmonic filters.
2008
The phase-only logarithmic radial harmonic (LRH) filter has been shown to be suitable for scale-invariant block object recognition. However, an important set of objects is the collection of contour functions that results from a digital edge extraction of the original block objects. These contour functions have a constant width that is independent of the scale of the original object. Therefore, since the energy of the contour objects decreases more slowly with the scale factor than does the energy of the block objects, the phase-only LRH filter has difficulties in the recognition tasks when these contour objects are used. We propose a modified LRH filter that permits the realization of a shi…
Quantitative analysis of crystal/grain sizes and their distributions in 2D and 3D
2011
Abstract We review methods to estimate the average crystal (grain) size and the crystal (grain) size distribution in solid rocks. Average grain sizes often provide the base for stress estimates or rheological calculations requiring the quantification of grain sizes in a rock’s microstructure. The primary data for grain size data are either 1D (i.e. line intercept methods), 2D (area analysis) or 3D (e.g., computed tomography, serial sectioning). These data have been used for different data treatments over the years, whereas several studies assume a certain probability function (e.g., logarithm, square root) to calculate statistical parameters as the mean, median, mode or the skewness of a cr…
Simulating term structure of interest rates with arbitrary marginals
2011
Decision models under uncertainty rely their analysis on scenarios of the economic factors. A key economic factor is the term structure of interest rates (yields). Simulation models of the yield curve usually assume that the conjugate distribution of the interest rates is lognormal. Dynamic models, like vector auto-regression, implicitly postulate that the logarithm of the interest rates is normally distributed. Statistical analyses have, however, shown that stationary transformations (yield changes) of the interest rates are substantially leptokurtic, thus posing serious doubts on the reliability of the available models. We propose in this paper a VARTA model (Biller and Nelson, 2003) to s…
The oxidation state of iron in silicic melt at 500 MPa water pressure
2002
Abstract The dependence of the ferric–ferrous ratio in silicate melts on oxygen fugacity was studied in the system SiO2(Qz)–NaAlSi3O8(Ab)–CaAl2Si2O8(An)–H2O using Mossbauer spectroscopy. Experiments were performed under water-saturated conditions at 500 MPa, and at temperatures of 850 and 950 °C, covering a range typical for magmatic processes. The oxygen fugacity was varied in the fO2 range from Cu–Cu2O buffer to slightly more reducing conditions than the wustite–magnetite buffer. The iron redox ratio was determined by analyzing the Mossbauer parameter distribution that was modeled based on experimental spectra collected at room temperature on the quenched samples. The obtained iron redox …
Digital signal processing for relaxation data conversion
2005
Abstract The origins, philosophy and basic practical aspects are considered for an approach of digital data transformations for broadband dielectric relaxation spectroscopy and other relaxation experiments carrying out direct and inverse integral transforms with kernels depending on the ratio or product of arguments. The approach is based on the concept that the mentioned data transformations represent a filtering problem on a logarithmic scale allowing one to implement the transforms by digital functional filters with the logarithmic sampling. As an example, digital Kramers–Kronig transformers are considered.
Power-aware design of MCML logarithmic adders
2010
This paper describes the low-power design of a MOS current-mode logarithmic adder. The adder utilizes the Brent-Kung tree structure. The design strategy adopted is very simple and effective. Moreover, it can be utilized also for other types of logarithmic adders. To validate it, several adders were designed in a TSMC CMOS 130nm technology. Results of simulations indicate that the proposed methodology offers a good starting point before fine-tuning the design by SPICE simulations. Finally, the tradeoff that can be realized between performance and power consumption is discussed.
Growth Kinetics of Wetting Layers at Surfaces
1990
Monte Carlo simulation of lattice gas models for the wetting transitions in systems with short range forces are described. A nearest-neighbor simple cubic lattice with nonconserved “Glauber dynamics” is used, applying a slab geometry (LxL cross section). It is shown that the growth proceeds in two stages: for short times t, the thickness of the wetting layer at an initially nonwet wall increases proportional to the logarithm of the time; for t » L2(lnL)2 the thickness increases proportional to t1/2/L. Generalizations to other systems are briefly discussed. Also two-dimensional growth of a wetting film at surface steps is considered, considering “terraces” of an LxM geometry with M»L as subs…