Value Of Scale Parameter Research Articles

Presenting Snow Grain Size and Shape Distributions in Northern Canada Using a New Photographic Device Allowing 2D and 3D Representation of Snow Grains

Geophysical properties of snow are known to be sensitive to climate variability and are of primary importance for hydrological and climatological process simulations. Numerous studies using passive microwaves have attempted to quantify snow from space, but the methods suffer from poor spatial resolution retrievals, combined with a great sensitivity to snow grain morphology. Those issues motivated work using active microwaves that are now core to space mission concept proposals currently under development. However, a clear limitation remains with regards to snow microstructure contribution to backscattering, especially in large depth hoar layers typical of polar snowpacks. This leads to difficulties retrieving Snow Water Equivalent (SWE) from space or developing radiative transfer models owing to a lack of field observations of snow microstructure. This paper presents an innovative technique to measure various snow grain metrics in the field where micro-photographs of snow grains are taken under angular directional LED lighting. The projected shadows are digitized so that a 3D reconstruction of the snow grains is possible and distribution functions can be proposed for various snow grain metrics and grain types. This device, dLED, has been used in several field campaigns and a very large dataset was collected and is presented in this paper. Distribution histograms from >160,000 digitized grains were produced for each metric for all grains considered as a whole dataset (unclassified), and also for each grain type: 1) Defragmented/broken (DF), 2) Depth Hoar (DH), 3) Facets (F), 4) Rounds (R) and 5) Precipitation Particles (PP). We selected distribution functions for each metric per grain time by analysing L-moment diagrams that summarize the shape of a probability distribution. Our results show that the logarithmic Kappa (LKAP) distribution is well suited to explain the snow grain metric distribution for each grain type. Location, scale and shape parameter values for each distribution are presented and a comparison with values derived from our shortwave infrared laser device, the InfraRed Integrating Sphere (IRIS), is provided. A discussion is presented on the pros and cons of the dLED and the use of the distributions presented in this paper for microwave radiative transfer modeling work.

Equivalence scales and the change in poverty levels across time: Turkish case

ABSTRACTEquivalence scales are used to adjust household income for household size and composition differences. The literature on poverty calculations have found sensitivity of poverty measurements to the choice of equivalence scales. In this study, we aim to estimate the sensitivity of the Turkish poverty rate and its change over time to the choice of equivalence scales. To that end, Household Budget Survey micro-level data are used and poverty rates are calculated for different equivalence scales. Results show that poverty rates differ sharply with the scale parameter. The change in poverty over time varies in absolute terms with most scale parameter values but only for high values of scale as a ratio of the initial period. Characteristics of poor households also change with scale alternatives.

Thermoelastic Damping of Functionally Graded Material Micro-Beam Resonators Based on the Modified Couple Stress Theory

Thermoelastic damping (TED) is one of the main internal energy dissipation mechanisms in micro-/nano-resonators. Accurate evaluation of TED is important in the design of micro-electromechanical systems and nano-electromechanical systems. In this paper, a theoretical analysis on the TED in functionally graded material (FGM) micro-beam resonators is presented. Equations of motion and the heat conduction equation governing the thermodynamic coupling free vibration of non-homogenous micro-beams are established based on the Euler–Bernoulli beam theory associated with the modified couple stress theory. Material properties of the FGM micro-beam are assumed to change in the depth direction as power-law functions. The layer-wise homogenization method is used for solving the heat conduction equation. By using the mathematical similarity of eigenvalue problem between the FGM beam and the reference homogeneous one, the complex natural frequency including TED is expressed in terms of the natural frequency of the isothermal homogenous beam. In the presented numerical results, influences of various characteristic parameters, such as beam thickness, material gradient index, structure size, vibration mode and boundary conditions, on TED are examined in detail. It shows that TED decreases with the increases in the values of length scale parameters because the latter lead to the increase in structural stiffness.

The Mapping of Land Use Using Object-Based Image Analysis (OBIA) in Klaten Regency

Klaten Regency is one of the regencies in Central Java Province that has an increasing population every year. This can cause an increase in built-up land for human activities. The built-up land needs to be monitored so that the construction is in accordance with the regional development plan so that it does not cause problems such as the occurrence of critical land. Therefore, it is necessary to monitor land use regularly. One method for monitoring land use is the remote sensing method. The remote sensing method is much more efficient in mapping land use because without having to survey the field. The remote sensing method utilizes satellite imagery data that can be processed for land use classification. This study uses the sentinel 2 satellite image data with the Object-Based Image Analysis (OBIA) algorithm to obtain land use classification. Sentinel 2 satellite imagery is a medium resolution image category with a spatial resolution of 10 meters. The land use classification can be used to see the distribution of built-up land in Klaten Regency without having to conduct a field survey. The results of the study obtained a segmentation scale parameter value of 60 and a merge scale parameter value of 85. The classification results obtained by 5 types of land use with OBIA. Agricultural land use dominates with an area of 50% of the total area.

Application of quantum self-frictional nonperturbative theory for the study of atomic anharmonic oscillator potentials and their arbitrary derivatives

The self-frictional (SF) nonperturbative theory, introduced by one of the authors, is used for the evaluation of the $$V^{{(p_{l}^{ * } )}}$$ and $$V^{(\alpha^{ * })}$$ atomic anharmonic oscillator potentials and their derivatives, where $$p_{l}^{*} = 2l + 2 - \alpha^{ * }$$ and $$\alpha^{ * }$$ represent the integer $$(\alpha^{ * } = \alpha ,\; - \infty < \alpha \le 2$$ ) or non-integer ( $$\alpha^{ * } \ne \alpha ,\,\,\, - \infty < \alpha^{ * } < 3$$ ) SF quantum numbers. This study is based on the use of complete sets of $$\text{L}_{{}}^{{\left( {p_{l}^{*}} \right)}}$$ and $$\text{L}_{{}}^{{\left( {\alpha^{ * }} \right)}}$$ SF polynomials. The dependence of the potentials and their derivatives from the nucleus distances is investigated. All of the obtained results are valid for the arbitrary values of quantum numbers, scaling parameters and SF quantum numbers.

Radar Cross Section Reduction of Metallic Plate Loaded with Via Hole Dielectric Substrate

Radar cross section (RCS) stealth technology has a major importance in the military applications. In this paper, RCS reduction of metallic sheet is investigated through loading it by dielectric substrate with tapered via holes. The via holes tapering are drilled in two approaches according to the choice of the reference hole radius. In the first approach, the via holes are tapered in a single direction from row to row and are kept fixed along the singlerow. A reduction on RCS of 13 dB below the unloaded case is achieved. The RCS reduction frequency band is shifted down by increasing the negative value of scaling parameter due to the reduction of the effective dielectric constant of the dielectric sheet. In the second approach, the holes are tapered along the off-diagonal directions where the tapering occurs along both row and column. A symmetrical structure around the main diagonal is produced. The reduction in RCS is achieved with the band from 11 to 12.75 GHz for different scaling coefficient values with best RCS reduction of 33.5 dB occurs at α=0.18. Symmetrical wide angle RCS reduction from -109o to 109o degrees is reached.

The effect of multidimensional temperature distribution on the vibrational characteristics of a size-dependent thick bi-directional functionally graded microplate

This article develops the modified couple stress theory to study the free vibration of bi-directional functionally graded microplates subjected to multidimensional temperature distribution. Third-order shear deformation and classical theories of plates are adapted for free vibration analysis of thick and thin microplates, respectively. Employing the third-order shear deformation theory, both normal and shear deformations are considered without the need for shear correction factor. Material of the bi-directional functionally graded microplate is graded smoothly through the length and thickness of the microplate. Gradient of the material is assumed to obey from the power law in terms of the volume fraction of the constituents. Assuming the uniform and nonuniform temperature distributions, the effect of thermal environment on dynamic behavior of the microplate is discussed in detail. Applying the Ritz method, the displacement field is expanded by admissible functions which satisfy the essential boundary conditions, and Hamilton principle is employed to determine the natural frequencies of the microplate. Developed model has been applied to determine the natural frequencies in problems of thin/thick, one-directional/bi-directional functionally graded, and homogeneous/nonhomogeneous microplates. Effects of parameters such as the thermal environment, power law indexes [Formula: see text] and length scale parameter on free vibration of these problems are studied in detail. The results show that higher values of length scale parameter and temperature rise decrease the natural frequency of the bi-directional functionally graded microplate. According to results obtained by classical and third-order shear deformation theories, the third-order shear deformation theory is proposed for vibration analysis of microplates with thickness-to-length ratio less than five.

Reliability Assessment of a Cement Industry by Application of Weibull Method

The financial cost of downtime can be very significant, especially in manufacturing industries. As a result, no business wants to experience downtime. In this study, the reliability of two identical machines code named GDA and GDB used in a cement manufacturing industry was assessed by analysis of failure times data of components in the machines by applying Weibull distribution method. The estimates of the Weibull parameters, θ and β were obtained using a reliability software tool ‘Windchill Quality Solutions 11.0 Tryout’ and the mean time to failure, failure rate and reliability of the machines was successfully determined. The result obtained showed that, the machines are undergoing rapid wear out as the values of the shape parameter obtained were greater than four. The plots of the failure rate also showed that the machines are in their wear out periods as the failure rate curves were observed to be increasing. The values of the mean time to failure of the two machines were found to be very close. The reliability of the machines was found to be increasing as their values of scale parameter, θ increases with machine GDA having the highest reliability.

Fractional Calculus Approach to Nonlocal Three-Dimensional Vibration Analysis of Plates

The nonlocal three-dimensional vibration analysis of rectangular plates is investigated within the framework of fractional calculus in the sense of the Caputo fractional derivative. To show the effect of the fractional derivative on nonlocality, the frequency spectra of the plates with different boundary conditions and symmetry modes are carried out for the different orders of the fractional derivative and different values of the length scale parameter . The vibration analysis is obtained by the Ritz energy method, whereas Chebyshev polynomials are used as admissible functions. The results of the frequency spectrum demonstrate that the nonlocal effect decreases and the results get closer to the values of the classical frequencies as the order of the fractional derivative approaches the classical derivative .

Drying characteristics and modeling of apple slices during microwave intermittent drying

AbstractDrying characteristics and quality of apple slices were studied using microwave intermittent drying at different microwave power density (2.2, 3.5, 4.8, and 6.1 W/g), sample thickness (3, 5, 7, and 9 mm) and heating time in each cycle (4, 5, 6, and 7 s). Results showed that the approximate constant rate drying periods and falling rate drying periods were found in all the curves. The drying time decreased with increasing microwave power density and heating time in each cycle, while increased significantly with the growth of sample thickness. Weibull distribution model could fit the drying curves well in all conditions (R2 &gt; 0.99) with the scale parameter values changed from 45.88 to 206.08 min and the shape parameters values varied from 1.514 to 1.69. The moisture effective diffusivity calculated by Weibull model ranged from 0.3217 × 10−9 to 1.435 × 10−9 m2·s−1. The flavor, texture and overall acceptability values displayed a decreasing tendency with the increase of microwave power density, while increased with the growth of thickness. And the shrinkage rates of apple slices showed a decline tendency with the increase of above parameters.Practical applicationsApple is a kind of popular and important fruits with high nutrient content, and it has been widely planted in China. Due to its high moisture content, fresh apples will subject to various deteriorative reactions during storage and thus lead to serious post‐harvest losses. Microwave drying technology has been widely used in dehydration of agricultural products in China because of the significant heating efficiency. However, the continuous microwave heating may easily cause the overheating of raw materials and undesirable changes in quality. Microwave intermittent drying (MID) was proposed on the basis of conventional microwave drying and regarded as an efficient processing method by solving the above issues. Currently this technology has been successfully applied to ginkgo fruits, yam and banana slices. Analyzing the effects of drying parameters on MID kinetics and quality of apple slices will have important significance for optimizing the processing efficiency and consumer acceptability of dried products.

Comparison of Two Priors in Bayesian Estimation for Parameter of Weibull Distribution

This present study purposes to conduct Bayesian inference for scale parameters, denoted by , from Weibull distribution. The prior distribution chosen in this study is the prior conjugate, that is inverse gamma and non-informative prior, namely Jeffreys’ prior. This research also aims to study several theoretical properties of posterior distribution based on prior used and then implement it to generated data and make comparison between both Bayes estimator as well. The method used to evaluate the best estimator is based on the smallest Mean Square Error (MSE). This study proved that Bayes estimator using conjugate prior produces parameter value that is better estimate than the non-informative prior since it produces smaller MSE value, for condition scale parameter value more than one based on analytic and simulation study. Meanwhile for scale parameter value less than one, it could not yielded the good estimated value.

Size-dependent nonlinear bending and vibration of flexoelectric nanobeam based on strain gradient theory

In this study, the nonlinear bending and free vibration of Timoshenko piezoelectric nanobeam incorporating flexoelectricity and surface effect are investigated for the first time. To take size effect into account, a size-dependent Timoshenko nanobeam model containing additional material length scale parameters is developed based on strain gradient theory. The governing equations and corresponding boundary conditions are obtained by electric enthalpy variation and Hamilton’s principle. By adjusting the values of material length scale parameters, the current Timoshenko piezoelectric nanobeam formulations can be transformed to those based on modified couple stress theory. The generalized differential quadrature method (GDQM) is employed to discretize governing differential equations and boundary conditions into a series of nonlinear algebraic equations. Then the algebraic equations are solved by using the Newton iteration method. It is found that strain gradient elastic effect, flexoelectricity, surface effect and applied electric voltage have significant influences on the nonlinear mechanical behaviors of nanobeam. Simulation results indicate that both the strain gradient effect and flexoelectric effect have considerable impacts on the electric field distribution in nanobeams. Moreover, the results also indicate that the influence of flexoelectricity is weakened to some extent due to the consideration of surface effect. The numerical analysis reveals that the present model can be considered reliable to quantitatively investigate size-dependent nonlinear bending and nonlinear free vibration of the piezoelectric nanobeam incorporating flexoelectric and surface effects.

Spectral analysis of temporal variability of nonlinear and nonstationary rainfall-runoff processes

This study deals with the time-dependent nonlinear response of catchments to the variations in rainfall. Both the rainfall and runoff discharge fields are treated to be nonstationary in time. A functional series representation, a generalization of the linear convolution integral, is employed to quantify the nonlinear relation between the input and output. The Fourier-Stieltjes representation approach is used to evaluate the variance of runoff discharge in the spectral frequency domain. The analysis based on the spectral solution for the runoff discharge variance clearly demonstrates that larger values of rainfall characteristic time scale or catchment size parameter lead to larger variability of the runoff discharge, while a larger catchment scale parameter leads to smaller variability of the runoff discharge.

Optimal replenishment policy for multi-item probabilistic inventory model with all-units discount

In this paper, we develop a multi item inventory model for the retailer by considering all-units discount offered by the supplier. Demands in this model are assumed to be probabilistic following a Gamma distribution with certain values of shape and scale parameters. The aim of the model is to determine the optimal replenishment policy that minimize the total inventory cost. The total inventory cost was composed from the purchasing, ordering, handling or storing and shortage costs. All shortages are handled by backorder. We compare the individual and joint replenishment policies for the model and develop an algorithm to find the optimal replenishment policy. Numerical examples are given to give a better understanding of the model in comparing the individual and joint replenishment policies. We also perform sensitivity analysis by changing values of shape and scale parameters of the demand distribution to analyse the effects on the optimal solution.

Characteristics of Near Surface Winds over Different Underlying Surfaces in China: Implications for Wind Power Development

Accurate wind and turbulence information are essential to wind energy research and utilization, among which wind shear and turbulence intensity/scale have seldom been investigated. In this paper, the observational data from the 100-m high wind towers in Xilinhot in Inner Mongolia (2009–10; grassland region), Huanghua in Hebei Province (2009–10; coastal flat region), and Xingzi County in Jiangxi Province (2010–11; mountain-lake region) are used to study the variations in near surface winds and turbulence characteristics related to the development of local wind energy over different underlying surfaces. The results indicate that (1) the percentage of the observed wind shear exponents exceeding 0.3 for the grassland region is 6%, while the percentage is 13% for the coastal flat region and 10% for the mountain-lake region. In other words, if the wind speed at 10 m is 10 m s−1, the percentage of the wind speed at 100 m exceeding 20 m s−1 for the grassland region is 6%, while the percentage is 13% for the coastal flat region and 10% for the mountain-lake region. (2) In terms of the turbulent intensity in the zonal, meridional, and vertical directions (Iu, Iv, and Iw, respectively), the frequencies of Iv /Iu < 0.8 in the grassland, coastal flat, and mountain-lake regions are 23%–29%, 32%–38%, and 30%–37%, respectively. Additionally, the frequencies of Iw / Iv < 0.5 in the grassland, coastal flat, and mountain-lake regions are 45%–75%, 52%–70%, and 43%–53%, respectively. The frequencies of Iv /Iu < 0.8 and Iw /Iu < 0.5 in each region mean that Iu is large and the air flow is unstable and fluctuating, which will damage the wind turbines. Therefore, these conditions do not meet the wind turbine design requirements, which must be considered separately. (3) At 50- and 70-m heights, the value of the turbulence scale parameter Λ in the grassland region is greater than that in the coastal flat region, and the latter is greater than that in the mountain-lake region. Therefore, under the same conditions, some parameters, e.g., the extreme directional change and extreme operating gust at the hub height in the grassland region, are greater than those in the coastal flat region, which are greater than those in the mountain-lake region. These results provide a reference for harnessing local wind energy resources and for the selection and design of wind turbines.

Investigation of wind speed characteristics and its energy potential in Makurdi, north central, Nigeria

This study investigates wind speed characteristics and its energy potential in Makurdi, in order to assess the prospect and availability of wind energy for electricity generation in the region. Wind speed data measured at 10 m were obtained from the Nigeria Meteorology Agency, Lagos. The data spanned from 1961–2014. Weibull distribution function was employed to determine wind energy potential in Makurdi. Results reveal that the period of highest potential for wind harvest was the peak of dry season (i.e. April) and that for lowest yield was the onset of dry season (i.e. November). Wind speed characteristics used for wind energy estimate was determined. Furthermore, high values of Weibull shape and scale parameters obtained in this study indicate the availability of wind speed and the windy nature of Makurdi. The wind power density of 86.85 W/m2 suggests that Makurdi wind can be used for electricity generation. Besides, monthly and annual mean wind speeds were above the minimum values (3.0–4.0 m/s) required for most wind turbines to operate. The wind profile and its characteristics depict Makurdi as a suitable site for wind power generation. Hence, there is huge prospect of wind power generation in Makurdi and its environs.

An investigation of back stress formulations under cyclic loading

A single material length parameter governs both the material size dependence and the predicted micro-structural behavior in most existing micro-structurally based continuum theories. As a consequence, smoothly varying field quantities are predicted which contrast recent years' experimental observations. In a previous work by the authors, addressing this matter, two new back stress formulations were proposed, and demonstrated to offer novel modeling capabilities in the localization behavior of geometrically necessary dislocation pile-up under monotonic loading. However, the cyclic behavior of these formulations remains to be investigated. The present work studies the new back stress formulations, within a non-work conjugate type higher order strain gradient crystal plasticity framework, and demonstrates their performance through the idealized single slip simple shear case. At high values of the material length scale parameter, a seemingly anomalous cyclic response is observed when deviating from the conventional type back stress formulation. Similar observations have recently been reported in other numerical studies, and the present work offers a discussion of the physical justification of such material behavior. It is found that the properties of the adopted formulations, in fact, open the possibility for modeling complex material behavior, tied to the presence of long range internal stresses due to dislocation pile-up. Moreover, the present study extends the discussion on micro-structure predictions as a consequence of the adopted back stress models.

On convergence of iterative method for determination of weibull parameters by maximum likelihood method

The Weibull distribution is frequently used for the assessment of wind energy potential and modeling of wind speed data. The parameters of Weibull distribution are determined by a number of methods; Maximum Likelihood Methods is one of them. The values of scale and shape parameters of Weibull distribution are found by the help of Maximum Likelihood function. Two different techniques are used to find the parameters. One is known as iterative method, in which a start value of ‘k’ is set and iterations are terminated when given criterion is reached. The second method is Newton Raphson method of finding roots. We report here a problem of non-convergence of iterative method. We suggest the Newton Raphson method as the best choice for finding the value of ‘k’ through Maximum Likelihood Method.

Evolutionary dynamics of the prisoner's dilemma with expellers

Expulsion refers to the widespread behavior of expelling intruders from the owners’ territories, which has not been considered in current models on the evolutionary dynamics of cooperation so far. In the context of prisoner’s dilemma, we present a simple game-theoretical model of expulsion in which punishing cooperators (i.e. expellers) are able to banish defectors from their own neighborhoods. In the mean-field limit, our theoretical analysis of prisoner’s dilemma with expellers shows that the increment of either vacant sites ratio or time scale parameter between pairwise interaction process and strategy updating process can slow down evolutionary speed though defection is the only stable fixed point anyway. In more realistic spatial settings, we provide both analytical and numerical results for the limiting case where pairwise interaction dynamics proceeds much faster than strategy updating dynamics. Using the extended pair approximation methods and Monte Carlo simulations, we show that the introduction of expellers not only promotes coevolution of expulsion and cooperation by means of both direct and indirect domain competition but also opens the gate to rich dynamical behaviors even if expulsion is costly. Phase diagrams reveal the occurrence of frozen as well as dynamical stationary states, between which continuous or discontinuous phase transition may happen. For intermediate ranges, we investigate numerically the coupled interplay between pairwise interaction dynamics and strategy updating dynamics, and show that the validity of main results for the limiting case can be extended to this general case. Interestingly, there exists an optimal value of time scale parameter that results in the maximum fraction of altruistic players, which resembles the coherence resonance phenomenon in dynamical systems. Our results may provide insights into understanding coevolutionary dynamics of expulsive and cooperative behavior in social dilemma situations.

On the nano-structural dependence of nonlocal dynamics and its relationship to the upper limit of nonlocal scale parameter

Nonlocal elasticity theory is one of the most popular theoretical approaches to investigate the intrinsic scale effect of nano-materials/structures. The coupling of an internal characteristic length and a material parameter can be regarded as a nonlocal scale parameter in nano-meters. The range of this non-dimensional scale parameter is from zero up to different values previously. There is no doubt that the zero nonlocal scale parameter corresponds to a situation without any nonlocal effect. However, the determination of a peak value for the scale parameter is still uncertain. In fact, we frequently ask a simple but unresolved question, i.e., how strong is the nonlocal scale effect? This question is equivalent to what the maximum value of the nonlocal scale parameter is, since it was introduced to characterize the scale effect theoretically. Until now, various maximum values have been selected without rigorous verifications. In this paper, the nano-structural dependence of nonlocal dynamical behavior is investigated to present the existence of an upper limit for the scale parameter. Through three typical examples, the size-dependent behavior of nonlocal dynamics for various nano-structures is analyzed. The upper limit of the scale parameter can be determined accordingly. It is shown that an interval for the scale parameter in the illustrative examples can be found on the basis of the nonlocal softening physical mechanism, in which the equivalent stiffness of nano-structures is weakened than that predicted by the classical continuum theory. The present study contributes to a fuzzy zone in nonlocal elasticity where people are puzzled over the question how to select the upper limit of the nonlocal scale parameter. It is not only beneficial to the refinement of the nonlocal theory of elasticity, and also useful for the exploration of similar theories in nano-mechanics.