The Importance of the Shape Parameter in a Bulk Parameterization Scheme to the Evolution of the Cloud Droplet Spectrum during Condensation

The shape parameter of the Gamma size distribution plays a key role in the evolution of the cloud droplet spectrum in the bulk parameterization schemes. However, due to the inaccurate specification of the shape parameter in the commonly used bulk double-moment schemes, the cloud droplet spectra cannot reasonably be described during the condensation process. Therefore, a newly-developed triple-parameter condensation scheme with the shape parameter diagnosed through the number concentration, cloud water content, and reflectivity factor of cloud droplets can be applied to improve the evolution of the cloud droplet spectrum. The simulation with the new parameterization scheme was compared to those with a high-resolution Lagrangian bin scheme, the double-moment schemes in a parcel model, and the observation in a 1.5D Eulerian model that consists of two cylinders. The new scheme with the shape parameter varying with time and space can accurately simulate the evolution of the cloud droplet spectrum. Furthermore, the volume-mean radius and cloud water content simulated with the new scheme match the Lagrangian analytical solutions well, and the errors are steady, within approximately 0.2%.

Dendritic tip selection during solidification of alloys:Insights from phase-field simulations

The effect of undercooling DT and the interface energy anisotropy parameter e4 on the shape of the equiaxed dendritic tip has been investigated by using a quantitative phase-field model for solidification of binary alloys.It was found that the tip radius r increases and the tip shape amplitude coefficient A4 decreases with the increase of the fitting range for all cases.The dendrite tip shape selection parameter sdecreases and then stabilizes with the increase of the fitting range,and sincreases with the increase of e4.The relationship between sand e4 follows a power-law function sµea 4,and a is independent of DT but dependent on the fitting range.Numerical results demonstrate that the predicted sis consistent with the curve of microscopic solvability theory(MST)for e4<0.02,and sobtained from our phase-field simulations is sensitive to the undercooling when e4 is fixed.

A Radial Basis Function Method with Improved Accuracy for Fourth Order Boundary Value Problems

Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used.

New cubic rational basis with tension shape parameters

By using the blossom approach, we construct four new cubic rational Bernsteinlike basis functions with two shape parameters, which form a normalized B-basis and include the cubic Bernstein basis and the cubic Said-Ball basis as special cases. Based on the new basis, we propose a class of C2 continuous cubic rational B-spline-like basis functions with two local shape parameters, which includes the cubic non-uniform B-spline basis as a special case.Their totally positive property is proved. In addition, we extend the cubic rational Bernsteinlike basis to a triangular domain which has three shape parameters and includes the cubic triangular Bernstein-B′ezier basis and the cubic triangular Said-Ball basis as special cases. The G1 continuous conditions are deduced for the joining of two patches. The shape parameters in the bases serve as tension parameters and play a foreseeable adjusting role on generating curves and patches.

Bézier curves with shape parameter

In this paper, Bézier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the Bézier curves with shape parameter. The Bézier basis curves with shape parameter have most properties of Bernstein basis and the Bézier curves. Moreover the shape parameter can adjust the curves’ shape with the same control polygon. As the increase of the shape parameter, the Bézier curves with shape parameter approximate to the control polygon. In the last, the Bézier surface with shape parameter is also constructed and it has most properties of Bézier surface.

MODIFIABLE QUARTIC AND QUINTIC CURVES WITH SHAPE-PARAMETERS

This paper presents a method for creating modificable quartic and quintic curves with shape parameters. The curves can achieve C 2 even C 3 continuity and unify both interpolation and approximation to the control points without solving a system of equations or inserting additional control points. They have the local properties like the cubic B spline. Besides, the quintic curve would be able globally to tend the control polygon.

Circular object recognition based on shape parameters

To recognize circular objects rapidly in satellite remote sensing imagery, an approach using their geometry properties is presented. The original image is segmented to be a binary one by one dimension maximum entropy threshold algorithm and the binary image is labeled with an algorithm based on recursion technique. Then, shape parameters of all labeled regions are calculated and those regions with shape parameters satisfying certain conditions are recognized as circular objects. The algorithm is described in detail, and comparison experiments with the randomized Hough transformation （RHT） are also provided. The experimental results on synthetic images and real images show that the proposed method has the merits of fast recognition rate, high recognition efficiency and the ability of anti-noise and anti-jamming. In addition, the method performs well when some circular objects are little deformed and partly misshapen.

Convexity-preserving interpolation of trigonometric polynomial curves with a shape parameter

In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate convexity-preserving in-terpolating transcendental curves;even constructing convexity-preserving interpolating polynomial curves,it is required to solve a system of equations or recur to a complicated iterative process. The method developed in this paper overcomes the above draw-backs. The basic idea is:first to construct a kind of trigonometric polynomial curves with a shape parameter,and interpolating trigonometric polynomial parametric curves with C2(or G1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then,the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter. Performing the method is easy and fast,and the curvature distribution of the resulting interpolating curves is always well-proportioned. Several numerical examples are shown to substantiate that our algorithm is not only correct but also usable.

Subtle Influence of the Weibull Shape Parameter on Homer Optimization Space of a Wind Diesel Hybrid Gen Set for Use in Southern Brazil

Wind power is an increasingly important alternative for obtaining energy supplies, both in large interconnected power systems and in smaller hybrid systems and even in backup systems. The temporal and spatial variability of the winds represent an obstacle to be overcome so that wind energy can be increasingly used. The capacity factor of wind farms shows how this variability impacts the operation of the plants and its value is of the order of 30% to 35%. The variability of the wind speed is influenced if the point of interest is on land or on sea, the shape of the surface, the proximity of water bodies, among other factors. The availability of wind is best described by the Weibull probability distribution, which has as one of its defining parameters one which is termed as shape parameter. This parameter is much higher as higher is the variability of the wind speed. This paper studies the subtle influence of Weibull shape parameter on the optimal combination of components in a wind diesel hybrid system, by means of computer simulations with the well known software Homer. The results indicate a relatively small influence (as expected) in the studied system, which appears particularly when the cost of diesel is higher and the availability of wind is lower.

Generate mesh with shape parameters

In CAD/CAM, mesh rather than smooth surface is only needed sometimes. A mesh-generating method from permanence principle of Coons patch is developed. A new mesh point is defined through local small subpatch and all mesh points are computed by a linear system with special symmetric block tridiagonal coefficient matrix. By simplification, the determinant of coefficient matrix is determined by determinants of submatrices. Condition of existence of solution is given. Whether coefficient matrix is singular can be judged by a simple polynomial function with the eigenvalue of submatrix as variable. Numerical examples demonstrate the effects of shape parameters.

Population structure of Araucaria angustifolia under distinct forest protection status:implications for management and conservation

Araucaria angustifolia is the dominant coniferous species in Brazil,a long-lived pioneer species and a supplier of valuable timber and non-timber products,which gives it key-species status.This study examines how A.angustifolia population structure affects the stand structure,and whether these relationships differ between protected and unprotected areas.The study was carried out on two protection status forests(national forest and urban forest)in a region of Atlantic mixed forest in ParanáState,southern Brazil.Skewness coefficient and the Weibull shape parameter described the population structure and its effects on species diversity and biomass stock.Population diameter distribution differed significantly between forests,with unbalanced structure in both,although regeneration was more abundant in the protected area.Skewness positively affected aboveground biomass whereas shape negatively affected it and species diversity.These relationships differed between protected and unprotected stands.The effect of A.angustifolia populations on stand structure was conditioned on protection status.Old-growth populations may have lower diversity and biomass stock even supporting large trees.Consequently,old-growth forests,can lead to wood loss through mortality,senescence,and declining populations,representing the waste of a valuable timber resource.These findings provide useful knowledge for forest management,species conservation,and the carbon market.

Local Radial Basis Function Methods: Comparison, Improvements, and Implementation

Radial Basis Function methods for scattered data interpolation and for the numerical solution of PDEs were originally implemented in a global manner. Subsequently, it was realized that the methods could be implemented more efficiently in a local manner and that the local approaches could match or even surpass the accuracy of the global implementations. In this work, three localization approaches are compared: a local RBF method, a partition of unity method, and a recently introduced modified partition of unity method. A simple shape parameter selection method is introduced and the application of artificial viscosity to stabilize each of the local methods when approximating time-dependent PDEs is reviewed. Additionally, a new type of quasi-random center is introduced which may be better choices than other quasi-random points that are commonly used with RBF methods. All the results within the manuscript are reproducible as they are included as examples in the freely available Python Radial Basis Function Toolbox.

Influence of the roughness and shape of quartz particles on their flotation kinetics

Surface roughness and shape play an important role on the behavior of particles in various processes such as flotation. In this re- search, the influence of different grinding methods on the surface roughness and shape characteristics of quartz particles as well as the effect of these parameters on the flotation of the particles was investigated. The surface roughness of the particles was determined by measuring their specific surface area via the gas adsorption method. The shape characteristics of the particles were measured and calculated by images obtained by scanning electron microscopy via an image analysis system. The flotation kinetics was determined using a laboratory flotation cell. The results showed that the particles of rod mill products have higher roughness and elongation ratio and lower roundness than the parti- cles of ball mill products. The flotation kinetics constant of the particles increased with their surface roughness increasing. Particles with higher elongation and lower roundness indicated higher floatability. In addition, the influence of the surface roughness on the flotation kinet- ics was greater than that of shape parameters.

Numerical Study of Air Chamber for Oscillating Water Column Wave Energy Convertor

Oscillating Water Column （OWC） wave energy converting system is one of the most widely used facilities all over the world. The air chamber is utilized to convert the wave energy into the pneumatic energy. The numerical wave tank based on the two-phase VOF model is established in the present study toinvestigate the operating performance of OWC air chamber. The RANS equations, standard k-ε turbulence model and dynamic mesh technology are employed in the numerical model. The effects of incident wave conditions and shape parameters on the wave energy converting efficiency are studied and the capability of the present numerical wave tank on the corresponding engineering application is validated.

A new type of the generalized Bézier curves

In this paper, we improve the generalized Bernstein basis functions introduced by Han, et al. The new basis functions not only inherit the most properties of the classical Bernstein basis functions, but also reserve the shape parameters that are similar to the shape parameters of the generalized Bernstein basis functions. The degree elevation algorithm and the conversion formulae between the new basis functions and the classical Bernstein basis functions are obtained. Also the new Q-Bezier curve and surface constructed by the new basis functions are given and their properties are discussed.

Prediction of rock brittleness using nondestructive methods for hard rock tunneling

Sand production is an undesired phenomenon occurring in unconsolidated formations due to shear failure and hydrodynamic forces. There have been many approaches developed to predict sand production and prevent it by changing drilling or production strategies. However, assumptions involved in these approaches have limited their applications to very specific scenarios. In this paper, an elliptical model based on the borehole shape is presented to predict the volume of sand produced during the drilling and depletion stages of oil and gas reservoirs. A shape factor parameter is introduced to estimate the changes in the geometry of the borehole as a result of shear failure. A carbonate reservoir from the south of Iran with a solid production history is used to show the application of the developed methodology. Deriving mathematical equations for determination of the shape factor based on different failure criteria indicate that the effect of the intermediate principal stress should be taken into account to achieve an accurate result. However, it should be noticed that the methodology presented can only be used when geomechanical parameters are accurately estimated prior to the production stage when using wells and field data.

Development of a mass model in estimating weight-wise particle size distribution using digital image processing

Particle size distribution of coarse aggregates through mechanical sieving gives results in terms of cumu- lative mass percent. But digital image processing generated size distribution of particles, while being fast and accurate, is often expressed in terms of area function or number of particles. In this paper, a mass model is developed which converts the image obtained size distribution to mass-wise distribution, mak- ing it readily comparable to mechanical sieving data. The concept of weight/particle ratio is introduced for mass reconstruction from 2D images of particle aggregates. Using this mass model, the effects of several particle shape parameters （such as major axis, minor axis, and equivalent diameter） on sieve-size of the particles is studied. It is shown that the sieve-size of a particle strongly depend upon the shape param- eters, 91% of its variation being explained by major axis, minor axis, bounding box length and equivalent diameter. Furthermore, minor axis gives an overall accurate estimate of particle sieve-size, error in mean size （D-50） being just 0.4%. However, sieve-size of smaller particles （〈20 ram） strongly depends upon the length of the smaller arm of the bounding box enclosing them and sieve-sizes of larger particles （〉20 mm） are highly correlated to their equivalent diameters. Multiple linear regression analysis has been used to generate overall mass-wise particle size distribution, considering the influences of all these shape parameters on particle sieve-size. Multiple linear regression generated overall mass-wise particle size distribution shows a strong correlation with sieve generated data. The adjusted R-square value of the regression analysis is found to be 99 percent （w.r,t cumulative frequency）. The method proposed in this paper provides a time-efficient way of producing accurate （up to 99%） mass-wise PSD using digital image processing and it can be used effectively to renlace the mechanical sieving.

Factors affecting accuracy of radial point interpolation meshfree method for 3-D solid mechanics

Recently,the radial point interpolation meshfree method has gained popularity owing to its advantages in large deformation and discontinuity problems,however,the accuracy of this method depends on many factors and their influences are not fully investigated yet.In this work,three main factors,i.e.,the shape parameters,the influence domain size,and the nodal distribution,on the accuracy of the radial point interpolation method(RPIM)are systematically studied and conclusive results are obtained.First,the effect of shape parameters(R,q)of the multi-quadric basis function on the accuracy of RPIM is examined via global search.A new interpolation error index,closely related to the accuracy of RPIM,is proposed.The distribution of various error indexes on the R q plane shows that shape parameters q[1.2,1.8]and R[0,1.5]can give good results for general 3-D analysis.This recommended range of shape parameters is examined by multiple benchmark examples in 3D solid mechanics.Second,through numerical experiments,an average of 30 40 nodes in the influence domain of a Gauss point is recommended for 3-D solid mechanics.Third,it is observed that the distribution of nodes has significant effect on the accuracy of RPIM although it has little effect on the accuracy of interpolation.Nodal distributions with better uniformity give better results.Furthermore,how the influence domain size and nodal distribution affect the selection of shape parameters and how the nodal distribution affects the choice of influence domain size are also discussed.

A UNIFIED THREE POINT APPROXIMATING SUBDIVISION SCHEME

In this paper, we propose a three point approximating subdivision scheme, with three shape parameters, that unifies three different existing three point approximating schemes. Some sufficient conditions for subdivision curve C0 to C3 continuity and convergence of the scheme for generating tensor product surfaces for certain ranges of parameters by using Laurent polynomial method are discussed. The systems of curve and surface design based on our scheme have been developed successfully in garment CAD especially for clothes modelling.

The Mean Deviation from the Median of the Dagum Distribution

The Dagum model is particularly suitable for the analysis of the distributions of economic quantities, such as income, assets and consumption. The purpose of this note is to derive the expression of the mean deviation from the median of the Dagum distribution to study the behavior of the scale and shape parameters in terms of absolute variability and in terms of relative variability.