General solutions of plane problem for power function curved cracks

A new exact and universal conformal mapping is proposed. Using Muskhelishvili＇s complex potential method, the plane elasticity problem of power function curved cracks is investigated with an arbitrary power of a natural number, and the general solutions of the stress intensity factors （SIFs） for mode I and mode II at the crack tip are obtained under the remotely uniform tensile loads. The present results can be reduced to the well-known solutions when the power of the function takes different natural numbers. Numerical examples are conducted to reveal the effects of the coefficient, the power, and the projected length along the x-axis of the power function curved crack on the SIFs for mode I and mode II.

Comments on “General solutions of plane problem for power function curved cracks”

An error has been found in Ref. [1]. In the case of n = 2, authors of Ref. [1] suggested the following conformal mapping function：

Preliminary Clinical Study of Real-time Three-dimensional Echo-cardiographic Volume-time Curve in Evaluating Left Ventricular Diastolic Function

The volume-time curve change in patients with normal left ventricular （LV） diastolic function and diastolic dysfunction was evaluated by real-time three-dimensional echocardiography （RT3DE）. LV diastolic dysfunction was defined by E＇〈A＇ in pulse-wave tissue Doppler for inter-ventricular septal （IVS） of mitral annulus. In 24 patients with LV diastolic dysfunction, including 12 patients with delayed relaxation （delayed relaxation group） and 12 patients with pseudo-normal function （pseudo-normal group） and 24 normal volunteers （control group）, data of full-volume image were acquired by real-time three-dimensional echocardiography and subjected to volume-time curve analysis. EDV （end-diastolic volume）, ESV （end-systolic volume）, LVEF （left ventricular ejection fraction）, PER （peak ejection rate）, PFR （peak filling rate） from RT3DE were examined in the three groups. Compared to the control group, PFR （diastolic filling index of RT3DE） was significantly reduced in the delayed relaxation group and pseudo-normal group （P〈0.05）. There were no significant differences in EDV, ESV, LVEE PER （P〉0.05）. It is concluded that PFR, as a diastolic filling index of RT3DE, can reflect the early diastolic function and serve as a new non-invasive, quick and accurate tool for clinical assessment of LV diastolic function.

Nonlinear thermo-mechanical stability of eccentrically stiffened functionally graded material sandwich doubly curved shallow shells with general sigmoid law and power law according to third-order shear deformation theory

In this paper, the nonlinear analysis of stability of functionally graded ma- terial （FGM） sandwich doubly curved shallow shells is studied under thermo-mechanical loads with material properties obeying the general sigmoid law and power law of four ma- terial models. Shells are reinforced by the FGM stiffeners and rest on elastic foundations. Theoretical formulations are derived by the third-order shear deformation theory （TSDT） with the von Karman-type nonlinearity taking into account the initial geometrical im- perfection and smeared stiffener technique. The explicit expressions for determining the critical buckling load and the post-buckling mechanical and thermal load-deflection curves are obtained by the Galerkin method. Two iterative algorithms are presented. The effects of the stiffeners, the thermal element, the distribution law of material, the initial imper- fection, the foundation, and the geometrical parameters on buckling and post-buckling of shells are investigated.

Improved theory of generalized meteo-ballistic weighting factor functions and their use

It follows from the analysis of artillery fire errors that approximately two-thirds of the inaccuracy of indirect artillery fire is caused by inaccuracies in the determination of the meteo parameters included in fire error budget model.Trajectories calculated under non-standard conditions are considered to be perturbed.The tools utilized for the analysis of perturbed trajectories are weighting factor functions(WFFs)which are a special kind of sensitivity functions.WFFs are used for calculation of meteo ballistic elements B(ballistic wind w B,densityρB,virtual temperatureτB,pressure p B)as well.We have found that the existing theory of WFF calculation has several significant shortcomings.The aim of the article is to present a new,improved theory of generalized WFFs that eliminates the deficiencies found.Using this theory will improve methods for designing firing tables,fire control systems algorithms,and meteo message generation algorithms.

Potential energy curve study on the ^3Π electronic states of GaX （X=F, Cl, and Br） molecules

The potential energy curves （PECs） of the 3Π states of GaX （X=F, Cl, and Br） molecules are calculated using the multireference configuration interaction method with a large contracted basis set aug-cc-pV5Z. The PECs are accurately fitted to analytical potential energy functions （APEFs） using the Murrell–Sorbie potential function. The spectroscopic parameters for the states are determined using the obtained APEFs, and compared with the theoretical and experimental data available presently in the literature.

METABALL-BASED TRANSITION SURFACES

Metaball-based constraint deformation technique is used to change the definition of r, the straight-line distance from a space point to a constraint center in the original calculation of the potential function. By replacing the parameter of the pararnetrized surface w with the straight-line distance r, a method of building transition surfaces according to cormected boundary curves and skeleton curves is proposed. The method has no restrictions on boundary curves that control the space shapes of transition surfaces or on types of skeleton curves, thus transition surfaces, which reach C^1 continuity and are more abundant in shapes and natural, can be obtained.

MRCI potential energy curves and analytical potential energy functions for the X^2Σ^+ and ~2Π states of BO molecule

The potential energy curves （PECs） of BO molecule, including ∑^＋and ∏ symmetries with doublet spin multiplicities, are obtained employing multi-reference configuration interaction （MRCI） method and Dunning＇s correlation consistent basis sets. The analytical potential energy functions （APEFs） are fitted using the Murrell-Sorbie （MS） function and the least square method. Based on the PECs, the spectroscopic constants of the states have been determined and compared with the theoretical and experimental results available to affirm the accuracy and liability of the calculations. The root-mean-square （RMS） errors between the fitted results and the ab initio values are too little in comparison with the chemical accuracy （349.755 cm^-1）. It is shown that the present APEFs are accurate and can display the interaction between the atoms well. The present APEFs can be used to construct more complicated APEF or do some dynamic investigations.

On well-posedness of two-phase nonlocal integral models for higher-order refined shear deformation beams

Due to the conflict between equilibrium and constitutive requirements,Eringen’s strain-driven nonlocal integral model is not applicable to nanostructures of engineering interest.As an alternative,the stress-driven model has been recently developed.In this paper,for higher-order shear deformation beams,the ill-posed issue(i.e.,excessive mandatory boundary conditions(BCs)cannot be met simultaneously)exists not only in strain-driven nonlocal models but also in stress-driven ones.The well-posedness of both the strain-and stress-driven two-phase nonlocal(TPN-Strain D and TPN-Stress D)models is pertinently evidenced by formulating the static bending of curved beams made of functionally graded(FG)materials.The two-phase nonlocal integral constitutive relation is equivalent to a differential law equipped with two restriction conditions.By using the generalized differential quadrature method(GDQM),the coupling governing equations are solved numerically.The results show that the two-phase models can predict consistent scale-effects under different supported and loading conditions.

A New Empirical Method for Constructing Capillary Pressure Curves from Conventional Logs in Low-Permeability Sandstones

Pore structure reflected from capillary pressure curves plays an important role in low-permeability formation evaluation. It is a common way to construct capillary pressure curves by Nuclear Magnetic Resonance（NMR） log. However, the method＇s efficiency will be severely affected if there is no NMR log data or it cannot reflect pore structure well. Therefore, on the basis of J function and diagenetic facies classification, a new empirical model for constructing capillary pressure curves from conventional logs is proposed here as a solution to the problem. This model includes porosity and the relative value of natural gamma rays as independent variables and the saturation of mercury injection as a dependent variable. According to the 51 core experimental data sets of three diagenetic facies from the bottom of the Upper Triassic in the western Ordos Basin, China, the model＇s parameters in each diagenetic facies are calibrated. Both self-checking and extrapolation tests show a positive effect, which demonstrates the high reliability of the proposed capillary pressure curve construction model. Based on the constructed capillary pressure curves, NMR T_2 spectra under fully brine-saturated conditions are mapped by a piecewise power function. A field study is then presented. Agreement can be seen between the mapped NMR T_2 spectra and the MRIL-Plog data in the location of the major peak, right boundary, distribution characteristics and T_2 logarithmic mean value. In addition, the capillary pressure curve construction model proposed in this paper is not affected by special log data or formation condition. It is of great importance in evaluating pore structure, predicting oil production and identifying oil layers through NMR log data in low-permeability sandstones.

Spatial pattern of grassland aboveground biomass and its environmental controls in the Eurasian steppe

Vegetation biomass is an important component of terrestrial ecosystem carbon stocks. Grasslands are one of the most widespread biomes worldwideplaying an important role in global carbon cycling. Thereforestudying spatial patterns of biomass and their correlations to environment in grasslands is fundamental to quantifying terrestrial carbon budgets. The Eurasian steppean important part of global grasslandsis the largest and relatively well preserved grassland in the world. In this studywe analyzed the spatial pattern of aboveground biomass（AGB）and correlations of AGB to its environment in the Eurasian steppe by meta-analysis. AGB data used in this study were derived from the harvesting method and were obtained from three data sources（literatureglobal NPP database at the Oak Ridge National Laboratory Distributed Active Archive Center（ORNL）some data provided by other researchers）. Our results demonstrated that：（1） as for the Eurasian steppe overallthe spatial variation in AGB exhibited significant horizontal and vertical zonality. In detailAGB showed an inverted parabola curve with the latitude and with the elevationwhile a parabola curve with the longitude. In additionthe spatial pattern of AGB had marked horizontal zonality in the Black Sea-Kazakhstan steppe subregion and the Mongolian Plateau steppe subregionwhile horizontal and vertical zonality in the Tibetan Plateau alpine steppe subregion.（2） Of the examined environmental variablesthe spatial variation of AGB was related to mean annual precipitation（MAP）mean annual temperature（MAT）mean annual solar radiation（MAR）soil Gravel contentsoil p H and soil organic content（SOC） at the depth of 0–30 cm. NeverthelessMAP dominated spatial patterns of AGB in the Eurasian steppe and its three subregions.（3） A Gaussian function was found between AGB and MAP in the Eurasian steppe overallwhich was primarily determined by unique patterns of grasslands and environment in the Tibetan Plateau. AGB was significantly positively related to MAP in the Black Sea-Kazakhstan steppe subregion（elevation 〈 3000 m）the Mongolian Plateau steppe subregion（elevation 〈 3000 m） and the surface（elevation ≥ 4800 m） of the Tibetan Plateau. Neverthelessthe spatial variation in AGB exhibited a Gaussian function curve with the increasing MAP in the east and southeast margins（elevation 〈 4800 m） of the Tibetan Plateau. This study provided more knowledge of spatial patterns of AGB and their environmental controls in grasslands than previous studies only conducted in local regions like the Inner Mongolian temperate grasslandthe Tibetan Plateau alpine grasslandetc.

An Inherent Probabilistic Aspect ofthe Hough Transform

in this paper a new property of the Hough transform is discovered, namely an inherent probabilistic aspect which is independent of the input image and embedded in the transformation process from the image space to the parameter space. It is shown that such a probabilistic aspect has a wide range of implica tions concerning the specification of implementation schemes and the performance of Hough transform. In particular, it is shown that in order to make the Hough transform really meaningful, an appropriate curve (surface) density function must be, either explicitly or implicitly, supplied during its implementation processi and that the widely used approach to uniformly discretizing parameter space in the literature is generally inadequate.

A New Definition of the Hough Transform

This paper's main contributions are three-fold. Firstly, it is shown that the two existing template matching-like definitions of the Hough transform in the literature areinadequate. Secondly, an inherent probabilistic aspect of the Hough transform embedded in the transformation process from image space to parameter space is clarified.Thirdly, a new definition of the Hough transform is proposed which takes into account both the intersection scheme between the mapping curve (or mapping surface) and accumulator cells and the inherent probabilistic characteristics.

Analysis on two novel spherical helical antennas

Two novel spherical helical antennas are designed by projecting the planar equiangular spiral antenna onto hemisphere and partial sphere surfaces.Their radiation properties are analyzed by the moment method with curved basis and test function,and the curves of the voltage standing wave ratio(VSWR),gain,polarization and pattern that change with frequency are also given,respectively.It can be seen that the circular polarization band of the novel hemispherical helical antenna is broader.The gain curve of the partial spherical helical antenna is flatter and the structure is simpler.