ANALYSIS OF STRESS FIELD NEAR CRACK TIP BASED ON ELECTRIC SATURATION MODEL

Within the framework of nonlinear eleetroelasticity, the stress field near to the crack tip in an infinite piezoelectric media subject to a far field uniform loading is studied by using an electrical strip saturation model and the complex variable method. And the emphasis is placed on the stress field near to the crack tip. The obtained solutions show that the normalized stress components at an arbitrary point near to the crack tip are determined by the angle of the point. Moreover, the stress components are independent of the distance from the point to the ori- gin of the coordinate. The distributions of in-plane stress components near to the crack tip are analyzed based on numerical results for PZT-SH. Compared with some related solutions, results show that the solutions are valid.

Complex variable approach in studying modified polarization saturation model in two-dimensional semipermeable piezoelectric media

A modified polarization saturation model is proposed and addressed math- ematically using a complex variable approach in two-dimensional （2D） semipermeable piezoelectric media. In this model, an existing polarization saturation （PS） model in 2D piezoelectric media is modified by considering a linearly varying saturated normal electric displacement load in place of a constant normal electric displacement load, applied on a saturated electric zone. A centre cracked infinite 2D piezoelectric domain subject to an arbitrary poling direction and in-plane electromechanical loadings is considered for the analytical and numerical studies. Here, the problem is mathematically modeled as a non-homogeneous Riemann-Hilbert problem in terms of unknown complex potential functions representing electric displacement and stress components. Having solved the Hilbert problem, the solutions to the saturated zone length, the crack opening displace- ment （COD）, the crack opening potential （COP）, and the local stress intensity factors （SIFs） are obtained in explicit forms. A numerical study is also presented for the proposed modified model, showing the effects of the saturation condition on the applied electrical loading, the saturation zone length, and the COP. The results of fracture parameters obtained from the proposed model are compared with the existing PS model subject to electrical loading, crack face conditions, and polarization angles.

Effect of gas saturation on P-wave velocity in tight sandstone

By measuring the variation of the P-and S-wave velocities of tight sandstone samples under water saturation,it was confirmed that with the decrease in water saturation,the P-wave velocity first decreased and then increased.The variation in velocity was influenced by the sandstone’s porosity.The commonly used Gassmann equation based on fluid substitution theory was studied.Comparing the calculated results with the measured data,it was found that the Gassmann equation agreed well with the measured data at high water saturation,but it could not explain the bending phenomenon of P-wave velocity at low saturation.This indicated that these equations could not accurately describe the relationship between fluid content and rock acoustic velocity.The reasons for this phenomenon were discussed through Taylor’s expansion.The coefficients of the fitting formula were calculated and verified by fitting the measured acoustic velocity changes of the cores.The relationship between P-wave velocity and saturation was discussed,which provides experimental support for calculating saturation using seismic and acoustic logging data.

Statistical fluctuations in a saturation laser model with correlated noises

We study the effects of correlations between quantum and pump noises on fluctuations of the laser intensity in a saturation laser model. An approximative Fokker-Planck equation and analytic expressions of the steady-state probability distribution function （SPD） of the laser system are derived. Based on the SPD, the normalized mean, the normalized variance, and the normalized skewness of the steady-state laser intensity are calculated numerically. The results indicate that （i） the correlation strength A of correlated noises always enhances the fluctuation of laser intensity; （ii） the correlation time v of correlated noises strengthens the fluctuation of laser intensity for the below-threshold case but τ weakens it for the above-threshold case.

Effects of correlations between the real and imaginary parts of quantum noise on intensity fluctuation for a saturation laser model

This paper studies the effects of cross-correlations between the real and imaginary parts of quantum noise on the laser intensity in a saturation laser model. It derives the analytic expressions of the intensity correlation function C（τ） and the associated relaxation time T（C） in the case of a stable locked phase resulting from the cross-correlation λq between the real and imaginary parts of quantum noise. Based on numerical computations it finds that the presence of cross correlations between the real and imaginary parts of quantum noise slow down the decay of intensity fluctuation, i.e., it causes the increase of intensity fluctuation.

Carbonate rocks resistivity determination using dual and triple porosity conductivity models

The rocks may be classified as Archie rocks or Non-Archie rocks,depending on the link between pore structure and resistivity of the rock.For carbonate rocks,keeping this factor in view,the applicability of Archie's law tends to be unreasonable and employing Archie's equation will ultimately lead to inaccurate estimates of the water saturation.Numerous investigators have reported models that forms a link between laboratory results and field well logs to determine water saturation in intricate pore systems.In case of complex systems,Archie's law fails to correctly define the resistivity-index curves.In addition,it is imperative to carry out investigations at lower saturation values in order to elaborate the non-Archie characteristics.This brings the dual and triple porosity conductivity models into the equation.As these models are essential in defining the considerable changes of the resistivity-index curves,both qualitatively and quantitatively.The linkage between the two models is depicted electrically in series or in parallel.Moreover,it is possible to have a combination of the two configurations.As a result,the experimental results can be modeled accurately using least parameters.This work presents two models to determine water saturation in carbonate rocks,containing dual and triple porosity systems.This study also investigates the impact of different influential parameters such as saturation exponents,conductivity ratios,and pore volume fraction of each network systems,on the new models.Finally,the effect of each parameter is individually studied and the sensitivity analysis on the RI curves is produced.A new approach to apply these models is also explained which requires the use of NMR log,mercury injection capillary pressure(MICP)measurement,and simple plotting techniques to determine the water saturation.The proposed new models help petrophysicists to estimate water saturation in Non-Archie rocks,containing double and triple porosity network systems.

A new integrated approach to resolve the saturation profile using high-resolution facies in heterogenous reservoirs

The saturation calculation in complex reservoirs remains a major challenge to the oil and gas industry.In simple formations,a tendency towards simple saturation models such as Archie or Simandoux for clean and shaly reservoirs respectively is always preferable.These models were found to be working effectively in homogeneous formations within which the porosity and permeability are linked in the light of a simple facies scheme.Where the rocks show some degrees of heterogeneity,the well-logs are usually affected by different factors.This adversely results in a compromised or averaged log profiles that may affect the saturation calculations.Four wells drilled across a shaly sand of high heterogeneity have been studied in the Perth Basin,Western Australia.The aim is to resolve the hydrocarbon saturation and explain the high productivity results,despite the high water saturation,obtained through a conducted formation well test across the interested reservoir zones.A new integration technique between a suite of conventional and advanced logging tools together with the capillary pressure measurements has been carried out to generate a high-resolution reservoir saturation profile,that is lithofacies dependent.Three different independent methods were used in the studied wells to calculate the saturation and to reduce the uncertainty of the final estimated profiles.The methods are the resistivity-based saturation,the NMR-based irreducible saturation,and a new application through saturation height modeling.Furthermore,through the workflow,an effective calibration for the magnetic resonance T2 cutoff has been applied that is supported by the excellent reservoir production behavior from such complex reservoir.The methodology will help resolve the saturation calculation as one of the most challenging reservoir parameters,particularly where the resistivity logs are affected in complicated shaly sand environments.The effectiveness of the workflow shines the possibility to predict high resolution facies and saturation profiles in the lack of resistivity logs.A further possibility can complete the analysis on real time basis,which can certainly provide facies and saturation profiles extended to the uncored wells.Application of this methodology in the uncored wells has shown very encouraging results in various well trajectories,either vertical,deviated or horizontal long boreholes.

Energy dependent growth of nucleon and inclusive charged hadron distributions

In the Color Glass Condensate formalism, charged hadron p T spectra in p＋p and p＋Pb collisions are studied by considering an energy-dependent broadening of nucleon density distribution. Then, in the glasma flux tube picture, the n-particle multiplicity distributions at different pseudo-rapidity ranges are investigated. Both the theoretical results show good agreement with the recent experimental data from ALICE and CMS at LHC energies.The predictive results for p T or multiplicity distributions in p＋p and p＋Pb collisions at the Large Hadron Collider are also given in this paper.

Net-Baryon and Net-Kaon Rapidity Distributions in Ultrarelativistic Heavy-Ion Collisions

In this paper,the gluon distribution is extracted from the KLR-AdS/CFT saturation model and used to investigate net-baryon and net-kaon rapidity distributions in ultrarelativistic heavy-ion collisions.With the same parameters of the saturation model fitting to HERA data and an χ 2 analysis of the overall constant C,the theoretical results are in good agreement with RHIC data in Au+Au collisions at √ s = 0.2 TeV.Then,we present the predictive results for net-baryon rapidity distributions in central Pb+Pb collisions at LHC energies of √ s = 2.76,3.94,and 5.52 TeV,and give the corresponding values of dN/dy for net-baryon at y = 0.

Indoor and outdoor people detection and shadow suppression by exploiting HSV color information

An adaptive background model based on max-imum statistical probability and a shadow suppression scheme for indoor and outdoor people detection by exploiting hue saturation value(HSV)color information is proposed.To obtain the initial background scene,the frequency of R,G,and B component values for each pixel at the same position in the learning sequence are respec-tively calculated;the R,G,and B component values with the biggest ratios are incorporated to model the initial background.The background maintenance,or the so-called background re-initiation,is also proposed to adapt to scene changes such as illumination changes and scene geometry changes.Moving cast shadows generally exhibit a challenge for accurate moving target detection.Based on the observation that a shadow cast on a background region lowers its brightness but does not change its chro-maticity significantly,we address this problem in the ar-ticle by exploiting HSV color information.In addition,quantitative metrics is introduced to evaluate the algo-rithm on a benchmark suite of indoor and outdoor video sequences.The experimental results are given to show the performance of the algorithm.

The Closeness of the τ-Standard Part of a Set

In this paper,the closeness of the τ-standard part of a set is discussed.Some related propositions of the τ-neighborhood system of a set are given.And then some related conclusions of the τ-monad of a set and the τ-standard part of a set are presented.And based on it,the necessary and sufficient conditions of the enlarged model and the saturated model are showed.Finally,some sufficient conditions that the τ-standard part of a set is closed are proved in the enlarged model and the saturated model.

Computer assessment of the composition of a generic wound by image processing

Aim:This paper addresses the assessment of the composition of a general wound,in terms of all identifiable categories of tissue and pigmentation in an attempt to improve accuracy in assessing and monitoring wound health.Materials and Methods:A knowledgebase of clusters was built into the hue,saturation and intensity(HSI)color space and then used for assessing wound composition.Based on the observation that the clusters are fairly distinct,two different algorithms,that is,Mahalanobis distance(MD)based and the rotated coordinate system(RCS)method,were used for classification.These methods exploit the shape,spread,and orientation of each cluster.Results:The clusters in the HSI color space,built from about 9,000(calibrated)pixels from 48 images of various wound beds,showed 8 fairly distinct regions.The inter-cluster distances were consistent with the visual appearance.The efficacy of the MD and RCS based methods in 120 experiments taken from a set of 15 test images(in terms of average percent-match)was found to be 91.55 and 93.71,respectively.Conclusion:Our investigations established eight categories of tissue and pigmentation in wound beds.These findings help to determine the stage of wound healing more accurately and comprehensively than typically permitted through use of the 4-color model reported in the literature for addressing specific wound types.