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格调论视阈中的杜诗“正变”论--兼及对明清格调论思维模式的考察 被引量:1
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作者 王顺贵 《学术论坛》 CSSCI 北大核心 2008年第9期160-163,共4页
"正变"论格调论是最为核心的理论命题,它决定着一个作家品第的高下优劣。杜诗"正变"一直是明清格调论关注的焦点,明代格调论从伸"正"诎"变"的视角出发,将杜甫置于"大家"之尴尬地位;... "正变"论格调论是最为核心的理论命题,它决定着一个作家品第的高下优劣。杜诗"正变"一直是明清格调论关注的焦点,明代格调论从伸"正"诎"变"的视角出发,将杜甫置于"大家"之尴尬地位;清代格调论则从杜甫人格与诗格的多维标举中,圆满地解决了杜诗"正"与"变"的问题。杜诗"正变"具有重要的诗学要义,它体现了明清格调论不同的思维模式,反映了明清格调派唐诗观的发展演变和审美观念的时代变迁。 展开更多
关键词 杜诗 “正变” 明清格调论 诗学要义
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A Fast Algorithm for Solving the Poisson Equations Based on the Discrete Cosine/Sine Transforms in the Finite Difference Method
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作者 LI Congcong WANG Danxia +1 位作者 JIA Hongen ZHANG Chenhui 《应用数学》 北大核心 2025年第3期651-669,共19页
To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical c... To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%. 展开更多
关键词 Phase-field model Finite difference method Fast Poisson solver(DC-T/DST) Explicit invariant energy quadratization Unconditional energy stability
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Normalized Solutions of Nonlinear Choquard Equations with Nonconstant Potential
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作者 LI Nan XU Liping 《应用数学》 北大核心 2025年第1期14-29,共16页
In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ... In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods. 展开更多
关键词 Nonlinear Choquard equation Potential function Variational method Normalized solution
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A New Class of Efficient Schemes for the Cahn-Hilliard-Navier-Stokes Equations
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作者 WANG Lijing WANG Danxia ZHANG Jianwen 《应用数学》 北大核心 2025年第3期607-624,共18页
In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary varia... In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary variable approaches.By using a new pressure correction method,the accuracy of the pressure has been greatly improved.Furthermore,one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step.In addition,we prove the unconditional energy stability of the schemes,rigorously.Finally,plenty of numerical simulations are carried out to verify the convergence rates,stability,and effectiveness of the proposed schemes numerically. 展开更多
关键词 Cahn-Hilliard-Navier-Stokes equation Scalar auxiliary variable Pressurecorrection Unconditional energy stability
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Two Second-Order Ecient Numerical Schemes for the Boussinesq Equations
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作者 LIU Fang WANG Danxia ZHANG Jianwen 《应用数学》 北大核心 2025年第1期114-129,共16页
In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,t... In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes. 展开更多
关键词 Scalar auxiliary variable approach Pressure-correction method Fully decoupled Unconditional stability Boussinesq equations
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Normalized Positive Ground State Solutions for Nonhomogeneous Kirchhoff Equations
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作者 ZHANG Xiaocang XU Liping 《应用数学》 北大核心 2025年第3期711-720,共10页
This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of norm... This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature. 展开更多
关键词 Normalized positive ground state solution Nonhomogeneous Kirchhoff equation Variational method Exponential critical growth Trapping potential
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许学夷的汉魏诗史观 被引量:2
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作者 陈斌 《福建师范大学学报(哲学社会科学版)》 CSSCI 北大核心 2006年第4期52-56,共5页
许学夷的汉魏诗史观,受明代七子派相关思想影响较大,但又自觉地对他们的观点予以驳正与补罅,从而在思路与学理上对明代的汉魏诗歌研究作出一定的推进。本文着重从两方面对他的汉魏诗史观作一评述,一是对格调派尊汉贬魏的诗史价值观的批... 许学夷的汉魏诗史观,受明代七子派相关思想影响较大,但又自觉地对他们的观点予以驳正与补罅,从而在思路与学理上对明代的汉魏诗歌研究作出一定的推进。本文着重从两方面对他的汉魏诗史观作一评述,一是对格调派尊汉贬魏的诗史价值观的批判,二是以“正变”说建构自己的汉魏诗史序列。 展开更多
关键词 许学夷 汉魏诗论 明代诗学 格调派 “正变”
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Improved Berry-Esseen Bound for Rademacher Sum
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作者 MA li YE Liu HAN Xin-Fang 《应用概率统计》 CSCD 北大核心 2024年第6期910-941,共32页
Let X=Σ_(i=1)^(n)a_(i)ξ_(i)be a Rademacher sum with Var(X)=1 and Z be a standard normal random variable.This paper concerns the upper bound of|P(X≤x)−P(Z≤x)|for any x∈R.Using the symmetric properties and R softwa... Let X=Σ_(i=1)^(n)a_(i)ξ_(i)be a Rademacher sum with Var(X)=1 and Z be a standard normal random variable.This paper concerns the upper bound of|P(X≤x)−P(Z≤x)|for any x∈R.Using the symmetric properties and R software,this paper gets the following improved Berry-Esseen type bound under some conditions,|P(X≤x)−P(Z≤x)|≤P(Z∈(0,a1)),∀x∈R,which is one of the modified conjecture proposed by Nathan K.and Ohad K. 展开更多
关键词 sum of i.i.d.random variables standard normal distribution QUANTILE Berry-Esseen upper bound
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A new apparatus for investigating stress,deformation and seepage coupling properties of rock fractures 被引量:2
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作者 刘才华 陈从新 《Journal of Central South University》 SCIE EI CAS 2011年第5期1662-1666,共5页
A true triaxial apparatus which is composed of three units was presented.The apparatus allows for investigations on deformation and seepage behaviors of a single rock fracture subjected to lateral stress and normal st... A true triaxial apparatus which is composed of three units was presented.The apparatus allows for investigations on deformation and seepage behaviors of a single rock fracture subjected to lateral stress and normal stress.The first unit has three jacks which can apply loads independently in three orthogonal directions.The second unit is used to supply water inflow,control seepage pressure and measure flow velocity in real time.The third unit is for measuring the normal deformation of rock fractures.Some tests for investigating the normal deformation and seepage behaviors of rock fractures subjected to normal and lateral loads on hard granite specimens with an artificial persistent fracture,were introduced.The results show that both the normal deformation and the hydraulic conductivity are influenced not only by the normal stress but also by the lateral stress.It is also shown that the aperture and the hydraulic conductivity decrease with the increasing normal stress but increase with the increasing lateral stress and both the aperture and the hydraulic conductivity obey exponential relationships with the normal stress and the lateral stress. 展开更多
关键词 true triaxial apparatus rock fractures normal stress lateral stress normal deformation seepage properties hydraulic conductivity
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Influences of pre-existing fracture on ground deformation induced by normal faulting in mixed ground conditions 被引量:9
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作者 蔡奇鹏 吴宏伟 +1 位作者 骆冠勇 胡平 《Journal of Central South University》 SCIE EI CAS 2013年第2期501-509,共9页
Physical model tests have been conducted by various researchers to investigate fault rupture propagation and ground deformation induced by bedrock faulting. However, the effects of pre-existing fracture on ground defo... Physical model tests have been conducted by various researchers to investigate fault rupture propagation and ground deformation induced by bedrock faulting. However, the effects of pre-existing fracture on ground deformation are not fully understood. In this work, six centrifuge tests are reported to investigate the influence of pre-existing fracture on ground deformation induced by normal faulting in sand, clay and nine-layered soil with interbedded sand and clay layers. Shear box tests were conducted to develop a filter paper technique, which was adopted in soil model preparation to simulate the effects of pre-existing fracture in centrifuge tests. Centrifuge test results show that ground deformation mechanism in clay, sand and nine-layered soil strata is classified as a stationary zone, a shearing zone and a rigid body zone. Inclination of the strain localization is governed by the dilatancy of soil material. Moreover, the pre-existing fracture provides a preferential path for ground deformation and results in a scarp at the ground surface in sand. On the contrary, fault ruptures are observed at the ground surface in clay and nine-layered soil strata. 展开更多
关键词 centrifuge modeling pre-existing fracture ground deformation normal faulting EARTHQUAKE
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Numerical simulation of intelligent compaction for subgrade construction 被引量:9
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作者 MA Yuan LUAN Ying-cheng +1 位作者 ZHANG Wei-guang ZHANG Yu-qing 《Journal of Central South University》 SCIE EI CAS CSCD 2020年第7期2173-2184,共12页
During the compaction of a road subgrade, the mechanical parameters of the soil mass change in real time, but current research assumes that these parameters remain unchanged. In order to address this discrepancy, this... During the compaction of a road subgrade, the mechanical parameters of the soil mass change in real time, but current research assumes that these parameters remain unchanged. In order to address this discrepancy, this paper establishes a relationship between the degree of compaction K and strain ε. The relationship between the compaction degree K and the shear strength of soil(cohesion c and frictional angle φ) was clearly established through indoor experiments. The subroutine UMAT in ABAQUS finite element numerical software was developed to realize an accurate calculation of the subgrade soil compaction quality. This value was compared and analyzed against the assumed compaction value of the model, thereby verifying the accuracy of the intelligent compaction calculation results for subgrade soil. On this basis, orthogonal tests of the influential factors(frequency, amplitude, and quality) for the degree of compaction and sensitivity analysis were carried out. Finally, the ‘acceleration intelligent compaction value’, which is based on the acceleration signal, is proposed for a compaction meter value that indicates poor accuracy. The research results can provide guidance and basis for further research into the accurate control of compaction quality for roadbeds and pavements. 展开更多
关键词 intelligent compaction numerical simulation dynamic change control indicators orthogonal experiment
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Modified constitutive model and workability of 7055 aluminium alloy in hot plastic compression 被引量:16
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作者 ZHANG Tao ZHANG Shao-hang +2 位作者 LI Lei LU Shi-hong GONG Hai 《Journal of Central South University》 SCIE EI CAS CSCD 2019年第11期2930-2942,共13页
To obtain flow behavior and workability of 7055 aluminium alloy during hot deformation,hot compression tests at different temperatures and strain rates are conducted.True stress?strain curves of 7055 aluminium alloy u... To obtain flow behavior and workability of 7055 aluminium alloy during hot deformation,hot compression tests at different temperatures and strain rates are conducted.True stress?strain curves of 7055 aluminium alloy under different conditions are obtained and the flow stress increases with ascending strain rate and descending temperature.For Arrhenius constitutive equation,each material parameter is set as a constant,which will bring forth large error for predicting flow behavior.In this work,material parameters are fitted as a function of temperature or strain rate based on experimental results and a modified constitutive equation is established for more accurate prediction of flow behavior of 7055 aluminium alloy.The effects of temperature and strain rate on power dissipation and instability are analyzed to establish a processing map of 7055 aluminium alloy.The dominant deformation mechanism for microstructure evolution at different deformation conditions can be determined and high efficiency of power dissipation may be achieved from power dissipation map.Meanwhile,proper processing parameters to avoid flow instability can be easily acquired in instability map.According to the processing map,optimized processing parameters of 7055 aluminium alloy are temperature of 673?723 K and strain rate of 0.01?0.4 s^?1,during which its efficiency of power dissipation is over 30%.Finite element method(FEM)is used to obtain optimized parameter in hot rolling process on the basis of processing map. 展开更多
关键词 7055 aluminium alloy flow behavior modified constitutive equation processing map optimized parameters
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Estimating probability curves of rock variables using orthogonal polynomials and sample moments 被引量:3
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作者 邓建 边利 《Journal of Central South University of Technology》 2005年第3期349-353,共5页
A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample ... A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample of observed values of a random variable could be conventional moments (moments about the origin or central moments) and probability-weighted moments (PWMs). Probability curves derived from orthogonal polynomials and conventional moments are probability density functions (PDF), and probability curves derived from orthogonal polynomials and PWMs are inverse cumulative density functions (CDF) of random variables. The proposed approach is verified by two most commonly-used theoretical standard distributions: normal and exponential distribution. Examples from observed data of uniaxial compressive strength of a rock and concrete strength data are presented for illustrative purposes. The results show that probability curves of rock variable can be accurately derived from orthogonal polynomials and sample moments. Orthogonal polynomials and PWMs enable more secure inferences to be made from relatively small samples about an underlying probability curve. 展开更多
关键词 rock variables probability curve orthogonal polynomials conventional moments probability-weighted moments
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Influence of radial forging process on strain inhomogeneity of hollow gear shaft using finite element method and orthogonal design 被引量:4
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作者 LI Hong-xu WANG Kai +5 位作者 LUO Rong ZHU Zi-zong DENG Shuai LUO Rong ZHANG Jing-yi FANG Fei-song 《Journal of Central South University》 SCIE EI CAS CSCD 2020年第6期1666-1677,共12页
Due to the current trend towards lightweight design in automotive industry,hollow stepped gear shafts for automobile and its radial forging process are widely investigated.Utilizing coupled finite element thermo-mecha... Due to the current trend towards lightweight design in automotive industry,hollow stepped gear shafts for automobile and its radial forging process are widely investigated.Utilizing coupled finite element thermo-mechanical model,radial forging process of a hollow stepped gear shaft for automobile was simulated.The optimal combination of three process parameters including initial temperature,rotation rate and radial reduction was also selected using orthogonal design method.To examine the strain inhomogeneity of the forging workpiece,the strain inhomogeneity factor was introduced.The results reveal that the maximum effective strain and the minimum effective strain appeared in the outermost and innermost zones of different cross sections for the hollow stepped gear shaft,respectively.Optimal forging parameters are determined as a combination of initial temperature of 780°C,rotation rate of 21°/stroke and radial reduction of 3 mm. 展开更多
关键词 radial forging process strain inhomogeneity orthogonal design coupled thermo-mechanical analysis finite element method
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Selective image enhancement method for low energy target information area
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作者 朱利 陈继锋 +1 位作者 秦辰 曾明 《Journal of Central South University of Technology》 EI 2006年第5期563-567,共5页
A selective subband enhancement method based on biorthogonal wavelet base is proposed. This novel image enhancement method is just for those images in which the energy of target information area is relatively lower. I... A selective subband enhancement method based on biorthogonal wavelet base is proposed. This novel image enhancement method is just for those images in which the energy of target information area is relatively lower. It includes two parts: one is enhancing the low frequency subband by wavelet decomposition and the other is building a new criterion based on entropy window to image evaluation. Experimental results show that this new scheme may result in a perfect image processing. 展开更多
关键词 wavelet transform biorthogonal wavelet basel selective subband enhancement entropy windowl lowfrequency subband
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Semi-empirical modeling of volumetric efficiency in engines equipped with variable valve timing system 被引量:1
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作者 Mostafa Ghajar Amir Hasan Ka Kaee Behrooz Mashadi 《Journal of Central South University》 SCIE EI CAS CSCD 2016年第12期3132-3142,共11页
Volumetric efficiency and air charge estimation is one of the most demanding tasks in control of today's internal combustion engines.Specifically,using three-way catalytic converter involves strict control of the ... Volumetric efficiency and air charge estimation is one of the most demanding tasks in control of today's internal combustion engines.Specifically,using three-way catalytic converter involves strict control of the air/fuel ratio around the stoichiometric point and hence requires an accurate model for air charge estimation.However,high degrees of complexity and nonlinearity of the gas flow in the internal combustion engine make air charge estimation a challenging task.This is more obvious in engines with variable valve timing systems in which gas flow is more complex and depends on more functional variables.This results in models that are either quite empirical(such as look-up tables),not having interpretability and extrapolation capability,or physically based models which are not appropriate for onboard applications.Solving these problems,a novel semi-empirical model was proposed in this work which only needed engine speed,load,and valves timings for volumetric efficiency prediction.The accuracy and generalizability of the model is shown by its test on numerical and experimental data from three distinct engines.Normalized test errors are 0.0316,0.0152 and 0.24 for the three engines,respectively.Also the performance and complexity of the model were compared with neural networks as typical black box models.While the complexity of the model is less than half of the complexity of neural networks,and its computational cost is approximately 0.12 of that of neural networks and its prediction capability in the considered case studies is usually more.These results show the superiority of the proposed model over conventional black box models such as neural networks in terms of accuracy,generalizability and computational cost. 展开更多
关键词 engine modeling modeling and simulation spark ignition engine volumetric efficiency variable valve timing
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A comparative study on three EOF analysis techniques using decades of Arctic sea-ice concentration data
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作者 陈新保 刘信陶 +1 位作者 李松年 Chow Annie 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第7期2681-2690,共10页
Change in Arctic sea ice extent is one of the indicators of global climate changes. Spatio-temporal change and change patterns can be identified using various methods to facilitate human understanding global climate c... Change in Arctic sea ice extent is one of the indicators of global climate changes. Spatio-temporal change and change patterns can be identified using various methods to facilitate human understanding global climate changes. Three empirical orthogonal function(EOF) techniques are discussed and applied to decades of sea-ice concentration(SIC) dataset in Arctic area for identifying independent patterns. It was found that: 1) discrepancies exist in magnitude and scope for each EOF pattern, however, the first two leading EOFs of variability possess high similarities in structure and shape; 2) Even though there are somewhat differences in amplitude of each PC mode, the first two leading PC modes maintain consistent in overall trend and periodicity; 3) There are significant discrepancies and inconsistencies in the third and fourth leading EOF and PC modes. The accuracies of three techniques are further validated in representing the physical phenomena of SIC anomaly patterns. 展开更多
关键词 empirical orthogonal functions sea-ice concentration comparative study patterns arctic
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OMHT method for weak signal processing of GPR and its application in identification of concrete micro-crack 被引量:5
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作者 LING Tong-hua ZHANG Liang +3 位作者 HUANG Fu GU Dan-ping YU Bin ZHANG Sheng 《Journal of Central South University》 SCIE EI CAS CSCD 2019年第11期3057-3065,共9页
In the light of the problem of weak reflection signals shielded by strong reflections from the concrete surface,the detection and the recognition of hidden micro-cracks in the shield tunnel lining were studied using t... In the light of the problem of weak reflection signals shielded by strong reflections from the concrete surface,the detection and the recognition of hidden micro-cracks in the shield tunnel lining were studied using the orthogonal matching pursuit and the Hilbert transform(OMHT method).First,according to the matching pursuit algorithm and the strong reflection-forming mechanism,and based on the sparse representation theory,a sparse dictionary,adapted to the characteristics of the strong reflection signal,was selected,and a matching decomposition of each signal was performed so that the weak target signal submerged in the strong reflection was displayed more strongly.Second,the Hilbert transform was used to extract multiple parameters,such as the instantaneous amplitude,the instantaneous frequency,and the instantaneous phase,from the processed signal,and the ground penetrating radar(GPR)image was comprehensively analyzed and determined from multiple angles.The results show that the OMHT method can accurately weaken the effect of the strong impedance interface and effectively enhance the weak reflected signal energy of hidden micro-crack in the shield tunnel segment.The resolution of the processed GPR image is greatly improved,and the reflected signal of the hidden micro-crack is easily visible,which proves the validity and accuracy of the analysis method. 展开更多
关键词 orthogonal matching pursuit Hilbert transform shield tunnel lining structure hidden micro-crack
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Effects of oxidation treatment on properties of SiO_(2f)/SiO_2-BN composites 被引量:1
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作者 LI Duan ZHANG Chang-rui +4 位作者 LI Bin CAO Feng WANG Si-qing YANG Bei LIU Kun 《Journal of Central South University》 SCIE EI CAS 2012年第1期30-35,共6页
The silica fiber reinforced silica and boron nitride-based composites (SiO2f/SiO2-BN) were prepared firstly via the sol-gel method and then the urea route, and the effects of oxidation treatment on the component, st... The silica fiber reinforced silica and boron nitride-based composites (SiO2f/SiO2-BN) were prepared firstly via the sol-gel method and then the urea route, and the effects of oxidation treatment on the component, structure, mechanical and dielectric properties of the composites were investigated. The results show that the oxidation treatment at 450 ℃ will not impair the structure of boron nitride, and carbon is the main impurity with the excessive urea. The density of SiO2f/SiO2-BN composites is 1.81 g/cm3, and the flexural strength and elastic modulus are 113.9 MPa and 36.5 GPa, respectively. After oxidation treatment, the density varies to 1.80 g/cm3, and the flexural strength and elastic modulus are decreased to 58.9 MPa and 9.4 GPa, respectively. The mechanical properties of the composites are severely damaged, but they still exhibit a good toughness. The composites show excellent dielectric properties with the dielectric constant and loss tangent being 3.22 and 0.003 9, respectively, which indicates that the oxidation treatment is ineffective to improve the dielectric properties of SiOzf/SiO2-BN composites. 展开更多
关键词 RADOME boron nitride urea route COMPOSITES oxidation treatment wave-transparent structure mechanical properties dielectric properties
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Analytical solution to one-dimensional consolidation in unsaturated soils under sinusoidal cyclic loading
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作者 冯君 巫锡勇 +1 位作者 朱宝龙 杨期祥 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第2期646-653,共8页
An analytical solution was presented to the unsaturated soil with a finite thickness under confinement in the lateral direction and sinusoidal cyclic loading in the vertical direction based on Fredlund's one-dimen... An analytical solution was presented to the unsaturated soil with a finite thickness under confinement in the lateral direction and sinusoidal cyclic loading in the vertical direction based on Fredlund's one-dimensional consolidation equation for unsaturated soil. The transfer relationship between the state vectors at the top surface and any depth was gained by applying the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy's law and Fick's law. The excess pore-air and pore-water pressures and settlement in the Laplace-transformed domain were obtained by using the Laplace transform with the initial and boundary conditions. The analytical solutions of the excess pore-air and pore-water pressures at any depth and settlement were obtained in the time domain by performing the inverse Laplace transforms. A typical example illustrates the consolidation characteristics of unsaturated soil under sinusoidal loading from analytical results. Finally, comparisons between the analytical solutions and results of the numerical method indicate that the analytical solution is correct. 展开更多
关键词 unsaturated soil analytical solution one-dimensional consolidation excess pore-water pressure excess pore-air pressure SETTLEMENT sinusoidal cyclic loading
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