The preferred orientation of clay minerals dominates the intrinsic anisotropy of shale. We introduce the clay lamination (CL) parameter to the Backus averaging method to describe the intrinsic shale anisotropy induc...The preferred orientation of clay minerals dominates the intrinsic anisotropy of shale. We introduce the clay lamination (CL) parameter to the Backus averaging method to describe the intrinsic shale anisotropy induced by the alignment of clay minerals. Then, we perform the inversion of CL and the Thomsen anisotropy parameters. The direct measurement of anisotropy is difficult because of the inability to measure the acoustic velocity in the vertical direction in boreholes and instrument limitations. By introducing the parameter CL, the inversion method provides reasonable estimates of the elastic anisotropy in the Longmaxi shale. The clay content is weakly correlated with the CL parameter. Moreover, the parameter CL is abnormally high at the bottom of the Longmaxi and Wufeng Formations, which are the target reservoirs. Finally, we construct rock physics templates to interpret well logging and reservoir properties.展开更多
Material properties of blank have a great effect on power spinning process of aluminum alloy parts with transverse inner rib.By using finite element(FE) and Taguchi method,the effects and significance of five key mate...Material properties of blank have a great effect on power spinning process of aluminum alloy parts with transverse inner rib.By using finite element(FE) and Taguchi method,the effects and significance of five key material parameters,namely,anisotropic index in thickness direction,yield strength,hardening exponent,strengthening factor and elastic modulus on the formability of inner rib,tendency of wall fracture and degree of inhomogeneous deformation of finished spun parts were obtained.The achievements provide an important guide for selecting reasonable spinning material,and are very significant for the optimum design and precision control of power spinning process of parts with transverse inner rib.展开更多
Based on the statistical analysis of blocking effect arising from anisotropic growth,the anisotropic effect on the kinetics of solid-state transformation was investigated.The result shows that the blocking effect lead...Based on the statistical analysis of blocking effect arising from anisotropic growth,the anisotropic effect on the kinetics of solid-state transformation was investigated.The result shows that the blocking effect leads to the retardation of transformation and then a regular behavior of varying Avrami exponent.Following previous analytical model,the formulations of Avrami exponent and effective activation energy accounting for blocking effect were obtained.The anisotropic effect on the transformation depends on two factors,non-blocking factor γ and blocking scale k,which directly acts on the dimensionality of growth.The effective activation energy is not affected by the anisotropic effect.The evolution of anisotropic effect with the fraction transformed is taken into account,showing that the anisotropic effect is more severe at the middle stage of transformation.展开更多
Uniaxial strain hardening exponent is not suitable for describing the strain hardening behaviors of the anisotropic materials, especially when material deforms in the multi-axial stress states. In this work, a novel m...Uniaxial strain hardening exponent is not suitable for describing the strain hardening behaviors of the anisotropic materials, especially when material deforms in the multi-axial stress states. In this work, a novel method was proposed to estimate the equivalent strain hardening exponent of anisotropic materials based on an equivalent energy method. By performing extensive finite element (FE) simulations of the spherical indentation on anisotropic materials, dimensionless function was proposed to correlate the strain hardening exponent of anisotropic materials with the indentation imprint parameters. And then, a mathematic expression on the strain hardening exponent of anisotropic materials with the indentation imprint was established to estimate the equivalent strain hardening exponent of anisotropic materials by directly solving this dimensionless function. Additionally, Meyer equation was modified to determine the yield stress of anisotropic materials. The effectiveness and reliability of the new method were verified by the numerical examples and by its application on the TC1M engineering material.展开更多
Using an exact solution of the one-dimensional quantum transverse-field Ising model, we calculate the critical exponents of the two-dimensional anisotropic classical Ising model (IM). We verify that the exponents ar...Using an exact solution of the one-dimensional quantum transverse-field Ising model, we calculate the critical exponents of the two-dimensional anisotropic classical Ising model (IM). We verify that the exponents are the same as those of isotropic claesical IM. Our approach provides an alternative means of obtaining and verifying these well-known results.展开更多
This article describes a proposal for a double index to estimate the isotropic components of unitary errors in a quantum computation circuit. In the context of this work the error is considered isotropic if it has sph...This article describes a proposal for a double index to estimate the isotropic components of unitary errors in a quantum computation circuit. In the context of this work the error is considered isotropic if it has spherical symmetry about the state of interest. The theoretical definition is given, as well the numerical approximation for practical purposes. The index is tested in some simple examples and the geometric distortion of the propagated error is studied for an inaccurate Shor 9-qubits correcting code.展开更多
Using the first principles calculations based on density functional theory, the crystal structure, elastic anisotropy, and electronic properties of carbon, silicon and their alloys (C12Si4, C8Si8, and C4Si12) in a m...Using the first principles calculations based on density functional theory, the crystal structure, elastic anisotropy, and electronic properties of carbon, silicon and their alloys (C12Si4, C8Si8, and C4Si12) in a monoclinic structure (C2/m) are investigated. The calculated results such as lattice parameters, elastic constants, bulk modulus, and shear modulus of C16 and Si16 in C2/m structure are in good accord with previous work. The elastic constants show that C16, Si16, and their alloys in C2/m structure are mechanically stable. The calculated results of universal anisotropy index, compression and shear anisotropy percent factors indicate that C-Si alloys present elastic anisotropy, and CsSis shows a greater anisotropy. The Poisson's ratio and the BIG value show that C8Si8 is ductile material and other four C-Si alloys are brittle materials. In addition, Debye temperature and average sound velocity are predicted utilizing elastic modulus and density of C-Si alloys. The band structure and the partial density of states imply that C16 and Si16 are indirect band gap semiconductors, while 612Si4, C8Si8, and C4Si12 are semi-metallic alloys.展开更多
The mechanical behaviors near the interface crack tip for mode Ⅰ of orthotropic bimaterial are researched. With the help of the complex function method and the undetermined coefficient method, non-oscillatory field i...The mechanical behaviors near the interface crack tip for mode Ⅰ of orthotropic bimaterial are researched. With the help of the complex function method and the undetermined coefficient method, non-oscillatory field if the singularity exponent is a real number, and oscillatory field if the singularity exponent is a complex number are discussed, respectively. For each case, the stress functions are constructed which contain twelve undetermined coefficients and an unknown singularity exponent. Based on the boundary conditions, the system of non-homogeneous linear equations is obtained. According to the necessary and sufficient condition for the existence of solution for the system of non-homogeneous linear equations, the singularity exponent is determined under appropriate condition using bimaterial parameters. Both the theoretical formulae of stress intensity factors and analytic solutions of stress or displacement field near the interface crack tip are given. When the two orthotropic materials are the same, the classical results for orthotropic single material are deduced.展开更多
Suppose F = Q(√-p1 pt) is an imaginary quadratic number field with distinct primes p1,..., pt,where pi≡ 1(mod 4)(i = 1,..., t- 1) and pt ≡ 3(mod 4). We express the possible values of the 8-rank r8 of the class grou...Suppose F = Q(√-p1 pt) is an imaginary quadratic number field with distinct primes p1,..., pt,where pi≡ 1(mod 4)(i = 1,..., t- 1) and pt ≡ 3(mod 4). We express the possible values of the 8-rank r8 of the class group of F in terms of a quadratic form Q over F2 which is defined by quartic symbols. In particular,we show that r8 is bounded by the isotropy index of Q.展开更多
基金supported by the Foundation of State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Effective Development(No.G5800-16-ZS-KFZY002)the NSFC and Sino PEC Joint Key Project(No.U1663207)the National Natural Science Foundation of China(No.41404090)
文摘The preferred orientation of clay minerals dominates the intrinsic anisotropy of shale. We introduce the clay lamination (CL) parameter to the Backus averaging method to describe the intrinsic shale anisotropy induced by the alignment of clay minerals. Then, we perform the inversion of CL and the Thomsen anisotropy parameters. The direct measurement of anisotropy is difficult because of the inability to measure the acoustic velocity in the vertical direction in boreholes and instrument limitations. By introducing the parameter CL, the inversion method provides reasonable estimates of the elastic anisotropy in the Longmaxi shale. The clay content is weakly correlated with the CL parameter. Moreover, the parameter CL is abnormally high at the bottom of the Longmaxi and Wufeng Formations, which are the target reservoirs. Finally, we construct rock physics templates to interpret well logging and reservoir properties.
基金Projects(50405039,50575186) supported by the National Natural Science Foundation of ChinaProject(50225518) supported by the National Natural Science Foundation of China for Distinguished Young ScholarsProject(2008AA04Z122) supported by the National High-tech Research and Development Program of China
文摘Material properties of blank have a great effect on power spinning process of aluminum alloy parts with transverse inner rib.By using finite element(FE) and Taguchi method,the effects and significance of five key material parameters,namely,anisotropic index in thickness direction,yield strength,hardening exponent,strengthening factor and elastic modulus on the formability of inner rib,tendency of wall fracture and degree of inhomogeneous deformation of finished spun parts were obtained.The achievements provide an important guide for selecting reasonable spinning material,and are very significant for the optimum design and precision control of power spinning process of parts with transverse inner rib.
基金Project (2011CB610403) supported by the National Basic Research Program of ChinaProject (51125002) supported by the National Funds for Distinguished Young Scientists of China+2 种基金Project (51071127) supported by the National Natural Science Foundation of ChinaProjects (09-QZ-2008,24-TZ-2009) supported by the Free Research Fund of State Key Laboratory of Solidification Processing,ChinaProject (CX201008) supported by the Doctorate Foundation of Northwestern Polytechnical University,China
文摘Based on the statistical analysis of blocking effect arising from anisotropic growth,the anisotropic effect on the kinetics of solid-state transformation was investigated.The result shows that the blocking effect leads to the retardation of transformation and then a regular behavior of varying Avrami exponent.Following previous analytical model,the formulations of Avrami exponent and effective activation energy accounting for blocking effect were obtained.The anisotropic effect on the transformation depends on two factors,non-blocking factor γ and blocking scale k,which directly acts on the dimensionality of growth.The effective activation energy is not affected by the anisotropic effect.The evolution of anisotropic effect with the fraction transformed is taken into account,showing that the anisotropic effect is more severe at the middle stage of transformation.
基金Project(51675431)supported by the National Natural Science Foundation of China
文摘Uniaxial strain hardening exponent is not suitable for describing the strain hardening behaviors of the anisotropic materials, especially when material deforms in the multi-axial stress states. In this work, a novel method was proposed to estimate the equivalent strain hardening exponent of anisotropic materials based on an equivalent energy method. By performing extensive finite element (FE) simulations of the spherical indentation on anisotropic materials, dimensionless function was proposed to correlate the strain hardening exponent of anisotropic materials with the indentation imprint parameters. And then, a mathematic expression on the strain hardening exponent of anisotropic materials with the indentation imprint was established to estimate the equivalent strain hardening exponent of anisotropic materials by directly solving this dimensionless function. Additionally, Meyer equation was modified to determine the yield stress of anisotropic materials. The effectiveness and reliability of the new method were verified by the numerical examples and by its application on the TC1M engineering material.
基金The project supported by National Natural Science Foundation of China under Grant No. 10347101 and the grant from Beijing Normal University
文摘Using an exact solution of the one-dimensional quantum transverse-field Ising model, we calculate the critical exponents of the two-dimensional anisotropic classical Ising model (IM). We verify that the exponents are the same as those of isotropic claesical IM. Our approach provides an alternative means of obtaining and verifying these well-known results.
文摘This article describes a proposal for a double index to estimate the isotropic components of unitary errors in a quantum computation circuit. In the context of this work the error is considered isotropic if it has spherical symmetry about the state of interest. The theoretical definition is given, as well the numerical approximation for practical purposes. The index is tested in some simple examples and the geometric distortion of the propagated error is studied for an inaccurate Shor 9-qubits correcting code.
基金Supported by the Natural Science Foundation of China under Grant No.61474089Open Fund of Key Laboratory of Complex Electromagnetic Environment Science and Technology,China Academy of Engineering Physics under Grant No.2015-0214.YY.K
文摘Using the first principles calculations based on density functional theory, the crystal structure, elastic anisotropy, and electronic properties of carbon, silicon and their alloys (C12Si4, C8Si8, and C4Si12) in a monoclinic structure (C2/m) are investigated. The calculated results such as lattice parameters, elastic constants, bulk modulus, and shear modulus of C16 and Si16 in C2/m structure are in good accord with previous work. The elastic constants show that C16, Si16, and their alloys in C2/m structure are mechanically stable. The calculated results of universal anisotropy index, compression and shear anisotropy percent factors indicate that C-Si alloys present elastic anisotropy, and CsSis shows a greater anisotropy. The Poisson's ratio and the BIG value show that C8Si8 is ductile material and other four C-Si alloys are brittle materials. In addition, Debye temperature and average sound velocity are predicted utilizing elastic modulus and density of C-Si alloys. The band structure and the partial density of states imply that C16 and Si16 are indirect band gap semiconductors, while 612Si4, C8Si8, and C4Si12 are semi-metallic alloys.
基金supported by the Natural Science Foundation of Shanxi Province (Grant No. 2011011021-3)
文摘The mechanical behaviors near the interface crack tip for mode Ⅰ of orthotropic bimaterial are researched. With the help of the complex function method and the undetermined coefficient method, non-oscillatory field if the singularity exponent is a real number, and oscillatory field if the singularity exponent is a complex number are discussed, respectively. For each case, the stress functions are constructed which contain twelve undetermined coefficients and an unknown singularity exponent. Based on the boundary conditions, the system of non-homogeneous linear equations is obtained. According to the necessary and sufficient condition for the existence of solution for the system of non-homogeneous linear equations, the singularity exponent is determined under appropriate condition using bimaterial parameters. Both the theoretical formulae of stress intensity factors and analytic solutions of stress or displacement field near the interface crack tip are given. When the two orthotropic materials are the same, the classical results for orthotropic single material are deduced.
基金supported by China Postdoctoral Science Foundation(Grant No.2013M541064)National Natural Science Foundation of China(Grant No.11371043)National Basic Research Program of China(Grant No.2013CB834202)
文摘Suppose F = Q(√-p1 pt) is an imaginary quadratic number field with distinct primes p1,..., pt,where pi≡ 1(mod 4)(i = 1,..., t- 1) and pt ≡ 3(mod 4). We express the possible values of the 8-rank r8 of the class group of F in terms of a quadratic form Q over F2 which is defined by quartic symbols. In particular,we show that r8 is bounded by the isotropy index of Q.