Based on the form of the n-dimensional generic power-law potential, the state equation and the heat capacity, the analytical expressions of the Joule-Thomson coefficient （3TC） for an ideal Bose gas are derived in n-...Based on the form of the n-dimensional generic power-law potential, the state equation and the heat capacity, the analytical expressions of the Joule-Thomson coefficient （3TC） for an ideal Bose gas are derived in n-dimensional potential. The effect of the spatial dimension and the external potential on the JTC are discussed, respectively. These results show that： （i） For the free ideal Bose gas, when n/s ≤ 2 （n is the spatial dimension, s is the momentum index in the relation between the energy and the momentum）, and T → Tc （Tc is the critical temperature）, the JTC can obviously improve by means of changing the throttle valve＇s shape and decreasing the spatial dimension of gases. （ii） For the inhomogeneous external potential, the discriminant △= [1 - y∏^ni=1（kT/εi）^1/tiГ（1/ti＋1）] （k is the Boltzmann Constant, T is the thermodynamic temperature, ε is the external field＇s energy）, is obtained. The potential makes the JTC increase when △ 〉 0, on the contrary, it makes the JTC decrease when A 〈△. （iii） In the homogenous strong external potential, the JTC gets the maximum on the condition of kTεi〈〈1.展开更多
The main goal of this paper is to determine the effect of an extra dimension on a traversable wormhole. Here an earlier study by the author [Phys. Rev. D 98, 064041 (2018)] is extended in several significant ways. To ...The main goal of this paper is to determine the effect of an extra dimension on a traversable wormhole. Here an earlier study by the author [Phys. Rev. D 98, 064041 (2018)] is extended in several significant ways. To begin with, the extra spatial dimension is assumed to be time dependent, while the redshift and shape functions, as well as the extra dimension, are functions of both r and l, the respective radial and extra coordinates;the last of these is therefore a function of r, l, and t. The main objective is to determine the conditions that allow the throat of the wormhole to be threaded with ordinary matter (by respecting the null energy condition) and that the same conditions lead to a violation of the null energy condition in the fifth dimension, which is therefore responsible for sustaining the wormhole. The dependence of the extra dimension on l and t is subject to additional conditions that are subsequently analyzed in this paper. Finally, the extra dimension may be extremely small or even curled up.展开更多
Traditional spatial clustering methods have the disadvantage of ＂hardware division＂, and can not describe the physical characteristics of spatial entity effectively. In view of the above, this paper sets forth a gen...Traditional spatial clustering methods have the disadvantage of ＂hardware division＂, and can not describe the physical characteristics of spatial entity effectively. In view of the above, this paper sets forth a general multi-dimensional cloud model, which describes the characteristics of spatial objects more reasonably according to the idea of non-homogeneous and non-symmetry. Based on infrastructures＇ classification and demarcation in Zhanjiang, a detailed interpretation of clustering results is made from the spatial distribution of membership degree of clustering, the comparative study of Fuzzy C-means and a coupled analysis of residential land prices. General multi-dimensional cloud model reflects the integrated char- acteristics of spatial objects better, reveals the spatial distribution of potential information, and realizes spatial division more accurately in complex circumstances. However, due to the complexity of spatial interactions between geographical entities, the generation of cloud model is a specific and challenging task.展开更多
Three high dimensional spatial standardization algorithms are used for diffusion tensor image(DTI)registration,and seven kinds of methods are used to evaluate their performances.Firstly,the template used in this paper...Three high dimensional spatial standardization algorithms are used for diffusion tensor image(DTI)registration,and seven kinds of methods are used to evaluate their performances.Firstly,the template used in this paper was obtained by spatial transformation of 16 subjects by means of tensor-based standardization.Then,high dimensional standardization algorithms for diffusion tensor images,including fractional anisotropy(FA)based diffeomorphic registration algorithm,FA based elastic registration algorithm and tensor-based registration algorithm,were performed.Finally,7 kinds of evaluation methods,including normalized standard deviation,dyadic coherence,diffusion cross-correlation,overlap of eigenvalue-eigenvector pairs,Euclidean distance of diffusion tensor,and Euclidean distance of the deviatoric tensor and deviatoric of tensors,were used to qualitatively compare and summarize the above standardization algorithms.Experimental results revealed that the high-dimensional tensor-based standardization algorithms perform well and can maintain the consistency of anatomical structures.展开更多
The filter made up of two gratings performs as a two-dimensional non-spatial filtering. This paper reports that the volume Bragg gratings are fabricated by interfering two collimated coherent laser beams in photopolym...The filter made up of two gratings performs as a two-dimensional non-spatial filtering. This paper reports that the volume Bragg gratings are fabricated by interfering two collimated coherent laser beams in photopolymer. Diffraction efficiency of a single grating is up to 78% in Bragg＇s condition, then a two-dimensional non-spatial filter, which consists of two volume Bragg gratings and a half-wave plate, enables the laser beam filtered in two dimensions with the diffraction efficiency of 54%. The Bragg＇s condition and effect of polarisation on performances of the two-dimension filter are also discussed.展开更多
A theory of （4＋1）-dimensional gravity is developed on the basis of the teleparallel theory equivalent to general relativity. The fundamental gravitational field variables are the five-dimensional vector fields （pe...A theory of （4＋1）-dimensional gravity is developed on the basis of the teleparallel theory equivalent to general relativity. The fundamental gravitational field variables are the five-dimensional vector fields （pentad）, defined globally on a manifold M, and gravity is attributed to the torsion. The Lagrangian density is quadratic in the torsion tensor. We then give the exact five-dimensional solution. The solution is a generalization of the familiar Schwarzschild and Kerr solutions of the four-dimensional teleparallel equivalent of general relativity. We also use the definition of the gravitational energy to calculate the energy and the spatial momentum.展开更多
This paper presents a gas-kinetic theory based multidimensional high-order method for the compressible Naiver–Stokes solutions. In our previous study, a spatially and temporally dependent third-order flux scheme with...This paper presents a gas-kinetic theory based multidimensional high-order method for the compressible Naiver–Stokes solutions. In our previous study, a spatially and temporally dependent third-order flux scheme with the use of a third-order gas distribution function is employed.However, the third-order flux scheme is quite complicated and less robust than the second-order scheme. In order to reduce its complexity and improve its robustness, the secondorder flux scheme is adopted instead in this paper, while the temporal order of method is maintained by using a two stage temporal discretization. In addition, its CPU cost is relatively lower than the previous scheme. Several test cases in two and three dimensions, containing high Mach number compressible flows and low speed high Reynolds number laminar flows, are presented to demonstrate the method capacity.展开更多
Various pattern evolutions are presented in one- and two-dimensional spatially coupled phase-conjugate systems （SCPCSs）. As the system parameters change, different patterns are obtained from the period-doubling of k...Various pattern evolutions are presented in one- and two-dimensional spatially coupled phase-conjugate systems （SCPCSs）. As the system parameters change, different patterns are obtained from the period-doubling of kink-antikinks in space to the spatiotemporal chaos in a one-dimensional SCPCS. The homogeneous symmetric states induce symmetry breaking from the four corners and the boundaries, finally leading to spatiotemporal chaos with the increase of the iteration time in a two-dimensional SCPCS. Numerical simulations are very helpful for understanding the complex optical phenomena.展开更多
Recently, a four-dimensional lattice spring model(4D-LSM) was developed to overcome the Poisson’s ratio limitation of the classical LSM by introducing the fourth-dimensional spatial interaction. In this work, some as...Recently, a four-dimensional lattice spring model(4D-LSM) was developed to overcome the Poisson’s ratio limitation of the classical LSM by introducing the fourth-dimensional spatial interaction. In this work, some aspects of the 4D-LSM on solving problems in geomechanics are investigated, such as the ability to reproduce elastic properties of geomaterials, the capability of solving heterogeneous problems,the accuracy on modelling stress wave propagation, the ability to solve dynamic fracturing and the parallel computational efficiency. Our results indicate that the 4D-LSM is promising to deal with problems in geomechanics.展开更多
土壤是具有高度异质性的复合体。早期的数字土壤制图研究主要关注水平方向的土壤空间变异和制图,对垂直方向空间变异和土壤三维制图考虑较少。近年来,三维地理信息技术和对地观测与探测技术的快速发展,极大地促进了土壤三维空间数据获...土壤是具有高度异质性的复合体。早期的数字土壤制图研究主要关注水平方向的土壤空间变异和制图,对垂直方向空间变异和土壤三维制图考虑较少。近年来,三维地理信息技术和对地观测与探测技术的快速发展,极大地促进了土壤三维空间数据获取、三维空间推测、三维数据模型、三维模型构建和可视化方法等方面的研究。本文对三维空间土壤推测与土壤模型构建的已有方法进行梳理和评述,以期为三维数字土壤制图的应用和发展提供建议。以三维土壤制图、三维GIS、三维数据模型、三维地质建模、三维可视化、土壤空间变异、空间推测、克里格插值、土壤-景观分析、深度函数、机器学习、地统计学、随机模拟等为关键词检索Web of Science数据库,基于相关度、引用率和文献来源等因素进一步筛选出重点文献进行分析。归纳整理了土壤空间变异性、三维空间土壤推测、三维空间数据模型和三维模型构建等关键技术的现有研究体系,对各种三维推测和建模方法的优缺点和适用场景作出评价。针对目前研究中存在的垂直方向土壤数据稀少、土壤三维推测精度低、三维模型质量待提高等问题,提出一些可行的研究思路。展开更多
In this paper, the concept of the equidistant conjugate points of a triangle to the n-dimensional Euclidean space is extended. The concept of equidistant conjugate point in high dimensional simplex is defined, and the...In this paper, the concept of the equidistant conjugate points of a triangle to the n-dimensional Euclidean space is extended. The concept of equidistant conjugate point in high dimensional simplex is defined, and the property of the equidistant conjugate points of a triangle is generalized to high dimensional simplex.展开更多
To correct a lower limb deformity, orthopedic surgeons must have an exact understanding of the deformity. In general, preoperative planning is carried out using anterior-posterior (AP) and lateral radiographs. However...To correct a lower limb deformity, orthopedic surgeons must have an exact understanding of the deformity. In general, preoperative planning is carried out using anterior-posterior (AP) and lateral radiographs. However, for severe cases with a combination of angular and rotational deformities of the lower limb, obtaining true AP and lateral radiographs is difficult and accurate calculation of the rotational deformity from radiographs is impossible. In this report, we propose to focus on preoperative assessment using three-dimensional (3D) reconstruction images of computed tomography (CT) scans for severe lower limb deformity in a patient with bilateral fibular hemimelia type II according to the Achterman- Kalamchi classification. She underwent bifocal deformity corrections of the bilateral tibiae using Taylor spatial frames in combination with the Ilizarov external fixator. Complete bony union was achieved, without angular deformity or limb length discrepancy.展开更多
基金Supported by Natural Science Foundation of Shaanxi Province under Grant No. 2007A02the Science Foundation of Baoji University of Science and Arts of China under Grant No. ZK0914
文摘Based on the form of the n-dimensional generic power-law potential, the state equation and the heat capacity, the analytical expressions of the Joule-Thomson coefficient （3TC） for an ideal Bose gas are derived in n-dimensional potential. The effect of the spatial dimension and the external potential on the JTC are discussed, respectively. These results show that： （i） For the free ideal Bose gas, when n/s ≤ 2 （n is the spatial dimension, s is the momentum index in the relation between the energy and the momentum）, and T → Tc （Tc is the critical temperature）, the JTC can obviously improve by means of changing the throttle valve＇s shape and decreasing the spatial dimension of gases. （ii） For the inhomogeneous external potential, the discriminant △= [1 - y∏^ni=1（kT/εi）^1/tiГ（1/ti＋1）] （k is the Boltzmann Constant, T is the thermodynamic temperature, ε is the external field＇s energy）, is obtained. The potential makes the JTC increase when △ 〉 0, on the contrary, it makes the JTC decrease when A 〈△. （iii） In the homogenous strong external potential, the JTC gets the maximum on the condition of kTεi〈〈1.
文摘The main goal of this paper is to determine the effect of an extra dimension on a traversable wormhole. Here an earlier study by the author [Phys. Rev. D 98, 064041 (2018)] is extended in several significant ways. To begin with, the extra spatial dimension is assumed to be time dependent, while the redshift and shape functions, as well as the extra dimension, are functions of both r and l, the respective radial and extra coordinates;the last of these is therefore a function of r, l, and t. The main objective is to determine the conditions that allow the throat of the wormhole to be threaded with ordinary matter (by respecting the null energy condition) and that the same conditions lead to a violation of the null energy condition in the fifth dimension, which is therefore responsible for sustaining the wormhole. The dependence of the extra dimension on l and t is subject to additional conditions that are subsequently analyzed in this paper. Finally, the extra dimension may be extremely small or even curled up.
基金National Natural Science Foundation of China, N0.40971102 Knowledge Innovation Project of the Chinese Academy of Sciences, No. KZCX2-YW-322 Special Grant for Postgraduates＇ Scientific Innovation and So- cial Practice in 2008
文摘Traditional spatial clustering methods have the disadvantage of ＂hardware division＂, and can not describe the physical characteristics of spatial entity effectively. In view of the above, this paper sets forth a general multi-dimensional cloud model, which describes the characteristics of spatial objects more reasonably according to the idea of non-homogeneous and non-symmetry. Based on infrastructures＇ classification and demarcation in Zhanjiang, a detailed interpretation of clustering results is made from the spatial distribution of membership degree of clustering, the comparative study of Fuzzy C-means and a coupled analysis of residential land prices. General multi-dimensional cloud model reflects the integrated char- acteristics of spatial objects better, reveals the spatial distribution of potential information, and realizes spatial division more accurately in complex circumstances. However, due to the complexity of spatial interactions between geographical entities, the generation of cloud model is a specific and challenging task.
基金Supported by the National Key Research and Development Program of China(2016YFC0100300)the National Natural Science Foundation of China(61402371,61771369)+1 种基金the Natural Science Basic Research Plan in Shaanxi Province of China(2017JM6008)the Fundamental Research Funds for the Central Universities of China(3102017zy032,3102018zy020)
文摘Three high dimensional spatial standardization algorithms are used for diffusion tensor image(DTI)registration,and seven kinds of methods are used to evaluate their performances.Firstly,the template used in this paper was obtained by spatial transformation of 16 subjects by means of tensor-based standardization.Then,high dimensional standardization algorithms for diffusion tensor images,including fractional anisotropy(FA)based diffeomorphic registration algorithm,FA based elastic registration algorithm and tensor-based registration algorithm,were performed.Finally,7 kinds of evaluation methods,including normalized standard deviation,dyadic coherence,diffusion cross-correlation,overlap of eigenvalue-eigenvector pairs,Euclidean distance of diffusion tensor,and Euclidean distance of the deviatoric tensor and deviatoric of tensors,were used to qualitatively compare and summarize the above standardization algorithms.Experimental results revealed that the high-dimensional tensor-based standardization algorithms perform well and can maintain the consistency of anatomical structures.
基金supported by the Joint Fund of the National Natural Science Foundation of China and the China Academy of Engineering Physics (NSAF) (Grant No. 10676038)
文摘The filter made up of two gratings performs as a two-dimensional non-spatial filtering. This paper reports that the volume Bragg gratings are fabricated by interfering two collimated coherent laser beams in photopolymer. Diffraction efficiency of a single grating is up to 78% in Bragg＇s condition, then a two-dimensional non-spatial filter, which consists of two volume Bragg gratings and a half-wave plate, enables the laser beam filtered in two dimensions with the diffraction efficiency of 54%. The Bragg＇s condition and effect of polarisation on performances of the two-dimension filter are also discussed.
基金National Natural Science Foundation of China （No. 41201407） Special funding of scientific research for public welfare industry of Ministry o Land and Resources （No. 201111009）
文摘A theory of （4＋1）-dimensional gravity is developed on the basis of the teleparallel theory equivalent to general relativity. The fundamental gravitational field variables are the five-dimensional vector fields （pentad）, defined globally on a manifold M, and gravity is attributed to the torsion. The Lagrangian density is quadratic in the torsion tensor. We then give the exact five-dimensional solution. The solution is a generalization of the familiar Schwarzschild and Kerr solutions of the four-dimensional teleparallel equivalent of general relativity. We also use the definition of the gravitational energy to calculate the energy and the spatial momentum.
文摘This paper presents a gas-kinetic theory based multidimensional high-order method for the compressible Naiver–Stokes solutions. In our previous study, a spatially and temporally dependent third-order flux scheme with the use of a third-order gas distribution function is employed.However, the third-order flux scheme is quite complicated and less robust than the second-order scheme. In order to reduce its complexity and improve its robustness, the secondorder flux scheme is adopted instead in this paper, while the temporal order of method is maintained by using a two stage temporal discretization. In addition, its CPU cost is relatively lower than the previous scheme. Several test cases in two and three dimensions, containing high Mach number compressible flows and low speed high Reynolds number laminar flows, are presented to demonstrate the method capacity.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10847110)
文摘Various pattern evolutions are presented in one- and two-dimensional spatially coupled phase-conjugate systems （SCPCSs）. As the system parameters change, different patterns are obtained from the period-doubling of kink-antikinks in space to the spatiotemporal chaos in a one-dimensional SCPCS. The homogeneous symmetric states induce symmetry breaking from the four corners and the boundaries, finally leading to spatiotemporal chaos with the increase of the iteration time in a two-dimensional SCPCS. Numerical simulations are very helpful for understanding the complex optical phenomena.
基金financially supported by the National Natural Science Foundation of China (Grant No. 1177020290)
文摘Recently, a four-dimensional lattice spring model(4D-LSM) was developed to overcome the Poisson’s ratio limitation of the classical LSM by introducing the fourth-dimensional spatial interaction. In this work, some aspects of the 4D-LSM on solving problems in geomechanics are investigated, such as the ability to reproduce elastic properties of geomaterials, the capability of solving heterogeneous problems,the accuracy on modelling stress wave propagation, the ability to solve dynamic fracturing and the parallel computational efficiency. Our results indicate that the 4D-LSM is promising to deal with problems in geomechanics.
文摘土壤是具有高度异质性的复合体。早期的数字土壤制图研究主要关注水平方向的土壤空间变异和制图,对垂直方向空间变异和土壤三维制图考虑较少。近年来,三维地理信息技术和对地观测与探测技术的快速发展,极大地促进了土壤三维空间数据获取、三维空间推测、三维数据模型、三维模型构建和可视化方法等方面的研究。本文对三维空间土壤推测与土壤模型构建的已有方法进行梳理和评述,以期为三维数字土壤制图的应用和发展提供建议。以三维土壤制图、三维GIS、三维数据模型、三维地质建模、三维可视化、土壤空间变异、空间推测、克里格插值、土壤-景观分析、深度函数、机器学习、地统计学、随机模拟等为关键词检索Web of Science数据库,基于相关度、引用率和文献来源等因素进一步筛选出重点文献进行分析。归纳整理了土壤空间变异性、三维空间土壤推测、三维空间数据模型和三维模型构建等关键技术的现有研究体系,对各种三维推测和建模方法的优缺点和适用场景作出评价。针对目前研究中存在的垂直方向土壤数据稀少、土壤三维推测精度低、三维模型质量待提高等问题,提出一些可行的研究思路。
基金Supported by the Technological Project of Jiangxi Province Education Department(GJJ 08389)
文摘In this paper, the concept of the equidistant conjugate points of a triangle to the n-dimensional Euclidean space is extended. The concept of equidistant conjugate point in high dimensional simplex is defined, and the property of the equidistant conjugate points of a triangle is generalized to high dimensional simplex.
文摘To correct a lower limb deformity, orthopedic surgeons must have an exact understanding of the deformity. In general, preoperative planning is carried out using anterior-posterior (AP) and lateral radiographs. However, for severe cases with a combination of angular and rotational deformities of the lower limb, obtaining true AP and lateral radiographs is difficult and accurate calculation of the rotational deformity from radiographs is impossible. In this report, we propose to focus on preoperative assessment using three-dimensional (3D) reconstruction images of computed tomography (CT) scans for severe lower limb deformity in a patient with bilateral fibular hemimelia type II according to the Achterman- Kalamchi classification. She underwent bifocal deformity corrections of the bilateral tibiae using Taylor spatial frames in combination with the Ilizarov external fixator. Complete bony union was achieved, without angular deformity or limb length discrepancy.
