The distribution of tailings lenticles reflects the sediment state of tailing dam, and has a great influence on the stability of the dam. In order to disclose the distribution law of tailings lenticles in theory, 12 g...The distribution of tailings lenticles reflects the sediment state of tailing dam, and has a great influence on the stability of the dam. In order to disclose the distribution law of tailings lenticles in theory, 12 geological cross-sections, including 7 cross-sections of tailings dam constructed by the upstream method and 5 cross-sections by the middle line method, were analyzed with box dimension method. The results show that the distribution of tailings lenticles has better fractal character with box dimension from 1.290 7 to 1.513 6. The box dimension of the tailings dam constructed by upstream method is nearly 1.50 and that by middle line method is 1.30. Thereby the values of lenticles dimension have obvious relation to the method of constructing dam, and reflect the sediment state of tailings dam with the rule that smaller value means better state.展开更多
In order to research the characteristic and mechanism of fracture of rock-like materials,the morphology of rock fracture surface under the breakages of uniaxial compression and triaxial compression was observed and me...In order to research the characteristic and mechanism of fracture of rock-like materials,the morphology of rock fracture surface under the breakages of uniaxial compression and triaxial compression was observed and measured by means of a new-type 3D laser scanning system.Based on geographic information system(GIS)technique,the fracture surfaces were 3D visualized and reestablished.According to GIS 3D statistics,the geometrical characteristics of fracture surfaces under different breakage conditions were analyzed,and then based on fractal theory,the change laws of fractal dimension of fracture surfaces were discussed under the conditions of different cell pressures and initial water contents of rock.Furthermore,the relationships between characteristics of fracture surface and mechanical properties of rock were discussed.The results indicate that cell pressure,initial water content,and mechanical parameters of rock are the important factors to influence on the geometrical characteristics of fracture surface.The research provides a new experimental method for quantitative study on the fracture characteristics of various materials under different breakage conditions.展开更多
Traditional fractal pattern design has some disadvantages such as inability to effectively reflect the characteristics of real scenery and texture. We propose a novel pattern design technique combining fractal geometr...Traditional fractal pattern design has some disadvantages such as inability to effectively reflect the characteristics of real scenery and texture. We propose a novel pattern design technique combining fractal geometry and image texture synthesis to solve these problems. We have improved Wei and Levoy (2000)’s texture synthesis algorithm by first using two-dimensional autocorrelation function to analyze the structure and distribution of textures, and then determining the size of L neighborhood. Several special fractal sets were adopted and HSL (Hue, Saturation, and Light) color space was chosen. The fractal structure was used to manipulate the texture synthesis in HSL color space where the pattern’s color can be adjusted conveniently. Experiments showed that patterns with different styles and different color characteristics can be more efficiently generated using the new technique.展开更多
Nonwovens' pore structures are very important to their mechanical and physical properties. And the pore structures are influenced by the fiber properties and fibers arrangement in web. In this paper, the fractal geom...Nonwovens' pore structures are very important to their mechanical and physical properties. And the pore structures are influenced by the fiber properties and fibers arrangement in web. In this paper, the fractal geometry, in combination with computer image anaysis, is used to express the irregularity of pore size distribution in nonwovens, and the effect of fiber properties on fractal dimension of pore size distribution is discussed by using simulated images which are composed of nonlinear staple fibers. The results show that the fiber properties, such as crimp, diameter, angular distribution, and especially the number of fibers prominently influence the pore structure.展开更多
Within today's product development process, various FE-simulations (finite element) for the functional validation of the desired characteristics are made to avoid expensive testing with real components. Those simul...Within today's product development process, various FE-simulations (finite element) for the functional validation of the desired characteristics are made to avoid expensive testing with real components. Those simulations are performed with great effort for discretization, use of simulations conditions, like taking different non-linearities (i.e., material behavior, etc.) into account, to create meaningful results. Despite knowing the effects of deformations occurring during the production processes, always the non-deformed design model of a CAD-system (computer aided design) is used for the FE-simulations. It seems rather doubtful that further refinement of simulation methods makes sense, if the real manufactured geometry of the component is not considered for in the simulation. For an efficient exploit of the potential of simulation methods, an approach has been developed which offers a geometry model for simulation based on the existing CAD-model but with integrated production deviations as soon as a first prototype is at hand by adapting the FE-mesh to the real, 3D surface detected geometry.展开更多
We propose a new Geographic Information System (GIS) three-dimensional (3D) data model based on conformal geometric algebra (CGA). In this approach, geographic objects of different dimensions are mapped to the corresp...We propose a new Geographic Information System (GIS) three-dimensional (3D) data model based on conformal geometric algebra (CGA). In this approach, geographic objects of different dimensions are mapped to the corresponding basic elements (blades) in Clifford algebra, and the expressions of multi-dimensional objects are unified without losing their geometric meaning. Geometric and topologic computations are also processed in a clear and coordinates-free way. Under the CGA framework, basic geometrics are constructed and expressed by the inner and outer operators. This expression combined geometrics of different dimensions and metric relations. We present the structure of the framework, data structure design, and the data storage, editing and updating mechanisms of the proposed 3D GIS data model. 3D GIS geometric and topological analyses are performed by CGA metric, geometric and topological operators using an object-oriented approach. Demonstrations with 3D residence district data suggest that our 3D data model expresses effectively geometric objects in different dimensions, which supports computation of both geometric and topological relations. The clear and effective expression and computation structure has the potential to support complex 3D GIS analysis, and spatio-temporal analysis.展开更多
The authors show that the self-similar set for a finite family of contractive similitudes (similarities, i.e., |fi(x) - fi(y)| = αi|x - y|, x,y ∈ RN, where 0 < αi < 1) is uniformly perfect except the case tha...The authors show that the self-similar set for a finite family of contractive similitudes (similarities, i.e., |fi(x) - fi(y)| = αi|x - y|, x,y ∈ RN, where 0 < αi < 1) is uniformly perfect except the case that it is a singleton. As a corollary, it is proved that this self-similar set has positive Hausdorff dimension provided that it is not a singleton. And a lower bound of the upper box dimension of the uniformly perfect sets is given. Meanwhile the uniformly perfect set with Hausdorff measure zero in its Hausdorff dimension is given.展开更多
Accurately characterizing the threedimensional geometric contacts between the crust of the Chinese mainland and adjacent regions is important for understanding the dynamics of this part of Asia from the viewpoint of g...Accurately characterizing the threedimensional geometric contacts between the crust of the Chinese mainland and adjacent regions is important for understanding the dynamics of this part of Asia from the viewpoint of global plate systems. In this pa per, a method is introduced to investigate the geometric contacts between the Eurasian and Indian plates at the Burma arc sub duction zone using earthquake source parameters based on the Slabl.0 model of Hayes et al. (2009, 2010). The distribution of earthquake focus depths positioned in 166 sections along the Burma Arc subduction zone boundary has been investigated. Linear plane fitting and curved surface fitting has been performed on each section. Threedimensional geometric contacts and the extent of subduction are defined quantitatively. Finally, the focal depth distribution is outlined for six typical sections along the Burma arc subduction zone, combining focal mechanisms with background knowledge of geologic structure. Possible dy namic interaction patterns are presented and discussed. This paper provides an elementary method for studying the geometric contact of the Chinese mainland crust with adjacent plates and serves as a global reference for dynamic interactions between plates and related geodynamic investigations.展开更多
During the last decade, a great deal of activity has been devoted to the calculation of the HilbertPoincar′e series of unitary highest weight representations and related modules in algebraic geometry. However,uniform...During the last decade, a great deal of activity has been devoted to the calculation of the HilbertPoincar′e series of unitary highest weight representations and related modules in algebraic geometry. However,uniform formulas remain elusive—even for more basic invariants such as the Gelfand-Kirillov dimension or the Bernstein degree, and are usually limited to families of representations in a dual pair setting. We use earlier work by Joseph to provide an elementary and intrinsic proof of a uniform formula for the Gelfand-Kirillov dimension of an arbitrary unitary highest weight module in terms of its highest weight. The formula generalizes a result of Enright and Willenbring(in the dual pair setting) and is inspired by Wang's formula for the dimension of a minimal nilpotent orbit.展开更多
Wintgen ideal submanifolds in space forms are those ones attaining equality at every point in the socalled DDVV inequality which relates the scalar curvature,the mean curvature and the normal scalar curvature.This pro...Wintgen ideal submanifolds in space forms are those ones attaining equality at every point in the socalled DDVV inequality which relates the scalar curvature,the mean curvature and the normal scalar curvature.This property is conformal invariant;hence we study them in the framework of Mbius geometry,and restrict to three-dimensional Wintgen ideal submanifolds in S5.In particular,we give Mbius characterizations for minimal ones among them,which are also known as(3-dimensional)austere submanifolds(in 5-dimensional space forms).展开更多
In this paper, we consider the exterior problem of the critical semilinear wave equation in three space dimensions with variable coefficients and prove the global existence of smooth solutions. As in the constant coef...In this paper, we consider the exterior problem of the critical semilinear wave equation in three space dimensions with variable coefficients and prove the global existence of smooth solutions. As in the constant coefficients case, we show that the energy cannot concentrate at any point (t, x) ∈ (0, ∞) ×Ω. For that purpose, following Ibrahim and Majdoub's paper in 2003, we use a geometric multiplier similar to the well-known Morawetz multiplier used in the constant coefficients case. We then use the comparison theorem from Riemannian geometry to estimate the error terms. Finally, using the Strichartz inequality as in Smith and Sogge's paper in 1995, we confirm the global existence.展开更多
This paper presents a method for extracting geometrical features of the joint probability density function(PDF)of two-dimensional systems based on its contour lines,with particular interests given to the number and po...This paper presents a method for extracting geometrical features of the joint probability density function(PDF)of two-dimensional systems based on its contour lines,with particular interests given to the number and position of peaks and craters.In order to detect those two types of structures,a series of horizontal planes are applied to truncate the joint PDF with contour lines generated.Starting with the analysis of contour lines in a single plane,shape characteristics of the peak and the crater can be reflected on the contour lines in the aspects of gradient direction and inclusion relationship.Aided by the properties of PDF,the information about gradient direction and inclusion relationship of contour lines can be obtained simultaneously if the contour tree is built.According to the contour tree,the contour lines can be classified as two groups.Then the corresponding relation between contour lines in different planes is discussed.Based on the corresponding relation,clustering analysis about contour lines belonging to the same group but having different heights is performed.Two sets of contour lines are finally obtained as the simplest expression of geometrical characteristics of a joint PDF.They can be used to obtain the number and position of each peak and crater.Three oscillators of different types are chosen to test this method,which shows that this method can pave the way for numerical calculation about the stochastic P-bifurcation of multi-dimensional systems.展开更多
A technique of coordinate transformation is devised to overcome the computational difficulty associated with the direct transformation between eigenfunctions of three components of the geometric momentum on two-dimens...A technique of coordinate transformation is devised to overcome the computational difficulty associated with the direct transformation between eigenfunctions of three components of the geometric momentum on two-dimensional spherical surface, and the computations are firstly carried out in new coordinates and secondly the results are transformed back into the original coordinates. The eigenfunctions of different components of geometric momentum is explicitly demonstrated to transform under the spatial rotations in the precise way we anticipate.展开更多
Korchmaros and Nagy [Hermitian codes from higher degree places. J Pure Appl Algebra, doi: 10. 1016/j.jpaa.2013.04.002, 2013] computed the Weierstrass gap sequence G(P) of the Hermitian function field Fq2 (H) at a...Korchmaros and Nagy [Hermitian codes from higher degree places. J Pure Appl Algebra, doi: 10. 1016/j.jpaa.2013.04.002, 2013] computed the Weierstrass gap sequence G(P) of the Hermitian function field Fq2 (H) at any place P of degree 3, and obtained an explicit formula of the Matthews-Michel lower bound on the minimum distance in the associated differential Hermitian code CΩ(D, mP) where the divisor D is, as usual, the sum of all but one 1-degree Fq2-rational places of Fq2 (H) and m is a positive integer. For plenty of values of m depending on q, this provided improvements on the designed minimum distance of CΩ(D, mP). Further improvements from G(P) were obtained by Korchmaros and Nagy relying on algebraic geometry. Here slightly weaker improvements are obtained from G(P) with the usual function-field method depending on linear series, Riemann-Roch theorem and Weierstrass semigroups. We also survey the known results on this subject.展开更多
文摘The distribution of tailings lenticles reflects the sediment state of tailing dam, and has a great influence on the stability of the dam. In order to disclose the distribution law of tailings lenticles in theory, 12 geological cross-sections, including 7 cross-sections of tailings dam constructed by the upstream method and 5 cross-sections by the middle line method, were analyzed with box dimension method. The results show that the distribution of tailings lenticles has better fractal character with box dimension from 1.290 7 to 1.513 6. The box dimension of the tailings dam constructed by upstream method is nearly 1.50 and that by middle line method is 1.30. Thereby the values of lenticles dimension have obvious relation to the method of constructing dam, and reflect the sediment state of tailings dam with the rule that smaller value means better state.
文摘In order to research the characteristic and mechanism of fracture of rock-like materials,the morphology of rock fracture surface under the breakages of uniaxial compression and triaxial compression was observed and measured by means of a new-type 3D laser scanning system.Based on geographic information system(GIS)technique,the fracture surfaces were 3D visualized and reestablished.According to GIS 3D statistics,the geometrical characteristics of fracture surfaces under different breakage conditions were analyzed,and then based on fractal theory,the change laws of fractal dimension of fracture surfaces were discussed under the conditions of different cell pressures and initial water contents of rock.Furthermore,the relationships between characteristics of fracture surface and mechanical properties of rock were discussed.The results indicate that cell pressure,initial water content,and mechanical parameters of rock are the important factors to influence on the geometrical characteristics of fracture surface.The research provides a new experimental method for quantitative study on the fracture characteristics of various materials under different breakage conditions.
基金Project supported by the Natural Science Foundation of Zhejiang Province (No. M603228), Zhejiang Science and Technology Plan Project, and Ningbo Science Foundation for Doctor, China
文摘Traditional fractal pattern design has some disadvantages such as inability to effectively reflect the characteristics of real scenery and texture. We propose a novel pattern design technique combining fractal geometry and image texture synthesis to solve these problems. We have improved Wei and Levoy (2000)’s texture synthesis algorithm by first using two-dimensional autocorrelation function to analyze the structure and distribution of textures, and then determining the size of L neighborhood. Several special fractal sets were adopted and HSL (Hue, Saturation, and Light) color space was chosen. The fractal structure was used to manipulate the texture synthesis in HSL color space where the pattern’s color can be adjusted conveniently. Experiments showed that patterns with different styles and different color characteristics can be more efficiently generated using the new technique.
文摘Nonwovens' pore structures are very important to their mechanical and physical properties. And the pore structures are influenced by the fiber properties and fibers arrangement in web. In this paper, the fractal geometry, in combination with computer image anaysis, is used to express the irregularity of pore size distribution in nonwovens, and the effect of fiber properties on fractal dimension of pore size distribution is discussed by using simulated images which are composed of nonlinear staple fibers. The results show that the fiber properties, such as crimp, diameter, angular distribution, and especially the number of fibers prominently influence the pore structure.
文摘Within today's product development process, various FE-simulations (finite element) for the functional validation of the desired characteristics are made to avoid expensive testing with real components. Those simulations are performed with great effort for discretization, use of simulations conditions, like taking different non-linearities (i.e., material behavior, etc.) into account, to create meaningful results. Despite knowing the effects of deformations occurring during the production processes, always the non-deformed design model of a CAD-system (computer aided design) is used for the FE-simulations. It seems rather doubtful that further refinement of simulation methods makes sense, if the real manufactured geometry of the component is not considered for in the simulation. For an efficient exploit of the potential of simulation methods, an approach has been developed which offers a geometry model for simulation based on the existing CAD-model but with integrated production deviations as soon as a first prototype is at hand by adapting the FE-mesh to the real, 3D surface detected geometry.
基金supported by National High Technology R & D Program of China (Grant No. 2009AA12Z205)Key Project of National Natural Science Foundation of China (Grant No. 40730527)National Natural Science Foundation of China (Grant No. 41001224)
文摘We propose a new Geographic Information System (GIS) three-dimensional (3D) data model based on conformal geometric algebra (CGA). In this approach, geographic objects of different dimensions are mapped to the corresponding basic elements (blades) in Clifford algebra, and the expressions of multi-dimensional objects are unified without losing their geometric meaning. Geometric and topologic computations are also processed in a clear and coordinates-free way. Under the CGA framework, basic geometrics are constructed and expressed by the inner and outer operators. This expression combined geometrics of different dimensions and metric relations. We present the structure of the framework, data structure design, and the data storage, editing and updating mechanisms of the proposed 3D GIS data model. 3D GIS geometric and topological analyses are performed by CGA metric, geometric and topological operators using an object-oriented approach. Demonstrations with 3D residence district data suggest that our 3D data model expresses effectively geometric objects in different dimensions, which supports computation of both geometric and topological relations. The clear and effective expression and computation structure has the potential to support complex 3D GIS analysis, and spatio-temporal analysis.
基金Project supported by the National Natural Science Foundation of China (No.10171090, No.10231040).
文摘The authors show that the self-similar set for a finite family of contractive similitudes (similarities, i.e., |fi(x) - fi(y)| = αi|x - y|, x,y ∈ RN, where 0 < αi < 1) is uniformly perfect except the case that it is a singleton. As a corollary, it is proved that this self-similar set has positive Hausdorff dimension provided that it is not a singleton. And a lower bound of the upper box dimension of the uniformly perfect sets is given. Meanwhile the uniformly perfect set with Hausdorff measure zero in its Hausdorff dimension is given.
基金supported by the National Science and Technology Support Plan Project (Grant No.2012BAK19B01-04)
文摘Accurately characterizing the threedimensional geometric contacts between the crust of the Chinese mainland and adjacent regions is important for understanding the dynamics of this part of Asia from the viewpoint of global plate systems. In this pa per, a method is introduced to investigate the geometric contacts between the Eurasian and Indian plates at the Burma arc sub duction zone using earthquake source parameters based on the Slabl.0 model of Hayes et al. (2009, 2010). The distribution of earthquake focus depths positioned in 166 sections along the Burma Arc subduction zone boundary has been investigated. Linear plane fitting and curved surface fitting has been performed on each section. Threedimensional geometric contacts and the extent of subduction are defined quantitatively. Finally, the focal depth distribution is outlined for six typical sections along the Burma arc subduction zone, combining focal mechanisms with background knowledge of geologic structure. Possible dy namic interaction patterns are presented and discussed. This paper provides an elementary method for studying the geometric contact of the Chinese mainland crust with adjacent plates and serves as a global reference for dynamic interactions between plates and related geodynamic investigations.
基金supported by National Natural Science Foundation of China(Grant No.11171324)the Hong Kong Research Grants Council under RGC Project(Grant No.60311)the Hong Kong University of Science and Technology under DAG S09/10.SC02.
文摘During the last decade, a great deal of activity has been devoted to the calculation of the HilbertPoincar′e series of unitary highest weight representations and related modules in algebraic geometry. However,uniform formulas remain elusive—even for more basic invariants such as the Gelfand-Kirillov dimension or the Bernstein degree, and are usually limited to families of representations in a dual pair setting. We use earlier work by Joseph to provide an elementary and intrinsic proof of a uniform formula for the Gelfand-Kirillov dimension of an arbitrary unitary highest weight module in terms of its highest weight. The formula generalizes a result of Enright and Willenbring(in the dual pair setting) and is inspired by Wang's formula for the dimension of a minimal nilpotent orbit.
基金supported by National Natural Science Foundation of China (Grant Nos. 10901006,11171004 and 11331002)
文摘Wintgen ideal submanifolds in space forms are those ones attaining equality at every point in the socalled DDVV inequality which relates the scalar curvature,the mean curvature and the normal scalar curvature.This property is conformal invariant;hence we study them in the framework of Mbius geometry,and restrict to three-dimensional Wintgen ideal submanifolds in S5.In particular,we give Mbius characterizations for minimal ones among them,which are also known as(3-dimensional)austere submanifolds(in 5-dimensional space forms).
基金supported by National Natural Science Foundation of China (Grant No. 10728101)National Basic Research Program of China+3 种基金Doctoral Program Foundation of the Ministry of Education of Chinathe "111" projectSGST 09DZ2272900supported by the Outstanding Doctoral Science Foundation Program of Fudan University
文摘In this paper, we consider the exterior problem of the critical semilinear wave equation in three space dimensions with variable coefficients and prove the global existence of smooth solutions. As in the constant coefficients case, we show that the energy cannot concentrate at any point (t, x) ∈ (0, ∞) ×Ω. For that purpose, following Ibrahim and Majdoub's paper in 2003, we use a geometric multiplier similar to the well-known Morawetz multiplier used in the constant coefficients case. We then use the comparison theorem from Riemannian geometry to estimate the error terms. Finally, using the Strichartz inequality as in Smith and Sogge's paper in 1995, we confirm the global existence.
基金supported by the National Program on Key Basic Research Project(Grant No.2014CB046805)National Natural Science Foundation of China(Grant No.11372211).
文摘This paper presents a method for extracting geometrical features of the joint probability density function(PDF)of two-dimensional systems based on its contour lines,with particular interests given to the number and position of peaks and craters.In order to detect those two types of structures,a series of horizontal planes are applied to truncate the joint PDF with contour lines generated.Starting with the analysis of contour lines in a single plane,shape characteristics of the peak and the crater can be reflected on the contour lines in the aspects of gradient direction and inclusion relationship.Aided by the properties of PDF,the information about gradient direction and inclusion relationship of contour lines can be obtained simultaneously if the contour tree is built.According to the contour tree,the contour lines can be classified as two groups.Then the corresponding relation between contour lines in different planes is discussed.Based on the corresponding relation,clustering analysis about contour lines belonging to the same group but having different heights is performed.Two sets of contour lines are finally obtained as the simplest expression of geometrical characteristics of a joint PDF.They can be used to obtain the number and position of each peak and crater.Three oscillators of different types are chosen to test this method,which shows that this method can pave the way for numerical calculation about the stochastic P-bifurcation of multi-dimensional systems.
基金Supported by National Natural Science Foundation of China under Grant No. 11175063
文摘A technique of coordinate transformation is devised to overcome the computational difficulty associated with the direct transformation between eigenfunctions of three components of the geometric momentum on two-dimensional spherical surface, and the computations are firstly carried out in new coordinates and secondly the results are transformed back into the original coordinates. The eigenfunctions of different components of geometric momentum is explicitly demonstrated to transform under the spatial rotations in the precise way we anticipate.
基金financially supported by the TAMOP-4.2.1/B-09/1/KONV-2010-0005 project
文摘Korchmaros and Nagy [Hermitian codes from higher degree places. J Pure Appl Algebra, doi: 10. 1016/j.jpaa.2013.04.002, 2013] computed the Weierstrass gap sequence G(P) of the Hermitian function field Fq2 (H) at any place P of degree 3, and obtained an explicit formula of the Matthews-Michel lower bound on the minimum distance in the associated differential Hermitian code CΩ(D, mP) where the divisor D is, as usual, the sum of all but one 1-degree Fq2-rational places of Fq2 (H) and m is a positive integer. For plenty of values of m depending on q, this provided improvements on the designed minimum distance of CΩ(D, mP). Further improvements from G(P) were obtained by Korchmaros and Nagy relying on algebraic geometry. Here slightly weaker improvements are obtained from G(P) with the usual function-field method depending on linear series, Riemann-Roch theorem and Weierstrass semigroups. We also survey the known results on this subject.