The problem of geometric non-linearity simulation for spacial cable system was solved by introducing the truss element based on corotational coordinate (CR) system, cable structure materials and node coordinates and a...The problem of geometric non-linearity simulation for spacial cable system was solved by introducing the truss element based on corotational coordinate (CR) system, cable structure materials and node coordinates and automatic refreshing algorithms for element internal force. And the shape-finding problem for maneuvering profile was solved with the Newton-Raphson based on energy convergence criteria with search function. This has avoided the regular truss element assumption extensively used in traditional methods and catenary elements which have difficulties in practical application because of the complicated formulas. The use of CR formulation has taken into account the stiffness outside the cable plane via a geometric stiffness matrix, realizing the 3D space analysis of a cable bridge and improving the efficiency and precision for the space geometric non-linearity analysis and cable structure, and enabling more precised simulation of geometric form finding and internal force of the large span suspension bridge main cable under construction.展开更多
This paper outlines the necessity of the knowledge representation for the geometrical shapes （KRGS）. We advocate that KRGS for being powerful must contain at least three major components, namely （1） fu...This paper outlines the necessity of the knowledge representation for the geometrical shapes （KRGS）. We advocate that KRGS for being powerful must contain at least three major components, namely （1） fuzzy logic scheme; （2） the machine learning technique; and （3） an integrated algebraic and logical reasoning. After arguing the need for using fuzzy expressions in spatial reasoning, then inducing the spatial graph generalized and maximal common part of the expressions is discussed. Finally, the integration of approximate references into spatial reasoning using absolute measurements is outlined. The integration here means that the satisfiability of a fuzzy spatial expression is conducted by both logical and algebraic reasoning.展开更多
In this paper,we study the Cauchy problem of an integrable evolution system,i.e.,the n-dimensional generalization of third-order symmetry of the well-known Landau-Lifshitz equation.By rewriting this equation in a geom...In this paper,we study the Cauchy problem of an integrable evolution system,i.e.,the n-dimensional generalization of third-order symmetry of the well-known Landau-Lifshitz equation.By rewriting this equation in a geometric form and applying the geometric energy method with a forth-order perturbation,we show the global well-posedness of the Cauchy problem in suitable Sobolev spaces.展开更多
Let Md be the moduli space of stable sheaves on P2with Hilbert polynomial dm+1.In this paper,we determine the effective and the nef cone of the space Md by natural geometric divisors.Main idea is to use the wall-cross...Let Md be the moduli space of stable sheaves on P2with Hilbert polynomial dm+1.In this paper,we determine the effective and the nef cone of the space Md by natural geometric divisors.Main idea is to use the wall-crossing on the space of Bridgeland stability conditions and to compute the intersection numbers of divisors with curves by using the Grothendieck-Riemann-Roch theorem.We also present the stable base locus decomposition of the space M6.As a byproduct,we obtain the Betti numbers of the moduli spaces,which confirm the prediction in physics.展开更多
Micropipette aspiration(MA) is widely applied in cell mechanics, however, at small deformations a common model corresponding to the MA is the half-space model wherein the finite cell size and cell compressibility are ...Micropipette aspiration(MA) is widely applied in cell mechanics, however, at small deformations a common model corresponding to the MA is the half-space model wherein the finite cell size and cell compressibility are neglected. This study extends the half-space model by accounting for the influence of cell geometry and compressibility(sphere model). Using a finite element analysis of cell aspiration into a micropipette, an elastic approximation formula of the aspirated length was derived for the sphere model. The approximation formula includes the geometry parameter of the sphere model(ζ = R/a, R is the radius of the cell, and a is the inner radius of the micropipette) and the Poisson's ratio v of the cell. The results indicate that the parameter and Poisson's ratio v markedly affect the aspirated length, particularly for small and v. When ζ→∞ and v→0.5,the approximation formula tends to the analytical solution for the half-space model. In the incompressible case(v = 0.5), within the general experimental range(ζ varying from 2 to 4), the difference between the analytical solution and the approximate one is significant, and is up to 29% of the approximation solution when ζ= 2. Additionally, parametere was introduced to evaluate the error of elastic moduli between the half-space model and sphere model. Based on the approximation formula, the ζ thresholds, beyond which e becomes larger than 10% and 20%, were derived.展开更多
基金National Science and Technology Support Program of China(No.2009BAG15B01)Key Programs for Science and Technology Development of Chinese Transportation Industry(No.2008-353-332-190)
文摘The problem of geometric non-linearity simulation for spacial cable system was solved by introducing the truss element based on corotational coordinate (CR) system, cable structure materials and node coordinates and automatic refreshing algorithms for element internal force. And the shape-finding problem for maneuvering profile was solved with the Newton-Raphson based on energy convergence criteria with search function. This has avoided the regular truss element assumption extensively used in traditional methods and catenary elements which have difficulties in practical application because of the complicated formulas. The use of CR formulation has taken into account the stiffness outside the cable plane via a geometric stiffness matrix, realizing the 3D space analysis of a cable bridge and improving the efficiency and precision for the space geometric non-linearity analysis and cable structure, and enabling more precised simulation of geometric form finding and internal force of the large span suspension bridge main cable under construction.
文摘This paper outlines the necessity of the knowledge representation for the geometrical shapes （KRGS）. We advocate that KRGS for being powerful must contain at least three major components, namely （1） fuzzy logic scheme; （2） the machine learning technique; and （3） an integrated algebraic and logical reasoning. After arguing the need for using fuzzy expressions in spatial reasoning, then inducing the spatial graph generalized and maximal common part of the expressions is discussed. Finally, the integration of approximate references into spatial reasoning using absolute measurements is outlined. The integration here means that the satisfiability of a fuzzy spatial expression is conducted by both logical and algebraic reasoning.
基金supported by National Basic Research Program of China(Grant No.2006CB805902)
文摘In this paper,we study the Cauchy problem of an integrable evolution system,i.e.,the n-dimensional generalization of third-order symmetry of the well-known Landau-Lifshitz equation.By rewriting this equation in a geometric form and applying the geometric energy method with a forth-order perturbation,we show the global well-posedness of the Cauchy problem in suitable Sobolev spaces.
基金supported by TJ Park Science Fellowship of POSCO TJ Park Foundation and National Research Foundation of Korea(Grant No.2013R1A1A2006037)
文摘Let Md be the moduli space of stable sheaves on P2with Hilbert polynomial dm+1.In this paper,we determine the effective and the nef cone of the space Md by natural geometric divisors.Main idea is to use the wall-crossing on the space of Bridgeland stability conditions and to compute the intersection numbers of divisors with curves by using the Grothendieck-Riemann-Roch theorem.We also present the stable base locus decomposition of the space M6.As a byproduct,we obtain the Betti numbers of the moduli spaces,which confirm the prediction in physics.
基金supported by the National Natural Science Foundation of China(Grant No.11032008)the Youth Fund of Taiyuan University of Technology
文摘Micropipette aspiration(MA) is widely applied in cell mechanics, however, at small deformations a common model corresponding to the MA is the half-space model wherein the finite cell size and cell compressibility are neglected. This study extends the half-space model by accounting for the influence of cell geometry and compressibility(sphere model). Using a finite element analysis of cell aspiration into a micropipette, an elastic approximation formula of the aspirated length was derived for the sphere model. The approximation formula includes the geometry parameter of the sphere model(ζ = R/a, R is the radius of the cell, and a is the inner radius of the micropipette) and the Poisson's ratio v of the cell. The results indicate that the parameter and Poisson's ratio v markedly affect the aspirated length, particularly for small and v. When ζ→∞ and v→0.5,the approximation formula tends to the analytical solution for the half-space model. In the incompressible case(v = 0.5), within the general experimental range(ζ varying from 2 to 4), the difference between the analytical solution and the approximate one is significant, and is up to 29% of the approximation solution when ζ= 2. Additionally, parametere was introduced to evaluate the error of elastic moduli between the half-space model and sphere model. Based on the approximation formula, the ζ thresholds, beyond which e becomes larger than 10% and 20%, were derived.
