In an arcjet thruster,the cathode and constrictor degrade with time,and the electrical arc discharge may become unsymmetrical.In this work,a three-dimensional numerical model of a hydrogen plasma arcjet is developed a...In an arcjet thruster,the cathode and constrictor degrade with time,and the electrical arc discharge may become unsymmetrical.In this work,a three-dimensional numerical model of a hydrogen plasma arcjet is developed and validated to study the effect of unsymmetrical electric arc discharge on thruster performance.The unsymmetrical arc discharge is realized by introducing a radial shift of the cathode so that the cathode tip offset is 80μm(25%of the constrictor radius).Simulations are conducted for both axially centered cathode(coaxial)and off-centered cathode(non-coaxial)configurations with identical propellant flow rates and input current.Simulations show asymmetrical arc discharge in the non-coaxial cathode configuration,resulting in azimuthally asymmetric Joule heating,species concentrations,and velocity field.This asymmetry continues as the plasma expands in the divergent section of the nozzle.Temperature,species concentrations,and axial velocity exhibit asymmetric radial distribution at the nozzle exit.The computed Joule heating was found to reduce with cathode shift,and consequently,the thrust and specific impulse of the thruster was decreased by about 6.6%.In the case of the non-coaxial cathode,geometric asymmetry also induces a small side thrust.展开更多
The buckling behavior of single layer space structure is very sensitive. The joint rigidity, moreover, is one of the main factors of stability which may determine the entire failure behavior. Thus, the reasonable stif...The buckling behavior of single layer space structure is very sensitive. The joint rigidity, moreover, is one of the main factors of stability which may determine the entire failure behavior. Thus, the reasonable stiffness of joint system, which is neither total pin assumption nor perfect fix condition, is very important to apply to the real single layer space one. Therefore, the purpose of this work was to investigate the buckling behavior of single layer space structure, using the development of the upgraded stiffness matrix for the joint rigidity. To derive tangential stiffness matrix, a displacement function was assumed using translational and rotational displacement at the node. The geometrical nonlinear analysis was simulated not only with perfect model but also with imperfect one. As a result, the one and two free nodal numerical models were investigated using derived stiffness matrix. It was figured out that the buckling load increases in proportion to joint rigidity with rise-span ratio. The stability of numerical model is very sensitive with the initial imperfection, responding of bifurcation in the structure.展开更多
In this paper,We study the global attractor and its properties on in nite lattice dynamical system FitzHugh-Nagumo in a weighted space lσ^2×lσ^2.We prove the existence and uniqueness of the solution to the latt...In this paper,We study the global attractor and its properties on in nite lattice dynamical system FitzHugh-Nagumo in a weighted space lσ^2×lσ^2.We prove the existence and uniqueness of the solution to the lattice dynamical system FitzHugh-Nagumo in lσ^2×lσ^2.Then we get a bounded absorbing set,which suggests the existence of global attractors.Finally,we study the uniform boundedness and the upper semicontinuity of the global attractor.展开更多
A quasi-structure factor method is used to show how sharp diffraction patterns are produced by aperiodic quasicrystals. Icosahedral symmetry is described for the tensor rank 3 solids with edge-sharing unit cells that ...A quasi-structure factor method is used to show how sharp diffraction patterns are produced by aperiodic quasicrystals. Icosahedral symmetry is described for the tensor rank 3 solids with edge-sharing unit cells that are pentagonally close packed in hierarchic structures having a geometric reciprocal lattice. The hierarchic symmetry replaces translational symmetry in crystal diffraction. Details in the calculation show how the symmetry is simulated in diffraction.展开更多
The geometric theory of quasicrystal structure is an important subject in quasicrystal research. The authors deduce the quasicrystal plane geometric lattices from the stereograms of quasicrystal space geometric lattic...The geometric theory of quasicrystal structure is an important subject in quasicrystal research. The authors deduce the quasicrystal plane geometric lattices from the stereograms of quasicrystal space geometric lattice , and put them together to form the geometric lattices of quasicrystal structures . The general characteristics of quasicrystal geometric lattices , the relation between structural models and geometric lattices , and the relation formula (k=0 , 2 , 4 , 6 , 8, 10,12) of the symmetric axis between quasicrystal and crystal are discussed based on the quasicrystal space geometric lattices. This is of significant in quasicrystal research .展开更多
In this paper, we obtain some geometric inequalities on the radii of inscribed sphere of a simplex and its subsimplex, as particular case of this paper, we obtain some main results of [1].
For the geometric parameters Q and q of Orlicz norm, we prove where This result improves the traditional estimations of Chen S. T., Rao, M. M. and Wu C.X.
The cross product in Euclidean space IR3 is an operation in which two vectors are associated to generate a third vector, also in space IR3. This product can be studied rewriting its basic equations in a matrix structu...The cross product in Euclidean space IR3 is an operation in which two vectors are associated to generate a third vector, also in space IR3. This product can be studied rewriting its basic equations in a matrix structure, more specifically in terms of determinants. Such a structure allows extending, for analogy, the ideas of the cross product for a type of the product of vectors in higher dimensions, through the systematic increase of the number of rows and columns in determinants that constitute the equations. So, in a n-dimensional space with Euclidean norm, we can associate n – 1 vectors and to obtain an n-th vector, with the same geometric characteristics of the product in three dimensions. This kind of operation is also a geometric interpretation of the product defined by Eckman [1]. The same analogies are also useful in the verification of algebraic properties of such products, based?on known properties of determinants.展开更多
New geometrical model of time is suggested where time of body’s motion is defined as the length of its trajectories in four-dimension space-time. Within suggested approach periodical motions in clocks correspond to d...New geometrical model of time is suggested where time of body’s motion is defined as the length of its trajectories in four-dimension space-time. Within suggested approach periodical motions in clocks correspond to definite length of four-dimension trajectories that is clocks appear to be standards for measurements of length in four-dimension space analogously as hard sticks are standards for measurements of length in three-dimension space. This means that space and time are entities of the same geometrical nature. A suggested interpretation of time leads to necessity of changes in general theory of relativity. These changes are unessential for body’s motion in weak gravitational field.展开更多
The four-dimensional character of Einstein’s spacetime is generally accepted in mainstream physics as beyond reasonable doubt correct. However the real problem is when we require scale invariance and that this spacet...The four-dimensional character of Einstein’s spacetime is generally accepted in mainstream physics as beyond reasonable doubt correct. However the real problem is when we require scale invariance and that this spacetime be four-dimensional on all scales. It is true that on our classical scale, the 4D decouples into 3D plus one time dimension and that on very large scale only the curvature of spacetime becomes noticeable. However the critical problem is that such spacetime must remain 4D no matter how small the scale we are probing is. This is something of crucial importance for quantum physics. The present work addresses this basic, natural and logical requirement and shows how many contradictory results and shortcomings of relativity and quantum gravity could be eliminated when we “complete” Einstein’s spacetime in such a geometrical gauge invariant way. Concurrently the work serves also as a review of the vast Literature on E-Infinity theory used here.展开更多
In this paper, we study the extremals of the curvature energy actions on non-null curves in the four-dimensional Lorentz-Minkowski space. We derive the motion equations and find three Killing fields along the generali...In this paper, we study the extremals of the curvature energy actions on non-null curves in the four-dimensional Lorentz-Minkowski space. We derive the motion equations and find three Killing fields along the generalized elastic curves. We also construct a cylindrical coordinate system using these Killing fields and express the generalized elastic curves by means of quadratures.展开更多
Let be a n-dimensional row vector space over a finite field For , let be a d-?dimensional subspace of . denotes the set of all the spaces which are the subspaces of and not the subspaces of except . We define the part...Let be a n-dimensional row vector space over a finite field For , let be a d-?dimensional subspace of . denotes the set of all the spaces which are the subspaces of and not the subspaces of except . We define the partial order on by ordinary inclusion (resp. reverse inclusion), and then is a poset, denoted by (resp. ). In this paper we show that both and are finite atomic lattices. Further, we discuss the geometricity of and , and obtain their characteristic polynomials.展开更多
Fuzzy concepts are introduced into structural optimization to solve fuzzyoptimization problems with a crisp objective function and fuzzy constraints, also a non-membershipfunction is used to convert fuzzy constrains i...Fuzzy concepts are introduced into structural optimization to solve fuzzyoptimization problems with a crisp objective function and fuzzy constraints, also a non-membershipfunction is used to convert fuzzy constrains into crisp constrains. Two models are discussed wherethe objective function considered is the volume of space frame and the fuzzy constrains are designlimits by the axial strength, slenderness, deflection, thickness and diameter of space frame member.展开更多
A unit cell geometrical structure was found with the use of symmetry operations corresponding to the point group C3. Based on the symmetry of space group R3, a 3D braided geometrical structure was obtained by transfor...A unit cell geometrical structure was found with the use of symmetry operations corresponding to the point group C3. Based on the symmetry of space group R3, a 3D braided geometrical structure was obtained by transforming the unit-cell. The features corresponding to this braided structure were studied. The fiber volume percentage and variational tendencies of the material were predicted by establishing a geometric model.展开更多
基金the Indian Space Research Organization(VSSC-ISRO)for funding this research through ISRO-IITM Cell。
文摘In an arcjet thruster,the cathode and constrictor degrade with time,and the electrical arc discharge may become unsymmetrical.In this work,a three-dimensional numerical model of a hydrogen plasma arcjet is developed and validated to study the effect of unsymmetrical electric arc discharge on thruster performance.The unsymmetrical arc discharge is realized by introducing a radial shift of the cathode so that the cathode tip offset is 80μm(25%of the constrictor radius).Simulations are conducted for both axially centered cathode(coaxial)and off-centered cathode(non-coaxial)configurations with identical propellant flow rates and input current.Simulations show asymmetrical arc discharge in the non-coaxial cathode configuration,resulting in azimuthally asymmetric Joule heating,species concentrations,and velocity field.This asymmetry continues as the plasma expands in the divergent section of the nozzle.Temperature,species concentrations,and axial velocity exhibit asymmetric radial distribution at the nozzle exit.The computed Joule heating was found to reduce with cathode shift,and consequently,the thrust and specific impulse of the thruster was decreased by about 6.6%.In the case of the non-coaxial cathode,geometric asymmetry also induces a small side thrust.
基金Project(12 High-tech Urban C11) supported by High-tech Urban Development Program of Ministry of Land,Transport and Maritime Affairs,Korea
文摘The buckling behavior of single layer space structure is very sensitive. The joint rigidity, moreover, is one of the main factors of stability which may determine the entire failure behavior. Thus, the reasonable stiffness of joint system, which is neither total pin assumption nor perfect fix condition, is very important to apply to the real single layer space one. Therefore, the purpose of this work was to investigate the buckling behavior of single layer space structure, using the development of the upgraded stiffness matrix for the joint rigidity. To derive tangential stiffness matrix, a displacement function was assumed using translational and rotational displacement at the node. The geometrical nonlinear analysis was simulated not only with perfect model but also with imperfect one. As a result, the one and two free nodal numerical models were investigated using derived stiffness matrix. It was figured out that the buckling load increases in proportion to joint rigidity with rise-span ratio. The stability of numerical model is very sensitive with the initial imperfection, responding of bifurcation in the structure.
基金Supported by The Scientic Research Foundation Funded by Hunan Provincial Education Department under grant 19A503Partially supported by Hunan Provincial Exploration of Undergraduate Research Learning and Innovative Experiment Project:2018XTUSJ008Hunan Provincial Natural Science Foundation of China under grant 2015JJ2144.
文摘In this paper,We study the global attractor and its properties on in nite lattice dynamical system FitzHugh-Nagumo in a weighted space lσ^2×lσ^2.We prove the existence and uniqueness of the solution to the lattice dynamical system FitzHugh-Nagumo in lσ^2×lσ^2.Then we get a bounded absorbing set,which suggests the existence of global attractors.Finally,we study the uniform boundedness and the upper semicontinuity of the global attractor.
文摘A quasi-structure factor method is used to show how sharp diffraction patterns are produced by aperiodic quasicrystals. Icosahedral symmetry is described for the tensor rank 3 solids with edge-sharing unit cells that are pentagonally close packed in hierarchic structures having a geometric reciprocal lattice. The hierarchic symmetry replaces translational symmetry in crystal diffraction. Details in the calculation show how the symmetry is simulated in diffraction.
文摘The geometric theory of quasicrystal structure is an important subject in quasicrystal research. The authors deduce the quasicrystal plane geometric lattices from the stereograms of quasicrystal space geometric lattice , and put them together to form the geometric lattices of quasicrystal structures . The general characteristics of quasicrystal geometric lattices , the relation between structural models and geometric lattices , and the relation formula (k=0 , 2 , 4 , 6 , 8, 10,12) of the symmetric axis between quasicrystal and crystal are discussed based on the quasicrystal space geometric lattices. This is of significant in quasicrystal research .
基金Supported by the First Class Key Course of Mathematics of Jiangsu Province(SXKYA1010)
文摘In this paper, we obtain some geometric inequalities on the radii of inscribed sphere of a simplex and its subsimplex, as particular case of this paper, we obtain some main results of [1].
文摘For the geometric parameters Q and q of Orlicz norm, we prove where This result improves the traditional estimations of Chen S. T., Rao, M. M. and Wu C.X.
文摘The cross product in Euclidean space IR3 is an operation in which two vectors are associated to generate a third vector, also in space IR3. This product can be studied rewriting its basic equations in a matrix structure, more specifically in terms of determinants. Such a structure allows extending, for analogy, the ideas of the cross product for a type of the product of vectors in higher dimensions, through the systematic increase of the number of rows and columns in determinants that constitute the equations. So, in a n-dimensional space with Euclidean norm, we can associate n – 1 vectors and to obtain an n-th vector, with the same geometric characteristics of the product in three dimensions. This kind of operation is also a geometric interpretation of the product defined by Eckman [1]. The same analogies are also useful in the verification of algebraic properties of such products, based?on known properties of determinants.
文摘New geometrical model of time is suggested where time of body’s motion is defined as the length of its trajectories in four-dimension space-time. Within suggested approach periodical motions in clocks correspond to definite length of four-dimension trajectories that is clocks appear to be standards for measurements of length in four-dimension space analogously as hard sticks are standards for measurements of length in three-dimension space. This means that space and time are entities of the same geometrical nature. A suggested interpretation of time leads to necessity of changes in general theory of relativity. These changes are unessential for body’s motion in weak gravitational field.
文摘The four-dimensional character of Einstein’s spacetime is generally accepted in mainstream physics as beyond reasonable doubt correct. However the real problem is when we require scale invariance and that this spacetime be four-dimensional on all scales. It is true that on our classical scale, the 4D decouples into 3D plus one time dimension and that on very large scale only the curvature of spacetime becomes noticeable. However the critical problem is that such spacetime must remain 4D no matter how small the scale we are probing is. This is something of crucial importance for quantum physics. The present work addresses this basic, natural and logical requirement and shows how many contradictory results and shortcomings of relativity and quantum gravity could be eliminated when we “complete” Einstein’s spacetime in such a geometrical gauge invariant way. Concurrently the work serves also as a review of the vast Literature on E-Infinity theory used here.
基金supported by the National Natural Science Foundation of China (No. 10671066)the Shanghai Leading Academic Discipline Project (No. B407)
文摘In this paper, we study the extremals of the curvature energy actions on non-null curves in the four-dimensional Lorentz-Minkowski space. We derive the motion equations and find three Killing fields along the generalized elastic curves. We also construct a cylindrical coordinate system using these Killing fields and express the generalized elastic curves by means of quadratures.
文摘Let be a n-dimensional row vector space over a finite field For , let be a d-?dimensional subspace of . denotes the set of all the spaces which are the subspaces of and not the subspaces of except . We define the partial order on by ordinary inclusion (resp. reverse inclusion), and then is a poset, denoted by (resp. ). In this paper we show that both and are finite atomic lattices. Further, we discuss the geometricity of and , and obtain their characteristic polynomials.
基金This work was financially supported by the National Natural Science Foundation of China(No.50078004).
文摘Fuzzy concepts are introduced into structural optimization to solve fuzzyoptimization problems with a crisp objective function and fuzzy constraints, also a non-membershipfunction is used to convert fuzzy constrains into crisp constrains. Two models are discussed wherethe objective function considered is the volume of space frame and the fuzzy constrains are designlimits by the axial strength, slenderness, deflection, thickness and diameter of space frame member.
文摘A unit cell geometrical structure was found with the use of symmetry operations corresponding to the point group C3. Based on the symmetry of space group R3, a 3D braided geometrical structure was obtained by transforming the unit-cell. The features corresponding to this braided structure were studied. The fiber volume percentage and variational tendencies of the material were predicted by establishing a geometric model.
