Hot compression tests of the extruded 7075Al/15%SiC (volume fraction) particle reinforced composite prepared by spray deposition were performed on Gleeble?1500 system in the temperature range of 300?450 °C and st...Hot compression tests of the extruded 7075Al/15%SiC (volume fraction) particle reinforced composite prepared by spray deposition were performed on Gleeble?1500 system in the temperature range of 300?450 °C and strain rate range of 0.001?1 s?1. The results indicate that the true stress?true strain curve almost exhibits rapid flow softening phenomenon without an obvious work hardening, and the stress decreases with increasing temperature and decreasing strain rate. Moreover, the stress levels are higher at temperature below 400 °C but lower at 450 °C compared with the spray deposited 7075Al alloy. Superplastic deformation characteristics are found at temperature of 450 °C and strain rate range of 0.001?0.1 s?1 with corresponding strain rate sensitivity of 0.72. The optimum parameters of hot working are determined to be temperature of 430?450 °C and strain rate of 0.001?0.05 s?1 based on processing map and optical microstructural observation.展开更多
In this paper,we consider quasi Einstein hypersurfaces in a hyperbolic space. The following theorem is obtained. Theorem Quasi Einstein hypersurfaces of a hyperbolic space are of constant curvature,where the dimension...In this paper,we consider quasi Einstein hypersurfaces in a hyperbolic space. The following theorem is obtained. Theorem Quasi Einstein hypersurfaces of a hyperbolic space are of constant curvature,where the dimension is large enough.展开更多
We first establish a integral inequality for compact maximal space-like subman ifolds in pseudo-Riemannian manifolds Np(n+p). Then, we investigate compact space-like sub manifolds and hupersurfaces with parallel secon...We first establish a integral inequality for compact maximal space-like subman ifolds in pseudo-Riemannian manifolds Np(n+p). Then, we investigate compact space-like sub manifolds and hupersurfaces with parallel second fundamental form in Np(n+p) and some other ambient spaces. We obtain some distribution theorems for the square norm of the second fundamental form.展开更多
In this paper, we study the relation between the excess of open manifolds and their topology by using the methods of comparison geometry. We prove that a complete open Riemmannian manifold with Ricci curvature negativ...In this paper, we study the relation between the excess of open manifolds and their topology by using the methods of comparison geometry. We prove that a complete open Riemmannian manifold with Ricci curvature negatively lower bounded is of finite topological type provided that the conjugate radius is bounded from below by a positive constant and its Excess is bounded by some function of its conjugate radius, which improves some results in [4].展开更多
In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular...In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green＇s integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cure-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.展开更多
In this paper, a rigidity theorem of hypersurface in real space form will be given. In addition, we obtain rigidity theorems of submanifold in sphere which improve the result of Hou and Xu.
A-manifolds and/3-manifolds, introduced by Gray （1978）, are two significant classes of Einstein-like Riemannian manifolds. A Riemannian manifold is Ricci parallel if and only if it is simultaneously an A-manifold an...A-manifolds and/3-manifolds, introduced by Gray （1978）, are two significant classes of Einstein-like Riemannian manifolds. A Riemannian manifold is Ricci parallel if and only if it is simultaneously an A-manifold and a B-manifold. The present paper proves that both focal submanifolds of each isoparametric hypersurface in unit spheres with g = 4 distinct principal curvatures are A-manifolds. As for the focal submanifolds with g = 6, m = 1 or 2, only one is an A-manifold, and neither is a B-manifold.展开更多
Recently,by combining a swirl flow with non-equilibrium condensation phenomena of condensate gas generated in a supersonic flow,a separating and extracting techniques of condensate gas have been developed.This techniq...Recently,by combining a swirl flow with non-equilibrium condensation phenomena of condensate gas generated in a supersonic flow,a separating and extracting techniques of condensate gas have been developed.This technique can reduce the size of the device and don't use chemicals.In the present study,by using a non-equilibrium condensation phenomenon of moist air occurred in the supersonic flow in the annular nozzle composed of an inher body and an outer nozzle with a swirl,the possibility of separation of the condensable gas and the effect of shape of nozzle inlet on the flow field were examined numerically.展开更多
Let Pt denote the tubular hypersurface of radius t around a given compatible submanifold in a symmetric space of arbitrary rank. The authors will obtain some relations between the integrated mean curvatures of P, and ...Let Pt denote the tubular hypersurface of radius t around a given compatible submanifold in a symmetric space of arbitrary rank. The authors will obtain some relations between the integrated mean curvatures of P, and their derivatives with respect to f. Moreover, the authors will emphasize the differences between the results obtained for rank one and arbitrary rank symmetric spaces.展开更多
Curvature properties are studied for the Sasaki metric on the （1, 1） tensor bundle of a Riemannian manifold. As an application, examples of almost para-Nordenian and para-Kahler-Nordenian B-metrics are constructed o...Curvature properties are studied for the Sasaki metric on the （1, 1） tensor bundle of a Riemannian manifold. As an application, examples of almost para-Nordenian and para-Kahler-Nordenian B-metrics are constructed on the （1, 1） tensor bundle by looking at the Sasaki metric. Also, with respect to the para-Nordenian B-structure, paraholomorphic conditions for the complete lifts of vector fields are analyzed.展开更多
Let E be a simply connected rational homology sphere. A pair of disjoint closed submanifolds M＋, M_ C ＋ are called dual to each other if the complement ~ - M＋ strongly homotopy retracts onto M- or vice-versa. In th...Let E be a simply connected rational homology sphere. A pair of disjoint closed submanifolds M＋, M_ C ＋ are called dual to each other if the complement ~ - M＋ strongly homotopy retracts onto M- or vice-versa. In this paper, we are concerned with the basic problem of which integral triples （n; m＋, m-） E Na can appear, where n ： dime - 1 and m＋ = codimM~ - 1. The problem is motivated by several fundamental aspects in differential geometry. （i） The theory of isoparametric/I）upin hypersurfaces in the unit sphere Sn＋l initiated by ]~lie Cartan, where M=t= are the focal manifolds of the isoparametric/Dupin hypersurface M C Snq-1, and m~= coincide with the multiplicities of principal curvatures of M. （ii） The Grove-Ziller construction of non-negatively curved Riemannian metrics on the Milnor exotic spheres ~, i.e., total spaces of smooth S3-bundles over $4 homeomorphic but not diffeomorphic to S7, where M~ P~ ~so（4） $3, P -＋ $4 the principal SO（4）-bundle of ~ and P~ the singular orbits of a cohomogeneity one SO（4） ~ SO（3）-action on P which are both of codimension 2. Based on the important result of Grove-Halperin, we provide a surprisingly simple answer, namely, if and only if one of the following holds true：m＋ =m- =n; 1 {1, 2,4, 8}; m＋=m_=1/3n∈ {1,2}; m＋=m_=1/4n∈{1,2}; m＋=m_=1/6n∈{1,2}; n In addition, if E is a homotopy sphere and the ratio n/m＋m-2 （for simplicity let us assume 2 ≤ m_ 〈 m＋）, we observe that the work of Stolz on the multiplicities of isoparametric hypersurfaces applies almost identically to conclude that, the pair can be realized if and only if, either （m＋, m_） = （5, 4） or m＋ ＋ m- ＋ 1 is divisible by the integer 5（m_） （see the table on Page 1551）, which is equivalent to the existence of （m- - 1） linearly independent vector fields on the sphere Sin＋＋m- by Adams＇ celebrated work. In contrast, infinitely many counterexamples are given if E is a rational homology sphere.展开更多
Experiments were carried out to eliminate the screech tone generated from a supersonic jet. Compressed air was passed through a circular convergent nozzle preceded by a straight tube of same diameter. In order to redu...Experiments were carried out to eliminate the screech tone generated from a supersonic jet. Compressed air was passed through a circular convergent nozzle preceded by a straight tube of same diameter. In order to reduce the jet screech a spherical reflector was used and placed at the nozzle exit. The placement of the spherical reflector at the nozzle exit controlled the location of the image source as well as minimized the sound pressure at the nozzle exit. The weak sound pressure did not excite the unstable disturbance at the exit. Thus the loop of the feedback mechanism could not be accomplished and the jet screech was eliminated. The technique of screech reduction with a flat plate was also examined and compared with the present method. A good and effective performance in canceling the screech component by the new method was found by the investigation. Experimental results indicate that the new system suppresses not only the screech tones but also the broadband noise components and reduces the overall noise of the jet flow. The spherical reflector was found very effective in reducing overall sound pressure level in the upstream region of the nozzle compared to a flat plate. The proposed spherical reflector can, accordingly, protect the upstream noise propagation.展开更多
Large-eddy simulation of a sonic injection from circular and elliptic injectors into a supersonic crossflow has been performed.The effects of injector geometry on various fundamental mechanisms dictating the intricate...Large-eddy simulation of a sonic injection from circular and elliptic injectors into a supersonic crossflow has been performed.The effects of injector geometry on various fundamental mechanisms dictating the intricate flow phenomena including shock/jet interaction,jet shear layer vortices and their evolution,jet penetration properties and the relevant turbulence behaviors have been studied systematically.As a jet issuing transversely into a supersonic crossflow,salient three-dimensional shock and vortical structures,such as bow,separation and barrel shocks,Mach disk,horseshoe vortex,jet shear layer vortices and vortex pairs,are induced.The shock structures exhibit considerable deformations in the circular injection,while their fluctuation becomes smaller in the elliptic injection.The jet shear layer vortices are generated at the jet periphery and their evolution characteristics are analyzed through tracing the centroid of these coherent structures.It is found that the jet from the elliptic injector spreads rapidly in the spanwise direction but suffers a reduction in the transverse penetration compared to the circular injection case.The turbulent fluctuations are amplified because of the jet/crossflow interaction.The vertical Reynolds normal stress is enhanced in the downstream of the jet because of the upwash velocity induced by the counter-rotating vortex pair.展开更多
基金Project(51271076)supported by the National Natural Science Foundation of China
文摘Hot compression tests of the extruded 7075Al/15%SiC (volume fraction) particle reinforced composite prepared by spray deposition were performed on Gleeble?1500 system in the temperature range of 300?450 °C and strain rate range of 0.001?1 s?1. The results indicate that the true stress?true strain curve almost exhibits rapid flow softening phenomenon without an obvious work hardening, and the stress decreases with increasing temperature and decreasing strain rate. Moreover, the stress levels are higher at temperature below 400 °C but lower at 450 °C compared with the spray deposited 7075Al alloy. Superplastic deformation characteristics are found at temperature of 450 °C and strain rate range of 0.001?0.1 s?1 with corresponding strain rate sensitivity of 0.72. The optimum parameters of hot working are determined to be temperature of 430?450 °C and strain rate of 0.001?0.05 s?1 based on processing map and optical microstructural observation.
文摘In this paper,we consider quasi Einstein hypersurfaces in a hyperbolic space. The following theorem is obtained. Theorem Quasi Einstein hypersurfaces of a hyperbolic space are of constant curvature,where the dimension is large enough.
文摘We first establish a integral inequality for compact maximal space-like subman ifolds in pseudo-Riemannian manifolds Np(n+p). Then, we investigate compact space-like sub manifolds and hupersurfaces with parallel second fundamental form in Np(n+p) and some other ambient spaces. We obtain some distribution theorems for the square norm of the second fundamental form.
基金Supported by the National Natural Science Foundation of China(10371047)
文摘In this paper, we study the relation between the excess of open manifolds and their topology by using the methods of comparison geometry. We prove that a complete open Riemmannian manifold with Ricci curvature negatively lower bounded is of finite topological type provided that the conjugate radius is bounded from below by a positive constant and its Excess is bounded by some function of its conjugate radius, which improves some results in [4].
基金Partially Supported by the Department of Science and Technology Through a Research Grant to RG(No.SR/FTP/MS-020/2010)
文摘In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green＇s integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cure-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.
文摘In this paper, a rigidity theorem of hypersurface in real space form will be given. In addition, we obtain rigidity theorems of submanifold in sphere which improve the result of Hou and Xu.
基金supported by National Natural Science Foundation of China(Grant No.11301027)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130003120008)+1 种基金the Beijing Natural Science Foundation(Grant No.1144013)the Fundamental Research Funds for the Central Universities(Grant No.2012CXQT09)
文摘A-manifolds and/3-manifolds, introduced by Gray （1978）, are two significant classes of Einstein-like Riemannian manifolds. A Riemannian manifold is Ricci parallel if and only if it is simultaneously an A-manifold and a B-manifold. The present paper proves that both focal submanifolds of each isoparametric hypersurface in unit spheres with g = 4 distinct principal curvatures are A-manifolds. As for the focal submanifolds with g = 6, m = 1 or 2, only one is an A-manifold, and neither is a B-manifold.
文摘Recently,by combining a swirl flow with non-equilibrium condensation phenomena of condensate gas generated in a supersonic flow,a separating and extracting techniques of condensate gas have been developed.This technique can reduce the size of the device and don't use chemicals.In the present study,by using a non-equilibrium condensation phenomenon of moist air occurred in the supersonic flow in the annular nozzle composed of an inher body and an outer nozzle with a swirl,the possibility of separation of the condensable gas and the effect of shape of nozzle inlet on the flow field were examined numerically.
文摘Let Pt denote the tubular hypersurface of radius t around a given compatible submanifold in a symmetric space of arbitrary rank. The authors will obtain some relations between the integrated mean curvatures of P, and their derivatives with respect to f. Moreover, the authors will emphasize the differences between the results obtained for rank one and arbitrary rank symmetric spaces.
基金Project supported by the Scientific and Technological Research Council of Turkey(No.TBAG-108T590)
文摘Curvature properties are studied for the Sasaki metric on the （1, 1） tensor bundle of a Riemannian manifold. As an application, examples of almost para-Nordenian and para-Kahler-Nordenian B-metrics are constructed on the （1, 1） tensor bundle by looking at the Sasaki metric. Also, with respect to the para-Nordenian B-structure, paraholomorphic conditions for the complete lifts of vector fields are analyzed.
基金supported by National Natural Science Foundation of China(Grant No.11431009)the Ministry of Education in China,and the Municipal Administration of Beijing
文摘Let E be a simply connected rational homology sphere. A pair of disjoint closed submanifolds M＋, M_ C ＋ are called dual to each other if the complement ~ - M＋ strongly homotopy retracts onto M- or vice-versa. In this paper, we are concerned with the basic problem of which integral triples （n; m＋, m-） E Na can appear, where n ： dime - 1 and m＋ = codimM~ - 1. The problem is motivated by several fundamental aspects in differential geometry. （i） The theory of isoparametric/I）upin hypersurfaces in the unit sphere Sn＋l initiated by ]~lie Cartan, where M=t= are the focal manifolds of the isoparametric/Dupin hypersurface M C Snq-1, and m~= coincide with the multiplicities of principal curvatures of M. （ii） The Grove-Ziller construction of non-negatively curved Riemannian metrics on the Milnor exotic spheres ~, i.e., total spaces of smooth S3-bundles over $4 homeomorphic but not diffeomorphic to S7, where M~ P~ ~so（4） $3, P -＋ $4 the principal SO（4）-bundle of ~ and P~ the singular orbits of a cohomogeneity one SO（4） ~ SO（3）-action on P which are both of codimension 2. Based on the important result of Grove-Halperin, we provide a surprisingly simple answer, namely, if and only if one of the following holds true：m＋ =m- =n; 1 {1, 2,4, 8}; m＋=m_=1/3n∈ {1,2}; m＋=m_=1/4n∈{1,2}; m＋=m_=1/6n∈{1,2}; n In addition, if E is a homotopy sphere and the ratio n/m＋m-2 （for simplicity let us assume 2 ≤ m_ 〈 m＋）, we observe that the work of Stolz on the multiplicities of isoparametric hypersurfaces applies almost identically to conclude that, the pair can be realized if and only if, either （m＋, m_） = （5, 4） or m＋ ＋ m- ＋ 1 is divisible by the integer 5（m_） （see the table on Page 1551）, which is equivalent to the existence of （m- - 1） linearly independent vector fields on the sphere Sin＋＋m- by Adams＇ celebrated work. In contrast, infinitely many counterexamples are given if E is a rational homology sphere.
文摘Experiments were carried out to eliminate the screech tone generated from a supersonic jet. Compressed air was passed through a circular convergent nozzle preceded by a straight tube of same diameter. In order to reduce the jet screech a spherical reflector was used and placed at the nozzle exit. The placement of the spherical reflector at the nozzle exit controlled the location of the image source as well as minimized the sound pressure at the nozzle exit. The weak sound pressure did not excite the unstable disturbance at the exit. Thus the loop of the feedback mechanism could not be accomplished and the jet screech was eliminated. The technique of screech reduction with a flat plate was also examined and compared with the present method. A good and effective performance in canceling the screech component by the new method was found by the investigation. Experimental results indicate that the new system suppresses not only the screech tones but also the broadband noise components and reduces the overall noise of the jet flow. The spherical reflector was found very effective in reducing overall sound pressure level in the upstream region of the nozzle compared to a flat plate. The proposed spherical reflector can, accordingly, protect the upstream noise propagation.
基金supported by the National Natural Science Foundation of China(Grant Nos.11132010 and 11072236)
文摘Large-eddy simulation of a sonic injection from circular and elliptic injectors into a supersonic crossflow has been performed.The effects of injector geometry on various fundamental mechanisms dictating the intricate flow phenomena including shock/jet interaction,jet shear layer vortices and their evolution,jet penetration properties and the relevant turbulence behaviors have been studied systematically.As a jet issuing transversely into a supersonic crossflow,salient three-dimensional shock and vortical structures,such as bow,separation and barrel shocks,Mach disk,horseshoe vortex,jet shear layer vortices and vortex pairs,are induced.The shock structures exhibit considerable deformations in the circular injection,while their fluctuation becomes smaller in the elliptic injection.The jet shear layer vortices are generated at the jet periphery and their evolution characteristics are analyzed through tracing the centroid of these coherent structures.It is found that the jet from the elliptic injector spreads rapidly in the spanwise direction but suffers a reduction in the transverse penetration compared to the circular injection case.The turbulent fluctuations are amplified because of the jet/crossflow interaction.The vertical Reynolds normal stress is enhanced in the downstream of the jet because of the upwash velocity induced by the counter-rotating vortex pair.
