A new non-decoupling three-dimensional guidance law is proposed for bank-to-turn （BTT） missiles with the motion coupling problem. In this method, the different geometry is taken for theoretically modeling on B-IT mi...A new non-decoupling three-dimensional guidance law is proposed for bank-to-turn （BTT） missiles with the motion coupling problem. In this method, the different geometry is taken for theoretically modeling on B-IT missiles＇ motion within the threedimensional style without information loss, and meanwhile, Liegroup is utilized to describe the line-of-sight （LOS） azimuth when the terminal angular constraints are considered. Under these cir- cumstances, a guidance kinematics model is established based on differential geometry. Then, corresponding to no terminal angular constraint and terminal angular constraints, guidance laws are re- spectively designed by using proportional control and generalized proportional-derivative （PD） control in SO（3） group. Eventually, simulation results validate that this developed method can effectively avoid the complexity of pure Lie-group method and the information loss of the traditional decoupling method as well.展开更多
Gaseous detonation propagating in a toroidal chamber was numerically studied for hydrogen/oxygen/nitrogen mixtures. The numerical method used is based on the three-dimensional Euler equations with detailed finiterate ...Gaseous detonation propagating in a toroidal chamber was numerically studied for hydrogen/oxygen/nitrogen mixtures. The numerical method used is based on the three-dimensional Euler equations with detailed finiterate chemistry. The results show that the calculated streak picture is in qualitative agreement with the picture recorded by a high speed streak camera from published literature. The three-dimensional flow field induced by a continuously rotating detonation was visualized and distinctive features of the rotating detonations were clearly depicted. Owing to the unconfined character of detonation wavelet, a deficit of detonation parameters was observed. Due to the effects of wall geometries, the strength of the outside detonation front is stronger than that of the inside portion. The detonation thus propagates with a constant circular velocity. Numerical simulation also shows three-dimensional rotating detonation structures, which display specific feature of the detonation- shock combined wave. Discrete burning gas pockets are formed due to instability of the discontinuity. It is believed that the present study could give an insight into the interest- ing properties of the continuously rotating detonation, and is thus beneficial to the design of continuous detonation propulsion systems.展开更多
Physics success is largely determined by using mathematics.Physics often themselves create the necessary mathematical apparatus.This article shows how you can construct a fractal calculus-mathematics of fractal geomet...Physics success is largely determined by using mathematics.Physics often themselves create the necessary mathematical apparatus.This article shows how you can construct a fractal calculus-mathematics of fractal geometry.In modem scientific literature often write from a firm that"there is no strict definition of fractals",to the more moderate that"objects in a certain sense,fractal and similar."We show that fractal geometry is a strict mathematical theory,defined by their axioms.This methodology allows the geometry of axiomatised naturally define fractal integrals and differentials.Consistent application on your input below the axiom gives the opportunity to develop effective methods of measurement of fractal dimension,geometri-cal interpretation of fractal derivative gain and open dual symmetry.展开更多
A new copper(Ⅱ) complex [Cu(PDA)(H 2O) 2] was synthesized and its structure was determined. Cu(Ⅱ) is five coordinated in a tetragonal pyramid geometry. The two coordinating water molecules are different and t...A new copper(Ⅱ) complex [Cu(PDA)(H 2O) 2] was synthesized and its structure was determined. Cu(Ⅱ) is five coordinated in a tetragonal pyramid geometry. The two coordinating water molecules are different and the two Cu-O bond lengths differ by nearly 0.02 nm. The whole crystal is linked to form a three dimensional network by means of hydrogen bonds. The X band ESR spectrum shows three different g tensors with a well resolved hyperfine structure in the g z signal, giving the ESR parameters g x=2 05, g y =2 065 and g z =2 29. The covalency of the coordinate bonds and the deviation from tetragonal pyramid geometry for the complex are discussed based on the ESR spectra.展开更多
The undirected graph to express engineering drawings is discussed .The principle to re-solve and reason the undirected graph is presented, and the algorithm finally transforms theundirected graph into the resolvable d...The undirected graph to express engineering drawings is discussed .The principle to re-solve and reason the undirected graph is presented, and the algorithm finally transforms theundirected graph into the resolvable directed graph. Therefore,a rapid and simple way is suppliedfor variational design. A prototype of this algorithm has been implemented, and some examplesare given.展开更多
As per Hawking and Bekenstein’s work on black holes, information resides on the surface and there is a limit on it amounting to a bit for every Planck area. It would seem therefore that extra dimensions would logical...As per Hawking and Bekenstein’s work on black holes, information resides on the surface and there is a limit on it amounting to a bit for every Planck area. It would seem therefore that extra dimensions would logically lead to a hyper-surface for a black hole and consequently a reduction of the corresponding information density due to the dilution effect of these additional dimensions. The present paper argues that the counterintuitive opposite of the above is what should be expected. This surprising result is a consequence of a well known theorem on measure concentration due to I. Dvoretzky.展开更多
We pioneered a study about how the geometric relationship of single-walled carbon nanotubes(SWCNT) is influenced by curvature factor and non-planar geometry factor in cylindrical coordinate system based on the assumpt...We pioneered a study about how the geometric relationship of single-walled carbon nanotubes(SWCNT) is influenced by curvature factor and non-planar geometry factor in cylindrical coordinate system based on the assumption of complete symmetry. The bond length and angle of every carbon-carbon bonds are determined by using the principle of the minimum energy. The results of the paper include(1) From the calculation result, the symmetry breaking appears for chiral carbon nanotubes, while the part symmetry appears for achiral carbon nanotubes with increasing curvature.(2) The synergistic effect of bond lengths and bond angles is first found.(3) We conclude that the influence of non-planar geometry factor can be completely ignored on bond lengths and bond angles when the curvature parameter has been included in the model.(4)The two fractal dimensions are given from the nanoscale to the macroscale for zigzag topology and armchair topology respectively. Fractal dimensions of SWCNT show special characteristics, varying with the length of SWCNT until the lengths approach infinity. The close and inevitable correlations among curvature, symmetry breaking and stability of SWCNTs can be summed up as: the increase of curvature causes symmetry breaking,and such symmetry breaking will further reduce the structural stability.展开更多
Complex nonlinear dynamic systems are ubiquitous in the landscapes and phenomena studied by earth sciences in general and by geomorphology in particular. Many natural landscape features have an aspect such as fractals...Complex nonlinear dynamic systems are ubiquitous in the landscapes and phenomena studied by earth sciences in general and by geomorphology in particular. Many natural landscape features have an aspect such as fractals. In the many geomorphologic phenomena such as river networks and coast lines this is visible. In recent years fractal geometry offers as an option for modeling river geometry and physical processes of rivers. The fractal dimension is a statistical quantity that indicates how a fractal scales with the shrink, the space occupied. This theory has the mathematical basis but also applied in geomorphology and also shown great success. Physical behavior of many natural processes as well as using fractal geometry is predictable relations. Behavior of complex natural phenomena as rivers has always been of interest to researchers. In this study using data basic maps, drainage networks map and Digital Elevation Model of the ground was prepared. Then applying the rules Horton-Strahler river network, fractal dimensions were calculated to examine the relationship between fractal dimension and some rivers geomorphic features were investigated. Results showed fractal dimension of watersheds have meaningful relations with factors such as shape form, area, bifurcation ratio and length ratio in the watersheds.展开更多
The quintessence of hyperbolic geometry is transferred to a transfinite Cantorian-fractal setting in the present work. Starting from the building block of E-infinity Cantorian spacetime theory, namely a quantum pre-pa...The quintessence of hyperbolic geometry is transferred to a transfinite Cantorian-fractal setting in the present work. Starting from the building block of E-infinity Cantorian spacetime theory, namely a quantum pre-particle zero set as a core and a quantum pre-wave empty set as cobordism or surface of the core, we connect the interaction of two such self similar units to a compact four dimensional manifold and a corresponding holographic boundary akin to the compactified Klein modular curve with SL(2,7) symmetry. Based on this model in conjunction with a 4D compact hy- perbolic manifold M(4) and the associated general theory, the so obtained ordinary and dark en- ergy density of the cosmos is found to be in complete agreement with previous analysis as well as cosmic measurements and observations such as WMAP and Type 1a supernova.展开更多
On the basis of nonlinear strain component formulations of three-dimensional continuum, this paper has derived the nonlinear strain component formulations of shells with initial geometric imperfections. The derivation...On the basis of nonlinear strain component formulations of three-dimensional continuum, this paper has derived the nonlinear strain component formulations of shells with initial geometric imperfections. The derivation is not confined to a special shell, therefore they possess general properties. These formulations provide the theoretical basis of the strain analysis for geometric nonlinear problems of shells with initial geometric imperfections.展开更多
In Comparison with the traditional point-by-point line generation method,the method we present is based on segment code in Pan-Euclidean geometric space and is quite different in re- spect of running speed and theoret...In Comparison with the traditional point-by-point line generation method,the method we present is based on segment code in Pan-Euclidean geometric space and is quite different in re- spect of running speed and theoretical basis.This paper presents an approach of using segment code to draw straight lines and shows the characteristics of a digital line.It is a newly proposed al- gorithm applicable in CAD.展开更多
基金supported by the National University of Defense Technology Innovation Support Project for Outstanding Graduate Student(B100303)
文摘A new non-decoupling three-dimensional guidance law is proposed for bank-to-turn （BTT） missiles with the motion coupling problem. In this method, the different geometry is taken for theoretically modeling on B-IT missiles＇ motion within the threedimensional style without information loss, and meanwhile, Liegroup is utilized to describe the line-of-sight （LOS） azimuth when the terminal angular constraints are considered. Under these cir- cumstances, a guidance kinematics model is established based on differential geometry. Then, corresponding to no terminal angular constraint and terminal angular constraints, guidance laws are re- spectively designed by using proportional control and generalized proportional-derivative （PD） control in SO（3） group. Eventually, simulation results validate that this developed method can effectively avoid the complexity of pure Lie-group method and the information loss of the traditional decoupling method as well.
基金This paper is supported by National Natural Science Foundation （No. 60871093, 60872126） and National Defense Prediction Foundation （No. 9140C80002080C80）, Guangdong Province Natural Science Foundation （No.8151806001000002）
基金supported by the National Natural Science Foundation of China (10872096)the Open Fund of State Key Laboratory of Explosion Science and Technology, Beijing University of Science and Technology (KFJJ09-13)
文摘Gaseous detonation propagating in a toroidal chamber was numerically studied for hydrogen/oxygen/nitrogen mixtures. The numerical method used is based on the three-dimensional Euler equations with detailed finiterate chemistry. The results show that the calculated streak picture is in qualitative agreement with the picture recorded by a high speed streak camera from published literature. The three-dimensional flow field induced by a continuously rotating detonation was visualized and distinctive features of the rotating detonations were clearly depicted. Owing to the unconfined character of detonation wavelet, a deficit of detonation parameters was observed. Due to the effects of wall geometries, the strength of the outside detonation front is stronger than that of the inside portion. The detonation thus propagates with a constant circular velocity. Numerical simulation also shows three-dimensional rotating detonation structures, which display specific feature of the detonation- shock combined wave. Discrete burning gas pockets are formed due to instability of the discontinuity. It is believed that the present study could give an insight into the interest- ing properties of the continuously rotating detonation, and is thus beneficial to the design of continuous detonation propulsion systems.
文摘Physics success is largely determined by using mathematics.Physics often themselves create the necessary mathematical apparatus.This article shows how you can construct a fractal calculus-mathematics of fractal geometry.In modem scientific literature often write from a firm that"there is no strict definition of fractals",to the more moderate that"objects in a certain sense,fractal and similar."We show that fractal geometry is a strict mathematical theory,defined by their axioms.This methodology allows the geometry of axiomatised naturally define fractal integrals and differentials.Consistent application on your input below the axiom gives the opportunity to develop effective methods of measurement of fractal dimension,geometri-cal interpretation of fractal derivative gain and open dual symmetry.
基金Supported by the National Natural Science Foundation of China(No.2 0 0 710 192 0 0 710 2 0 and5 0 172 0 2 ) and the Re-search Fund for Doctoral Program of Higher Education.
文摘A new copper(Ⅱ) complex [Cu(PDA)(H 2O) 2] was synthesized and its structure was determined. Cu(Ⅱ) is five coordinated in a tetragonal pyramid geometry. The two coordinating water molecules are different and the two Cu-O bond lengths differ by nearly 0.02 nm. The whole crystal is linked to form a three dimensional network by means of hydrogen bonds. The X band ESR spectrum shows three different g tensors with a well resolved hyperfine structure in the g z signal, giving the ESR parameters g x=2 05, g y =2 065 and g z =2 29. The covalency of the coordinate bonds and the deviation from tetragonal pyramid geometry for the complex are discussed based on the ESR spectra.
文摘The undirected graph to express engineering drawings is discussed .The principle to re-solve and reason the undirected graph is presented, and the algorithm finally transforms theundirected graph into the resolvable directed graph. Therefore,a rapid and simple way is suppliedfor variational design. A prototype of this algorithm has been implemented, and some examplesare given.
文摘As per Hawking and Bekenstein’s work on black holes, information resides on the surface and there is a limit on it amounting to a bit for every Planck area. It would seem therefore that extra dimensions would logically lead to a hyper-surface for a black hole and consequently a reduction of the corresponding information density due to the dilution effect of these additional dimensions. The present paper argues that the counterintuitive opposite of the above is what should be expected. This surprising result is a consequence of a well known theorem on measure concentration due to I. Dvoretzky.
基金National Natural Science Foundation of China (No. 10602028)Student Research Train Program of BeiHang University
文摘We pioneered a study about how the geometric relationship of single-walled carbon nanotubes(SWCNT) is influenced by curvature factor and non-planar geometry factor in cylindrical coordinate system based on the assumption of complete symmetry. The bond length and angle of every carbon-carbon bonds are determined by using the principle of the minimum energy. The results of the paper include(1) From the calculation result, the symmetry breaking appears for chiral carbon nanotubes, while the part symmetry appears for achiral carbon nanotubes with increasing curvature.(2) The synergistic effect of bond lengths and bond angles is first found.(3) We conclude that the influence of non-planar geometry factor can be completely ignored on bond lengths and bond angles when the curvature parameter has been included in the model.(4)The two fractal dimensions are given from the nanoscale to the macroscale for zigzag topology and armchair topology respectively. Fractal dimensions of SWCNT show special characteristics, varying with the length of SWCNT until the lengths approach infinity. The close and inevitable correlations among curvature, symmetry breaking and stability of SWCNTs can be summed up as: the increase of curvature causes symmetry breaking,and such symmetry breaking will further reduce the structural stability.
文摘Complex nonlinear dynamic systems are ubiquitous in the landscapes and phenomena studied by earth sciences in general and by geomorphology in particular. Many natural landscape features have an aspect such as fractals. In the many geomorphologic phenomena such as river networks and coast lines this is visible. In recent years fractal geometry offers as an option for modeling river geometry and physical processes of rivers. The fractal dimension is a statistical quantity that indicates how a fractal scales with the shrink, the space occupied. This theory has the mathematical basis but also applied in geomorphology and also shown great success. Physical behavior of many natural processes as well as using fractal geometry is predictable relations. Behavior of complex natural phenomena as rivers has always been of interest to researchers. In this study using data basic maps, drainage networks map and Digital Elevation Model of the ground was prepared. Then applying the rules Horton-Strahler river network, fractal dimensions were calculated to examine the relationship between fractal dimension and some rivers geomorphic features were investigated. Results showed fractal dimension of watersheds have meaningful relations with factors such as shape form, area, bifurcation ratio and length ratio in the watersheds.
文摘The quintessence of hyperbolic geometry is transferred to a transfinite Cantorian-fractal setting in the present work. Starting from the building block of E-infinity Cantorian spacetime theory, namely a quantum pre-particle zero set as a core and a quantum pre-wave empty set as cobordism or surface of the core, we connect the interaction of two such self similar units to a compact four dimensional manifold and a corresponding holographic boundary akin to the compactified Klein modular curve with SL(2,7) symmetry. Based on this model in conjunction with a 4D compact hy- perbolic manifold M(4) and the associated general theory, the so obtained ordinary and dark en- ergy density of the cosmos is found to be in complete agreement with previous analysis as well as cosmic measurements and observations such as WMAP and Type 1a supernova.
文摘On the basis of nonlinear strain component formulations of three-dimensional continuum, this paper has derived the nonlinear strain component formulations of shells with initial geometric imperfections. The derivation is not confined to a special shell, therefore they possess general properties. These formulations provide the theoretical basis of the strain analysis for geometric nonlinear problems of shells with initial geometric imperfections.
文摘In Comparison with the traditional point-by-point line generation method,the method we present is based on segment code in Pan-Euclidean geometric space and is quite different in re- spect of running speed and theoretical basis.This paper presents an approach of using segment code to draw straight lines and shows the characteristics of a digital line.It is a newly proposed al- gorithm applicable in CAD.
