In this paper, based on the Schrfdinger equation and the ψ mapping theory, the accurate expression for the gradient of resonating valence bond superconducting phase Θ^2s is found. The expression of Δ↓Θ^2s is just...In this paper, based on the Schrfdinger equation and the ψ mapping theory, the accurate expression for the gradient of resonating valence bond superconducting phase Θ^2s is found. The expression of Δ↓Θ^2s is just the velocity flow without considering the coefficient. The curl of Δ↓Θ^2s is where the vortex lies, and has important relation to δ2(ψ) and an important relation to the zero points of resonating valence bond superconducting order parameter ψ. The topological structure of the vortex is characterized by the ψ-mapping topological numbers Hopf-index and Brouwer degrees. The Ginzberg-Landau equation in resonating valence bond state also is discussed in this theory. The magnetic property is discussed also.展开更多
Optical vortices as topological objects exist ubiquitously in nature.In this paper,by making use of the Duan's topological current theory,we investigate the topology in the closed and knotted optical vortices.The ...Optical vortices as topological objects exist ubiquitously in nature.In this paper,by making use of the Duan's topological current theory,we investigate the topology in the closed and knotted optical vortices.The topological inner structure of the optical vortices are obtained,and the linking of the knotted optical vortices is also given.展开更多
It is hypothesized that steady anguilliform swimming motion of aquatic animals is purely reactive such that no net vortex wake is left downstream. This is versus carangiform and tunniform swimming of fish, where vorte...It is hypothesized that steady anguilliform swimming motion of aquatic animals is purely reactive such that no net vortex wake is left downstream. This is versus carangiform and tunniform swimming of fish, where vortex streams are shed from tail, fins, and body. But there the animal movements are such to produce partial vortex cancellation downstream in maximizing propulsive efficiency. In anguilliform swimming characteristic of the eel family, it is argued that the swimming motions are configured by the animal such that vortex shedding does not occur at all. However, the propulsive thrust in this case is higher order in the motion amplitude, so that relatively large coils are needed to produce relatively small thrust; the speeds of anguilliform swimmers are less than the carangiform and tunniforrn, which develop first order thrusts via lifting processes. Results of experimentation on live lamprey are compared to theoretical prediction which assumes the no-wake hypothesis. Two-dimensional analysis is first performed to set the concept. This is followed by three-dimensional analysis using slender-body theory. Slender-body theory has been applied by others in studying anguilliform swimming, as it is ideally suited to the geometry of the lamprey and other eel-like animals. The agreement between this new approach based on the hypothesis of wakeless swimming and the experiments is remarkably good in spite of the physical complexities.展开更多
The stall behavior in a single-stage low-speed axial compressor under rotating inlet distortion (RID) is investigatedin the first half of this paper. The tests demonstrate that the tip leakage flow (TLF) plays an impo...The stall behavior in a single-stage low-speed axial compressor under rotating inlet distortion (RID) is investigatedin the first half of this paper. The tests demonstrate that the tip leakage flow (TLF) plays an important rolein triggering rotating stall. The tracking of the spike-like disturbances caused by the spillage of TLV indicates thatmost of such spike-like disturbances will be smeared by non-distorted sector and the growth of the spike-like disturbancesactually relate closely to how and how often the path of the propagating disturbances come across thepath of the rotating distorted sector. In the second half of this paper, micro air injections are applied to test the effectbehavior of TLF on stall inception. Contrasts to without micro air injections, the spike-like disturbances aremuch fewer, so the possibilities that spike-like disturbances may trigger rotating stall are fewer too. As a result,the compressor gets a lower mass flow rate at stall for both co-rotating inlet distortion and counter-rotating inletdistortion.展开更多
Nonlinear parabolized stability equations are employed in this work to investigate the nonlinear development of the G6rtler insta- bility up to the saturation stage. The perturbed boundary layer is highly inflectional...Nonlinear parabolized stability equations are employed in this work to investigate the nonlinear development of the G6rtler insta- bility up to the saturation stage. The perturbed boundary layer is highly inflectional both in the normalwise and spanwise directions and receptive to the secondary instabilities. The Floquet theory is applied to solve the fundamental, subharmonic and detuned secondary instabilities. With the Gortler-vortices-distorted base flow, two classes of secondary disturbances, i.e. odd modes and even modes, are identified according to the eigenfunctions of the disturbances. These modes may result in different patterns in the late stages of the transition process. Li and Malik [ 1 ] have shown the sinuous and varicose types of breakdown originating from the odd and even modes. The current study focuses on the four most amplified modes termed the even modes I & Ⅱ and odd modes I & lI. Odd mode II was missing in the work of Li and Malik [1] probably due to their inviscid simplifeation. The detuned modes are confirmed to be less amplifed than the fundamental (for the odd mode I) and subharmonic modes (for even modes I & II and the odd mode II).展开更多
The research on scroll profiles theory at present mainly is aiming at the single profile and its amelioration or parameter optimization,not aiming at the natural characteristic of the profiles equation of scroll profi...The research on scroll profiles theory at present mainly is aiming at the single profile and its amelioration or parameter optimization,not aiming at the natural characteristic of the profiles equation of scroll profiles itself.Thus,the intrinsic differential equation bearing on arc-length and tangent direction angle was studied.Using the inherent differential equation and general functional theory,the conversion ideas between the expression of intrinsic differential equation and the expression in Cartesian coordinate was studied,and the condition of involutes characteristic was presented.The detailed analysis of four typical scroll profiles was given.According to the four typical scroll profiles and based on the method of Taylor series,the unified formation of general functional integration scroll profiles was established,which perfected general theory of scroll profiles increasingly.The envelope method to seek conjugation engagement profiles was studied.The unified general functional equation of scroll profiles represented the admissible function scrolls and the conjugation engagement characteristic of which was studied.The engagement condition of conjugation scroll profiles and the expression in Cartesian coordinate of conjugation scroll profiles of general functional integration scroll profiles were educed.Therefore,the restriction of inherent characteristics of single scroll profiles model is broken through.Solid modeling and machine tool path simulation can bridge the gap between design and manufacture which is essential for the design and manufacture of scroll compressors.With this method a perfect solid model can be achieved,which leads to an optimal design in terms of quality,delivery time and cost.The presentation of unified formation of general functional integration scroll profiles represents foundation factor of instinct characteristics of scroll profiles,which widens the design method of scroll compressor for automobile air conditioning.展开更多
文摘In this paper, based on the Schrfdinger equation and the ψ mapping theory, the accurate expression for the gradient of resonating valence bond superconducting phase Θ^2s is found. The expression of Δ↓Θ^2s is just the velocity flow without considering the coefficient. The curl of Δ↓Θ^2s is where the vortex lies, and has important relation to δ2(ψ) and an important relation to the zero points of resonating valence bond superconducting order parameter ψ. The topological structure of the vortex is characterized by the ψ-mapping topological numbers Hopf-index and Brouwer degrees. The Ginzberg-Landau equation in resonating valence bond state also is discussed in this theory. The magnetic property is discussed also.
基金supported by National Natural Science Foundation of China
文摘Optical vortices as topological objects exist ubiquitously in nature.In this paper,by making use of the Duan's topological current theory,we investigate the topology in the closed and knotted optical vortices.The topological inner structure of the optical vortices are obtained,and the linking of the knotted optical vortices is also given.
文摘It is hypothesized that steady anguilliform swimming motion of aquatic animals is purely reactive such that no net vortex wake is left downstream. This is versus carangiform and tunniform swimming of fish, where vortex streams are shed from tail, fins, and body. But there the animal movements are such to produce partial vortex cancellation downstream in maximizing propulsive efficiency. In anguilliform swimming characteristic of the eel family, it is argued that the swimming motions are configured by the animal such that vortex shedding does not occur at all. However, the propulsive thrust in this case is higher order in the motion amplitude, so that relatively large coils are needed to produce relatively small thrust; the speeds of anguilliform swimmers are less than the carangiform and tunniforrn, which develop first order thrusts via lifting processes. Results of experimentation on live lamprey are compared to theoretical prediction which assumes the no-wake hypothesis. Two-dimensional analysis is first performed to set the concept. This is followed by three-dimensional analysis using slender-body theory. Slender-body theory has been applied by others in studying anguilliform swimming, as it is ideally suited to the geometry of the lamprey and other eel-like animals. The agreement between this new approach based on the hypothesis of wakeless swimming and the experiments is remarkably good in spite of the physical complexities.
基金The support of National Natural Science Foundation of China through Grant 50676094 and 50736007 are gratefully acknowledged.
文摘The stall behavior in a single-stage low-speed axial compressor under rotating inlet distortion (RID) is investigatedin the first half of this paper. The tests demonstrate that the tip leakage flow (TLF) plays an important rolein triggering rotating stall. The tracking of the spike-like disturbances caused by the spillage of TLV indicates thatmost of such spike-like disturbances will be smeared by non-distorted sector and the growth of the spike-like disturbancesactually relate closely to how and how often the path of the propagating disturbances come across thepath of the rotating distorted sector. In the second half of this paper, micro air injections are applied to test the effectbehavior of TLF on stall inception. Contrasts to without micro air injections, the spike-like disturbances aremuch fewer, so the possibilities that spike-like disturbances may trigger rotating stall are fewer too. As a result,the compressor gets a lower mass flow rate at stall for both co-rotating inlet distortion and counter-rotating inletdistortion.
基金supported by the National Natural Science Foundation of China(Grant Nos.10932005 and 11202115)
文摘Nonlinear parabolized stability equations are employed in this work to investigate the nonlinear development of the G6rtler insta- bility up to the saturation stage. The perturbed boundary layer is highly inflectional both in the normalwise and spanwise directions and receptive to the secondary instabilities. The Floquet theory is applied to solve the fundamental, subharmonic and detuned secondary instabilities. With the Gortler-vortices-distorted base flow, two classes of secondary disturbances, i.e. odd modes and even modes, are identified according to the eigenfunctions of the disturbances. These modes may result in different patterns in the late stages of the transition process. Li and Malik [ 1 ] have shown the sinuous and varicose types of breakdown originating from the odd and even modes. The current study focuses on the four most amplified modes termed the even modes I & Ⅱ and odd modes I & lI. Odd mode II was missing in the work of Li and Malik [1] probably due to their inviscid simplifeation. The detuned modes are confirmed to be less amplifed than the fundamental (for the odd mode I) and subharmonic modes (for even modes I & II and the odd mode II).
基金supported by the National Natural Science Foundation of China (Grant No 50805149)China Postdoctoral Science Foundation (Grant No 20090450166/201003669)+2 种基金Chongqing Municipal Intellectual Property Office Special FoundationChongqing Science and Technology Commission Key Project Foundation (CSTC) (Grant No 2009AB3234)Chongqing University Innovation Group Team Project (Grant No KJTD201019)
文摘The research on scroll profiles theory at present mainly is aiming at the single profile and its amelioration or parameter optimization,not aiming at the natural characteristic of the profiles equation of scroll profiles itself.Thus,the intrinsic differential equation bearing on arc-length and tangent direction angle was studied.Using the inherent differential equation and general functional theory,the conversion ideas between the expression of intrinsic differential equation and the expression in Cartesian coordinate was studied,and the condition of involutes characteristic was presented.The detailed analysis of four typical scroll profiles was given.According to the four typical scroll profiles and based on the method of Taylor series,the unified formation of general functional integration scroll profiles was established,which perfected general theory of scroll profiles increasingly.The envelope method to seek conjugation engagement profiles was studied.The unified general functional equation of scroll profiles represented the admissible function scrolls and the conjugation engagement characteristic of which was studied.The engagement condition of conjugation scroll profiles and the expression in Cartesian coordinate of conjugation scroll profiles of general functional integration scroll profiles were educed.Therefore,the restriction of inherent characteristics of single scroll profiles model is broken through.Solid modeling and machine tool path simulation can bridge the gap between design and manufacture which is essential for the design and manufacture of scroll compressors.With this method a perfect solid model can be achieved,which leads to an optimal design in terms of quality,delivery time and cost.The presentation of unified formation of general functional integration scroll profiles represents foundation factor of instinct characteristics of scroll profiles,which widens the design method of scroll compressor for automobile air conditioning.