TOPOLOGICAL STRUCTURES OF VORTEX AND HELICITY ANALYSIS

The topological structures of the vortex filaments and vortex tubes with an exact solution of a straight spiral vortex tube are discussed. It is found that there are some confusions about the calculation of the helicity of a knotted vortex filament and some linked vortex filaments by using different methods. How to unify these methods is explained and the right results are given. (Edited author abstract) 5 Refs.

Topological Structure-Modulated Collagen Carbon as Two-in-One Energy Storage Configuration toward Ultrahigh Power and Energy Density

Efficient energy storage devices with suitable electrode materials,that integrate high power and high energy,are the crucial requisites of the renewable power source,which have unwrapped new possibilities in the sustainable development of energy and the environment.Herein,a facile collagen microstructure modulation strategy is proposed to construct a nitrogen/oxygen dual-doped hierarchically porous carbon fiber with ultrahigh specific surface area(2788 m^(2)g^(-1))and large pore volume(4.56 cm^(3)g^(-1))via local microfibrous breakage/disassembly of natural structured proteins.Combining operando spectroscopy and density functional theory unveil that the dual-heteroatom doping could effectively regulate the electronic structure of carbon atom framework with enhanced electric conductivity and electronegativity as well as decreased diffusion resistance in favor of rapid pseudocapacitive-dominated Li^(+)-storage(353 mAh g^(-1)at 10 A g^(-1)).Theoretical calculations reveal that the tailored micro-/mesoporous structures favor the rapid charge transfer and ion storage,synergistically realizing high capacity and superior rate performance for NPCF-H cathode(75.0 mAh g^(-1)at 30 A g^(-1)).The assembled device with NPCF-H as both anode and cathode achieves extremely high energy density(200 Wh kg^(-1))with maximum power density(42600 W kg^(-1))and ultralong lifespan(80%capacity retention over 10000 cycles).

Topological structures of transition metal dichalcogenides: A review on fabrication, effects, applications, and potential

Transition metal dichalcogenides(TMDs)have received tremendous attention owing to their potential for optoelectronic applications.Topological structures,such as wrinkles,folds,and scrolls,have been generated on TMDs,thereby exhibiting novel physical properties with improved optoelectronic performance,making them attractive prospects for both basic understanding and advanced applications in optoelectronics.In this review,the methods for fabricating wrinkles,folds,and scrolls on TMDs are outlined,including modification of the fabrication and transfer processes,and manipulation via auxiliary polymers.The effects on their physical and electronic properties are also discussed,with particular paid to the energy band structure,single-photon sources,second harmonic generation(SHG),and interlayer coupling.In comparison to pristine TMDs,these topologies exhibit great advantages in optoelectronic devices,such as field-effect transistors and photodetectors.Finally,existing challenges and opportunities of wrinkled,folded,and scrolled TMDs are outlined and an outlook is presented.

TOPOLOGY AND VORTEX STRUCTURES OF A CURVING TURBINE CASCADE WITH TIP CLEARANCE (Ⅰ)- EXPERIMENTAL MODEL AND TOPOLOGICAL FLOW PATTERNS ON BOTH ENDWALLS AND BLADE SURFACES

By means of ink trace visualization of the flows in conventional straight, positively curved and negatively curved cascades with tip clearance, and measurement of the aerodynamic parameters in the transverse section, and by appling topology theory, the structures on both endwalls and blade surfaces were analyzed. Compared with conventional straight cascade, blade positive curving eliminates the separation line of the upper passage vortex and leads the secondary vortex to change from close separation to open separation, while blade negative curving effects merely the positions of singular points and the intensities and scales of vortex.

TOPOLOGY AND VORTEX STRUCTURES OF A CURVING TURBINE CASCADE WITH TIP CLEARANCE (Ⅱ)- TOPOLOGICAL FLOW PATTERN AND VORTEX STRUCTURE IN THE TRANSVERSE SECTION OF A BLADE CASCADE

By means of ink trace visualization of the flows in conventional straight, positively curved and negatively curved cascades with tip clearance, and measurement of the aerodynamic parameters in transverse section, and by appling topology theory, the topological structures and vortex structure in the transverse section of a blade cascade were analyzed. Compared with conventional straight cascade, blade positive curving eliminates the separation line of the upper passage vortex, and leads the secondary vortex to change from close separation to open separation, while blade negative curving effects merely the positions of singular points and the intensities and scales of vortex.

THE TOPOLOGICAL OPTIMIZATION FOR TRUSS STRUCTURES WITH STRESS CONSTRAINTS BASED ON THE EXIST-NULL COMBINED MODEL

A new exist-null combined model is proposed for the structural topology optimization. The model is applied to the topology optimization of the truss with stress constraints. Satisfactory computational result can be obtained with more rapid and more stable convergence as compared with the cross-sectional optimization. This work also shows that the presence of independent and continuous topological variable motivates the research of structural topology optimization.

Elimination of cracks in stainless steel casings via 3D printed sand molds with an internal topology structure

The important supporting component in a gas turbine is the casing,which has the characteristics of large size,complex structure,and thin wall.In the context of existing 3DP sand casting processes,casting crack defects are prone to occur.This leads to an increase in the scrap rate of casings,causing significant resource wastage.Additionally,the presence of cracks poses a significant safety hazard after the casings are put into service.The generation of different types of crack defects in stainless steel casings is closely related to casting stress and the high-temperature concession of the sand mold.Therefore,the types and causes of cracks in stainless steel casing products,based on their structural characteristics,were systematically analyzed.Various sand molds with different internal topology designs were printed using the 3DP technology to investigate the impact of sand mold structures on high-temperature concession.The optimal sand mold structure was used to cast casings,and the crack suppression effect was verified by analyzing its eddy current testing results.The experimental results indicate that the skeleton structure has an excellent effect on suppressing cracks in the casing.This research holds important theoretical and engineering significance in improving the quality of casing castings and reducing production costs.

Space Topologies and Their Dual Space Topologies for Conventional Functional Space Topologies

In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(Rn) of functions of class C∞ on Rn which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C∞ with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.

Study on local topology model of low/high streak structures in wall-bounded turbulence by tomographic time-resolved particle image velocimetry

The relationship between the in the logarithmic law （log-law） region of bursting event and the low/high-speed streak a turbulent boundary layer is investigated. A tomographic time-resolved particle image velocimetry （TRPIV） system is used to measure the instantaneous three-dimensional-three-component （3D-3C） velocity field. The momentum thickness based Reynolds number is about 2 460. The topological information in the log-law region is obtained experimentally. It is found that the existence of the quadrupole topological structure implies a three-pair hairpin-like vortex packet, which is in connection with the low/high-speed streak. An idealized 3D topological model is then proposed to characterize the observed hairpin vortex packet and low/high-speed streak.

STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM(Ⅰ)

Based on the work discussed on the former study, this article first starts from the mathematical model of a kind of complicated financial system, and analyses all possible things that the model shows in the operation of our country's macro_financial system: balance, stable periodic, fractal, Hopf_bifurcation, the relationship between parameters and Hopf_bifurcation, and chaotic motion etc. By the changes of parameters of all economic meanings, the conditions on which the complicated behaviors occur in such a financial system, and the influence of the adjustment of the macro_economic policies and adjustment of some parameter on the whole financial system behavior have been analyzed. This study will deepen people's understanding of the lever function of all kinds of financial policies.

Topology and Vortex Structures of Turbine Cascade with Different Tip Clearances

This paper uses the topology theory to analyze the surface flowspectrums of straight, positively curved and negatively curvedcascades with relative tip clearances of 0.023 and 0.036, findsapparent differences of topology and vortex structures in the bladetip and the suction side wall corner of single type of cascade withthis two clearances, and studies the mechanism of the differenceformation as well as their effects o the energy loss.

Topological analysis of plasma flow control on corner separation in a highly loaded compressor cascade

In this paper, flow behavior and topology structure in a highly loaded compressor cascade with and without plasma aerodynamic actuation （PAA） are investigated. Streamline pattern, total pressure loss coefficient, outlet flow angle and topological analysis are considered to study the effect and mechanism of the plasma flow control on corner separation. Results presented include the boundary layer flow behavior, effects of three types of PAA on separated flows and performance parameters, topology structures and sequences of singular points with and without PAA. Two separation lines, reversed flow and backflow exist on the suction surface. The cross flow on the endwall is an important element for the comer separation. PAA can reduce the undertuming and overturning as well as the total pressure loss, leading to an overall increase of flow turning and enhancement of aerodynamic performance. PAA can change the topology structure, sequences of singular points and their corresponding separation lines. Types II and III PAA are much more efficient in controlling comer separation and enhancing aerodynamic performances than type I.

STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM(Ⅱ)

Based on the work discussed on the former study, this article first starts from the mathematical model of a kind of complicated financial system, and analyses all possible things that the model shows in the operation of our country's macro_financial system: balance, stable periodic, fractal, Hopf_bifurcation, the relationship between parameters and Hopf_bifurcation, and chaotic motion etc. By the changes of parameters of all economic meanings, the conditions on which the complicated behaviors occur in such a financial system, and the influence of the adjustment of the macro_economic policies and adjustment of some parameter on the whole financial system behavior have been analyzed. This study will deepen people's understanding of the lever function of all kinds of financial policies.

TOPOLOGICAL STRUCTURE OF RENORM ALIZATION CONSTANTS I N QUANTUM FIELD THEORY AT SHORT DISTANCE KUNMING COLLABRATION OF MULTIHADRON DYNAMIOS

The anomalous dimensions of the quantum fields are the Hausdorff dimensiongrad. The present candidate of the renormalization constant is the generalized Cantor discontinuum. The Hausdorff dimensiongrad of the Minkowski space time is based upon the point set with σ-length on light cone.

Concurrent multi-scale design optimization of composite frame structures using the Heaviside penalization of discrete material model

This paper deals with the concurrent multi-scale optimization design of frame structure composed of glass or carbon fiber reinforced polymer laminates. In the composite frame structure, the fiber winding angle at the micro-material scale and the geometrical parameter of components of the frame in the macro-structural scale are introduced as the independent variables on the two geometrical scales. Considering manufacturing requirements, discrete fiber winding angles are specified for the micro design variable. The improved Heaviside penalization discrete material optimization interpolation scheme has been applied to achieve the discrete optimization design of the fiber winding angle. An optimization model based on the minimum structural compliance and the specified fiber material volume constraint has been established. The sensitivity information about the two geometrical scales design variables are also deduced considering the characteristics of discrete fiber winding angles. The optimization results of the fiber winding angle or the macro structural topology on the two single geometrical scales, together with the concurrent two-scale optimization, is separately studied and compared in the paper. Numerical examples in the paper show that the concurrent multi-scale optimization can further explore the coupling effect between the macro-structure and micro-material of the composite to achieve an ultralight design of the composite frame structure. The novel two geometrical scales optimization model provides a new opportunity for the design of composite structure in aerospace and other industries.

A review of the design methods of complex topology structures for 3D printing

As a matter of fact,most natural structures are complex topology structures with intricate holes or irregular surface morphology.These structures can be used as lightweight infill,porous scaffold,energy absorber or micro-reactor.With the rapid advancement of 3D printing,the complex topology structures can now be efficiently and accurately fabricated by stacking layered materials.The novel manufacturing technology and application background put forward new demands and challenges to the current design methodologies of complex topology structures.In this paper,a brief review on the development of recent complex topology structure design methods was provided;meanwhile,the limitations of existing methods and future work are also discussed in the end.

Community detection with consideration of non-topological information

In a network described by a graph, only topological structure information is considered to determine how the nodes are connected by edges. Non-topological information denotes that which cannot be determined directly from topological information. This paper shows, by a simple example where scientists in three research groups and one external group form four communities, that in some real world networks non-topological information （in this example, the research group affiliation） dominates community division. If the information has some influence on the network topological structure, the question arises as to how to find a suitable algorithm to identify the communities based only on the network topology. We show that weighted Newman algorithm may be the best choice for this example. We believe that this idea is general for real-world complex networks.

Topological structure effect on far-infrared spectra in a GaAs/InAs nanoring

On the basis of the growth mechanism of a GaAs/InAs nanoring, we propose a fine model which reflects the confinement details of real nanoring. Through calculations of the two-electron energy and far-infrared （FIR） spectra, we find that the ring topological structure and electron-electron interaction have great influence on the FIR spectra. The two unknown transition peaks in the experiment are determined theoretically. The theoretical results are in good agreement with the experiments.

TOPOLOGICAL STRUCTURE OF THE SINGULAR POINTS OF THE THIRD ORDER PHASE LOCKED LOOP EQUATIONS WITH THE CHARACTER OF DETECTED PHASE BEING g(φ)=(1+k)sinφ/(1+kcosφ)

In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with the character of detected phase being g(?) =(1+k)sin?/1+kcos?.

Topological Structure of Vortex Solution in Jackiw-Pi Model

By using φ-mapping method,we discuss the topological structure of the self-duality solution in Jackiw-Pimodel in terms of gauge potential decomposition.We set up relationship between Chern-Simons vortex solution andtopological number,which is determined by Hopf index and Brouwer degree.We also give the quantization of flux inthis ease.Then,we study the angular momentum of the vortex,which can be expressed in terms of,the flux.