This is a survey of local and global classification results concerning Dupin hypersurfaces in S^(n)(or R^(n))that have been obtained in the context of Lie sphere geometry.The emphasis is on results that relate Dupin h...This is a survey of local and global classification results concerning Dupin hypersurfaces in S^(n)(or R^(n))that have been obtained in the context of Lie sphere geometry.The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres.Along with these classification results,many important concepts from Lie sphere geometry,such as curvature spheres,Lie curvatures,and Legendre lifts of submanifolds of S^(n)(or R^(n)),are described in detail.The paper also contains several important constructions of Dupin hypersurfaces with certain special properties.展开更多
Collisions between objects are a relatively common phenomenon in nature.Analyses of collision processes can greatly contribute to solving problems such as impact-rub faults and particle impacts.The coefficient of rest...Collisions between objects are a relatively common phenomenon in nature.Analyses of collision processes can greatly contribute to solving problems such as impact-rub faults and particle impacts.The coefficient of restitution is a critical parameter in the analysis of collision processes.Many experiments have shown that the coefficient of restitution is closely related to the plate thickness,and the smaller the plate thickness,the more inaccurate the coefficient of restitution predicted by the existing model,which seriously affects the process of collision analysis.To remedy this shortcoming,this paper proposes a plate thickness influence factor with the ratio of sphere diameter to plate thickness as the variable.The plate thickness influence factor can optimize the coefficient of restitution model to effectively predict the coefficient of restitution of impacting elastoplastic spheres with finite plate thickness.Finally,the validity of the new model is verified using a large amount of experimental data.展开更多
Sodium-sulfur(Na-S)and potassium-sulfur(K-S)batteries for use at room temperature have received widespread attention because of the abundance and low cost of their raw materials and their high energy density.However,t...Sodium-sulfur(Na-S)and potassium-sulfur(K-S)batteries for use at room temperature have received widespread attention because of the abundance and low cost of their raw materials and their high energy density.However,their development is restricted by the shuttling of polysulfides,large volume expansion and poor conductivity.To overcome these obstacles,an effective approach is to use carbon-based materials with abundant space for the sulfur that has sulfiphilic sites to immobilize it,and a high electrical conductivity.Hollow carbon spheres(HCSs)with a controllable structure and composition are promising for this purpose.We consider recent progress in optimizing the electrochemical performance of Na-/K-S batteries by using these materials.First,the advantages of HCSs,their synthesis methods,and strategies for preparing HCSs/sulfur composite materials are reviewed.Second,the use of HCSs in Na-/K-S batteries,along with mechanisms underlying the resulting performance improvement,are discussed.Finally,prospects for the further development of HCSs for metal−S batteries are presented.展开更多
Incorporating a selenium(Se)positive electrode into aluminum(Al)-ion batteries is an effective strategy for improving the overall battery performance.However,the cycling stability of Se positive electrodes has challen...Incorporating a selenium(Se)positive electrode into aluminum(Al)-ion batteries is an effective strategy for improving the overall battery performance.However,the cycling stability of Se positive electrodes has challenges due to the dissolution of intermediate reaction products.In this work,we aim to harness the advantages of Se while reducing its limitations by preparing a core-shell mesoporous carbon hollow sphere with a titanium nitride(C@TiN)host to load 63.9wt%Se as the positive electrode material for Al-Se batteries.Using the physical and chemical confinement offered by the hollow mesoporous carbon and TiN,the obtained core-shell mesoporous carbon hollow spheres coated with Se(Se@C@TiN)display superior utilization of the active material and remarkable cycling stability.As a result,Al-Se batteries equipped with the as-prepared Se@C@TiN composite positive electrodes show an initial discharge specific capacity of 377 mAh·g^(-1)at a current density of 1000 mA·g^(-1)while maintaining a discharge specific capacity of 86.0 mAh·g^(-1)over 200 cycles.This improved cycling performance is ascribed to the high electrical conductivity of the core-shell mesoporous carbon hollow spheres and the unique three-dimensional hierarchical architecture of Se@C@TiN.展开更多
Electrochemical CO_(2) reduction to produce value-added chemicals and fuels is one of the research hotspots in the field of energy conversion.The development of efficient catalysts with high conductivity and readily a...Electrochemical CO_(2) reduction to produce value-added chemicals and fuels is one of the research hotspots in the field of energy conversion.The development of efficient catalysts with high conductivity and readily accessible active sites for CO_(2) electroreduction remains challenging yet indispensable.In this work,a reliable poly(ethyleneimine)(PEI)-assisted strategy is developed to prepare a hollow carbon nanocomposite comprising a single-site Ni-modified carbon shell and confined Ni nanoparticles(NPs)(denoted as Ni@NHCS),where PEI not only functions as a mediator to induce the highly dispersed growth of Ni NPs within hollow carbon spheres,but also as a nitrogen precursor to construct highly active atomically-dispersed Ni-Nx sites.Benefiting from the unique structural properties of Ni@NHCS,the aggregation and exposure of Ni NPs can be effectively prevented,while the accessibility of abundant catalytically active Ni-Nx sites can be ensured.As a result,Ni@NHCS exhibits a high CO partial current density of 26.9 mA cm^(-2) and a Faradaic efficiency of 93.0% at-1.0 V vs.RHE,outperforming those of its PEI-free analog.Apart from the excellent activity and selectivity,the shell confinement effect of the hollow carbon sphere endows this catalyst with long-term stability.The findings here are anticipated to help understand the structure-activity relationship in Ni-based carbon catalyst systems for electrocatalytic CO_(2) reduction.Furthermore,the PEI-assisted synthetic concept is potentially applicable to the preparation of high-performance metal-based nanoconfined materials tailored for diverse energy conversion applications and beyond.展开更多
The paper is devoted to a spherically symmetric problem of General Relativity (GR) for a fluid sphere. The problem is solved within the framework of a special geometry of the Riemannian space induced by gravitation. A...The paper is devoted to a spherically symmetric problem of General Relativity (GR) for a fluid sphere. The problem is solved within the framework of a special geometry of the Riemannian space induced by gravitation. According to this geometry, the four-dimensional Riemannian space is assumed to be Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate. Such interpretation of the Riemannian space allows us to obtain complete set of GR equations for the external empty space and the internal spaces for incompressible and compressible perfect fluids. The obtained analytical solution for an incompressible fluid is compared with the Schwarzchild solution. For a sphere consisting of compressible fluid or gas, a numerical solution is presented and discussed.展开更多
We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We ...We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We provide the mathematical definitions of Hamiltonians and obtain new results for both models, in particular the resolvents equations, spectral properties and some scattering quantities.展开更多
Rechargeable magnesium batteries(RMBs),as one of the most promising candidates for efficient energy storage devices with high energy,power density and high safety,have attracted increasing attention.However,searching ...Rechargeable magnesium batteries(RMBs),as one of the most promising candidates for efficient energy storage devices with high energy,power density and high safety,have attracted increasing attention.However,searching for suitable cathode materials with fast diffusion kinetics and exploring their magnesium storage mechanisms remains a great challenge.Cu S submicron spheres,made by a facile low-temperature synthesis strategy,were applied as the high-performance cathode for RMBs in this work,which can deliver a high specific capacity of 396mAh g^(-1)at 20 mA g^(-1) and a remarkable rate capacity of 250 m Ah g^(-1)at 1000 mA g^(-1).The excellent rate performance can be assigned to the nano needle-like particles on the surface of Cu S submicron spheres,which can facilitate the diffusion kinetics of Mg^(2+).Further storage mechanism investigations illustrate that the Cu S cathodes experience a two-step conversion reaction controlled by diffusion during the electrochemical reaction process.This work could make a contribution to the study of the enhancement of diffusion kinetics of Mg2+and the reaction mechanism of RMBs.展开更多
The strong metal-support interaction inducing combined effect plays a crucial role in the catalysis reaction. Herein, we revealed that the combined advantages of MoSe_(2), Ru, and hollow carbon spheres in the form of ...The strong metal-support interaction inducing combined effect plays a crucial role in the catalysis reaction. Herein, we revealed that the combined advantages of MoSe_(2), Ru, and hollow carbon spheres in the form of Ru nanoparticles(NPs) anchored on a two-dimensionally ordered MoSe_(2) nanosheet-embedded mesoporous hollow carbon spheres surface(Ru/MoSe_(2)@MHCS) for the largely boosted hydrogen evolution reaction(HER) performance. The combined advantages from the conductive support, oxyphilic MoSe_(2), and Ru active sites imparted a strong synergistic effect and charge redistribution in the Ru periphery which induced high catalytic activity, stability, and kinetics for HER. Specifically, the obtained Ru/MoSe_(2)@MHCS required a small overpotential of 25.5 and 38.4 mV to drive the kinetic current density of 10 mA cm^(-2)both in acid and alkaline media, respectively, which was comparable to that of the Pt/C catalyst. Experimental and theoretical results demonstrated that the charge transfer from MoSe_(2) to Ru NPs enriched the electronic density of Ru sites and thus facilitated hydrogen adsorption and water dissociation. The current work showed the significant interfacial engineering in Ru-based catalysts development and catalysis promotion effect understanding via the metal-support interaction.展开更多
Iron is commonly used as a structural and shielding material in nuclear devices. The accuracy of its nuclear data is critical for the design of nuclear devices. The evaluation data of ^(56)Fe isotopes in the latest ve...Iron is commonly used as a structural and shielding material in nuclear devices. The accuracy of its nuclear data is critical for the design of nuclear devices. The evaluation data of ^(56)Fe isotopes in the latest version of the CENDL-3.2 library from China was significantly updated. This new data must be tested before it can be used. To test the reliability of this data and assess the shielding effect, a shielding benchmark experiment was conducted with natural Fe spherical samples using a pulsed deuterium–tritium neutron source at the China Institute of Atomic Energy(CIAE). The leakage neutron spectra from the natural spherical iron samples with different thicknesses(4.5, 7.5, and 12 cm) were measured between 0.8 and 16 MeV after interacting with 14 MeV neutrons using the time-of-flight method. The simulation results were obtained by Monte Carlo simulations by employing the Fe data from the CENDL-3.2, ENDF/B-VIII.0, and JEDNL-5.0 libraries. The measured and simulated leakage neutron spectra and penetration rates were compared, demonstrating that the CENDL-3.2 library performs sufficiently overall. The simulation results of the other two libraries were underestimated for scattering at the continuum energy level.展开更多
Failure of irregular rock samples may provide implications in the rapid estimation of rock strength,which is imperative in rock engineering practice.In this work,analytical,experimental and numerical investigations we...Failure of irregular rock samples may provide implications in the rapid estimation of rock strength,which is imperative in rock engineering practice.In this work,analytical,experimental and numerical investigations were carried out to study the mechanical properties and failure characteristics of rock spheres under paired point loads.Analytical solutions indicted that with the increase in sample size(contact angle)and decrease in Poisson’s ratio,the uneven tensile stress in theta direction decreased.Then laboratory experiments were carried out to investigate the load characteristics and failure mode of spherical marble samples with different sizes subjected to a pair of diametral point loads.The discrete element method(DEM)was adopted to study the failure process of rock spheres.The effect of the sphere diameter on the point load contact angle was examined in terms of peak load,crushed zone distribution and energy dissipation.Experimental and numerical results showed that the samples primarily fail in tension,with crushed zones formed at both loading points.With increase in the sample size,the contact angle,crushed area and total work increase.As the specimen diameter increases from 30 mm to 50 mm,the peak load on the specimen increases from 3.6 kN to 8.8 kN,and the percentage of crushed zone(ratio of crushing zone to sample radius,d/r)increased from 0.191 to 0.262.The results of the study have implications for understanding the failure of irregular rock specimens under point loading conditions and their size effects.展开更多
To develop and utilize marine resources in the deep sea, the higher requirements for floating structures, which are operated in marine environment for a long term, have been put forward. Reasonable structure type and ...To develop and utilize marine resources in the deep sea, the higher requirements for floating structures, which are operated in marine environment for a long term, have been put forward. Reasonable structure type and accurate force analysis are favorable guarantees to improve the survival performance and working performance of the floating structures. Floating spheres fastened by mooring cable were widely used in floating structures. In this paper, the wave forces of the floating sphere are efficiently and accurately calculated by solving the geometric relationship between the non-submerged floating sphere and wave surface. Combined with the hydrodynamic calculation of mooring cables based on the lumped mass method, the coupled motion model of multi-floating spheres fastened by multi-mooring cable was established under wave action. Furthermore, according to the floating structures fastened by mooring cable in the actual ocean engineering, the topological method of multi-mooring cables fastening the multifloating spheres was expounded from simple to complex. Finally, the modeling method and preliminarily hydrodynamic characteristics of the fastened floating structures, including the mooring system of renewable energy devices, ocean buoy, and coral nursery, were presented and analyzed in detail. The obtained results showed that the method for calculating the wave force on the floating sphere developed in this paper can accurately describe the motion process of the floating mooring sphere and the force on the mooring cable. Also, the topological method of multiple buoys and multiple mooring cables could efficiently establish various numerical hydrodynamic models of fastened buoys in ocean engineering.展开更多
This paper studies two isometric problems between unit spheres of Banach spaces.In the first part,we introduce and study the Figiel type problem of isometric embeddings between unit spheres.However,the classical Figie...This paper studies two isometric problems between unit spheres of Banach spaces.In the first part,we introduce and study the Figiel type problem of isometric embeddings between unit spheres.However,the classical Figiel theorem on the whole space cannot be trivially generalized to this case,and this is pointed out by a counterexample.After establishing this,we find a natural necessary condition required by the existence of the Figiel operator.Furthermore,we prove that when X is a space with the T-property,this condition is also sufficient for an isometric embedding T:S_(X)→S_(Y) to admit the Figiel operator.This answers the Figiel type problem on unit spheres for a large class of spaces.In the second part,we consider the extension of bijectiveε-isometries between unit spheres of two Banach spaces.It is shown that every bijectiveε-isometry between unit spheres of a local GL-space and another Banach space can be extended to be a bijective 5ε-isometry between the corresponding unit balls.In particular,whenε=0,this recovers the MUP for local GL-spaces obtained in[40].展开更多
This paper presents a novel experiment to observe the whole water entry process of a free-falling sphere into a regular wave.A time-accurate synchronizing system modulates the moment elaborately to ensure the sphere i...This paper presents a novel experiment to observe the whole water entry process of a free-falling sphere into a regular wave.A time-accurate synchronizing system modulates the moment elaborately to ensure the sphere impacting onto the water surface at the desirable wave phase.Four high-speed cameras focus locally to measure the high-precision size of the cavity evolution.Meanwhile,the aggregated field view of the camera array covers both the splash above the free surface and the entire cavity in the wave.The detailed methodologies are described and verified for the hardware set-up and the image post-processing.The theoretical maximum deviation is 1.7%on the space scale.The integral morphology of the cavity is captured precisely in the coordinate system during the sphere penetrates through the water at four representative wave phases and the still water.The result shows that the horizontal velocity of the fluid particle in the wave impels the cavity and changes the shape distinctly.Notably,the wave motion causes the cavity to pinch offearlier at the wave trough phase and later at the wave crest phase than in the still water.The wave motion influences the falling process of the sphere slightly in the present parameters.展开更多
In this paper,we propose a novel approach to visualizing global geographical information:a panoramic sphere in an immersive environment.The whole geographical surface can be observed through the rotating of heads as t...In this paper,we propose a novel approach to visualizing global geographical information:a panoramic sphere in an immersive environment.The whole geographical surface can be observed through the rotating of heads as the viewpoint of the panoramic sphere is inside the sphere.We compared three approaches to visualizing the earth for rendering the geographical information in a virtual reality environment.On the tasks of terrestrial and marine geographical information,we compare the visualization effects on a)a globe,b)a flat map and c)a panoramic sphere.Terrestrial geographical information tasks include the area comparison and direction determination.Marine geographical information tasks contain the visualization of sea surface temperature and sea surface currents.For terrestrial geographical information tasks,the experimental results show that the panoramic sphere outperforms the globe and the flat map,with a higher average accuracy and a shorter time.On marine geographical information task,the panoramic sphere visualization is also superior to the flat map and the globe in an immersive environment for the sea surface temperature data and the sea surface current fields.In all three visualization experiments,the panoramic sphere is most preferred by the participants,particularly for global,transcontinental and transoceanic needs.展开更多
The paper is devoted to a spherically symmetric problem of General Relativity (GR) for an elastic solid sphere. Originally developed to describe gravitation in continuum (vacuum, gas, fluid and solid) GR does not prov...The paper is devoted to a spherically symmetric problem of General Relativity (GR) for an elastic solid sphere. Originally developed to describe gravitation in continuum (vacuum, gas, fluid and solid) GR does not provide the complete set of equations for solids and, in contrast to the Newton gravitation theory, does not allow us to study the stresses induced by gravitation in solids, because the compatibility equations which are attracted in the Euclidean space for this purpose do not exist in the Riemannian space. To solve the problem within the framework of GR, a special geometry of the Riemannian space induced by gravitation is proposed. According to this geometry, the four-dimensional Riemannian space is assumed to be Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate. Such interpretation of the Riemannian space in GR allows us to supplement the conservation equations for the energy-momentum tensor with compatibility equations of the theory of elasticity and to arrive to the complete set of equations for stresses. The analytical solution of the Einstein equations for the empty space surrounding the sphere and the numerical solution for the internal space inside the sphere with the proposed geometry are presented and discussed.展开更多
Energy conversion technologies like fuel cells and metal-air batteries require oxygen reduction reaction(ORR)electrocatalysts with low cost and high catalytic activity.Herein,N-doped carbon spheres(N-CS)with rich micr...Energy conversion technologies like fuel cells and metal-air batteries require oxygen reduction reaction(ORR)electrocatalysts with low cost and high catalytic activity.Herein,N-doped carbon spheres(N-CS)with rich micropore structure have been synthesized by a facile two-step method,which includes the polymerization of pyrrole and formaldehyde and followed by a facile pyrolysis process.During the preparation,zinc chloride(ZnCl2)was utilized as a catalyst to promote polymerization and provide a hypersaline environment.In addition,the morphology,defect content and activity area of the resultant N-CS catalysts could be regulated by controlling the content of ZnCl2.The optimum N-CS-1 catalyst demonstrated much better catalytic activity and durability towards ORR in alkaline conditions than commercial 20 wt%Pt/C catalysts,of which the half-wave potential reached 0.844 V vs.RHE.When applied in the Zn-air batteries as cathode catalysts,N-CS-1 showed a maximum power density of 175 mW cm^(-2) and long-term discharging stability of over 150 h at 10 mA cm^(-2),which outperformed 20 wt%Pt/C.The excellent performance could be due to its ultrahigh specific surface area of 1757 m2 g1 and rich micropore channels structure.Meanwhile,this work provides an efficient method to synthesize an ultrahigh surface porous carbon material,especially for catalyst application.展开更多
文摘This is a survey of local and global classification results concerning Dupin hypersurfaces in S^(n)(or R^(n))that have been obtained in the context of Lie sphere geometry.The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres.Along with these classification results,many important concepts from Lie sphere geometry,such as curvature spheres,Lie curvatures,and Legendre lifts of submanifolds of S^(n)(or R^(n)),are described in detail.The paper also contains several important constructions of Dupin hypersurfaces with certain special properties.
基金Supported by Joint Fund of the Ministry of Education of China (Grant No.8091B022203)Youth Talent Support Project (Grant No.2022-JCJQ-QT-059)。
文摘Collisions between objects are a relatively common phenomenon in nature.Analyses of collision processes can greatly contribute to solving problems such as impact-rub faults and particle impacts.The coefficient of restitution is a critical parameter in the analysis of collision processes.Many experiments have shown that the coefficient of restitution is closely related to the plate thickness,and the smaller the plate thickness,the more inaccurate the coefficient of restitution predicted by the existing model,which seriously affects the process of collision analysis.To remedy this shortcoming,this paper proposes a plate thickness influence factor with the ratio of sphere diameter to plate thickness as the variable.The plate thickness influence factor can optimize the coefficient of restitution model to effectively predict the coefficient of restitution of impacting elastoplastic spheres with finite plate thickness.Finally,the validity of the new model is verified using a large amount of experimental data.
文摘Sodium-sulfur(Na-S)and potassium-sulfur(K-S)batteries for use at room temperature have received widespread attention because of the abundance and low cost of their raw materials and their high energy density.However,their development is restricted by the shuttling of polysulfides,large volume expansion and poor conductivity.To overcome these obstacles,an effective approach is to use carbon-based materials with abundant space for the sulfur that has sulfiphilic sites to immobilize it,and a high electrical conductivity.Hollow carbon spheres(HCSs)with a controllable structure and composition are promising for this purpose.We consider recent progress in optimizing the electrochemical performance of Na-/K-S batteries by using these materials.First,the advantages of HCSs,their synthesis methods,and strategies for preparing HCSs/sulfur composite materials are reviewed.Second,the use of HCSs in Na-/K-S batteries,along with mechanisms underlying the resulting performance improvement,are discussed.Finally,prospects for the further development of HCSs for metal−S batteries are presented.
基金supported by the National Natural Science Foundation of China(No.52374350)China Postdoctoral Science Foundation(Nos.2020M680347 and 2021T140051)the Fundamental Research Funds for the Central Universities(No.FRF-TP-20-045A1)。
文摘Incorporating a selenium(Se)positive electrode into aluminum(Al)-ion batteries is an effective strategy for improving the overall battery performance.However,the cycling stability of Se positive electrodes has challenges due to the dissolution of intermediate reaction products.In this work,we aim to harness the advantages of Se while reducing its limitations by preparing a core-shell mesoporous carbon hollow sphere with a titanium nitride(C@TiN)host to load 63.9wt%Se as the positive electrode material for Al-Se batteries.Using the physical and chemical confinement offered by the hollow mesoporous carbon and TiN,the obtained core-shell mesoporous carbon hollow spheres coated with Se(Se@C@TiN)display superior utilization of the active material and remarkable cycling stability.As a result,Al-Se batteries equipped with the as-prepared Se@C@TiN composite positive electrodes show an initial discharge specific capacity of 377 mAh·g^(-1)at a current density of 1000 mA·g^(-1)while maintaining a discharge specific capacity of 86.0 mAh·g^(-1)over 200 cycles.This improved cycling performance is ascribed to the high electrical conductivity of the core-shell mesoporous carbon hollow spheres and the unique three-dimensional hierarchical architecture of Se@C@TiN.
文摘Electrochemical CO_(2) reduction to produce value-added chemicals and fuels is one of the research hotspots in the field of energy conversion.The development of efficient catalysts with high conductivity and readily accessible active sites for CO_(2) electroreduction remains challenging yet indispensable.In this work,a reliable poly(ethyleneimine)(PEI)-assisted strategy is developed to prepare a hollow carbon nanocomposite comprising a single-site Ni-modified carbon shell and confined Ni nanoparticles(NPs)(denoted as Ni@NHCS),where PEI not only functions as a mediator to induce the highly dispersed growth of Ni NPs within hollow carbon spheres,but also as a nitrogen precursor to construct highly active atomically-dispersed Ni-Nx sites.Benefiting from the unique structural properties of Ni@NHCS,the aggregation and exposure of Ni NPs can be effectively prevented,while the accessibility of abundant catalytically active Ni-Nx sites can be ensured.As a result,Ni@NHCS exhibits a high CO partial current density of 26.9 mA cm^(-2) and a Faradaic efficiency of 93.0% at-1.0 V vs.RHE,outperforming those of its PEI-free analog.Apart from the excellent activity and selectivity,the shell confinement effect of the hollow carbon sphere endows this catalyst with long-term stability.The findings here are anticipated to help understand the structure-activity relationship in Ni-based carbon catalyst systems for electrocatalytic CO_(2) reduction.Furthermore,the PEI-assisted synthetic concept is potentially applicable to the preparation of high-performance metal-based nanoconfined materials tailored for diverse energy conversion applications and beyond.
文摘The paper is devoted to a spherically symmetric problem of General Relativity (GR) for a fluid sphere. The problem is solved within the framework of a special geometry of the Riemannian space induced by gravitation. According to this geometry, the four-dimensional Riemannian space is assumed to be Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate. Such interpretation of the Riemannian space allows us to obtain complete set of GR equations for the external empty space and the internal spaces for incompressible and compressible perfect fluids. The obtained analytical solution for an incompressible fluid is compared with the Schwarzchild solution. For a sphere consisting of compressible fluid or gas, a numerical solution is presented and discussed.
文摘We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We provide the mathematical definitions of Hamiltonians and obtain new results for both models, in particular the resolvents equations, spectral properties and some scattering quantities.
基金the support from the Fundamental Research Funds for the Central Universities of Chongqing University(No.2020CDCGCL005)。
文摘Rechargeable magnesium batteries(RMBs),as one of the most promising candidates for efficient energy storage devices with high energy,power density and high safety,have attracted increasing attention.However,searching for suitable cathode materials with fast diffusion kinetics and exploring their magnesium storage mechanisms remains a great challenge.Cu S submicron spheres,made by a facile low-temperature synthesis strategy,were applied as the high-performance cathode for RMBs in this work,which can deliver a high specific capacity of 396mAh g^(-1)at 20 mA g^(-1) and a remarkable rate capacity of 250 m Ah g^(-1)at 1000 mA g^(-1).The excellent rate performance can be assigned to the nano needle-like particles on the surface of Cu S submicron spheres,which can facilitate the diffusion kinetics of Mg^(2+).Further storage mechanism investigations illustrate that the Cu S cathodes experience a two-step conversion reaction controlled by diffusion during the electrochemical reaction process.This work could make a contribution to the study of the enhancement of diffusion kinetics of Mg2+and the reaction mechanism of RMBs.
基金supported by the National Natural Science Foundation of China (21972124, 22272148)the Priority Academic Program Development of Jiangsu Higher Education Institution。
文摘The strong metal-support interaction inducing combined effect plays a crucial role in the catalysis reaction. Herein, we revealed that the combined advantages of MoSe_(2), Ru, and hollow carbon spheres in the form of Ru nanoparticles(NPs) anchored on a two-dimensionally ordered MoSe_(2) nanosheet-embedded mesoporous hollow carbon spheres surface(Ru/MoSe_(2)@MHCS) for the largely boosted hydrogen evolution reaction(HER) performance. The combined advantages from the conductive support, oxyphilic MoSe_(2), and Ru active sites imparted a strong synergistic effect and charge redistribution in the Ru periphery which induced high catalytic activity, stability, and kinetics for HER. Specifically, the obtained Ru/MoSe_(2)@MHCS required a small overpotential of 25.5 and 38.4 mV to drive the kinetic current density of 10 mA cm^(-2)both in acid and alkaline media, respectively, which was comparable to that of the Pt/C catalyst. Experimental and theoretical results demonstrated that the charge transfer from MoSe_(2) to Ru NPs enriched the electronic density of Ru sites and thus facilitated hydrogen adsorption and water dissociation. The current work showed the significant interfacial engineering in Ru-based catalysts development and catalysis promotion effect understanding via the metal-support interaction.
基金supported by the National Natural Science Foundation of China (No. 11775311)。
文摘Iron is commonly used as a structural and shielding material in nuclear devices. The accuracy of its nuclear data is critical for the design of nuclear devices. The evaluation data of ^(56)Fe isotopes in the latest version of the CENDL-3.2 library from China was significantly updated. This new data must be tested before it can be used. To test the reliability of this data and assess the shielding effect, a shielding benchmark experiment was conducted with natural Fe spherical samples using a pulsed deuterium–tritium neutron source at the China Institute of Atomic Energy(CIAE). The leakage neutron spectra from the natural spherical iron samples with different thicknesses(4.5, 7.5, and 12 cm) were measured between 0.8 and 16 MeV after interacting with 14 MeV neutrons using the time-of-flight method. The simulation results were obtained by Monte Carlo simulations by employing the Fe data from the CENDL-3.2, ENDF/B-VIII.0, and JEDNL-5.0 libraries. The measured and simulated leakage neutron spectra and penetration rates were compared, demonstrating that the CENDL-3.2 library performs sufficiently overall. The simulation results of the other two libraries were underestimated for scattering at the continuum energy level.
文摘Failure of irregular rock samples may provide implications in the rapid estimation of rock strength,which is imperative in rock engineering practice.In this work,analytical,experimental and numerical investigations were carried out to study the mechanical properties and failure characteristics of rock spheres under paired point loads.Analytical solutions indicted that with the increase in sample size(contact angle)and decrease in Poisson’s ratio,the uneven tensile stress in theta direction decreased.Then laboratory experiments were carried out to investigate the load characteristics and failure mode of spherical marble samples with different sizes subjected to a pair of diametral point loads.The discrete element method(DEM)was adopted to study the failure process of rock spheres.The effect of the sphere diameter on the point load contact angle was examined in terms of peak load,crushed zone distribution and energy dissipation.Experimental and numerical results showed that the samples primarily fail in tension,with crushed zones formed at both loading points.With increase in the sample size,the contact angle,crushed area and total work increase.As the specimen diameter increases from 30 mm to 50 mm,the peak load on the specimen increases from 3.6 kN to 8.8 kN,and the percentage of crushed zone(ratio of crushing zone to sample radius,d/r)increased from 0.191 to 0.262.The results of the study have implications for understanding the failure of irregular rock specimens under point loading conditions and their size effects.
基金financially supported by the National Natural Science Foundation of China (Grant No.52101330)the Basic Scientific Research Foundation of Zhejiang Provincial Universities (Grant No.2022J004)。
文摘To develop and utilize marine resources in the deep sea, the higher requirements for floating structures, which are operated in marine environment for a long term, have been put forward. Reasonable structure type and accurate force analysis are favorable guarantees to improve the survival performance and working performance of the floating structures. Floating spheres fastened by mooring cable were widely used in floating structures. In this paper, the wave forces of the floating sphere are efficiently and accurately calculated by solving the geometric relationship between the non-submerged floating sphere and wave surface. Combined with the hydrodynamic calculation of mooring cables based on the lumped mass method, the coupled motion model of multi-floating spheres fastened by multi-mooring cable was established under wave action. Furthermore, according to the floating structures fastened by mooring cable in the actual ocean engineering, the topological method of multi-mooring cables fastening the multifloating spheres was expounded from simple to complex. Finally, the modeling method and preliminarily hydrodynamic characteristics of the fastened floating structures, including the mooring system of renewable energy devices, ocean buoy, and coral nursery, were presented and analyzed in detail. The obtained results showed that the method for calculating the wave force on the floating sphere developed in this paper can accurately describe the motion process of the floating mooring sphere and the force on the mooring cable. Also, the topological method of multiple buoys and multiple mooring cables could efficiently establish various numerical hydrodynamic models of fastened buoys in ocean engineering.
基金the National Nature Science Foundation of China(11671214,11971348,12071230)the Hundred Young Academia Leaders Program of Nankai University(63223027,ZB22000105)+1 种基金the Undergraduate Education and Teaching Project of Nankai University(NKJG2022053)the National College Students’Innovation and Entrepreneurship Training Program of Nankai University(202210055048)。
文摘This paper studies two isometric problems between unit spheres of Banach spaces.In the first part,we introduce and study the Figiel type problem of isometric embeddings between unit spheres.However,the classical Figiel theorem on the whole space cannot be trivially generalized to this case,and this is pointed out by a counterexample.After establishing this,we find a natural necessary condition required by the existence of the Figiel operator.Furthermore,we prove that when X is a space with the T-property,this condition is also sufficient for an isometric embedding T:S_(X)→S_(Y) to admit the Figiel operator.This answers the Figiel type problem on unit spheres for a large class of spaces.In the second part,we consider the extension of bijectiveε-isometries between unit spheres of two Banach spaces.It is shown that every bijectiveε-isometry between unit spheres of a local GL-space and another Banach space can be extended to be a bijective 5ε-isometry between the corresponding unit balls.In particular,whenε=0,this recovers the MUP for local GL-spaces obtained in[40].
基金sponsored by the National Natural Sci-ence Foundation of China(Grant Nos.12102262,U22136010 and 11632012).
文摘This paper presents a novel experiment to observe the whole water entry process of a free-falling sphere into a regular wave.A time-accurate synchronizing system modulates the moment elaborately to ensure the sphere impacting onto the water surface at the desirable wave phase.Four high-speed cameras focus locally to measure the high-precision size of the cavity evolution.Meanwhile,the aggregated field view of the camera array covers both the splash above the free surface and the entire cavity in the wave.The detailed methodologies are described and verified for the hardware set-up and the image post-processing.The theoretical maximum deviation is 1.7%on the space scale.The integral morphology of the cavity is captured precisely in the coordinate system during the sphere penetrates through the water at four representative wave phases and the still water.The result shows that the horizontal velocity of the fluid particle in the wave impels the cavity and changes the shape distinctly.Notably,the wave motion causes the cavity to pinch offearlier at the wave trough phase and later at the wave crest phase than in the still water.The wave motion influences the falling process of the sphere slightly in the present parameters.
基金This research was funded by the Science and Technology Innovation Project for Laoshan Laboratory(No.LSKJ202204303)the National Natural Science Foundation of China(No.42030406)+1 种基金the Fundamental Research Funds for the Central Universities(No.202261006)the ESANRSCC Scientific Cooperation Project on Earth Observation Science and Applications:Dragon 5(No.58393).
文摘In this paper,we propose a novel approach to visualizing global geographical information:a panoramic sphere in an immersive environment.The whole geographical surface can be observed through the rotating of heads as the viewpoint of the panoramic sphere is inside the sphere.We compared three approaches to visualizing the earth for rendering the geographical information in a virtual reality environment.On the tasks of terrestrial and marine geographical information,we compare the visualization effects on a)a globe,b)a flat map and c)a panoramic sphere.Terrestrial geographical information tasks include the area comparison and direction determination.Marine geographical information tasks contain the visualization of sea surface temperature and sea surface currents.For terrestrial geographical information tasks,the experimental results show that the panoramic sphere outperforms the globe and the flat map,with a higher average accuracy and a shorter time.On marine geographical information task,the panoramic sphere visualization is also superior to the flat map and the globe in an immersive environment for the sea surface temperature data and the sea surface current fields.In all three visualization experiments,the panoramic sphere is most preferred by the participants,particularly for global,transcontinental and transoceanic needs.
文摘The paper is devoted to a spherically symmetric problem of General Relativity (GR) for an elastic solid sphere. Originally developed to describe gravitation in continuum (vacuum, gas, fluid and solid) GR does not provide the complete set of equations for solids and, in contrast to the Newton gravitation theory, does not allow us to study the stresses induced by gravitation in solids, because the compatibility equations which are attracted in the Euclidean space for this purpose do not exist in the Riemannian space. To solve the problem within the framework of GR, a special geometry of the Riemannian space induced by gravitation is proposed. According to this geometry, the four-dimensional Riemannian space is assumed to be Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate. Such interpretation of the Riemannian space in GR allows us to supplement the conservation equations for the energy-momentum tensor with compatibility equations of the theory of elasticity and to arrive to the complete set of equations for stresses. The analytical solution of the Einstein equations for the empty space surrounding the sphere and the numerical solution for the internal space inside the sphere with the proposed geometry are presented and discussed.
基金financially supported by the National Key R&D Program of China (No. 2018YFB0104000 and No. 2019YFA0210300)National Nature Science Foundation of China (No.21571189 and No.21671200)+3 种基金Natural Science Foundation of Jiangsu Province (BK20200991)Hunan Provincial Science and Technology Plan Project of China (No. 2019GK2033, No. 2017TP1001, CPS2019K06 and No. 2018RS3009)Postdoctoral International Exchange Program Funding of China (No. [2018]115)China Postdoctoral Science Foundation (2019M652802)
文摘Energy conversion technologies like fuel cells and metal-air batteries require oxygen reduction reaction(ORR)electrocatalysts with low cost and high catalytic activity.Herein,N-doped carbon spheres(N-CS)with rich micropore structure have been synthesized by a facile two-step method,which includes the polymerization of pyrrole and formaldehyde and followed by a facile pyrolysis process.During the preparation,zinc chloride(ZnCl2)was utilized as a catalyst to promote polymerization and provide a hypersaline environment.In addition,the morphology,defect content and activity area of the resultant N-CS catalysts could be regulated by controlling the content of ZnCl2.The optimum N-CS-1 catalyst demonstrated much better catalytic activity and durability towards ORR in alkaline conditions than commercial 20 wt%Pt/C catalysts,of which the half-wave potential reached 0.844 V vs.RHE.When applied in the Zn-air batteries as cathode catalysts,N-CS-1 showed a maximum power density of 175 mW cm^(-2) and long-term discharging stability of over 150 h at 10 mA cm^(-2),which outperformed 20 wt%Pt/C.The excellent performance could be due to its ultrahigh specific surface area of 1757 m2 g1 and rich micropore channels structure.Meanwhile,this work provides an efficient method to synthesize an ultrahigh surface porous carbon material,especially for catalyst application.