In this note we study subplanes of order q of the projective plane Π=PG( 2, q 3 ) and the ruled varieties V 2 5 of Σ=PG( 6,q ) using the spatial representation of Π in Σ, by fixing a hyperplane Σ ′ with a regula...In this note we study subplanes of order q of the projective plane Π=PG( 2, q 3 ) and the ruled varieties V 2 5 of Σ=PG( 6,q ) using the spatial representation of Π in Σ, by fixing a hyperplane Σ ′ with a regular spread of planes. First are shown some configurations of the affine q-subplanes. Then to prove that a variety V 2 5 of Σ represents a non-affine subplane of order q of Π, after having shown basic incidence properties of it, such a variety V 2 5 is constructed by choosing appropriately the two directrix curves in two complementary subspaces of Σ. The result can be translated into further incidence properties of the affine points of V 2 5 . Then a maximal bundle of varieties V 2 5 having in common one directrix cubic curve is constructed.展开更多
The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods.Tilted perturbation refers to the fact that perturbations form an angleθ∈(0,π/2)with the direc...The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods.Tilted perturbation refers to the fact that perturbations form an angleθ∈(0,π/2)with the direction of the basic flows.By defining an energy functional,it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for tilted streamwise perturbation when the Reynolds number is below a certain critical value and the boundary conditions are either rigid or stress-free.In the case of stress-free boundaries,by taking advantage of the poloidal-toroidal decomposition of a solenoidal field to define energy functionals,it can be even shown that plane parallel shear flows are unconditionally nonlinearly exponentially stable for all Reynolds numbers,where the tilted perturbation can be either spanwise or streamwise.展开更多
Structural planes play an important role in controlling the stability of rock engineering,and the influence of structural planes should be considered in the design and construction process of rock engineering.In this ...Structural planes play an important role in controlling the stability of rock engineering,and the influence of structural planes should be considered in the design and construction process of rock engineering.In this paper,mechanical properties,constitutive theory,and numerical application of structural plane are studied by a combination method of laboratory tests,theoretical derivation,and program development.The test results reveal the change laws of various mechanical parameters under different roughness and normal stress.At the pre-peak stage,a non-stationary model of shear stiffness is established,and threedimensional empirical prediction models for initial shear stiffness and residual stage roughness are proposed.The nonlinear constitutive models are established based on elasto-plastic mechanics,and the algorithms of the models are developed based on the return mapping algorithm.According to a large number of statistical analysis results,empirical prediction models are proposed for model parameters expressed by structural plane characteristic parameters.Finally,the discrete element method(DEM)is chosen to embed the constitutive models for practical application.The running programs of the constitutive models have been compiled into the discrete element model library.The comparison results between the proposed model and the Mohr-Coulomb slip model show that the proposed model can better describe nonlinear changes at different stages,and the predicted shear strength,peak strain and shear stiffness are closer to the test results.The research results of the paper are conducive to the accurate evaluation of structural plane in rock engineering.展开更多
A nuclear explosion in the rock mass medium can produce strong shock waves,seismic shocks,and other destructive effects,which can cause extreme damage to the underground protection infrastructures.With the increase in...A nuclear explosion in the rock mass medium can produce strong shock waves,seismic shocks,and other destructive effects,which can cause extreme damage to the underground protection infrastructures.With the increase in nuclear explosion power,underground protection engineering enabled by explosion-proof impact theory and technology ushered in a new challenge.This paper proposes to simulate nuclear explosion tests with on-site chemical explosion tests in the form of multi-hole explosions.First,the mechanism of using multi-hole simultaneous blasting to simulate a nuclear explosion to generate approximate plane waves was analyzed.The plane pressure curve at the vault of the underground protective tunnel under the action of the multi-hole simultaneous blasting was then obtained using the impact test in the rock mass at the site.According to the peak pressure at the vault plane,it was divided into three regions:the stress superposition region,the superposition region after surface reflection,and the approximate plane stress wave zone.A numerical simulation approach was developed using PFC and FLAC to study the peak particle velocity in the surrounding rock of the underground protective cave under the action of multi-hole blasting.The time-history curves of pressure and peak pressure partition obtained by the on-site multi-hole simultaneous blasting test and numerical simulation were compared and analyzed,to verify the correctness and rationality of the formation of an approximate plane wave in the simulated nuclear explosion.This comparison and analysis also provided a theoretical foundation and some research ideas for the ensuing study on the impact of a nuclear explosion.展开更多
The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurat...The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurate andunstable when applied. Therefore, developing new elements within the framework of the generalized variationalprinciple is of great significance. In this paper, an 8-node plane hybrid finite element with 15 parameters (PHQ8-15β) is developed for structural mechanics problems based on the Hellinger-Reissner variational principle.According to the design principle of Pian, 15 unknown parameters are adopted in the selection of stress modes toavoid the zero energy modes.Meanwhile, the stress functions within each element satisfy both the equilibrium andthe compatibility relations of plane stress problems. Subsequently, numerical examples are presented to illustrate theeffectiveness and robustness of the proposed finite element. Numerical results show that various common lockingbehaviors of plane elements can be overcome. The PH-Q8-15β element has excellent performance in all benchmarkproblems, especially for structures with varying cross sections. Furthermore, in bending problems, the reasonablemesh shape of the new element for curved edge structures is analyzed in detail, which can be a useful means toimprove numerical accuracy.展开更多
This paper reviews works on the dynamic analysis of flexible and rigid pavements under moving vehicles on the basis of continuum-based plane strain models and linear theories.The purpose of this review is to provide i...This paper reviews works on the dynamic analysis of flexible and rigid pavements under moving vehicles on the basis of continuum-based plane strain models and linear theories.The purpose of this review is to provide in-formation about the existing works on the subject,critically discuss them and make suggestions for further research.The reviewed papers are presented on the basis of the various models for pavement-vehicle systems and the various methods for dynamically analyzing these systems.Flexible pavements are modeled by a homogeneous or layered half-plane with isotropic or anisotropic and linear elastic,viscoelastic or poroelastic material behavior.Rigid pavements are modeled by a beam or plate on a homogeneous or layered half-plane with material properties like the ones for flexible pavements.The vehicles are modeled as concentrated or distributed over a finite area loads moving with constant or time dependent speed.The above pavement-vehicle models are dynamically analyzed by analytical,analytical/numerical or purely numerical methods working in the time or frequency domain.Representative examples are presented to illustrate the models and methods of analysis,demonstrate their merits and assess the effects of the various parameters on pavement response.The paper closes with con-clusions and suggestions for further research in the area.The significance of this research effort has to do with the presentation of the existing literature on the subject in a critical and easy to understand way with the aid of representative examples and the identification of new research areas.展开更多
This paper studies the clan temples in four periods,namely,the development period(early Ming Dynasty and before),the shaping period(mid-Ming Dynasty to early Qing Dynasty),the maturity period(mid-Qing Dynasty),and the...This paper studies the clan temples in four periods,namely,the development period(early Ming Dynasty and before),the shaping period(mid-Ming Dynasty to early Qing Dynasty),the maturity period(mid-Qing Dynasty),and the programmed period(late Qing Dynasty),analyzes and summarizes their prototypical planform features and attempts to summarize and construct a genealogy of the architectural characteristics of the plane shape of clan temples.During the Ming and Qing dynasties,Guangfu ancestral halls in general showed a journey of development from a centripetal-single-linear-multi-linear-grid pattern,forming the unique Guangsanlu classic pattern in the Guangfu area.展开更多
Rapid capacity decay and sluggish reaction kinetics are major barriers hindering the applications of manganese-based cathode materials for aqueous zinc-ion batteries.Herein,the effects of crystal plane on the in-situ ...Rapid capacity decay and sluggish reaction kinetics are major barriers hindering the applications of manganese-based cathode materials for aqueous zinc-ion batteries.Herein,the effects of crystal plane on the in-situ transformation behavior and electrochemical performance of manganese-based cathode is discussed.A comprehensive discussion manifests that the exposed(100)crystal plane is beneficial to the phase transformation from tunnel-structured MnO_(2) to layer-structured ZnMn_(3)O_(7)·3H_(2)O,which plays a critical role for the high reactivity,high capacity,fast diffusion kinetics and long cycling stability.Additionally,a two-stage zinc storage mechanism can be demonstrated,involving continuous activation reaction and phase transition reaction.As expected,it exhibits a high capacity of 275 mAh g^(-1)at 100 mA g^(-1),a superior durability over 1000 cycles and good rate capability.This study may open new windows toward developing advanced cathodes for ZIBs,and facilitate the applications of ZIBs in large-scale energy storage system.展开更多
For the aqueous Zn-ion battery,dendrite formation,corrosion,and interfacial parasitic reactions are major issues,which greatly inhibits their practical application.How to develop a method of Zn construction or treatme...For the aqueous Zn-ion battery,dendrite formation,corrosion,and interfacial parasitic reactions are major issues,which greatly inhibits their practical application.How to develop a method of Zn construction or treatment to solve these issues for Zn anodes are still great challenges.Herein,a simple and cheap metal passivation technique is proposed for Zn anodes from a corrosion science perspective.Similar to the metal anticorrosion engineering,the formed interfacial protective layer in a chemical way can sufficiently solve the corrosion issues.Furthermore,the proposed passivity approach can reconstruct Zn surface-preferred crystal planes,exposing more(002)planes and improving surface hydrophilicity,which inhibits the formation of Zn dendrites and hydrogen evolution effectively.As expected,the passivated Zn achieves outstanding cycling life(1914 h)with low voltage polarization(<40 mV).Even at 6 mA cm^(−2) and 3 mA h cm^(−2),it can achieve stable Zn deposition over 460 h.The treated Zn anode coupled with MnO_(2) cathode shows prominently reinforced full batteries service life,making it a potential Zn anode candidate for excellent performance aqueous Zn-ion batteries.The proposed passivation approach provides a guideline for other metal electrodes preparation in various batteries and establishes the connections between corrosion science and batteries.展开更多
文摘In this note we study subplanes of order q of the projective plane Π=PG( 2, q 3 ) and the ruled varieties V 2 5 of Σ=PG( 6,q ) using the spatial representation of Π in Σ, by fixing a hyperplane Σ ′ with a regular spread of planes. First are shown some configurations of the affine q-subplanes. Then to prove that a variety V 2 5 of Σ represents a non-affine subplane of order q of Π, after having shown basic incidence properties of it, such a variety V 2 5 is constructed by choosing appropriately the two directrix curves in two complementary subspaces of Σ. The result can be translated into further incidence properties of the affine points of V 2 5 . Then a maximal bundle of varieties V 2 5 having in common one directrix cubic curve is constructed.
基金supported by the National Natural Science Foundation of China(21627813)。
文摘The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods.Tilted perturbation refers to the fact that perturbations form an angleθ∈(0,π/2)with the direction of the basic flows.By defining an energy functional,it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for tilted streamwise perturbation when the Reynolds number is below a certain critical value and the boundary conditions are either rigid or stress-free.In the case of stress-free boundaries,by taking advantage of the poloidal-toroidal decomposition of a solenoidal field to define energy functionals,it can be even shown that plane parallel shear flows are unconditionally nonlinearly exponentially stable for all Reynolds numbers,where the tilted perturbation can be either spanwise or streamwise.
基金This work presented in this paper was funded by the National Natural Science Foundation of China(Grant Nos.51478031 and 51278046)Shenzhen Science and Technology Innovation Fund(Grant No.FA24405041).The authors are grateful to the editor and reviewers for discerning comments on this paper.
文摘Structural planes play an important role in controlling the stability of rock engineering,and the influence of structural planes should be considered in the design and construction process of rock engineering.In this paper,mechanical properties,constitutive theory,and numerical application of structural plane are studied by a combination method of laboratory tests,theoretical derivation,and program development.The test results reveal the change laws of various mechanical parameters under different roughness and normal stress.At the pre-peak stage,a non-stationary model of shear stiffness is established,and threedimensional empirical prediction models for initial shear stiffness and residual stage roughness are proposed.The nonlinear constitutive models are established based on elasto-plastic mechanics,and the algorithms of the models are developed based on the return mapping algorithm.According to a large number of statistical analysis results,empirical prediction models are proposed for model parameters expressed by structural plane characteristic parameters.Finally,the discrete element method(DEM)is chosen to embed the constitutive models for practical application.The running programs of the constitutive models have been compiled into the discrete element model library.The comparison results between the proposed model and the Mohr-Coulomb slip model show that the proposed model can better describe nonlinear changes at different stages,and the predicted shear strength,peak strain and shear stiffness are closer to the test results.The research results of the paper are conducive to the accurate evaluation of structural plane in rock engineering.
基金supported by the General Program of the National Natural Science Foundation of China(Grant No.52074295)the Special Fund for Basic Scientific Research Business Expenses of Central Universities(Grant No.2022YJSSB06)supported by State Key Laboratory for Geomechanics and Deep Underground Engineering,China University of Mining and technology,Beijing,China(Grant No.SKLGDUEK202217).
文摘A nuclear explosion in the rock mass medium can produce strong shock waves,seismic shocks,and other destructive effects,which can cause extreme damage to the underground protection infrastructures.With the increase in nuclear explosion power,underground protection engineering enabled by explosion-proof impact theory and technology ushered in a new challenge.This paper proposes to simulate nuclear explosion tests with on-site chemical explosion tests in the form of multi-hole explosions.First,the mechanism of using multi-hole simultaneous blasting to simulate a nuclear explosion to generate approximate plane waves was analyzed.The plane pressure curve at the vault of the underground protective tunnel under the action of the multi-hole simultaneous blasting was then obtained using the impact test in the rock mass at the site.According to the peak pressure at the vault plane,it was divided into three regions:the stress superposition region,the superposition region after surface reflection,and the approximate plane stress wave zone.A numerical simulation approach was developed using PFC and FLAC to study the peak particle velocity in the surrounding rock of the underground protective cave under the action of multi-hole blasting.The time-history curves of pressure and peak pressure partition obtained by the on-site multi-hole simultaneous blasting test and numerical simulation were compared and analyzed,to verify the correctness and rationality of the formation of an approximate plane wave in the simulated nuclear explosion.This comparison and analysis also provided a theoretical foundation and some research ideas for the ensuing study on the impact of a nuclear explosion.
基金the National Natural Science Foundation of China(No.11572210).
文摘The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurate andunstable when applied. Therefore, developing new elements within the framework of the generalized variationalprinciple is of great significance. In this paper, an 8-node plane hybrid finite element with 15 parameters (PHQ8-15β) is developed for structural mechanics problems based on the Hellinger-Reissner variational principle.According to the design principle of Pian, 15 unknown parameters are adopted in the selection of stress modes toavoid the zero energy modes.Meanwhile, the stress functions within each element satisfy both the equilibrium andthe compatibility relations of plane stress problems. Subsequently, numerical examples are presented to illustrate theeffectiveness and robustness of the proposed finite element. Numerical results show that various common lockingbehaviors of plane elements can be overcome. The PH-Q8-15β element has excellent performance in all benchmarkproblems, especially for structures with varying cross sections. Furthermore, in bending problems, the reasonablemesh shape of the new element for curved edge structures is analyzed in detail, which can be a useful means toimprove numerical accuracy.
文摘This paper reviews works on the dynamic analysis of flexible and rigid pavements under moving vehicles on the basis of continuum-based plane strain models and linear theories.The purpose of this review is to provide in-formation about the existing works on the subject,critically discuss them and make suggestions for further research.The reviewed papers are presented on the basis of the various models for pavement-vehicle systems and the various methods for dynamically analyzing these systems.Flexible pavements are modeled by a homogeneous or layered half-plane with isotropic or anisotropic and linear elastic,viscoelastic or poroelastic material behavior.Rigid pavements are modeled by a beam or plate on a homogeneous or layered half-plane with material properties like the ones for flexible pavements.The vehicles are modeled as concentrated or distributed over a finite area loads moving with constant or time dependent speed.The above pavement-vehicle models are dynamically analyzed by analytical,analytical/numerical or purely numerical methods working in the time or frequency domain.Representative examples are presented to illustrate the models and methods of analysis,demonstrate their merits and assess the effects of the various parameters on pavement response.The paper closes with con-clusions and suggestions for further research in the area.The significance of this research effort has to do with the presentation of the existing literature on the subject in a critical and easy to understand way with the aid of representative examples and the identification of new research areas.
文摘This paper studies the clan temples in four periods,namely,the development period(early Ming Dynasty and before),the shaping period(mid-Ming Dynasty to early Qing Dynasty),the maturity period(mid-Qing Dynasty),and the programmed period(late Qing Dynasty),analyzes and summarizes their prototypical planform features and attempts to summarize and construct a genealogy of the architectural characteristics of the plane shape of clan temples.During the Ming and Qing dynasties,Guangfu ancestral halls in general showed a journey of development from a centripetal-single-linear-multi-linear-grid pattern,forming the unique Guangsanlu classic pattern in the Guangfu area.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.51932011 and 52072411)Science and technology innovation Program of Hunan Province(Grant no.2021RC3001)Natural Science Foundation of Hunan Province(Grant no.2021JJ20060,2018RS3019 and 2019JJ30033).
文摘Rapid capacity decay and sluggish reaction kinetics are major barriers hindering the applications of manganese-based cathode materials for aqueous zinc-ion batteries.Herein,the effects of crystal plane on the in-situ transformation behavior and electrochemical performance of manganese-based cathode is discussed.A comprehensive discussion manifests that the exposed(100)crystal plane is beneficial to the phase transformation from tunnel-structured MnO_(2) to layer-structured ZnMn_(3)O_(7)·3H_(2)O,which plays a critical role for the high reactivity,high capacity,fast diffusion kinetics and long cycling stability.Additionally,a two-stage zinc storage mechanism can be demonstrated,involving continuous activation reaction and phase transition reaction.As expected,it exhibits a high capacity of 275 mAh g^(-1)at 100 mA g^(-1),a superior durability over 1000 cycles and good rate capability.This study may open new windows toward developing advanced cathodes for ZIBs,and facilitate the applications of ZIBs in large-scale energy storage system.
基金financialy supported by the National Key R&D Program of China(Grant No.2018YFB0905400)the National Natural Science Foundation of China(Grant Nos.22075331,51702376)+2 种基金the Fundamental Research Funds for the Central Universities(19lgzd02)the Guangdong Pearl River Talents Plan(2019QN01L117)the National Thousand Youth Talents Project of the Chinese Government
文摘For the aqueous Zn-ion battery,dendrite formation,corrosion,and interfacial parasitic reactions are major issues,which greatly inhibits their practical application.How to develop a method of Zn construction or treatment to solve these issues for Zn anodes are still great challenges.Herein,a simple and cheap metal passivation technique is proposed for Zn anodes from a corrosion science perspective.Similar to the metal anticorrosion engineering,the formed interfacial protective layer in a chemical way can sufficiently solve the corrosion issues.Furthermore,the proposed passivity approach can reconstruct Zn surface-preferred crystal planes,exposing more(002)planes and improving surface hydrophilicity,which inhibits the formation of Zn dendrites and hydrogen evolution effectively.As expected,the passivated Zn achieves outstanding cycling life(1914 h)with low voltage polarization(<40 mV).Even at 6 mA cm^(−2) and 3 mA h cm^(−2),it can achieve stable Zn deposition over 460 h.The treated Zn anode coupled with MnO_(2) cathode shows prominently reinforced full batteries service life,making it a potential Zn anode candidate for excellent performance aqueous Zn-ion batteries.The proposed passivation approach provides a guideline for other metal electrodes preparation in various batteries and establishes the connections between corrosion science and batteries.
