A set of permutations is called sign-balanced if the set contains the same number of even permutations as odd permutations.Let S_(n)(σ_(1),σ_(2),...,σ_(r))denote the set of permutations in the symmetric group S_(n)...A set of permutations is called sign-balanced if the set contains the same number of even permutations as odd permutations.Let S_(n)(σ_(1),σ_(2),...,σ_(r))denote the set of permutations in the symmetric group S_(n)which avoid patternsσ_(1),σ_(2),...,σ_(r).The aim of this paper is to investigate when,for certain patternsσ_(1),σ_(2),...,σ_(r),S_(n)(σ_(1),σ_(2),...,σ_(r))is sign-balanced for every integer n>1.We prove that for any{σ_(1),σ_(2),...,σ_(r)}?S_3,if{σ_(1),σ_(2),...,σ_(r)}is sign-balanced except for{132,213,231,312},then S_(n)(σ_(1),σ_(2),...,σ_(r))is sign-balanced for every integer n>1.In addition,we give some results in the case of avoiding some patterns of length 4.展开更多
This paper presents the non-associative and non-commutative properties of the 123-avoiding patterns of Aunu permutation patterns. The generating function of the said patterns has been reported earlier by the author [1...This paper presents the non-associative and non-commutative properties of the 123-avoiding patterns of Aunu permutation patterns. The generating function of the said patterns has been reported earlier by the author [1] [2]. The paper describes how these non-associative and non commutative properties can be established by using the Cayley table on which a binary operation is defined to act on the 123-avoiding and 132-avoiding patterns of Aunu permutations using a pairing scheme. Our results have generated larger matrices from permutations of points of the Aunu patterns of prime cardinality. It follows that the generated symbols can be used in further studies and analysis in cryptography and game theory thereby providing an interdisciplinary approach and applications of these important permutation patterns.展开更多
This paper presents a fringe-carrier method that eliminates sign ambiguity of transient moire fringes which can be used to automatically determine the relative orders. A fringe carrier is preset in the static state of...This paper presents a fringe-carrier method that eliminates sign ambiguity of transient moire fringes which can be used to automatically determine the relative orders. A fringe carrier is preset in the static state of the specimen and the dynamic in-plane displacements are recorded as the modulation to the frequency of the carrier fringes when the specimen is loaded by impact. According to a modulating criterion developed from the modulation degree, the fringes of the transient moire patterns keep monotonical in orders so that they can be automatically encoded in grey levels by a digital image system. The moire orders purely caused by dynamic loadings are evaluated by subtracting the grey-value of the unmodulated carrier image from that of the modulated carrier images encoded by their orders. With the subtracted moire orders the strain components can be obtained, and, correspondingly, the histograms of dynamic displacement moire images are shown with order variation by image-difference.展开更多
Moiré patterns on HOPG were studied with scanning tunneling microscopy （STM）. The results reveal that the observed Moiré patterns originate from the defects locating several layers below the surface, which...Moiré patterns on HOPG were studied with scanning tunneling microscopy （STM）. The results reveal that the observed Moiré patterns originate from the defects locating several layers below the surface, which presents the first experimental evidence supporting the prediction that in HOPG the nanoscale electronic waves can propagate through several layers without obvious decay.展开更多
Using the Lindemann criterion,we analyzed the quantum and thermal melting of electronic/excitonic crystals recently discovered in two-dimensional(2D)semiconductor moirépatterns.We show that the finite 2D screenin...Using the Lindemann criterion,we analyzed the quantum and thermal melting of electronic/excitonic crystals recently discovered in two-dimensional(2D)semiconductor moirépatterns.We show that the finite 2D screening of the atomically thin material can suppress(enhance)the inter-site Coulomb(dipolar)interaction strength,thus inhibits(facilitates)the formation of the electronic(excitonic)crystal.Meanwhile,a strong enough moiréconfinement is found to be essential for realizing the crystal phase with a wavelength near 10 nm or shorter.From the calculated Lindemann ratio which quantifies the fluctuation of the site displacement,we estimate that the crystal will melt into a liquid above a critical temperature ranging from several tens Kelvin to above 100 K(depending on the system parameters).展开更多
A new method for constructing digital-strain-field-image from a moire pattern with the help of digital image processing technique is proposed in this paper. The digital-strain-field-image expresses the strain values d...A new method for constructing digital-strain-field-image from a moire pattern with the help of digital image processing technique is proposed in this paper. The digital-strain-field-image expresses the strain values directly by its grey levels. The digital-strain-field-image can be obtained by making a differentiation for the digital moire pattern and doing a simple division operation. This image not only gives the visual strain field distribution, but also gives the strain values of every point. This method is simple and applicable and has satisfactory accuracy.展开更多
Fishburn permutations are in bijection with several important combinatorial structures including interval orders.In this paper,we use the method of generating trees to enumerate two classes of pattern-avoiding Fishbur...Fishburn permutations are in bijection with several important combinatorial structures including interval orders.In this paper,we use the method of generating trees to enumerate two classes of pattern-avoiding Fishburn permutations subject to 7 classical statistics simultaneously.The classes of our interest are(321,312)-avoiding and(321,4123)-avoiding Fishburn permutations.The statistics of our interest are ascents,descents,inversions,right-to-left maxima,right-to-left minima,left-to-right maxima and left-to-right minima.Our results generalize a result by Egge.展开更多
A novel method to separate and simultaneously record the Moiréinterferometry fringe patterns of three deformation fields with only one CCD camera is developed;details of its operation principle,key points and err...A novel method to separate and simultaneously record the Moiréinterferometry fringe patterns of three deformation fields with only one CCD camera is developed;details of its operation principle,key points and error analysis are presented.With this technique,the deformation in U,V and W fields can be measured simultaneously,so dynamic test with comprehensive information can be performed.The advantage of this technique over other similar techniques lies in its simplicity,easy implementation and low cost.An application of this technique is given to show its feasibility.Technical problems that may be caused with this technique are also analyzed.展开更多
With the ever-growing number of base stations(BSs)and user equipments(UEs)in ultra-dense networks(UDN),reusing the same pilot sequences among the cells is inevitable.With pilot reuse scheme,the channel estimation obta...With the ever-growing number of base stations(BSs)and user equipments(UEs)in ultra-dense networks(UDN),reusing the same pilot sequences among the cells is inevitable.With pilot reuse scheme,the channel estimation obtained at a BS contains not only the desired channel-state information(CSI)but also interference from neighboring cells,which can severely degrade CSI estimation performance and adversely affect communication performance.In this paper we consider a pilot contamination avoidance based on pilot pattern design for UDN where the pilot reuse employed and the interfering users from neighboring cells may be not at lower power levels at the BS compared to the in-cell users.We present a novel statistical interference model of sub-carriers to describe the non-deterministic interference from neighboring cells.Then,we provide a pilot pattern design model with non-uniform pilot distribution.Based on this,a pilot contamination avoidance based on pilot pattern design is proposed where pilot reuse scheme and the non-deterministic interference from neighboring cells are taken into consideration.Unlike existing interference mitigation approaches,the proposed method eliminates interference through the method of interference avoidance and can be applied to different kinds of channel estimation algorithms.Simulation results showed that the proposed approach can effectively avoid the interference and ensure the accuracy of channel estimation.展开更多
In moiré-patterned van der Waals structures of transition metal dichalcogenides,correlated insulators can form under integer and fractional fillings,whose transport properties are governed by various quasiparticl...In moiré-patterned van der Waals structures of transition metal dichalcogenides,correlated insulators can form under integer and fractional fillings,whose transport properties are governed by various quasiparticle excitations including holons,doublons and interlayer exciton insulators.Here we theoretically investigate the nearest-neighbor inter-site hoppings of holons and interlayer exciton insulators.Our analysis indicates that these hopping strengths are significantly enhanced compared to that of a single carrier.The underlying mechanism can be attributed to the strong Coulomb interaction between carriers at different sites.For the interlayer exciton insulator consisting of a holon and a carrier in different layers,we have also obtained its effective Bohr radius and energy splitting between the ground and the first-excited states.展开更多
Interplay between topology and magnetism can give rise to exotic properties in topological materials.Two-dimensional bismuth has been extensively studied owing to its topological states with a strong spin-orbit coupli...Interplay between topology and magnetism can give rise to exotic properties in topological materials.Two-dimensional bismuth has been extensively studied owing to its topological states with a strong spin-orbit coupling,and 1T-VTe_(2)monolayer theoretically predicted to host an intrinsic magnetism as experimentally suggested.In this work,we successfully constructed a vertical heterostructure composed of the two-dimensional Bi(110)monolayer and 1T-VTe_(2)monolayer by using molecular beam epitaxy(MBE).Scanning tunneling microscopy(STM)measurements revealed that the growth of Bi preferably occurs along the step edges of the VTe_(2)monolayer,forming a Bi(110)monolayer on top of the VTe_(2)monolayer next to a peripheral Bi bilayer.The Bi(100)/VTe_(2)heterostructure exhibits a specific lattice registry with a well-defined moiréperiodicity.Scanning tunneling spectroscopy(STS)measurements further unveiled an universal suppression in the local density-of-states at the boundary of the Bi(110)/VTe_(2)bilayer.By examining the atomic structures of Bi(110)boundaries,we found this effect does not originate from the previously proposed atomic reconstruction at the step edge of Bi(110),but is likely related to the magnetic properties of the VTe_(2)monolayer.展开更多
This paper presents a study on bioinspired closed-loop Central Pattern Generator(CPG)based control of a robot fish for obstacle avoidance and direction tracking.The biomimetic robot fish is made of a rigid head with a...This paper presents a study on bioinspired closed-loop Central Pattern Generator(CPG)based control of a robot fish for obstacle avoidance and direction tracking.The biomimetic robot fish is made of a rigid head with a pair of pectoral fins,a wire-driven active body covered with soft skin,and a compliant tail.The CPG model consists of four input parameters:the flapping amplitude,the flapping angular velocity,the flapping offset,and the time ratio between the beat phase and the restore phase in flapping.The robot fish is equipped with three infrared sensors mounted on the left,front and right of the robot fish,as well as an inertial measurement unit,from which the surrounding obstacles and moving direction can be sensed.Based on these sensor signals,the closed-loop CPG-based control can drive the robot fish to avoid obstacles and to track designated directions.Four sets of experiments are presented,including avoiding a static obstacle,avoiding a moving obstacle,tracking a designated direction and tracking a designated direction with an obstacle in the path.The experiment results indicated that the presented control strategy worked well and the robot fish can accomplish the obstacle avoidance and direction tracking effectively.展开更多
Space swarms,enabled by the miniaturization of spacecraft,have the potential capability to lower costs,increase efficiencies,and broaden the horizons of space missions.The formation control problem of large-scale spac...Space swarms,enabled by the miniaturization of spacecraft,have the potential capability to lower costs,increase efficiencies,and broaden the horizons of space missions.The formation control problem of large-scale spacecraft swarms flying around an elliptic orbit is considered.The objective is to drive the entire formation to produce a specified spatial pattern.The relative motion between agents becomes complicated as the number of agents increases.Hence,a density-based method is adopted,which concerns the density evolution of the entire swarm instead of the trajectories of individuals.The density-based method manipulates the density evolution with Partial Differential Equations(PDEs).This density-based control in this work has two aspects,global pattern control of the whole swarm and local collision-avoidance between nearby agents.The global behavior of the swarm is driven via designing velocity fields.For each spacecraft,the Q-guidance steering law is adopted to track the desired velocity with accelerations in a distributed manner.However,the final stable velocity field is required to be zero in the classical density-based approach,which appears as an obstacle from the viewpoint of astrodynamics since the periodic relative motion is always time-varying.To solve this issue,a novel transformation is constructed based on the periodic solutions of Tschauner-Hempel(TH)equations.The relative motion in Cartesian coordinates is then transformed into a new coordinate system,which permits zero-velocity in a stable configuration.The local behavior of the swarm,such as achieving collision avoidance,is achieved via a carefully-designed local density estimation algorithm.Numerical simulations are provided to demonstrate the performance of this approach.展开更多
A hybrid technique of combining moire measurement and analytical solution is developed to separate the normal and the tangential components of distributed contact stresses between two co-plane bodies. The moire interf...A hybrid technique of combining moire measurement and analytical solution is developed to separate the normal and the tangential components of distributed contact stresses between two co-plane bodies. The moire interfe-rometry offers the displacement fields near the deformed contact zone, from which the tangential strains and boundary slopes of the deformed configurations can be evaluated. Those experimental results provide boundary conditions for the discrete integration of Flamant＇s solutions, to inversely compute the separated components of the contact stresses.展开更多
In van der Waals heterostructures of atomically thin 2D materials, the inevitable lattice mismatch and twisting between the building blocks always lead to the formation of Moire pattern, which is a periodic spatial pa...In van der Waals heterostructures of atomically thin 2D materials, the inevitable lattice mismatch and twisting between the building blocks always lead to the formation of Moire pattern, which is a periodic spatial pattern of varying atomic registries. Theory has predicted that such a nanoscale moire landscape can endow excitons highly intriguing properties (Science Advances 3, e1701696 (2017)), including their confinement in an array of quantum dot like potential traps with circularly polarized valley optical selection rules.展开更多
Moirépatterns in physics are interference fringes produced when a periodic template is stacked on another similar one with different displacement and twist angles.The phonon in two-dimensional(2D)material affecte...Moirépatterns in physics are interference fringes produced when a periodic template is stacked on another similar one with different displacement and twist angles.The phonon in two-dimensional(2D)material affected by moirépatterns in the lattice shows various novel physical phenomena,such as frequency shift,different linewidth,and mediation to the superconductivity.This review gives a brief overview of phonons in 2D moirésuperlattice.First,we introduce the theory of the moiréphonon modes based on a continuum approach using the elastic theory and discuss the effect of the moirépattern on phonons in 2D materials such as graphene and MoS_(2).Then,we discuss the electron-phonon coupling(EPC)modulated by moirépatterns,which can be detected by the spectroscopy methods.Furthermore,the phonon-mediated unconventional superconductivity in 2D moirésuperlattice is introduced.The theory of phonon-mediated superconductivity in moirésuperlattice sets up a general framework,which promises to predict the response of superconductivity to various perturbations,such as disorder,magnetic field,and electric displacement field.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12061030)the Natural Science Foundation of Hainan Province(Grant No.122RC652)2023 Excellent Science and Technology Innovation Team of Jiangsu Province Universities(Real-Time Industrial Internet of Things).
文摘A set of permutations is called sign-balanced if the set contains the same number of even permutations as odd permutations.Let S_(n)(σ_(1),σ_(2),...,σ_(r))denote the set of permutations in the symmetric group S_(n)which avoid patternsσ_(1),σ_(2),...,σ_(r).The aim of this paper is to investigate when,for certain patternsσ_(1),σ_(2),...,σ_(r),S_(n)(σ_(1),σ_(2),...,σ_(r))is sign-balanced for every integer n>1.We prove that for any{σ_(1),σ_(2),...,σ_(r)}?S_3,if{σ_(1),σ_(2),...,σ_(r)}is sign-balanced except for{132,213,231,312},then S_(n)(σ_(1),σ_(2),...,σ_(r))is sign-balanced for every integer n>1.In addition,we give some results in the case of avoiding some patterns of length 4.
文摘This paper presents the non-associative and non-commutative properties of the 123-avoiding patterns of Aunu permutation patterns. The generating function of the said patterns has been reported earlier by the author [1] [2]. The paper describes how these non-associative and non commutative properties can be established by using the Cayley table on which a binary operation is defined to act on the 123-avoiding and 132-avoiding patterns of Aunu permutations using a pairing scheme. Our results have generated larger matrices from permutations of points of the Aunu patterns of prime cardinality. It follows that the generated symbols can be used in further studies and analysis in cryptography and game theory thereby providing an interdisciplinary approach and applications of these important permutation patterns.
基金The project supported by Alexander von Humboldt Foundation or Germany and the National Natural Science Foundation of China
文摘This paper presents a fringe-carrier method that eliminates sign ambiguity of transient moire fringes which can be used to automatically determine the relative orders. A fringe carrier is preset in the static state of the specimen and the dynamic in-plane displacements are recorded as the modulation to the frequency of the carrier fringes when the specimen is loaded by impact. According to a modulating criterion developed from the modulation degree, the fringes of the transient moire patterns keep monotonical in orders so that they can be automatically encoded in grey levels by a digital image system. The moire orders purely caused by dynamic loadings are evaluated by subtracting the grey-value of the unmodulated carrier image from that of the modulated carrier images encoded by their orders. With the subtracted moire orders the strain components can be obtained, and, correspondingly, the histograms of dynamic displacement moire images are shown with order variation by image-difference.
文摘Moiré patterns on HOPG were studied with scanning tunneling microscopy （STM）. The results reveal that the observed Moiré patterns originate from the defects locating several layers below the surface, which presents the first experimental evidence supporting the prediction that in HOPG the nanoscale electronic waves can propagate through several layers without obvious decay.
基金support by the National Natural Science Foundation of China(Grant No.12274477)the Department of Science and Technology of Guangdong Province of China(Grant No.2019QN01X061)。
文摘Using the Lindemann criterion,we analyzed the quantum and thermal melting of electronic/excitonic crystals recently discovered in two-dimensional(2D)semiconductor moirépatterns.We show that the finite 2D screening of the atomically thin material can suppress(enhance)the inter-site Coulomb(dipolar)interaction strength,thus inhibits(facilitates)the formation of the electronic(excitonic)crystal.Meanwhile,a strong enough moiréconfinement is found to be essential for realizing the crystal phase with a wavelength near 10 nm or shorter.From the calculated Lindemann ratio which quantifies the fluctuation of the site displacement,we estimate that the crystal will melt into a liquid above a critical temperature ranging from several tens Kelvin to above 100 K(depending on the system parameters).
文摘A new method for constructing digital-strain-field-image from a moire pattern with the help of digital image processing technique is proposed in this paper. The digital-strain-field-image expresses the strain values directly by its grey levels. The digital-strain-field-image can be obtained by making a differentiation for the digital moire pattern and doing a simple division operation. This image not only gives the visual strain field distribution, but also gives the strain values of every point. This method is simple and applicable and has satisfactory accuracy.
基金National Natural Science Foundation of China(Grant No.12171362)。
文摘Fishburn permutations are in bijection with several important combinatorial structures including interval orders.In this paper,we use the method of generating trees to enumerate two classes of pattern-avoiding Fishburn permutations subject to 7 classical statistics simultaneously.The classes of our interest are(321,312)-avoiding and(321,4123)-avoiding Fishburn permutations.The statistics of our interest are ascents,descents,inversions,right-to-left maxima,right-to-left minima,left-to-right maxima and left-to-right minima.Our results generalize a result by Egge.
文摘A novel method to separate and simultaneously record the Moiréinterferometry fringe patterns of three deformation fields with only one CCD camera is developed;details of its operation principle,key points and error analysis are presented.With this technique,the deformation in U,V and W fields can be measured simultaneously,so dynamic test with comprehensive information can be performed.The advantage of this technique over other similar techniques lies in its simplicity,easy implementation and low cost.An application of this technique is given to show its feasibility.Technical problems that may be caused with this technique are also analyzed.
基金This work was supported in part by the Chongqing Research Program of Basic Research and Frontier Technology under Grant cstc2019jcyj-msxmX0233in part by Science and Technology Research Program of Chongqing Education Commission of China under Grant KJQN201901125,Grant KJQN201901103in part by the Scientific Research Foundation of Chongqing University of Technology under Grant 2019ZD42,Grant 2019ZD63.
文摘With the ever-growing number of base stations(BSs)and user equipments(UEs)in ultra-dense networks(UDN),reusing the same pilot sequences among the cells is inevitable.With pilot reuse scheme,the channel estimation obtained at a BS contains not only the desired channel-state information(CSI)but also interference from neighboring cells,which can severely degrade CSI estimation performance and adversely affect communication performance.In this paper we consider a pilot contamination avoidance based on pilot pattern design for UDN where the pilot reuse employed and the interfering users from neighboring cells may be not at lower power levels at the BS compared to the in-cell users.We present a novel statistical interference model of sub-carriers to describe the non-deterministic interference from neighboring cells.Then,we provide a pilot pattern design model with non-uniform pilot distribution.Based on this,a pilot contamination avoidance based on pilot pattern design is proposed where pilot reuse scheme and the non-deterministic interference from neighboring cells are taken into consideration.Unlike existing interference mitigation approaches,the proposed method eliminates interference through the method of interference avoidance and can be applied to different kinds of channel estimation algorithms.Simulation results showed that the proposed approach can effectively avoid the interference and ensure the accuracy of channel estimation.
基金support by the National Natural Sci-ence Foundation of China(Grant No.12274477)the De-partment of Science and Technology of Guangdong Provincein China(Grant No.2019QN01X061)。
文摘In moiré-patterned van der Waals structures of transition metal dichalcogenides,correlated insulators can form under integer and fractional fillings,whose transport properties are governed by various quasiparticle excitations including holons,doublons and interlayer exciton insulators.Here we theoretically investigate the nearest-neighbor inter-site hoppings of holons and interlayer exciton insulators.Our analysis indicates that these hopping strengths are significantly enhanced compared to that of a single carrier.The underlying mechanism can be attributed to the strong Coulomb interaction between carriers at different sites.For the interlayer exciton insulator consisting of a holon and a carrier in different layers,we have also obtained its effective Bohr radius and energy splitting between the ground and the first-excited states.
基金financially supported by the National Key Research and Development Program of China(Grant No.2021YFA1400403)the National Natural Science Foundation of China(Grant Nos.12374183,92165205)+2 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20233001)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302800)the Fundamental Research Funds for the Central Universities(Grant No.020414380207).
文摘Interplay between topology and magnetism can give rise to exotic properties in topological materials.Two-dimensional bismuth has been extensively studied owing to its topological states with a strong spin-orbit coupling,and 1T-VTe_(2)monolayer theoretically predicted to host an intrinsic magnetism as experimentally suggested.In this work,we successfully constructed a vertical heterostructure composed of the two-dimensional Bi(110)monolayer and 1T-VTe_(2)monolayer by using molecular beam epitaxy(MBE).Scanning tunneling microscopy(STM)measurements revealed that the growth of Bi preferably occurs along the step edges of the VTe_(2)monolayer,forming a Bi(110)monolayer on top of the VTe_(2)monolayer next to a peripheral Bi bilayer.The Bi(100)/VTe_(2)heterostructure exhibits a specific lattice registry with a well-defined moiréperiodicity.Scanning tunneling spectroscopy(STS)measurements further unveiled an universal suppression in the local density-of-states at the boundary of the Bi(110)/VTe_(2)bilayer.By examining the atomic structures of Bi(110)boundaries,we found this effect does not originate from the previously proposed atomic reconstruction at the step edge of Bi(110),but is likely related to the magnetic properties of the VTe_(2)monolayer.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(class A)(Grant No.XDA22040203)the Fundamental Research Funds for the Central Universities(Grant No.2019XX01)+1 种基金GDNRC[2020]031the Natural Science Foundation of Guangdong Province(Grant No.2020A1515010621).
文摘This paper presents a study on bioinspired closed-loop Central Pattern Generator(CPG)based control of a robot fish for obstacle avoidance and direction tracking.The biomimetic robot fish is made of a rigid head with a pair of pectoral fins,a wire-driven active body covered with soft skin,and a compliant tail.The CPG model consists of four input parameters:the flapping amplitude,the flapping angular velocity,the flapping offset,and the time ratio between the beat phase and the restore phase in flapping.The robot fish is equipped with three infrared sensors mounted on the left,front and right of the robot fish,as well as an inertial measurement unit,from which the surrounding obstacles and moving direction can be sensed.Based on these sensor signals,the closed-loop CPG-based control can drive the robot fish to avoid obstacles and to track designated directions.Four sets of experiments are presented,including avoiding a static obstacle,avoiding a moving obstacle,tracking a designated direction and tracking a designated direction with an obstacle in the path.The experiment results indicated that the presented control strategy worked well and the robot fish can accomplish the obstacle avoidance and direction tracking effectively.
基金co-supported by the Strategic Priority Program on Space Science of the Chinese Academy of Sciences (No.XDA15014902)the Key Research Program of the Chinese Academy of Sciences (No. ZDRW-KT-2019-1-0102)
文摘Space swarms,enabled by the miniaturization of spacecraft,have the potential capability to lower costs,increase efficiencies,and broaden the horizons of space missions.The formation control problem of large-scale spacecraft swarms flying around an elliptic orbit is considered.The objective is to drive the entire formation to produce a specified spatial pattern.The relative motion between agents becomes complicated as the number of agents increases.Hence,a density-based method is adopted,which concerns the density evolution of the entire swarm instead of the trajectories of individuals.The density-based method manipulates the density evolution with Partial Differential Equations(PDEs).This density-based control in this work has two aspects,global pattern control of the whole swarm and local collision-avoidance between nearby agents.The global behavior of the swarm is driven via designing velocity fields.For each spacecraft,the Q-guidance steering law is adopted to track the desired velocity with accelerations in a distributed manner.However,the final stable velocity field is required to be zero in the classical density-based approach,which appears as an obstacle from the viewpoint of astrodynamics since the periodic relative motion is always time-varying.To solve this issue,a novel transformation is constructed based on the periodic solutions of Tschauner-Hempel(TH)equations.The relative motion in Cartesian coordinates is then transformed into a new coordinate system,which permits zero-velocity in a stable configuration.The local behavior of the swarm,such as achieving collision avoidance,is achieved via a carefully-designed local density estimation algorithm.Numerical simulations are provided to demonstrate the performance of this approach.
基金the National Basic Research Program(2007CB935602)the National Natural Science Foundation of China(90607004)the ICM Fund of CAEP(42105080106).
文摘A hybrid technique of combining moire measurement and analytical solution is developed to separate the normal and the tangential components of distributed contact stresses between two co-plane bodies. The moire interfe-rometry offers the displacement fields near the deformed contact zone, from which the tangential strains and boundary slopes of the deformed configurations can be evaluated. Those experimental results provide boundary conditions for the discrete integration of Flamant＇s solutions, to inversely compute the separated components of the contact stresses.
文摘In van der Waals heterostructures of atomically thin 2D materials, the inevitable lattice mismatch and twisting between the building blocks always lead to the formation of Moire pattern, which is a periodic spatial pattern of varying atomic registries. Theory has predicted that such a nanoscale moire landscape can endow excitons highly intriguing properties (Science Advances 3, e1701696 (2017)), including their confinement in an array of quantum dot like potential traps with circularly polarized valley optical selection rules.
基金National Natural Science Foundation of China(12074371)CAS Interdisciplinary Innovation Team,Strategic Priority Research Program of Chinese Academy of Sciences(XDB28000000)。
文摘Moirépatterns in physics are interference fringes produced when a periodic template is stacked on another similar one with different displacement and twist angles.The phonon in two-dimensional(2D)material affected by moirépatterns in the lattice shows various novel physical phenomena,such as frequency shift,different linewidth,and mediation to the superconductivity.This review gives a brief overview of phonons in 2D moirésuperlattice.First,we introduce the theory of the moiréphonon modes based on a continuum approach using the elastic theory and discuss the effect of the moirépattern on phonons in 2D materials such as graphene and MoS_(2).Then,we discuss the electron-phonon coupling(EPC)modulated by moirépatterns,which can be detected by the spectroscopy methods.Furthermore,the phonon-mediated unconventional superconductivity in 2D moirésuperlattice is introduced.The theory of phonon-mediated superconductivity in moirésuperlattice sets up a general framework,which promises to predict the response of superconductivity to various perturbations,such as disorder,magnetic field,and electric displacement field.
