Based on the substitution rule and symmetry, we propose a method to generate an octagonal quasilattice consisting ofsquare and rhombus tiles. Local configurations and Ammann lines are used to guide the growth of the t...Based on the substitution rule and symmetry, we propose a method to generate an octagonal quasilattice consisting ofsquare and rhombus tiles. Local configurations and Ammann lines are used to guide the growth of the tiles in a quasiperiodicorder. The structure obtained is a perfect eight-fold symmetric quasilattice, which is confirmed by the radial distributionfunction and the diffraction pattern.展开更多
A phoxonic crystal waveguide with the glide symmetry is designed,in which both electromagnetic and elastic waves can propagate along the glide plane at the same time.Due to the glide symmetry,the bands of the phoxonic...A phoxonic crystal waveguide with the glide symmetry is designed,in which both electromagnetic and elastic waves can propagate along the glide plane at the same time.Due to the glide symmetry,the bands of the phoxonic crystal super-cell degenerate in pairs at the boundary of the Brillouin zone.This is the so-called band-sticking effect and it causes the appearance of gapless guided-modes.By adjusting the magnitude of the glide dislocation the edge bandgaps,the bandgap of the guided-modes at the boundary of the Brillouin zone,can be further adjusted.The photonic and phononic guided-modes can then possess only one mode for a certain frequency with relatively low group velocities,achieving single-mode guided-bands with relatively flat dispersion relationship.In addition,there exists acousto-optic interaction in the cavity constructed by the glide plane.The proposed waveguide has potential applications in the design of novel optomechanical devices.展开更多
The exploration of spin symmetry (SS) in nuclear physics has been instrumental in identifying atomic nucleus structures.In this study,we solve the Dirac equation from the relativistic mean field (RMF) in complex momen...The exploration of spin symmetry (SS) in nuclear physics has been instrumental in identifying atomic nucleus structures.In this study,we solve the Dirac equation from the relativistic mean field (RMF) in complex momentum representation.We investigated SS and its breaking in single-particle resonant states within deformed nuclei,with a focus on the illustrative nucleus168Er.This was the initial discovery of a resonant spin doublet in a deformed nucleus,with the expectation of the SS approaching the continuum threshold.With increasing single-particle energy,the splitting of the resonant spin doublets widened significantly.This escalating splitting implies diminishing adherence to the SS,indicating a departure from the expected behavior as the energy levels increase.We also analyzed the width of the resonant states,showing that lower orbital angular momentum resonances possess shorter decay times and that SS is preserved within broad resonant doublets,as opposed to narrow resonant doublets.Comparing the radial density of the upper components for the bound-state and resonant-state doublets,it becomes evident that while SS is well-preserved in the bound states,it deteriorates in the resonant states.The impact of nuclear deformation (β_(2)) on SS was examined,demonstrating that an increase in β_(2) resulted in higher energy and width splitting in the resonant spin doublets,which is attributed to increased component mixing.Furthermore,the sensitivity of spin doublets to various potential parameters such as surface diffuseness (a),radius (R),and depth (Σ0) is discussed,emphasizing the role of these parameters in SS.This study provides valuable insights into the behavior of spin doublets in deformed nuclei and their interplay with the nuclear structure,thereby advancing our understanding of SS in the resonance state.展开更多
We propose the new field potential by maintaining both the symmetry of the scalar gauge and the conservation law keeping N?ether’s theorem, while disregarding the symmetry of the vector gauge. The new potential forms...We propose the new field potential by maintaining both the symmetry of the scalar gauge and the conservation law keeping N?ether’s theorem, while disregarding the symmetry of the vector gauge. The new potential forms like the well-type potential where a particle behaves almost freely but is very hard to escape without external energy, which can be interpreted as local confinement and asymptotic freedom. By assuming a 2-dimensional metric tensor in 4-dimensional space-time, we suggest the existence of 3 kinds of particles that resemble QCD with 3 color charges. We also show that the mass term exists but comes to zero and derive the charge and spin values. We can regard the particle with this new potential as a gluon, and the interaction in this well-type potential as a strong interaction for the properties of mass, charge, spin, and its behavior. We suggest the eight-fold way with this new particle, which is similar to the existing method based on SU (3) symmetry. Even though the strong interaction has been analyzed in the standard model and string theory, we build a new consistent model based on the theory of relativity including Riemann geometry, and show the unification of gravitational and strong interactional field.展开更多
The kagome superconductor CsV_(3)Sb_(5) has attracted widespread attention due to its rich correlated electron states including superconductivity, charge density wave(CDW), nematicity, and pair density wave. Notably, ...The kagome superconductor CsV_(3)Sb_(5) has attracted widespread attention due to its rich correlated electron states including superconductivity, charge density wave(CDW), nematicity, and pair density wave. Notably, the modulation of the intertwined electronic orders by the chemical doping is significant to illuminate the cooperation/competition between multiple phases in kagome superconductors. In this study, we have synthesized a series of tantalum-substituted Cs(V_(1-x)Ta_(x))_(3)Sb_(5) by a modified self-flux method. Electrical transport measurements reveal that CDW is suppressed gradually and becomes undetectable as the doping content of x is over 0.07. Concurrently, the superconductivity is enhanced monotonically from T_(c) ~ 2.8 K at x = 0 to 5.2 K at x = 0.12. Intriguingly, in the absence of CDW, Cs(V_(1-x)Ta_(x))_(3)Sb_(5)(x = 0.12) crystals exhibit a pronounced two-fold symmetry of the in-plane angular-dependent magnetoresistance(AMR) in the superconducting state, indicating the anisotropic superconducting properties in the Cs(V_(1-x)Ta_(x))_(3)Sb_(5). Our findings demonstrate that Cs(V_(1-x)Ta_(x))_(3)Sb_(5) with the non-trivial band topology is an excellent platform to explore the superconductivity mechanism and intertwined electronic orders in quantum materials.展开更多
We present a method using Zernike moments for quantifying rotational and reflectional symmetries in scanning transmission electron microscopy(STEM)images,aimed at improving structural analysis of materials at the atom...We present a method using Zernike moments for quantifying rotational and reflectional symmetries in scanning transmission electron microscopy(STEM)images,aimed at improving structural analysis of materials at the atomic scale.This technique is effective against common imaging noises and is potentially suited for low-dose imaging and identifying quantum defects.We showcase its utility in the unsupervised segmentation of polytypes in a twisted bilayer TaS_(2),enabling accurate differentiation of structural phases and monitoring transitions caused by electron beam effects.This approach enhances the analysis of structural variations in crystalline materials,marking a notable advancement in the characterization of structures in materials science.展开更多
This paper deals with the radial symmetry of positive solutions to the nonlocal problem(-Δ)_(γ)~su=b(x)f(u)in B_(1){0},u=h in R~N B_(1),where b:B_1→R is locally Holder continuous,radially symmetric and decreasing i...This paper deals with the radial symmetry of positive solutions to the nonlocal problem(-Δ)_(γ)~su=b(x)f(u)in B_(1){0},u=h in R~N B_(1),where b:B_1→R is locally Holder continuous,radially symmetric and decreasing in the|x|direction,F:R→R is a Lipschitz function,h:B_1→R is radially symmetric,decreasing with respect to|x|in R^(N)/B_(1),B_(1) is the unit ball centered at the origin,and(-Δ)_γ~s is the weighted fractional Laplacian with s∈(0,1),γ∈[0,2s)defined by(-△)^(s)_(γ)u(x)=CN,slimδ→0+∫R^(N)/B_(δ)(x)u(x)-u(y)/|x-y|N+2s|y|^(r)dy.We consider the radial symmetry of isolated singular positive solutions to the nonlocal problem in whole space(-Δ)_(γ)^(s)u(x)=b(x)f(u)in R^(N)\{0},under suitable additional assumptions on b and f.Our symmetry results are derived by the method of moving planes,where the main difficulty comes from the weighted fractional Laplacian.Our results could be applied to get a sharp asymptotic for semilinear problems with the fractional Hardy operators(-Δ)^(s)u+μ/(|x|^(2s))u=b(x)f(u)in B_(1)\{0},u=h in R^(N)\B_(1),under suitable additional assumptions on b,f and h.展开更多
AIM:To investigate the symmetry of upper eyelid in patients with unilateral mild and moderate blepharoptosis who underwent unilateral minimally invasive combined fascia sheath(CFS)suspension.METHODS:A retrospective st...AIM:To investigate the symmetry of upper eyelid in patients with unilateral mild and moderate blepharoptosis who underwent unilateral minimally invasive combined fascia sheath(CFS)suspension.METHODS:A retrospective study of patients who underwent unilateral minimally invasive CFS suspension surgery between January 2018 and December 2021.Inclusion criteria included unilateral mild and moderate ptosis,good levator muscle function(>9 mm)and follow-up of at least 6mo.Pre-and post-operative symmetry was graded subjectively for marginal reflex distance 1(MRD1),tarsal platform show(TPS)and eyebrow fat span(BFS).A t-test was used to evaluate MRD1,TPS and BFS asymmetry by calculating delta values.The Bézier curve tool of the Image J software was used to extract the upper eyelid contours,where the symmetry was measured by the percentage of overlapping curvatures(POC).RESULTS:Totally 105 patients(105 eyelids)were included(mild group,n=84;moderate group,n=21).Postoperatively,all patients increased MRD1 and decreased TPS in the ptotic eye while maintaining unchanged BFS.The asymmetric delta value for MRD1 was measured to be 1.48±0.86 preoperatively,and it decreased to 0.58±0.67 postoperatively in all cases(P=0.0004).In patients with mild ptosis,the asymmetry value of TPS fell significantly from 1.15±0.62 to 0.68±0.38(P=0.0187).The symmetry of the upper eyelid contour increased in all subgroups of patients,with a POC of 59.39%±13.45%preoperatively and POC of 78.29%±13.80%postoperatively.CONCLUSION:Minimally invasive CFS suspension is proved to be an effective means of improving the symmetry of unilateral ptosis in terms of MRD1(all subgroups),POC(all subgroups)and TPS(only mild group),whereas BFS is unaffected.展开更多
We investigate the electronic structure of NbGeSb with non-symmorphic symmetry.We employ angle-resolved photoemission spectroscopy(ARPES)to observe and identify the bulk and surface states over the Brillouin zone.By u...We investigate the electronic structure of NbGeSb with non-symmorphic symmetry.We employ angle-resolved photoemission spectroscopy(ARPES)to observe and identify the bulk and surface states over the Brillouin zone.By utilizing high-energy photons,we identify the bulk Fermi surface and bulk nodal line along the direction X–R,while the Fermi surface of the surface state is observed by using low-energy photons.We observe the splitting of surface bands away from the high-symmetry point X.The density functional theory calculations on bulk and 1 to 5-layer slab models,as well as spin textures of NbGeSb,verify that the band splitting could be attributed to the Rashba-like spin–orbit coupling caused by space-inversion-symmetry breaking at the surface.These splitted surface bands cross with each other,forming two-dimensional Weyl-like crossings that are protected by mirror symmetry.Our findings provide insights into the two-dimensional topological and symmetry-protected band inversion of surface states.展开更多
Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation al...Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation allows the Burgers-STO(BSTO)decomposition,two types of reducible coupled BSTO decompositions and the BSTO-KdV decomposition.Furthermore,we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO decompositions.Using the framework of standard Lie point symmetry theory,these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.展开更多
The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the K...The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while ‘the half-quantum vortex street' is observed in the other component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence, and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately0.18, which is less than the stability condition 0.28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin–orbit coupling disrupts the symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize the Kármán vortex street in a system.展开更多
We report progress towards a modern scientific description of thermodynamic properties of fluids following the discovery (in 2012) of a coexisting critical density hiatus and a supercritical mesophase defined by perco...We report progress towards a modern scientific description of thermodynamic properties of fluids following the discovery (in 2012) of a coexisting critical density hiatus and a supercritical mesophase defined by percolation transitions. The state functions density ρ(p,T), and Gibbs energy G(p,T), of fluids, e.g. CO<sub>2</sub>, H<sub>2</sub>O and argon exhibit a symmetry characterised by the rigidity, ω = (dp/dρ)<sub>T</sub>, between gaseous and liquid states along any isotherm from critical (T<sub>c</sub>) to Boyle (T<sub>B</sub>) temperatures, on either side of the supercritical mesophase. Here, using experimental data for fluid argon, we investigate the low-density cluster physics description of an ideal dilute gas that obeys Dalton’s partial pressure law. Cluster expansions in powers of density relate to a supercritical liquid-phase rigidity symmetry (RS) line (ω = ρ<sub>rs</sub>(T) = RT) to gas phase virial coefficients. We show that it is continuous in all derivatives, linear within stable fluid phase, and relates analytically to the Boyle-work line (BW) (w = (p/ρ)<sub>T</sub> = RT), and to percolation lines of gas (PB) and liquid (PA) phases by: ρ<sub>BW</sub>(T) = 2ρ<sub>PA</sub>(T) = 3ρ<sub>PB</sub>(T) = 3ρ<sub>RS</sub>(T)/2 for T T<sub>B</sub>. These simple relationships arise, because the higher virial coefficients (b<sub>n</sub>, n ≥ 4) cancel due to clustering equilibria, or become negligible at all temperatures (0 T T<sub>B</sub>)<sub> </sub>within the gas phase. The Boyle-work line (p/ρ<sub>BW</sub>)<sub>T</sub> is related exactly at lower densities as T → T<sub>B</sub>, and accurately for liquid densities, by ρ<sub>BW</sub>(T) = −(b<sub>2</sub>/b<sub>3</sub>)<sub>T</sub>. The RS line, ω(T) = RT, defines a new liquid-density ground-state physical constant (ρ<sub>RS</sub>(0) = (2/3)ρ<sub>BW</sub>(0) for argon). Given the gas-liquid rigidity symmetry, the entire thermodynamic state functions below T<sub>B</sub> are obtainable from b<sub>2</sub>(T). A BW-line ground-state crystal density ρ<sub>BW</sub>(0) can be defined by the pair potential minimum. The Ar<sub>2</sub> pair potential, ∅ij</sub>(r<sub>ij</sub>) determines b<sub>2</sub>(T) analytically for all T. This report, therefore, advances the salient objective of liquid-state theory: an argon p(ρ,T) Equation-of-state is obtained from ∅<sub>ij</sub>(r<sub>ij</sub>) for all fluid states, without any adjustable parameters.展开更多
The nuclear charge radius plays a vital role in determining the equation of state of isospin asymmetric nuclear matter.Based on the correlation between the differences in charge radii of mirror-partner nuclei and the ...The nuclear charge radius plays a vital role in determining the equation of state of isospin asymmetric nuclear matter.Based on the correlation between the differences in charge radii of mirror-partner nuclei and the slope parameter(L)of symmetry energy at the nuclear saturation density,an analysis of the calibrated slope parameter L was performed in finite nuclei.In this study,relativistic and nonrelativistic energy density functionals were employed to constrain the nuclear symmetry energy through the available databases of the mirror-pair nuclei^(36)Ca–^(36)S,^(38)Ca–^(38)Ar,and ^(54)Ni–^(54)Fe.The deduced nuclear symmetry energy was located in the range 29.89–31.85 MeV,and L of the symmetry energy essentially covered the range 22.50–51.55 MeV at the saturation density.Moreover,the extracted L_(s) at the sensitivity density p_(s)=0.10 fm^(-3) was located in the interval range 30.52–39.76 MeV.展开更多
In this paper,we investigate the complex symmetric structure of Toeplitz operators T_(φ)on the Hardy space over the bidisk.We first characterize the weighted composition operators,W_(u,v)which are J-symmetric and uni...In this paper,we investigate the complex symmetric structure of Toeplitz operators T_(φ)on the Hardy space over the bidisk.We first characterize the weighted composition operators,W_(u,v)which are J-symmetric and unitary.As a consequence,we characterize conjugations of the form A_(u,v).In addition,a class of conjugations of the form C_(λ,a)is introduced.We show that the class of conjugations C_(λ,a)coincides with the class of conjugations A_(u,v);we then characterize the complex symmetry of the Toeplitz operators T_(φ)with respect to the conjugation C_(λ,a).展开更多
Two(3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion(CRE) method. Through localization of residual symmetries, symmetry reduction solutions of t...Two(3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion(CRE) method. Through localization of residual symmetries, symmetry reduction solutions of the two equations are obtained. The CRE method is applied to the two equations to obtain new B?cklund transformations from which a type of interesting interaction solution between solitons and periodic waves is generated.展开更多
We first confirm an idea obtained from first-principles calculations,which is in line with symmetry theory:Although superatomic molecular orbitals(SAMOs) can be classified according to their angular momentum similar t...We first confirm an idea obtained from first-principles calculations,which is in line with symmetry theory:Although superatomic molecular orbitals(SAMOs) can be classified according to their angular momentum similar to atomic orbitals,SAMOs with the same angular momentum split due to the point group symmetry of superatoms.Based on this idea,we develop a method to quantitatively modulate the splitting spacing of molecular orbitals in a superatom by changing its structural symmetry or by altering geometric parameters with the same symmetry through expansion and compression processes.Moreover,the modulation of the position crossover is achieved between the lowest unoccupied molecular orbital and the highest occupied molecular orbital originating from the splitting of different angular momenta,leading to an effective reduction in system energy.This phenomenon is in line with the implication of the Jahn–Teller effect.This work provides insights into understanding and regulating the electronic structures of superatoms.展开更多
The goal of our research was to determine a coupling between information theory, geometry and multi-dimensional projections. This was accomplished after preliminary mathematics was presented to determine an alternativ...The goal of our research was to determine a coupling between information theory, geometry and multi-dimensional projections. This was accomplished after preliminary mathematics was presented to determine an alternative method for the illustration of multi-dimensional spaces. That was developed with a unique series that gives structure to integer exponents of power sets. The desired coupling is concisely illustrated in a single figure which includes three cyclic phases that are isomorphic to the three phases of Euclidian, rectangular cuboids. The series enables projections between n- and m-dimensional volumes. The associated figure also illustrates how vertical and/or horizontal symmetry breaking or symmetry emits or absorbs information.展开更多
We investigate the fractional heat equation with fractional translation in both time and position with different fractional orders.As examples,we consider a rod and anα-disk with an initial constant temperature and d...We investigate the fractional heat equation with fractional translation in both time and position with different fractional orders.As examples,we consider a rod and anα-disk with an initial constant temperature and discuss their cooling processes in the examined formalism.展开更多
We study the space of stability conditions on K3 surfaces from the perspective of mirror symmetry. This is done in the attractor backgrounds(moduli). We find certain highly non-generic behaviors of marginal stability ...We study the space of stability conditions on K3 surfaces from the perspective of mirror symmetry. This is done in the attractor backgrounds(moduli). We find certain highly non-generic behaviors of marginal stability walls(a key notion in the study of wall crossings)in the space of stability conditions. These correspond via mirror symmetry to some nongeneric behaviors of special Lagrangians in an attractor background. The main results can be understood as a mirror correspondence in a synthesis of the homological mirror conjecture and SYZ mirror conjecture.展开更多
The main goal of this article is to present a new result of a possible approach to the geometrical description of the birth and evolution of the universe. The novelty of the article is that it is possible to explain t...The main goal of this article is to present a new result of a possible approach to the geometrical description of the birth and evolution of the universe. The novelty of the article is that it is possible to explain the nature of supersymmetry in terms of the geometric representation of the wave function and to propose a mechanism of spontaneous symmetry breaking of the excitation of the universe with different degrees of freedom. It is under such conditions that the well-known spontaneous symmetry breaking occurs and individual excitation acquires mass. At the same time, a phase transition of the first kind occurs with the formation of a new phase.展开更多
基金the National Natural Science Foun-dation of China(Grant No.11674102)。
文摘Based on the substitution rule and symmetry, we propose a method to generate an octagonal quasilattice consisting ofsquare and rhombus tiles. Local configurations and Ammann lines are used to guide the growth of the tiles in a quasiperiodicorder. The structure obtained is a perfect eight-fold symmetric quasilattice, which is confirmed by the radial distributionfunction and the diffraction pattern.
基金Project supported by the National Natural Science Foundation of China(Grant No.12064025)the Natural Science Foundation of Jiangxi Province,China(Grant No.20212ACB202006)+1 种基金the Major Discipline Academic and Technical Leaders Training Program of Jiangxi Province,China(Grant No.20204BCJ22012)the Open Project of the Key Laboratory of Radar Imaging and Microwave Photonic Technology of the Education Ministry of China.
文摘A phoxonic crystal waveguide with the glide symmetry is designed,in which both electromagnetic and elastic waves can propagate along the glide plane at the same time.Due to the glide symmetry,the bands of the phoxonic crystal super-cell degenerate in pairs at the boundary of the Brillouin zone.This is the so-called band-sticking effect and it causes the appearance of gapless guided-modes.By adjusting the magnitude of the glide dislocation the edge bandgaps,the bandgap of the guided-modes at the boundary of the Brillouin zone,can be further adjusted.The photonic and phononic guided-modes can then possess only one mode for a certain frequency with relatively low group velocities,achieving single-mode guided-bands with relatively flat dispersion relationship.In addition,there exists acousto-optic interaction in the cavity constructed by the glide plane.The proposed waveguide has potential applications in the design of novel optomechanical devices.
基金supported by the National Natural Science Foundation of China(No.11935001)the Natural Science Foundation of Anhui Province(No.2008085MA26).
文摘The exploration of spin symmetry (SS) in nuclear physics has been instrumental in identifying atomic nucleus structures.In this study,we solve the Dirac equation from the relativistic mean field (RMF) in complex momentum representation.We investigated SS and its breaking in single-particle resonant states within deformed nuclei,with a focus on the illustrative nucleus168Er.This was the initial discovery of a resonant spin doublet in a deformed nucleus,with the expectation of the SS approaching the continuum threshold.With increasing single-particle energy,the splitting of the resonant spin doublets widened significantly.This escalating splitting implies diminishing adherence to the SS,indicating a departure from the expected behavior as the energy levels increase.We also analyzed the width of the resonant states,showing that lower orbital angular momentum resonances possess shorter decay times and that SS is preserved within broad resonant doublets,as opposed to narrow resonant doublets.Comparing the radial density of the upper components for the bound-state and resonant-state doublets,it becomes evident that while SS is well-preserved in the bound states,it deteriorates in the resonant states.The impact of nuclear deformation (β_(2)) on SS was examined,demonstrating that an increase in β_(2) resulted in higher energy and width splitting in the resonant spin doublets,which is attributed to increased component mixing.Furthermore,the sensitivity of spin doublets to various potential parameters such as surface diffuseness (a),radius (R),and depth (Σ0) is discussed,emphasizing the role of these parameters in SS.This study provides valuable insights into the behavior of spin doublets in deformed nuclei and their interplay with the nuclear structure,thereby advancing our understanding of SS in the resonance state.
文摘We propose the new field potential by maintaining both the symmetry of the scalar gauge and the conservation law keeping N?ether’s theorem, while disregarding the symmetry of the vector gauge. The new potential forms like the well-type potential where a particle behaves almost freely but is very hard to escape without external energy, which can be interpreted as local confinement and asymptotic freedom. By assuming a 2-dimensional metric tensor in 4-dimensional space-time, we suggest the existence of 3 kinds of particles that resemble QCD with 3 color charges. We also show that the mass term exists but comes to zero and derive the charge and spin values. We can regard the particle with this new potential as a gluon, and the interaction in this well-type potential as a strong interaction for the properties of mass, charge, spin, and its behavior. We suggest the eight-fold way with this new particle, which is similar to the existing method based on SU (3) symmetry. Even though the strong interaction has been analyzed in the standard model and string theory, we build a new consistent model based on the theory of relativity including Riemann geometry, and show the unification of gravitational and strong interactional field.
基金Project supported by the National Key R&D Program of China(Grant No.2022YFA1204100)the National Natural Science Foundation of China(Grant No.62488201)+1 种基金the Chinese Academy of Sciences(Grant Nos.XDB33030000,ZDBS-SSW-WHC001,YSBR-003,and YSBR-053)Innovation Program of Quantum Science and Technology(Grant No.2021ZD0302700)。
文摘The kagome superconductor CsV_(3)Sb_(5) has attracted widespread attention due to its rich correlated electron states including superconductivity, charge density wave(CDW), nematicity, and pair density wave. Notably, the modulation of the intertwined electronic orders by the chemical doping is significant to illuminate the cooperation/competition between multiple phases in kagome superconductors. In this study, we have synthesized a series of tantalum-substituted Cs(V_(1-x)Ta_(x))_(3)Sb_(5) by a modified self-flux method. Electrical transport measurements reveal that CDW is suppressed gradually and becomes undetectable as the doping content of x is over 0.07. Concurrently, the superconductivity is enhanced monotonically from T_(c) ~ 2.8 K at x = 0 to 5.2 K at x = 0.12. Intriguingly, in the absence of CDW, Cs(V_(1-x)Ta_(x))_(3)Sb_(5)(x = 0.12) crystals exhibit a pronounced two-fold symmetry of the in-plane angular-dependent magnetoresistance(AMR) in the superconducting state, indicating the anisotropic superconducting properties in the Cs(V_(1-x)Ta_(x))_(3)Sb_(5). Our findings demonstrate that Cs(V_(1-x)Ta_(x))_(3)Sb_(5) with the non-trivial band topology is an excellent platform to explore the superconductivity mechanism and intertwined electronic orders in quantum materials.
基金funding support from the National Research Foundation (Competitive Research Program grant number NRF-CRP16-2015-05)the National University of Singapore Early Career Research Award+1 种基金supported by the Eric and Wendy Schmidt AI in Science Postdoctoral Fellowshipa Schmidt Sciences program。
文摘We present a method using Zernike moments for quantifying rotational and reflectional symmetries in scanning transmission electron microscopy(STEM)images,aimed at improving structural analysis of materials at the atomic scale.This technique is effective against common imaging noises and is potentially suited for low-dose imaging and identifying quantum defects.We showcase its utility in the unsupervised segmentation of polytypes in a twisted bilayer TaS_(2),enabling accurate differentiation of structural phases and monitoring transitions caused by electron beam effects.This approach enhances the analysis of structural variations in crystalline materials,marking a notable advancement in the characterization of structures in materials science.
基金supported by the NSFC(12001252)the Jiangxi Provincial Natural Science Foundation(20232ACB211001)。
文摘This paper deals with the radial symmetry of positive solutions to the nonlocal problem(-Δ)_(γ)~su=b(x)f(u)in B_(1){0},u=h in R~N B_(1),where b:B_1→R is locally Holder continuous,radially symmetric and decreasing in the|x|direction,F:R→R is a Lipschitz function,h:B_1→R is radially symmetric,decreasing with respect to|x|in R^(N)/B_(1),B_(1) is the unit ball centered at the origin,and(-Δ)_γ~s is the weighted fractional Laplacian with s∈(0,1),γ∈[0,2s)defined by(-△)^(s)_(γ)u(x)=CN,slimδ→0+∫R^(N)/B_(δ)(x)u(x)-u(y)/|x-y|N+2s|y|^(r)dy.We consider the radial symmetry of isolated singular positive solutions to the nonlocal problem in whole space(-Δ)_(γ)^(s)u(x)=b(x)f(u)in R^(N)\{0},under suitable additional assumptions on b and f.Our symmetry results are derived by the method of moving planes,where the main difficulty comes from the weighted fractional Laplacian.Our results could be applied to get a sharp asymptotic for semilinear problems with the fractional Hardy operators(-Δ)^(s)u+μ/(|x|^(2s))u=b(x)f(u)in B_(1)\{0},u=h in R^(N)\B_(1),under suitable additional assumptions on b,f and h.
基金Supported by Tianjin Key Medical Discipline Construction Project(No.TJYXZDXK-016A).
文摘AIM:To investigate the symmetry of upper eyelid in patients with unilateral mild and moderate blepharoptosis who underwent unilateral minimally invasive combined fascia sheath(CFS)suspension.METHODS:A retrospective study of patients who underwent unilateral minimally invasive CFS suspension surgery between January 2018 and December 2021.Inclusion criteria included unilateral mild and moderate ptosis,good levator muscle function(>9 mm)and follow-up of at least 6mo.Pre-and post-operative symmetry was graded subjectively for marginal reflex distance 1(MRD1),tarsal platform show(TPS)and eyebrow fat span(BFS).A t-test was used to evaluate MRD1,TPS and BFS asymmetry by calculating delta values.The Bézier curve tool of the Image J software was used to extract the upper eyelid contours,where the symmetry was measured by the percentage of overlapping curvatures(POC).RESULTS:Totally 105 patients(105 eyelids)were included(mild group,n=84;moderate group,n=21).Postoperatively,all patients increased MRD1 and decreased TPS in the ptotic eye while maintaining unchanged BFS.The asymmetric delta value for MRD1 was measured to be 1.48±0.86 preoperatively,and it decreased to 0.58±0.67 postoperatively in all cases(P=0.0004).In patients with mild ptosis,the asymmetry value of TPS fell significantly from 1.15±0.62 to 0.68±0.38(P=0.0187).The symmetry of the upper eyelid contour increased in all subgroups of patients,with a POC of 59.39%±13.45%preoperatively and POC of 78.29%±13.80%postoperatively.CONCLUSION:Minimally invasive CFS suspension is proved to be an effective means of improving the symmetry of unilateral ptosis in terms of MRD1(all subgroups),POC(all subgroups)and TPS(only mild group),whereas BFS is unaffected.
基金Project supported by the National Key Research and Development Program of China(Grant No.2022YFA1403803)H.M.is supported by the Fundamental Research Funds for the Central Universities,and the Research Funds of Renmin University of China(Grant No.22XNH099)+7 种基金The results of DFT calculations described in this paper are supported by HPC Cluster of ITP-CAS.M.L.is supported by the National Natural Science Foundation of China(Grant No.12204536)the Fundamental Research Funds for the Central Universities,and the Research Funds of People’s Public Security University of China(PPSUC)(Grant No.2023JKF02ZK09)T.L.X.is supported by the National Key R&D Program of China(Grant No.2019YFA0308602)the National Natural Science Foundation of China(Grant Nos.12074425 and 11874422)Y.Y.W.is supported by the National Natural Science Foundation of China(Grant No.12104011)H.Y.L.is supported by the National Natural Science Foundation of China(Grant No.12074213)the Major Basic Program of Natural Science Foundation of Shandong Province(Grant No.ZR2021ZD01)the Project of Introduction and Cultivation for Young Innovative Talents in Colleges and Universities of Shandong Province.
文摘We investigate the electronic structure of NbGeSb with non-symmorphic symmetry.We employ angle-resolved photoemission spectroscopy(ARPES)to observe and identify the bulk and surface states over the Brillouin zone.By utilizing high-energy photons,we identify the bulk Fermi surface and bulk nodal line along the direction X–R,while the Fermi surface of the surface state is observed by using low-energy photons.We observe the splitting of surface bands away from the high-symmetry point X.The density functional theory calculations on bulk and 1 to 5-layer slab models,as well as spin textures of NbGeSb,verify that the band splitting could be attributed to the Rashba-like spin–orbit coupling caused by space-inversion-symmetry breaking at the surface.These splitted surface bands cross with each other,forming two-dimensional Weyl-like crossings that are protected by mirror symmetry.Our findings provide insights into the two-dimensional topological and symmetry-protected band inversion of surface states.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12235007, 11975131, and 12275144)the K. C. Wong Magna Fund in Ningbo Universitythe Natural Science Foundation of Zhejiang Province of China (Grant No. LQ20A010009)
文摘Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation allows the Burgers-STO(BSTO)decomposition,two types of reducible coupled BSTO decompositions and the BSTO-KdV decomposition.Furthermore,we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO decompositions.Using the framework of standard Lie point symmetry theory,these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12065022 and 12147213)。
文摘The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while ‘the half-quantum vortex street' is observed in the other component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence, and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately0.18, which is less than the stability condition 0.28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin–orbit coupling disrupts the symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize the Kármán vortex street in a system.
文摘We report progress towards a modern scientific description of thermodynamic properties of fluids following the discovery (in 2012) of a coexisting critical density hiatus and a supercritical mesophase defined by percolation transitions. The state functions density ρ(p,T), and Gibbs energy G(p,T), of fluids, e.g. CO<sub>2</sub>, H<sub>2</sub>O and argon exhibit a symmetry characterised by the rigidity, ω = (dp/dρ)<sub>T</sub>, between gaseous and liquid states along any isotherm from critical (T<sub>c</sub>) to Boyle (T<sub>B</sub>) temperatures, on either side of the supercritical mesophase. Here, using experimental data for fluid argon, we investigate the low-density cluster physics description of an ideal dilute gas that obeys Dalton’s partial pressure law. Cluster expansions in powers of density relate to a supercritical liquid-phase rigidity symmetry (RS) line (ω = ρ<sub>rs</sub>(T) = RT) to gas phase virial coefficients. We show that it is continuous in all derivatives, linear within stable fluid phase, and relates analytically to the Boyle-work line (BW) (w = (p/ρ)<sub>T</sub> = RT), and to percolation lines of gas (PB) and liquid (PA) phases by: ρ<sub>BW</sub>(T) = 2ρ<sub>PA</sub>(T) = 3ρ<sub>PB</sub>(T) = 3ρ<sub>RS</sub>(T)/2 for T T<sub>B</sub>. These simple relationships arise, because the higher virial coefficients (b<sub>n</sub>, n ≥ 4) cancel due to clustering equilibria, or become negligible at all temperatures (0 T T<sub>B</sub>)<sub> </sub>within the gas phase. The Boyle-work line (p/ρ<sub>BW</sub>)<sub>T</sub> is related exactly at lower densities as T → T<sub>B</sub>, and accurately for liquid densities, by ρ<sub>BW</sub>(T) = −(b<sub>2</sub>/b<sub>3</sub>)<sub>T</sub>. The RS line, ω(T) = RT, defines a new liquid-density ground-state physical constant (ρ<sub>RS</sub>(0) = (2/3)ρ<sub>BW</sub>(0) for argon). Given the gas-liquid rigidity symmetry, the entire thermodynamic state functions below T<sub>B</sub> are obtainable from b<sub>2</sub>(T). A BW-line ground-state crystal density ρ<sub>BW</sub>(0) can be defined by the pair potential minimum. The Ar<sub>2</sub> pair potential, ∅ij</sub>(r<sub>ij</sub>) determines b<sub>2</sub>(T) analytically for all T. This report, therefore, advances the salient objective of liquid-state theory: an argon p(ρ,T) Equation-of-state is obtained from ∅<sub>ij</sub>(r<sub>ij</sub>) for all fluid states, without any adjustable parameters.
基金supported by the Key Laboratory of High Precision Nuclear Spectroscopy,Institute of Modern Physics,Chinese Academy of Sciences,the National Natural Science Foundation of China(Nos.12135004,11635003,11961141004,12275025,and 11975096)the Fundamental Research Funds for Central Universities(No.2020NTST06).
文摘The nuclear charge radius plays a vital role in determining the equation of state of isospin asymmetric nuclear matter.Based on the correlation between the differences in charge radii of mirror-partner nuclei and the slope parameter(L)of symmetry energy at the nuclear saturation density,an analysis of the calibrated slope parameter L was performed in finite nuclei.In this study,relativistic and nonrelativistic energy density functionals were employed to constrain the nuclear symmetry energy through the available databases of the mirror-pair nuclei^(36)Ca–^(36)S,^(38)Ca–^(38)Ar,and ^(54)Ni–^(54)Fe.The deduced nuclear symmetry energy was located in the range 29.89–31.85 MeV,and L of the symmetry energy essentially covered the range 22.50–51.55 MeV at the saturation density.Moreover,the extracted L_(s) at the sensitivity density p_(s)=0.10 fm^(-3) was located in the interval range 30.52–39.76 MeV.
基金partially the National Natural Science Foundation of China(11771340,12101179,12171373)。
文摘In this paper,we investigate the complex symmetric structure of Toeplitz operators T_(φ)on the Hardy space over the bidisk.We first characterize the weighted composition operators,W_(u,v)which are J-symmetric and unitary.As a consequence,we characterize conjugations of the form A_(u,v).In addition,a class of conjugations of the form C_(λ,a)is introduced.We show that the class of conjugations C_(λ,a)coincides with the class of conjugations A_(u,v);we then characterize the complex symmetry of the Toeplitz operators T_(φ)with respect to the conjugation C_(λ,a).
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11975156 and 12175148)。
文摘Two(3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion(CRE) method. Through localization of residual symmetries, symmetry reduction solutions of the two equations are obtained. The CRE method is applied to the two equations to obtain new B?cklund transformations from which a type of interesting interaction solution between solitons and periodic waves is generated.
基金supported by the National Natural Science Foundation of China(Grant Nos.11974136 and 11674123)。
文摘We first confirm an idea obtained from first-principles calculations,which is in line with symmetry theory:Although superatomic molecular orbitals(SAMOs) can be classified according to their angular momentum similar to atomic orbitals,SAMOs with the same angular momentum split due to the point group symmetry of superatoms.Based on this idea,we develop a method to quantitatively modulate the splitting spacing of molecular orbitals in a superatom by changing its structural symmetry or by altering geometric parameters with the same symmetry through expansion and compression processes.Moreover,the modulation of the position crossover is achieved between the lowest unoccupied molecular orbital and the highest occupied molecular orbital originating from the splitting of different angular momenta,leading to an effective reduction in system energy.This phenomenon is in line with the implication of the Jahn–Teller effect.This work provides insights into understanding and regulating the electronic structures of superatoms.
文摘The goal of our research was to determine a coupling between information theory, geometry and multi-dimensional projections. This was accomplished after preliminary mathematics was presented to determine an alternative method for the illustration of multi-dimensional spaces. That was developed with a unique series that gives structure to integer exponents of power sets. The desired coupling is concisely illustrated in a single figure which includes three cyclic phases that are isomorphic to the three phases of Euclidian, rectangular cuboids. The series enables projections between n- and m-dimensional volumes. The associated figure also illustrates how vertical and/or horizontal symmetry breaking or symmetry emits or absorbs information.
基金supported by the Internal Project of Excellent Research of the Faculty of Science of Hradec KrálovéUniversity(Grant No.2022/2218)。
文摘We investigate the fractional heat equation with fractional translation in both time and position with different fractional orders.As examples,we consider a rod and anα-disk with an initial constant temperature and discuss their cooling processes in the examined formalism.
文摘We study the space of stability conditions on K3 surfaces from the perspective of mirror symmetry. This is done in the attractor backgrounds(moduli). We find certain highly non-generic behaviors of marginal stability walls(a key notion in the study of wall crossings)in the space of stability conditions. These correspond via mirror symmetry to some nongeneric behaviors of special Lagrangians in an attractor background. The main results can be understood as a mirror correspondence in a synthesis of the homological mirror conjecture and SYZ mirror conjecture.
文摘The main goal of this article is to present a new result of a possible approach to the geometrical description of the birth and evolution of the universe. The novelty of the article is that it is possible to explain the nature of supersymmetry in terms of the geometric representation of the wave function and to propose a mechanism of spontaneous symmetry breaking of the excitation of the universe with different degrees of freedom. It is under such conditions that the well-known spontaneous symmetry breaking occurs and individual excitation acquires mass. At the same time, a phase transition of the first kind occurs with the formation of a new phase.
