We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameteri...We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.展开更多
This paper is concerned with the (2+1)-dimensional Burgers' and heat types of equations.All of the geometic vector fields of the equations are obtained,an optimal system of the equation is presented.Especially,the...This paper is concerned with the (2+1)-dimensional Burgers' and heat types of equations.All of the geometic vector fields of the equations are obtained,an optimal system of the equation is presented.Especially,the Bcklund transformations (BTs) for the Burgers' equations are constructed based on the symmetry.Then,all of the symmetry reductions are provided in terms of the optimal system method,and the exact explicit solutions are investigated by the symmetry reductions and Bcklund transformations.展开更多
We investigate the quantum numbers of the pentaquark states Pc+,which are composed of 4(three flavors)quarks and an antiquark,by analyzing their inherent nodal structure in this paper.Assuming that the four quarks for...We investigate the quantum numbers of the pentaquark states Pc+,which are composed of 4(three flavors)quarks and an antiquark,by analyzing their inherent nodal structure in this paper.Assuming that the four quarks form a tetrahedron or a square,and the antiquark is at the ground state,we determine the nodeless structure of the states with orbital angular moment L≤3,and in turn,the accessible low-lying states.Since the inherent nodal structure depends only on the inherent geometric symmetry,we propose the quantum numbers JPof the low-lying pentaquark states P_c^+may be■,■,■and■,independent of dynamical models.展开更多
In this work,we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics,scientific fields,and ocean engineering.This equation will be reduced to the Korteweg-de Vries...In this work,we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics,scientific fields,and ocean engineering.This equation will be reduced to the Korteweg-de Vries equation via using the perturbation analysis.We derive the corresponding vectors,symmetry reduction and explicit solutions for this equation.We readily obtain Bäcklund transformation associated with truncated Painlevéexpansion.We also examine the related conservation laws of this equation via using the multiplier method.Moreover,we investigate the reciprocal Bäcklund transformations of the derived conservation laws for the first time.展开更多
Three dimensional space is said to be spherically symmetric if it admits SO(3) as the group of isometries. Under this symmetry condition, the Einstein’s Field equations for vacuum, yields the Schwarzschild Metric as ...Three dimensional space is said to be spherically symmetric if it admits SO(3) as the group of isometries. Under this symmetry condition, the Einstein’s Field equations for vacuum, yields the Schwarzschild Metric as the unique solution, which essentially is the statement of the well known Birkhoff’s Theorem. Geometrically speaking this theorem claims that the pseudo-Riemanian space-times provide more isometries than expected from the original metric holonomy/ansatz. In this paper we use the method of Lie Symmetry Analysis to analyze the Einstein’s Vacuum Field Equations so as to obtain the Symmetry Generators of the corresponding Differential Equation. Additionally, applying the Noether Point Symmetry method we have obtained the conserved quantities corresponding to the generators of the Schwarzschild Lagrangian and paving way to reformulate the Birkhoff’s Theorem from a different approach.展开更多
The SERS spectrum of C_(60) was obtained by using silver mirror. From the SERS spectrum of C_(60) and the IR spectrum of C_(60), we proposed that C_(60) adsorbed on the silver mirror adopts a more ellipsoidal shape.
Objective To discuss the etiology,course of diseases and prognosis of symmetry peripheral entrapment enuropathies of upper extremity. Methods The etiology, clinical scale and resluts of 14 cases were analyzed betwen 1...Objective To discuss the etiology,course of diseases and prognosis of symmetry peripheral entrapment enuropathies of upper extremity. Methods The etiology, clinical scale and resluts of 14 cases were analyzed betwen 1999 and April 2002. Results In the bilateral tunnel syndrome, the excellent and good rate was 60% at the original side and 80% at the contralateral side occurred later. In the bilateral carpal tunnel syndrome, the excellent and good rate was 67% at the original side and 89% at the contralateral side occurred later. Conclusion The main etiological factor of the bilateral cubital tunnel syndrome was the elbow eversion deformity. The lesions of synovium contributed mainly to the symmetry carpal tunnel syndrome. The symmetry peripheral entrapment neuropathies of upper extremity should be operated on as soon as possible when diagnosis had been made for enhancement of treatment outcome. 5 refs,2 tabs.展开更多
This paper is devoted to the investigation of the Landau–Ginzburg–Higgs equation(LGHe),which serves as a mathematical model to understand phenomena such as superconductivity and cyclotron waves.The LGHe finds applic...This paper is devoted to the investigation of the Landau–Ginzburg–Higgs equation(LGHe),which serves as a mathematical model to understand phenomena such as superconductivity and cyclotron waves.The LGHe finds applications in various scientific fields,including fluid dynamics,plasma physics,biological systems,and electricity-electronics.The study adopts Lie symmetry analysis as the primary framework for exploration.This analysis involves the identification of Lie point symmetries that are admitted by the differential equation.By leveraging these Lie point symmetries,symmetry reductions are performed,leading to the discovery of group invariant solutions.To obtain explicit solutions,several mathematical methods are applied,including Kudryashov's method,the extended Jacobi elliptic function expansion method,the power series method,and the simplest equation method.These methods yield solutions characterized by exponential,hyperbolic,and elliptic functions.The obtained solutions are visually represented through 3D,2D,and density plots,which effectively illustrate the nature of the solutions.These plots depict various patterns,such as kink-shaped,singular kink-shaped,bell-shaped,and periodic solutions.Finally,the paper employs the multiplier method and the conservation theorem introduced by Ibragimov to derive conserved vectors.These conserved vectors play a crucial role in the study of physical quantities,such as the conservation of energy and momentum,and contribute to the understanding of the underlying physics of the system.展开更多
In this paper,we use the symmetry of the Lie group analysis as one of the powerful tools that deals with the wide class of fractional order differential equations in the Riemann–Liouville concept.In this study,first,...In this paper,we use the symmetry of the Lie group analysis as one of the powerful tools that deals with the wide class of fractional order differential equations in the Riemann–Liouville concept.In this study,first,we employ the classical and nonclassical Lie symmetries(LS)to acquire similarity reductions of the nonlinear fractional far field Korteweg–de Vries(KdV)equation,and second,we find the related exact solutions for the derived generators.Finally,according to the LS generators acquired,we construct conservation laws for related classical and nonclassical vector fields of the fractional far field KdV equation.展开更多
As one of the paradigmatic models of non-equilibrium systems, the asymmetric simple exclusion process（ASEP） has been widely used to study many physical, chemical, and biological systems. The ASEP shows a range of no...As one of the paradigmatic models of non-equilibrium systems, the asymmetric simple exclusion process（ASEP） has been widely used to study many physical, chemical, and biological systems. The ASEP shows a range of nontrivial macroscopic phenomena, among which, the spontaneous symmetry breaking has gained a great deal of attention. Nevertheless,as a basic problem, it has been controversial whether there exist one or two symmetry-broken phases in the ASEP. Based on the mean field analysis and current minimization principle, this paper demonstrates that one of the broken-symmetry phases does not exist in a bidirectional two-lane ASEP with narrow entrances. Moreover, an exponential decay feature is observed,which has been used to predict the phase boundary in the thermodynamic limit. Our findings might be generalized to other ASEP models and thus deepen the understanding of the spontaneous symmetry breaking in non-equilibrium systems.展开更多
Unconventional magnetism,including altermagnetism and unconventional compensated magnetism,characterized by its duality of real-space antiferromagnetic alignment and momentum-space spin splitting,has garnered widespre...Unconventional magnetism,including altermagnetism and unconventional compensated magnetism,characterized by its duality of real-space antiferromagnetic alignment and momentum-space spin splitting,has garnered widespread attention.While altermagnetism has been extensively studied,research on unconventional compensated magnetism remains very rare.In particular,unconventional compensated magnetic materials are only theoretically predicted and have not yet been synthesized experimentally.In this study,based on symmetry analysis and frst-principles electronic structure calculations,we predict that LaMn_(2)SbO_(6)is an unconventional compensated magnetic semiconductor.Given that the Mn ions at opposite spin lattice cannot be connected by any symmetry,the spin splitting in LaMn_(2)SbO_(6)is isotropic.More importantly,LaMn_(2)SbO_(6)has already been synthesized experimentally,and its magnetic structure has been confrmed by neutron scattering experiments.Therefore,LaMn_(2)SbO_(6)serves as an excellent material platform for investigating the novel physical properties of unconventional compensated magnetic materials.展开更多
Intrinsic two-dimensional(2D)ferromagnetic(FM)semiconductors have attracted extensive attentions for their potential applications in next-generation spintronics devices.In recent years,the van der Waals material VI_(3...Intrinsic two-dimensional(2D)ferromagnetic(FM)semiconductors have attracted extensive attentions for their potential applications in next-generation spintronics devices.In recent years,the van der Waals material VI_(3) has been experimentally found to be an intrinsic FM semiconductor.However,the electronic structure of the VI_(3) is not fully understood.To reveal why the VI_(3)is a ferromagnetic semiconductor with strong out-of-plane anisotropy,we systematically studied the electronic structure of the monolayer VI_(3).Our results confirm that the monolayer VI_(3) is a Mott insulator,and d^(2) electrons occupy a_(g) and e_(g)^(π+) orbitals.The half-metallic state is a metastable state with a total energy 0.7 e V higher than the ferromagnetic Mott insulating state.Furthermore,our study confirmed that the VI_(3)exhibits the out-of-plane magnetic anisotropy,which originates from d^(2) electrons occupying low-lying agand egπ+orbitals.Since the orbital angular momentum of the e_(g)^(π+) state is not completely quenched,the VI_(3) has the out-of-plane anisotropy under interplay between the spin-orbit coupling and crystal field.Our study provides valuable guidance for the design of 2D magnetic materials with pronounced out-of-plane anisotropy.展开更多
As a celebrated nonlinear water wave equation,the Davey–Stewartson equation is widely studied by researchers,especially in the field of mathematical physics.On the basis of the Riemann–Liouville fractional derivativ...As a celebrated nonlinear water wave equation,the Davey–Stewartson equation is widely studied by researchers,especially in the field of mathematical physics.On the basis of the Riemann–Liouville fractional derivative,the time-fractional Davey–Stewartson equation is investigated in this paper.By application of the Lie symmetry analysis approach,the Lie point symmetries and symmetry groups are obtained.At the same time,the similarity reductions are derived.Furthermore,the equation is converted to a system of fractional partial differential equations and a system of fractional ordinary differential equations in the sense of Riemann–Liouville fractional derivative.By virtue of the symmetry corresponding to the scalar transformation,the equation is converted to a system of fractional ordinary differential equations in the sense of Erdélyi–Kober fractional integro-differential operators.By using Noether’s theorem and Ibragimov’s new conservation theorem,the conserved vectors and the conservation laws are derived.Finally,the traveling wave solutions are achieved and plotted.展开更多
The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible third grade fluid bounded by an infinite porous plate is studied with the Hall effect. An external uniform magnetic field is a...The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible third grade fluid bounded by an infinite porous plate is studied with the Hall effect. An external uniform magnetic field is applied perpendicular to the plate and the fluid motion is subjected to a uniform suction and injection. Similarity transformations are employed to reduce the non-linear equations governing the flow under discussion to two ordinary differential equations （with and without dispersion terms）. Using the finite difference scheme, numerical solutions represented by graphs with reference to the various involved parameters of interest are discussed and appropriate conclusions are drawn.展开更多
In this article,we explore the famous Selkov–Schnakenberg(SS)system of coupled nonlinear partial differential equations(PDEs)for Lie symmetry analysis,self-adjointness,and conservation laws.Moreover,miscellaneous sol...In this article,we explore the famous Selkov–Schnakenberg(SS)system of coupled nonlinear partial differential equations(PDEs)for Lie symmetry analysis,self-adjointness,and conservation laws.Moreover,miscellaneous soliton solutions like dark,bright,periodic,rational,Jacobian elliptic function,Weierstrass elliptic function,and hyperbolic solutions of the SS system will be achieved by a well-known technique called sub-ordinary differential equations.All these results are displayed graphically by 3D,2D,and contour plots.展开更多
We investigate the Einstein field equations corresponding to the Weyl-Lewis-Papapetrou form for an axisymmetric rotating field by using the classical symmetry method. Using the invafiance group properties of the gover...We investigate the Einstein field equations corresponding to the Weyl-Lewis-Papapetrou form for an axisymmetric rotating field by using the classical symmetry method. Using the invafiance group properties of the governing system of partial differential equations （PDEs） and admitting a Lie group of point transformations with commuting infinitesimal generators, we obtain exact solutions to the system of PDEs describing the Einstein field equations. Some appropriate canonical variables are characterized that transform the equations at hand to an equivalent system of ordinary differential equations and some physically important analytic solutions of field equations are constructed. Also, the class of axially symmetric solutions of Einstein field equations including the Papapetrou solution as a particular case has been found.展开更多
In this paper, the Lie symmetry analysis method is applied to the time-fractional Boussinesq–Burgers system which is used to describe shallow water waves near an ocean coast or in a lake.We obtain all the Lie symmetr...In this paper, the Lie symmetry analysis method is applied to the time-fractional Boussinesq–Burgers system which is used to describe shallow water waves near an ocean coast or in a lake.We obtain all the Lie symmetries admitted by the system and use them to reduce the fractional partial differential equations with a Riemann–Liouville fractional derivative to some fractional ordinary differential equations with an Erdélyi–Kober fractional derivative, thereby getting some exact solutions of the reduced equations. For power series solutions, we prove their convergence and show the dynamic analysis of their truncated graphs. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equations studied.展开更多
In this manuscript, we first perform a complete Lie symmetry classification for a higher-dimensional shallow water wave equation and then construct the corresponding reduced equations with the obtained Lie symmetries....In this manuscript, we first perform a complete Lie symmetry classification for a higher-dimensional shallow water wave equation and then construct the corresponding reduced equations with the obtained Lie symmetries. Moreover, with the extended <em>F</em>-expansion method, we obtain several new nonlinear wave solutions involving differentiable arbitrary functions, expressed by Jacobi elliptic function, Weierstrass elliptic function, hyperbolic function and trigonometric function.展开更多
Two-dimensional(2D)topological insulators with symmetry-protected helical edge states have drawn significant interest.The recently synthesized layered2D electride BaCu features a monolayer structure with intriguing ba...Two-dimensional(2D)topological insulators with symmetry-protected helical edge states have drawn significant interest.The recently synthesized layered2D electride BaCu features a monolayer structure with intriguing band crossings near Fermi level and a low exfoliation energy.In this study,firstprinciples calculations combined with symmetry analysis reveal that the BaCu monolayer behaves as a 2D topological insulator(TI)nature.When integrated with a 30°twisted√3 p×√3 hexagonal boron nitride(h-BN)supercell,the resulting twistedα/β-BaCu/BN heterobilayers exhibit 2D Weyl points and type-III Dirac points,respectively,demonstrating that twist angle can effectively modulate topological properties.Interestingly,ab initio molecular dynamics(AIMD)simulations reveal a spontaneous transition fromthe metastableβ-BaCu/BN toα-BaCu/BN configuration,indicating a low energy barrier and highlighting the potential for propertymodulation,emphasizing the versatility of twisted structures for tuning topological states.This work establishes a robust platform for exploring twist-angleinduced topological electride states,broadening the scope for future investigations.展开更多
In this paper,Lie symmetry analysis method is applied to one type of mathematical physics equations named the(2+1)-dimensional fractional Hirota-Maccari system.All Lie symmetries and the corresponding conserved vector...In this paper,Lie symmetry analysis method is applied to one type of mathematical physics equations named the(2+1)-dimensional fractional Hirota-Maccari system.All Lie symmetries and the corresponding conserved vectors for the system are obtained.The one-dimensional optimai system is utilized to reduce the aimed equations with Riemann-Liouville fractional derivative to the(1+1)-dimensional fractional partial differential equations with Erdelyi-Kober fractional derivative.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 60673006 and 60533060)the Program for New Century Excellent Talents in University (No. NCET-05-0275), Chinathe IDeA Network of Biomedical Research Excellence Grant (No. 5P20RR01647206) from National Institutes of Health (NIH), USA
文摘We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11171041 and 10971018the Natural Science Foundation of Shandong Province under Grant No.ZR2010AM029+1 种基金the Promotive Research Fund for Young and Middle-Aged Scientists of Shandong Province under Grant No.BS2010SF001the Doctoral Foundation of Binzhou University under Grant No.2009Y01
文摘This paper is concerned with the (2+1)-dimensional Burgers' and heat types of equations.All of the geometic vector fields of the equations are obtained,an optimal system of the equation is presented.Especially,the Bcklund transformations (BTs) for the Burgers' equations are constructed based on the symmetry.Then,all of the symmetry reductions are provided in terms of the optimal system method,and the exact explicit solutions are investigated by the symmetry reductions and Bcklund transformations.
基金supported by the National Natural Science Foundation of China under Contracts No.11435001,No.11775041the National Key Basic Research Program of China under Contract No.2015CB856900。
文摘We investigate the quantum numbers of the pentaquark states Pc+,which are composed of 4(three flavors)quarks and an antiquark,by analyzing their inherent nodal structure in this paper.Assuming that the four quarks form a tetrahedron or a square,and the antiquark is at the ground state,we determine the nodeless structure of the states with orbital angular moment L≤3,and in turn,the accessible low-lying states.Since the inherent nodal structure depends only on the inherent geometric symmetry,we propose the quantum numbers JPof the low-lying pentaquark states P_c^+may be■,■,■and■,independent of dynamical models.
基金supported by Natural Science Foundation of Hebei Province,China(Grant No.A2018207030)Youth Key Program of Hebei University of Economics and Business(2018QZ07)+2 种基金Key Program of Hebei University of Economics and Business(2020ZD11)Youth Team Support Program of Hebei University of Economics and BusinessNational Natural Science Foundation of China(Grant No.11801133)。
文摘In this work,we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics,scientific fields,and ocean engineering.This equation will be reduced to the Korteweg-de Vries equation via using the perturbation analysis.We derive the corresponding vectors,symmetry reduction and explicit solutions for this equation.We readily obtain Bäcklund transformation associated with truncated Painlevéexpansion.We also examine the related conservation laws of this equation via using the multiplier method.Moreover,we investigate the reciprocal Bäcklund transformations of the derived conservation laws for the first time.
文摘Three dimensional space is said to be spherically symmetric if it admits SO(3) as the group of isometries. Under this symmetry condition, the Einstein’s Field equations for vacuum, yields the Schwarzschild Metric as the unique solution, which essentially is the statement of the well known Birkhoff’s Theorem. Geometrically speaking this theorem claims that the pseudo-Riemanian space-times provide more isometries than expected from the original metric holonomy/ansatz. In this paper we use the method of Lie Symmetry Analysis to analyze the Einstein’s Vacuum Field Equations so as to obtain the Symmetry Generators of the corresponding Differential Equation. Additionally, applying the Noether Point Symmetry method we have obtained the conserved quantities corresponding to the generators of the Schwarzschild Lagrangian and paving way to reformulate the Birkhoff’s Theorem from a different approach.
文摘The SERS spectrum of C_(60) was obtained by using silver mirror. From the SERS spectrum of C_(60) and the IR spectrum of C_(60), we proposed that C_(60) adsorbed on the silver mirror adopts a more ellipsoidal shape.
文摘Objective To discuss the etiology,course of diseases and prognosis of symmetry peripheral entrapment enuropathies of upper extremity. Methods The etiology, clinical scale and resluts of 14 cases were analyzed betwen 1999 and April 2002. Results In the bilateral tunnel syndrome, the excellent and good rate was 60% at the original side and 80% at the contralateral side occurred later. In the bilateral carpal tunnel syndrome, the excellent and good rate was 67% at the original side and 89% at the contralateral side occurred later. Conclusion The main etiological factor of the bilateral cubital tunnel syndrome was the elbow eversion deformity. The lesions of synovium contributed mainly to the symmetry carpal tunnel syndrome. The symmetry peripheral entrapment neuropathies of upper extremity should be operated on as soon as possible when diagnosis had been made for enhancement of treatment outcome. 5 refs,2 tabs.
基金the South African National Space Agency (SANSA) for funding this work
文摘This paper is devoted to the investigation of the Landau–Ginzburg–Higgs equation(LGHe),which serves as a mathematical model to understand phenomena such as superconductivity and cyclotron waves.The LGHe finds applications in various scientific fields,including fluid dynamics,plasma physics,biological systems,and electricity-electronics.The study adopts Lie symmetry analysis as the primary framework for exploration.This analysis involves the identification of Lie point symmetries that are admitted by the differential equation.By leveraging these Lie point symmetries,symmetry reductions are performed,leading to the discovery of group invariant solutions.To obtain explicit solutions,several mathematical methods are applied,including Kudryashov's method,the extended Jacobi elliptic function expansion method,the power series method,and the simplest equation method.These methods yield solutions characterized by exponential,hyperbolic,and elliptic functions.The obtained solutions are visually represented through 3D,2D,and density plots,which effectively illustrate the nature of the solutions.These plots depict various patterns,such as kink-shaped,singular kink-shaped,bell-shaped,and periodic solutions.Finally,the paper employs the multiplier method and the conservation theorem introduced by Ibragimov to derive conserved vectors.These conserved vectors play a crucial role in the study of physical quantities,such as the conservation of energy and momentum,and contribute to the understanding of the underlying physics of the system.
文摘In this paper,we use the symmetry of the Lie group analysis as one of the powerful tools that deals with the wide class of fractional order differential equations in the Riemann–Liouville concept.In this study,first,we employ the classical and nonclassical Lie symmetries(LS)to acquire similarity reductions of the nonlinear fractional far field Korteweg–de Vries(KdV)equation,and second,we find the related exact solutions for the derived generators.Finally,according to the LS generators acquired,we construct conservation laws for related classical and nonclassical vector fields of the fractional far field KdV equation.
基金Project supported by the National Basic Research Program of China(Grant No.2012CB725404)the National Natural Science Foundation of China(Grant Nos.11422221 and 11672289)
文摘As one of the paradigmatic models of non-equilibrium systems, the asymmetric simple exclusion process（ASEP） has been widely used to study many physical, chemical, and biological systems. The ASEP shows a range of nontrivial macroscopic phenomena, among which, the spontaneous symmetry breaking has gained a great deal of attention. Nevertheless,as a basic problem, it has been controversial whether there exist one or two symmetry-broken phases in the ASEP. Based on the mean field analysis and current minimization principle, this paper demonstrates that one of the broken-symmetry phases does not exist in a bidirectional two-lane ASEP with narrow entrances. Moreover, an exponential decay feature is observed,which has been used to predict the phase boundary in the thermodynamic limit. Our findings might be generalized to other ASEP models and thus deepen the understanding of the spontaneous symmetry breaking in non-equilibrium systems.
基金supported by the National Natural Science Foundation of China(Grant Nos.12204533,12434009,and 62476278)the National Key R&D Program of China(Grant No.2024YFA1408601)+1 种基金the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No.24XNKJ15)。
文摘Unconventional magnetism,including altermagnetism and unconventional compensated magnetism,characterized by its duality of real-space antiferromagnetic alignment and momentum-space spin splitting,has garnered widespread attention.While altermagnetism has been extensively studied,research on unconventional compensated magnetism remains very rare.In particular,unconventional compensated magnetic materials are only theoretically predicted and have not yet been synthesized experimentally.In this study,based on symmetry analysis and frst-principles electronic structure calculations,we predict that LaMn_(2)SbO_(6)is an unconventional compensated magnetic semiconductor.Given that the Mn ions at opposite spin lattice cannot be connected by any symmetry,the spin splitting in LaMn_(2)SbO_(6)is isotropic.More importantly,LaMn_(2)SbO_(6)has already been synthesized experimentally,and its magnetic structure has been confrmed by neutron scattering experiments.Therefore,LaMn_(2)SbO_(6)serves as an excellent material platform for investigating the novel physical properties of unconventional compensated magnetic materials.
基金partially supported by the Natural Science Foundation of Hubei Province(No.2022CFC030)the Science and Technology Research Project of Hubei Provincial Department of Education(No.D20212603)+2 种基金Hubei University of Arts and Science(No.2020kypytd002)the support from National Natural Science Foundation of China(No.22303098)the support from Anhui Provincial Natural Science Foundation(No.1908085MA10)。
文摘Intrinsic two-dimensional(2D)ferromagnetic(FM)semiconductors have attracted extensive attentions for their potential applications in next-generation spintronics devices.In recent years,the van der Waals material VI_(3) has been experimentally found to be an intrinsic FM semiconductor.However,the electronic structure of the VI_(3) is not fully understood.To reveal why the VI_(3)is a ferromagnetic semiconductor with strong out-of-plane anisotropy,we systematically studied the electronic structure of the monolayer VI_(3).Our results confirm that the monolayer VI_(3) is a Mott insulator,and d^(2) electrons occupy a_(g) and e_(g)^(π+) orbitals.The half-metallic state is a metastable state with a total energy 0.7 e V higher than the ferromagnetic Mott insulating state.Furthermore,our study confirmed that the VI_(3)exhibits the out-of-plane magnetic anisotropy,which originates from d^(2) electrons occupying low-lying agand egπ+orbitals.Since the orbital angular momentum of the e_(g)^(π+) state is not completely quenched,the VI_(3) has the out-of-plane anisotropy under interplay between the spin-orbit coupling and crystal field.Our study provides valuable guidance for the design of 2D magnetic materials with pronounced out-of-plane anisotropy.
基金the National Natural Science Foundation of China(Grant No.11975143)。
文摘As a celebrated nonlinear water wave equation,the Davey–Stewartson equation is widely studied by researchers,especially in the field of mathematical physics.On the basis of the Riemann–Liouville fractional derivative,the time-fractional Davey–Stewartson equation is investigated in this paper.By application of the Lie symmetry analysis approach,the Lie point symmetries and symmetry groups are obtained.At the same time,the similarity reductions are derived.Furthermore,the equation is converted to a system of fractional partial differential equations and a system of fractional ordinary differential equations in the sense of Riemann–Liouville fractional derivative.By virtue of the symmetry corresponding to the scalar transformation,the equation is converted to a system of fractional ordinary differential equations in the sense of Erdélyi–Kober fractional integro-differential operators.By using Noether’s theorem and Ibragimov’s new conservation theorem,the conserved vectors and the conservation laws are derived.Finally,the traveling wave solutions are achieved and plotted.
文摘The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible third grade fluid bounded by an infinite porous plate is studied with the Hall effect. An external uniform magnetic field is applied perpendicular to the plate and the fluid motion is subjected to a uniform suction and injection. Similarity transformations are employed to reduce the non-linear equations governing the flow under discussion to two ordinary differential equations （with and without dispersion terms）. Using the finite difference scheme, numerical solutions represented by graphs with reference to the various involved parameters of interest are discussed and appropriate conclusions are drawn.
文摘In this article,we explore the famous Selkov–Schnakenberg(SS)system of coupled nonlinear partial differential equations(PDEs)for Lie symmetry analysis,self-adjointness,and conservation laws.Moreover,miscellaneous soliton solutions like dark,bright,periodic,rational,Jacobian elliptic function,Weierstrass elliptic function,and hyperbolic solutions of the SS system will be achieved by a well-known technique called sub-ordinary differential equations.All these results are displayed graphically by 3D,2D,and contour plots.
文摘We investigate the Einstein field equations corresponding to the Weyl-Lewis-Papapetrou form for an axisymmetric rotating field by using the classical symmetry method. Using the invafiance group properties of the governing system of partial differential equations （PDEs） and admitting a Lie group of point transformations with commuting infinitesimal generators, we obtain exact solutions to the system of PDEs describing the Einstein field equations. Some appropriate canonical variables are characterized that transform the equations at hand to an equivalent system of ordinary differential equations and some physically important analytic solutions of field equations are constructed. Also, the class of axially symmetric solutions of Einstein field equations including the Papapetrou solution as a particular case has been found.
文摘In this paper, the Lie symmetry analysis method is applied to the time-fractional Boussinesq–Burgers system which is used to describe shallow water waves near an ocean coast or in a lake.We obtain all the Lie symmetries admitted by the system and use them to reduce the fractional partial differential equations with a Riemann–Liouville fractional derivative to some fractional ordinary differential equations with an Erdélyi–Kober fractional derivative, thereby getting some exact solutions of the reduced equations. For power series solutions, we prove their convergence and show the dynamic analysis of their truncated graphs. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equations studied.
文摘In this manuscript, we first perform a complete Lie symmetry classification for a higher-dimensional shallow water wave equation and then construct the corresponding reduced equations with the obtained Lie symmetries. Moreover, with the extended <em>F</em>-expansion method, we obtain several new nonlinear wave solutions involving differentiable arbitrary functions, expressed by Jacobi elliptic function, Weierstrass elliptic function, hyperbolic function and trigonometric function.
基金support from the National Natural Science Foundation of China (Grants No. 12074013, No. 12204138 and No. 12204419)the National Science Fund for Distinguished Young Scholars (Grant No. T2225027). The calculations were carried out using supercomputers at the Hefei Advanced Computing Center. We also thank for the fruitful discussions with Rui Wang and Zhaopeng Guo.
文摘Two-dimensional(2D)topological insulators with symmetry-protected helical edge states have drawn significant interest.The recently synthesized layered2D electride BaCu features a monolayer structure with intriguing band crossings near Fermi level and a low exfoliation energy.In this study,firstprinciples calculations combined with symmetry analysis reveal that the BaCu monolayer behaves as a 2D topological insulator(TI)nature.When integrated with a 30°twisted√3 p×√3 hexagonal boron nitride(h-BN)supercell,the resulting twistedα/β-BaCu/BN heterobilayers exhibit 2D Weyl points and type-III Dirac points,respectively,demonstrating that twist angle can effectively modulate topological properties.Interestingly,ab initio molecular dynamics(AIMD)simulations reveal a spontaneous transition fromthe metastableβ-BaCu/BN toα-BaCu/BN configuration,indicating a low energy barrier and highlighting the potential for propertymodulation,emphasizing the versatility of twisted structures for tuning topological states.This work establishes a robust platform for exploring twist-angleinduced topological electride states,broadening the scope for future investigations.
文摘In this paper,Lie symmetry analysis method is applied to one type of mathematical physics equations named the(2+1)-dimensional fractional Hirota-Maccari system.All Lie symmetries and the corresponding conserved vectors for the system are obtained.The one-dimensional optimai system is utilized to reduce the aimed equations with Riemann-Liouville fractional derivative to the(1+1)-dimensional fractional partial differential equations with Erdelyi-Kober fractional derivative.
