Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transiti...Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transition in a Hubbard model by using the dynamical mean-field theory and introduce the local quantum state fidelity to depict the Mott metal–insulator transition. The local quantum state fidelity provides a convenient approach to determining the critical point of the Mott transition. Additionally, it presents a consistent description of the two distinct forms of the Mott transition points.展开更多
One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the...One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the change of certain topological invariant.A new gapless semimetallic state emerges at each topological quantum critical point.Here we perform a renormalization group analysis to investigate the stability of such critical points against perturbations induced by random scalar potential and random vector potential.We find that the quantum critical point between double-Weyl semimetal and band insulator is unstable and can be easily turned into a compressible diffusive metal by any type of weak disorder.The quantum critical point between triple-Weyl semimetal and band insulator flows to a stable strong-coupling fixed point if the system contains a random vector potential merely along the z-axis,but becomes a compressible diffusive metal when other types of disorders exist.展开更多
We study the critical scaling and dynamical signatures of fractionalized excitations at two different deconfined quantum critical points(DQCPs)in an S=1/2 spin chain using the time evolution of infinite matrix product...We study the critical scaling and dynamical signatures of fractionalized excitations at two different deconfined quantum critical points(DQCPs)in an S=1/2 spin chain using the time evolution of infinite matrix product states.The scaling of the correlation functions and the dispersion of the conserved current correlations explicitly show the emergence of enhanced continuous symmetries at these DQCPs.The dynamical structure factors in several different channels reveal the development of deconfined fractionalized excitations at the DQCPs.Furthermore,we find an effective spin-charge separation at the DQCP between the ferromagnetic(FM)and valence bond solid(VBS)phases,and identify two continua associated with different types of fractionalized excitations at the DQCP between the X-direction and Z-direction FM phases.Our findings not only provide direct evidence for the DQCP in one dimension but also shed light on exploring the DQCP in higher dimensions.展开更多
The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics,raising fundamental questions on the nature of quantum phase transitions.Here we unveil t...The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics,raising fundamental questions on the nature of quantum phase transitions.Here we unveil the behaviour of emergent symmetry involving two extraordinarily representative phenomena,i.e.,the deconfined quantum critical point(DQCP)and the quantum spin liquid(QSL)state.Via large-scale tensor network simulations,we study a spatially anisotropic spin-1/2 square-lattice frustrated antiferromagnetic(AFM)model,namely the J1x-J1y-J2 model,which contains anisotropic nearestneighbor couplings J1x,J1y and the next nearest neighbor coupling J2.For small J1y/J1x,by tuning J2,a direct continuous transition between the AFM and valence bond solid phase is observed.With growing J1y/J1x,a gapless QSL phase gradually emerges between the AFM and VBS phases.We observe an emergent O(4)symmetry along the AFM–VBS transition line,which is consistent with the prediction of DQCP theory.Most surprisingly,we find that such an emergent O(4)symmetry holds for the whole QSL–VBS transition line as well.These findings reveal the intrinsic relationship between the QSL and DQCP from categorical symmetry point of view,and strongly constrain the quantum field theory description of the QSL phase.The phase diagram and critical exponents presented in this paper are of direct relevance to future experiments on frustrated magnets and cold atom systems.展开更多
We propose the transverse velocity(β_T) dependence of the anti-deuteron to deuteron ratio as a new observable to search for the QCD critical point in heavy-ion collisions.The QCD critical point can attract the system...We propose the transverse velocity(β_T) dependence of the anti-deuteron to deuteron ratio as a new observable to search for the QCD critical point in heavy-ion collisions.The QCD critical point can attract the system evolution trajectory in the QCD phase diagram,which is known as the focusing effect.To quantify this effect,we employ the thermal and hadronic transport model to simulate the dynamical particle emission along a hypothetical focusing trajectory near the critical point.We found that the focusing effect can lead to anomalous β_T dependence on ■/p,■/d and ■/~3 He ratios.We examined the β_T dependence of ■/p and ■/d ratios of central Au+Au collisions at ■=7.7 to 200 GeV measured by the STAR experiment at RHIC.Surprisingly,we only observe a negative slope in β_T dependence of ■/d ratio at ■=19.6 GeV,which indicates the trajectory evolution has passed through the critical region.In the future,we could constrain the location of the critical point and/or width of the critical region by conducting precise measurements on the β_T dependence of the ■/d ratio at different energies and rapidity.展开更多
Existing critical point theories including metric and topological critical point theories are difficult to be applied directly to some concrete problems in particular polyhedral settings,because the notions of critica...Existing critical point theories including metric and topological critical point theories are difficult to be applied directly to some concrete problems in particular polyhedral settings,because the notions of critical sets could be either very vague or too large.To overcome these difficulties,we develop the critical point theory for nonsmooth but Lipschitzian functions defined on convex polyhedrons.This yields natural extensions of classical results in the critical point theory,such as the Liusternik-Schnirelmann multiplicity theorem.More importantly,eigenvectors for some eigenvalue problems involving graph 1-Laplacian coincide with critical points of the corresponding functions on polytopes,which indicates that the critical point theory proposed in the present paper can be applied to study the nonlinear spectral graph theory.展开更多
A critical point symmetry(CPS) for odd-odd nuclei is built in the core-particle coupling scheme with the even-even core assumed to follow the spherical to triaxially deformed shape phase transition. It is shown that t...A critical point symmetry(CPS) for odd-odd nuclei is built in the core-particle coupling scheme with the even-even core assumed to follow the spherical to triaxially deformed shape phase transition. It is shown that the model Hamiltonian can be approximately solved with the solutions being expressed in terms of the Bessel functions of irrational orders. In particular, the CPS predicts that collective multiple chiral doublets may exist in transitional odd-odd systems.展开更多
The Bohr Hamiltonian with axially deformed shape confined in a quasi-exactly solvable decatic β-part potential is studied.It is shown that the decatic model can well reproduce the X(5)model results as far as the ener...The Bohr Hamiltonian with axially deformed shape confined in a quasi-exactly solvable decatic β-part potential is studied.It is shown that the decatic model can well reproduce the X(5)model results as far as the energy ratios in the ground and beta band and related B(E2)values are concerned.Fitting results to the low-lying energy ratios and relevant B(E2)values of even-even X(5)candidates ^(150)Nd,^(156)Dy,^(164)Yb,^(168)Hf,^(174)Yb,^(176,178,180)Os,and ^(188,190)Os show that the decatic model provides the best fitting results for the energy ratios,while the X(5)model is the best at reproducing the B(E2)values of these nuclei,in which the beta-bandhead energy is lower than that of the gamma band.While for even-even nuclei,such as ^(154,156,158)Gd,with bandhead energies of the beta and gamma bands more or less equal within the X(5)critical point to the axially deformed region,our numerical analysis indicates that the decatic model is better than the X(5)model in describing both the low-lying level energies and related B(E2)values.展开更多
In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of computer algebra system MATHEMAT...In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of computer algebra system MATHEMATICA, the first 8 quasi Lyapunov constants are deduced. As a result, the necessary and sufficient conditions to have a center are obtained. The fact that there exist 8 small amplitude limit cycles created from the three-order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems.展开更多
The quantum critical regime marks a zone in the phase diagram where quantum fluctuation around the critical point plays a significant role at finite temperatures.While it is of great physical interest,simulation of th...The quantum critical regime marks a zone in the phase diagram where quantum fluctuation around the critical point plays a significant role at finite temperatures.While it is of great physical interest,simulation of the quantum critical regime can be difficult on a classical computer due to its intrinsic complexity.Herein,we propose a variational approach,which minimizes the variational free energy,to simulate and locate the quantum critical regime on a quantum computer.The variational quantum algorithm adopts an ansatz by performing an unitary operator on a product of a single-qubit mixed state,in which the entropy can be analytically obtained from the initial state,and thus the free energy can be accessed conveniently.With numeral simulation,using the one-dimensional Kitaev model as a demonstration we show that the quantum critical regime can be identified by accurately evaluating the temperature crossover line.Moreover,the dependencies of both the correlation length and the phase coherence time with temperature are evaluated for the thermal states.Our work suggests a practical way as well as a first step for investigating quantum critical systems at finite temperatures on quantum devices with few qubits.展开更多
In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infin...In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature.展开更多
Supercritical CO_(2)(SCO_(2))Brayton cycle has received more and more attention in the field of power generation due to its high cycle efficiency and compact structure.SCO_(2) compressor is the core component of the c...Supercritical CO_(2)(SCO_(2))Brayton cycle has received more and more attention in the field of power generation due to its high cycle efficiency and compact structure.SCO_(2) compressor is the core component of the cycle,and the improvement of its performance is the key to improving the efficiency of the entire cycle.However,the operation of the SCO_(2) compressor near the critical point has brought many design and operation problems.Based on the Reynolds Averaged Navier-Stokes(RANS)model,the performance and flow field of SCO_(2) centrifugal compressors based on different CO_(2) working fluid models are numerically investigated in this paper.The stability and convergence of the compressor steady-state simulation are also discussed.The results show that the fluid based on the Span-Wanger(SW)equation can obtain a more ideal compressor performance curve and capture a more accurate flow field structure,while the CO_(2) ideal gas is not suitable for the calculation of SCO_(2) centrifugal compressors.But its flow field can be used as the initial flow field for numerical calculation of centrifugal compressor based on CO_(2) real gas.展开更多
We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under som...We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under some suitable assumptions,we prove the existence of a ground state solution of the equation.Additionally,we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.展开更多
In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate cri...In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.展开更多
In this study, the constant volume, visual method is used to measure the critical point of CO2+toluene, CO2+cyclohexane, CO2+n-butyraldehyde, CO2+i-butyraldehyde, CO2+methanol and CO2+alcohol binary systems. The relat...In this study, the constant volume, visual method is used to measure the critical point of CO2+toluene, CO2+cyclohexane, CO2+n-butyraldehyde, CO2+i-butyraldehyde, CO2+methanol and CO2+alcohol binary systems. The relationship between critical point and the concentration of the entrainer for different substances has been discussed, and the comparison of the phase behavior of single component system and that of binary systems have been carried out.展开更多
We study a quasilinear elliptic equation with polynomial growth coefficients. The existence of infinitely many solutions is obtained by a dual method and a nonsmooth critical point theory.
The magnetic phase diagram of rare-earth perovskite compound,GdScO3,has been investigated by magnetization and heat capacity.The system undergoes an antiferromagnetic phase transition at TN=2.6 K,with an easy axis of ...The magnetic phase diagram of rare-earth perovskite compound,GdScO3,has been investigated by magnetization and heat capacity.The system undergoes an antiferromagnetic phase transition at TN=2.6 K,with an easy axis of magnetization along the a axis.The magnetization measurements show that it exists a spin-flop transition around 0.3 T for the applied field along the a axis.The critical magnetic field for the antiferromagnetic-to-paramagnetic transition is near 3.2 T when temperature approaches zero.By scaling susceptibilities,we presume this point(B=3.2 T,T=0 K)might be a fieldinduced quantum critical point and the magnetic critical fluctuations can even be felt above TN.展开更多
The existence of homoclinic solutions for the second-order p-Laplacian differential system( ρ( t) Φp( u'( t))) '-s( t) Φp( u( t))+ λf( t,u( t)) = 0 with impulsive effects Δ( ρ( tj) Φp( u'( tj))) = I...The existence of homoclinic solutions for the second-order p-Laplacian differential system( ρ( t) Φp( u'( t))) '-s( t) Φp( u( t))+ λf( t,u( t)) = 0 with impulsive effects Δ( ρ( tj) Φp( u'( tj))) = Ij( u( tj)) is studied. By using three critical points theorem and variational methods, the sufficient condition is established to guarantee that this p-Laplacian differential system with impulsive effects has at least one nontrivial homoclinic solution. Besides,an example is presented to illustrate the main result in the end of this paper.展开更多
More and more experimental results show that Darcy’s law is not fully applicable in low permeability media,and non-Darcy flow has been identified.In this paper we reviewed the research of non-Darcy flow experiments i...More and more experimental results show that Darcy’s law is not fully applicable in low permeability media,and non-Darcy flow has been identified.In this paper we reviewed the research of non-Darcy flow experiments in low-permeability media in recent decades,discuss the existence of non-Darcy flow,and summarize its constitutive equations.The reasons for the threshold gradient were also discussed and summarized for the criterion of the critical point of non-Darcy flow.On this basis,the future development of non-Darcy flow experiments in the rock and clay media were discussed,in order to provide a certain reference for subsequent research on seepage laws in low permeability media.展开更多
One of the fundamental properties of an ad hoc network is its connectivity. Maintaining connectivity in wireless networks is extremely difficult due to dynamic changing topology of MANETs. There are several techniques...One of the fundamental properties of an ad hoc network is its connectivity. Maintaining connectivity in wireless networks is extremely difficult due to dynamic changing topology of MANETs. There are several techniques to understand the connectivity level for a given network topology. In this paper, we examine the existing methods and discuss the issues and challenges that are still insurmountable in order to enhance the connectivity properties of wireless multi hop networks.展开更多
基金Project supported by the Scientific Research Foundation for Youth Academic Talent of Inner Mongolia University (Grant No.1000023112101/010)the Fundamental Research Funds for the Central Universities of China (Grant No.JN200208)+2 种基金supported by the National Natural Science Foundation of China (Grant No.11474023)supported by the National Key Research and Development Program of China (Grant No.2021YFA1401803)the National Natural Science Foundation of China (Grant Nos.11974051 and 11734002)。
文摘Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transition in a Hubbard model by using the dynamical mean-field theory and introduce the local quantum state fidelity to depict the Mott metal–insulator transition. The local quantum state fidelity provides a convenient approach to determining the critical point of the Mott transition. Additionally, it presents a consistent description of the two distinct forms of the Mott transition points.
基金the Natural Science Foundation of Anhui Province,China(Grant No.2208085MA11)the National Natural Science Foundation of China(Grants Nos.11974356,12274414,and U1832209)。
文摘One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the change of certain topological invariant.A new gapless semimetallic state emerges at each topological quantum critical point.Here we perform a renormalization group analysis to investigate the stability of such critical points against perturbations induced by random scalar potential and random vector potential.We find that the quantum critical point between double-Weyl semimetal and band insulator is unstable and can be easily turned into a compressible diffusive metal by any type of weak disorder.The quantum critical point between triple-Weyl semimetal and band insulator flows to a stable strong-coupling fixed point if the system contains a random vector potential merely along the z-axis,but becomes a compressible diffusive metal when other types of disorders exist.
基金Project supported by the National Science Foundation of China(Grant No.12174441)the Fundamental Research Funds for the Central Universities,Chinathe Research Funds of Remnin University of China(Grant No.18XNLG24)。
文摘We study the critical scaling and dynamical signatures of fractionalized excitations at two different deconfined quantum critical points(DQCPs)in an S=1/2 spin chain using the time evolution of infinite matrix product states.The scaling of the correlation functions and the dispersion of the conserved current correlations explicitly show the emergence of enhanced continuous symmetries at these DQCPs.The dynamical structure factors in several different channels reveal the development of deconfined fractionalized excitations at the DQCPs.Furthermore,we find an effective spin-charge separation at the DQCP between the ferromagnetic(FM)and valence bond solid(VBS)phases,and identify two continua associated with different types of fractionalized excitations at the DQCP between the X-direction and Z-direction FM phases.Our findings not only provide direct evidence for the DQCP in one dimension but also shed light on exploring the DQCP in higher dimensions.
基金supported by the National Key R&D Program of China(2022YFA1403700)the National Natural Science Foundation of China(NSFC)and the Research Grants Council(RGC)Joint Research Scheme of the Hong Kong Research Grants Council(N-CUHK427/18)+4 种基金the National Natural Science Foundation of China(12141402)supported by the Science,Technology and Innovation Commission of Shenzhen Municipality(ZDSYS20190902092905285)Guangdong Basic and Applied Basic Research Foundation(2020B1515120100)Center for Computational Science and Engineering at Southern University of Science and Technology.S.S.G.was supported by the National Natural Science Foundation of China(11874078 and 11834014)the Dongguan Key Laboratory of Artificial Intelligence Design for Advanced Materials.
文摘The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics,raising fundamental questions on the nature of quantum phase transitions.Here we unveil the behaviour of emergent symmetry involving two extraordinarily representative phenomena,i.e.,the deconfined quantum critical point(DQCP)and the quantum spin liquid(QSL)state.Via large-scale tensor network simulations,we study a spatially anisotropic spin-1/2 square-lattice frustrated antiferromagnetic(AFM)model,namely the J1x-J1y-J2 model,which contains anisotropic nearestneighbor couplings J1x,J1y and the next nearest neighbor coupling J2.For small J1y/J1x,by tuning J2,a direct continuous transition between the AFM and valence bond solid phase is observed.With growing J1y/J1x,a gapless QSL phase gradually emerges between the AFM and VBS phases.We observe an emergent O(4)symmetry along the AFM–VBS transition line,which is consistent with the prediction of DQCP theory.Most surprisingly,we find that such an emergent O(4)symmetry holds for the whole QSL–VBS transition line as well.These findings reveal the intrinsic relationship between the QSL and DQCP from categorical symmetry point of view,and strongly constrain the quantum field theory description of the QSL phase.The phase diagram and critical exponents presented in this paper are of direct relevance to future experiments on frustrated magnets and cold atom systems.
基金Supported in part by the National Natural Science Foundation of China(11890711,11575069,11828501 and 11861131009)Fundamental Research Funds for the Central Universities(CCNU19QN054)+1 种基金Nanhu Scholar Program for Young Scholars of XYNUCCNU-QLPL Innovation Fund(QLPL201801)
文摘We propose the transverse velocity(β_T) dependence of the anti-deuteron to deuteron ratio as a new observable to search for the QCD critical point in heavy-ion collisions.The QCD critical point can attract the system evolution trajectory in the QCD phase diagram,which is known as the focusing effect.To quantify this effect,we employ the thermal and hadronic transport model to simulate the dynamical particle emission along a hypothetical focusing trajectory near the critical point.We found that the focusing effect can lead to anomalous β_T dependence on ■/p,■/d and ■/~3 He ratios.We examined the β_T dependence of ■/p and ■/d ratios of central Au+Au collisions at ■=7.7 to 200 GeV measured by the STAR experiment at RHIC.Surprisingly,we only observe a negative slope in β_T dependence of ■/d ratio at ■=19.6 GeV,which indicates the trajectory evolution has passed through the critical region.In the future,we could constrain the location of the critical point and/or width of the critical region by conducting precise measurements on the β_T dependence of the ■/d ratio at different energies and rapidity.
基金supported by National Natural Science Foundation of China(Grant Nos.11822102 and 11421101)supported by Beijing Academy of Artificial Intelligence(BAAI)supported by the project funded by China Postdoctoral Science Foundation(Grant No.BX201700009)。
文摘Existing critical point theories including metric and topological critical point theories are difficult to be applied directly to some concrete problems in particular polyhedral settings,because the notions of critical sets could be either very vague or too large.To overcome these difficulties,we develop the critical point theory for nonsmooth but Lipschitzian functions defined on convex polyhedrons.This yields natural extensions of classical results in the critical point theory,such as the Liusternik-Schnirelmann multiplicity theorem.More importantly,eigenvectors for some eigenvalue problems involving graph 1-Laplacian coincide with critical points of the corresponding functions on polytopes,which indicates that the critical point theory proposed in the present paper can be applied to study the nonlinear spectral graph theory.
基金supported by the National Natural Science Foundation of China(Grant Nos.11875158,11675094,and 11875075)。
文摘A critical point symmetry(CPS) for odd-odd nuclei is built in the core-particle coupling scheme with the even-even core assumed to follow the spherical to triaxially deformed shape phase transition. It is shown that the model Hamiltonian can be approximately solved with the solutions being expressed in terms of the Bessel functions of irrational orders. In particular, the CPS predicts that collective multiple chiral doublets may exist in transitional odd-odd systems.
基金Support from the National Natural Science Foundation of China(11675071,12175097)the Liaoning Provincial Universities Overseas Training Program(2019GJWYB024)+2 种基金the U.S.National Science Foundation(OIA-1738287 and PHY-1913728)the Southeastern Universities Research Associationthe LSU-LNNU joint research program(9961)is acknowledged.
文摘The Bohr Hamiltonian with axially deformed shape confined in a quasi-exactly solvable decatic β-part potential is studied.It is shown that the decatic model can well reproduce the X(5)model results as far as the energy ratios in the ground and beta band and related B(E2)values are concerned.Fitting results to the low-lying energy ratios and relevant B(E2)values of even-even X(5)candidates ^(150)Nd,^(156)Dy,^(164)Yb,^(168)Hf,^(174)Yb,^(176,178,180)Os,and ^(188,190)Os show that the decatic model provides the best fitting results for the energy ratios,while the X(5)model is the best at reproducing the B(E2)values of these nuclei,in which the beta-bandhead energy is lower than that of the gamma band.While for even-even nuclei,such as ^(154,156,158)Gd,with bandhead energies of the beta and gamma bands more or less equal within the X(5)critical point to the axially deformed region,our numerical analysis indicates that the decatic model is better than the X(5)model in describing both the low-lying level energies and related B(E2)values.
基金Supported by the Natural Science Foundation of Shandong Province (Grant No. Y2007A17)
文摘In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of computer algebra system MATHEMATICA, the first 8 quasi Lyapunov constants are deduced. As a result, the necessary and sufficient conditions to have a center are obtained. The fact that there exist 8 small amplitude limit cycles created from the three-order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems.
基金supported by the National Natural Science Foundation of China(Grant No.12005065)the Guangdong Basic and Applied Basic Research Fund(Grant No.2021A1515010317)。
文摘The quantum critical regime marks a zone in the phase diagram where quantum fluctuation around the critical point plays a significant role at finite temperatures.While it is of great physical interest,simulation of the quantum critical regime can be difficult on a classical computer due to its intrinsic complexity.Herein,we propose a variational approach,which minimizes the variational free energy,to simulate and locate the quantum critical regime on a quantum computer.The variational quantum algorithm adopts an ansatz by performing an unitary operator on a product of a single-qubit mixed state,in which the entropy can be analytically obtained from the initial state,and thus the free energy can be accessed conveniently.With numeral simulation,using the one-dimensional Kitaev model as a demonstration we show that the quantum critical regime can be identified by accurately evaluating the temperature crossover line.Moreover,the dependencies of both the correlation length and the phase coherence time with temperature are evaluated for the thermal states.Our work suggests a practical way as well as a first step for investigating quantum critical systems at finite temperatures on quantum devices with few qubits.
文摘In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature.
文摘Supercritical CO_(2)(SCO_(2))Brayton cycle has received more and more attention in the field of power generation due to its high cycle efficiency and compact structure.SCO_(2) compressor is the core component of the cycle,and the improvement of its performance is the key to improving the efficiency of the entire cycle.However,the operation of the SCO_(2) compressor near the critical point has brought many design and operation problems.Based on the Reynolds Averaged Navier-Stokes(RANS)model,the performance and flow field of SCO_(2) centrifugal compressors based on different CO_(2) working fluid models are numerically investigated in this paper.The stability and convergence of the compressor steady-state simulation are also discussed.The results show that the fluid based on the Span-Wanger(SW)equation can obtain a more ideal compressor performance curve and capture a more accurate flow field structure,while the CO_(2) ideal gas is not suitable for the calculation of SCO_(2) centrifugal compressors.But its flow field can be used as the initial flow field for numerical calculation of centrifugal compressor based on CO_(2) real gas.
基金supported by National Natural Science Foundation of China(11971202)Outstanding Young foundation of Jiangsu Province(BK20200042)。
文摘We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under some suitable assumptions,we prove the existence of a ground state solution of the equation.Additionally,we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.
基金supported by the Natural Science Foundation of China(11771166,12071169)the Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT17R46。
文摘In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.
基金This work was supported by the National Natural Science Foundation of Chinathe Research Fund for the Doctoral Program of Higher Education(20076004,2000001005).
文摘In this study, the constant volume, visual method is used to measure the critical point of CO2+toluene, CO2+cyclohexane, CO2+n-butyraldehyde, CO2+i-butyraldehyde, CO2+methanol and CO2+alcohol binary systems. The relationship between critical point and the concentration of the entrainer for different substances has been discussed, and the comparison of the phase behavior of single component system and that of binary systems have been carried out.
基金supported in part by the National Natural Science Foundation of China(11261070)
文摘We study a quasilinear elliptic equation with polynomial growth coefficients. The existence of infinitely many solutions is obtained by a dual method and a nonsmooth critical point theory.
基金The work at SUSTech was supported by the National Natural Science Foundation of China(Grant No.11974157)Part of this work was also supported by the National Natural Science Foundation of China(Grant No.11875265)+1 种基金the Scientific Instrument Developing Project of the Chinese Academy of Sciences(3He-based neutron polarization devices)the Institute of High Energy Physics,the Chinese Academy of Sciences.Kan X C and Tian M L were supported by the National Natural Science Foundation of China(Grant No.51802002).
文摘The magnetic phase diagram of rare-earth perovskite compound,GdScO3,has been investigated by magnetization and heat capacity.The system undergoes an antiferromagnetic phase transition at TN=2.6 K,with an easy axis of magnetization along the a axis.The magnetization measurements show that it exists a spin-flop transition around 0.3 T for the applied field along the a axis.The critical magnetic field for the antiferromagnetic-to-paramagnetic transition is near 3.2 T when temperature approaches zero.By scaling susceptibilities,we presume this point(B=3.2 T,T=0 K)might be a fieldinduced quantum critical point and the magnetic critical fluctuations can even be felt above TN.
基金National Natural Science Foundations of China(No.11271371,No.10971229)
文摘The existence of homoclinic solutions for the second-order p-Laplacian differential system( ρ( t) Φp( u'( t))) '-s( t) Φp( u( t))+ λf( t,u( t)) = 0 with impulsive effects Δ( ρ( tj) Φp( u'( tj))) = Ij( u( tj)) is studied. By using three critical points theorem and variational methods, the sufficient condition is established to guarantee that this p-Laplacian differential system with impulsive effects has at least one nontrivial homoclinic solution. Besides,an example is presented to illustrate the main result in the end of this paper.
基金This study was supported by Natural Science Foundation of Hubei Province of China(No.2018CFB258)State Key Laboratory of Groundwater Protection and Utilization of Coal Mining(SHJT-17-42.9)College Student Innovation Project of Yangtze University(No.2019428 and No.2019422).
文摘More and more experimental results show that Darcy’s law is not fully applicable in low permeability media,and non-Darcy flow has been identified.In this paper we reviewed the research of non-Darcy flow experiments in low-permeability media in recent decades,discuss the existence of non-Darcy flow,and summarize its constitutive equations.The reasons for the threshold gradient were also discussed and summarized for the criterion of the critical point of non-Darcy flow.On this basis,the future development of non-Darcy flow experiments in the rock and clay media were discussed,in order to provide a certain reference for subsequent research on seepage laws in low permeability media.
文摘One of the fundamental properties of an ad hoc network is its connectivity. Maintaining connectivity in wireless networks is extremely difficult due to dynamic changing topology of MANETs. There are several techniques to understand the connectivity level for a given network topology. In this paper, we examine the existing methods and discuss the issues and challenges that are still insurmountable in order to enhance the connectivity properties of wireless multi hop networks.
