In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o...In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.展开更多
In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE,this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypersu...In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE,this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypersurfaces F(x)with degenerate critical points and proves that[F(x)](+)(lambda)is a distribution-valued meromorphic of lambda is an element of C under some assumptions on F(x).Next,the authors use the Normal form theory of Arnold and prove that for a hypersurface F(x)=0 with A(mu)type degenerate critical point at x=0,F-+(lambda)is a distribution-valued meromorphic function of lambda.展开更多
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
In this paper foe bifurcation of critical points for the quadratic systems of type(II)and (III) is investigated. and an answer to the problem given in[1] is given.
Suppose A,B and C are the bounded linear operators on a Hilbert space H, when A has a generalized inverse A - such that (AA -) *=AA - and B has a generalized inverse B - such that (B -B) *=B -B,the general cha...Suppose A,B and C are the bounded linear operators on a Hilbert space H, when A has a generalized inverse A - such that (AA -) *=AA - and B has a generalized inverse B - such that (B -B) *=B -B,the general characteristic forms for the critical points of the map F p:X→‖ A X B-C ‖ p p (1<p<∞), have been obtained, it is a generalization for P J Maher's result about p=2. Similarly, the same question has been discussed for several operators.展开更多
Deconfined quantum critical points(DQCPs)have been proposed as a class of continuous quantum phase transitions occurring between two ordered phases with distinct symmetry-breaking patterns,beyond the conventional fram...Deconfined quantum critical points(DQCPs)have been proposed as a class of continuous quantum phase transitions occurring between two ordered phases with distinct symmetry-breaking patterns,beyond the conventional framework of Landau-Ginzburg-Wilson(LGW)theory.At the DQCP,the system exhibits emergent gauge fields,fractionalized excitations,and enhanced symmetries.展开更多
The conventional Kibble–Zurek mechanism,describing driven dynamics across critical points based on the adiabatic-impulse scenario(AIS),has attracted broad attention.However,the driven dynamics at the tricritical poin...The conventional Kibble–Zurek mechanism,describing driven dynamics across critical points based on the adiabatic-impulse scenario(AIS),has attracted broad attention.However,the driven dynamics at the tricritical point with two independent relevant directions have not been adequately studied.Here,we employ the time-dependent variational principle to study the driven critical dynamics at a one-dimensional supersymmetric Ising tricritical point.For the relevant direction along the Ising critical line,the AIS apparently breaks down.Nevertheless,we find that the critical dynamics can still be described by finite-time scaling in which the driving rate has a dimension of r_(μ)=z+1/v_(μ)with z and v_(μ)being the dynamic exponent and correlation length exponent in this direction,respectively.For driven dynamics along another direction,the driving rate has a dimension of r_(p)=z+1/v_(p)with v_(p)being another correlation length exponent.Our work brings a new fundamental perspective into nonequilibrium critical dynamics near the tricritical point,which could be realized in programmable quantum processors in Rydberg atomic systems.展开更多
We study the global qualitative properties of the well-known Kukles systems (1) below. Firstly, the number of critical points in case (1) has a center or a fine focus.
In order to provide a reference for the further study of microbial contamination in the pork production process. Microbial contamination of pigs came from three slaughterhouses were detected, and critical control poin...In order to provide a reference for the further study of microbial contamination in the pork production process. Microbial contamination of pigs came from three slaughterhouses were detected, and critical control points in the progress of hog slaughter and processing were analyzed. The results showed that microbial con- taminatian existed in the entire slaughter and processing progress, including shower and assassination bloodletting, separation of the internal organs, chopping boards, workshop environment, personal hygiene of the operators, etc. , which should be paid more attention to. The results indicated that reasonable protection measures should be carried out, disinfection awareness of the operators should be improved, and regular disinfection should be ruled under the condition of continu- ous operation.展开更多
Up to now, the primary method for studying critical porosity and porous media are experimental measurements and data analysis. There are few references on how to numerically calculate porosity at the critical point, p...Up to now, the primary method for studying critical porosity and porous media are experimental measurements and data analysis. There are few references on how to numerically calculate porosity at the critical point, pore fluid-related parameters, or framework-related parameters. So in this article, we provide a method for calculating these elastic parameters and use this method to analyze gas-bearing samples. We first derive three linear equations for numerical calculations. They are the equation of density p versus porosity Ф, density times the square of compressional wave velocity p Vp^2 versus porosity, and density times the square of shear wave velocity pVs^2 versus porosity. Here porosity is viewed as an independent variable and the other parameters are dependent variables. We elaborate on the calculation steps and provide some notes. Then we use our method to analyze gas-bearing sandstone samples. In the calculations, density and P- and S-velocities are input data and we calculate eleven relative parameters for porous fluid, framework, and critical point. In the end, by comparing our results with experiment measurements, we prove the viability of the method.展开更多
In this paper, we consider the problem of existence as well as multiplicity results for a bi-harmonic equation under the Navier boundary conditions： △2 u = K（x）u p , u 〉 0 in Ω , △u = u = 0 on Ω , where Ω is ...In this paper, we consider the problem of existence as well as multiplicity results for a bi-harmonic equation under the Navier boundary conditions： △2 u = K（x）u p , u 〉 0 in Ω , △u = u = 0 on Ω , where Ω is a smooth domain in R n , n 5, and p ＋ 1 = 2 n n 4 is the critical Sobolev exponent. We obtain highlightly a new criterion of existence, which provides existence results for a dense subset of positive functions, and generalizes Bahri-Coron type criterion in dimension six. Our argument gives also estimates on the Morse index of the obtained solutions and extends some known results. Moreover, it provides, for generic K, Morse inequalities at infinity, which delivers lower bounds for the number of solutions. As further applications of this Morse theoretical approach, we prove more existence results.展开更多
This paper is concerned with the harmonic equation(P;) : ?u = 0, u > 0 in B;and ?u/?ν+(（n-2）/2)u =(（n-2）/2) Ku;on S;where B;is the unit ball in R;, n ≥ 4 with Euclidean metric g;, ?B;= S;is its boundary, K is...This paper is concerned with the harmonic equation(P;) : ?u = 0, u > 0 in B;and ?u/?ν+(（n-2）/2)u =(（n-2）/2) Ku;on S;where B;is the unit ball in R;, n ≥ 4 with Euclidean metric g;, ?B;= S;is its boundary, K is a function on S;and ε is a small positive parameter. We construct solutions of the subcritical equation(P;) which blow up at one critical point of K. We give also a sufficient condition on the function K to ensure the nonexistence of solutions for(P;) which blow up at one point. Finally, we prove a nonexistence result of single peaked solutions for the supercritical equation(P;).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
In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value ...In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.展开更多
In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear SchrSdinger equatio...In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear SchrSdinger equations with negative parameter which arose from the study of self-channeling of high-power ultrashort laser in matter.展开更多
The performance of supercritical fluid (SCF) as a solvent can be greatly affected by addition of anentrainer to the system. In this study, a constant volume visual method is used to measure the critical point ofCO2+n-...The performance of supercritical fluid (SCF) as a solvent can be greatly affected by addition of anentrainer to the system. In this study, a constant volume visual method is used to measure the critical point ofCO2+n-butyraldehyde, CO2+ i-butyraldehyde and CO2+alcohol binary systems and CO2+entrainer+trisodiumsalt of tri-(m-sulfonphenyl)phosphine (TPPTS) ternary systems, which provides us good theoretical basis for super-critical extraction and chemical reaction. The relationship between critical point and concentration of the entrainerare discussed. The phase behavior of binary system and that of ternary system are compared. The relationshipbetween the concentration of TPPTS and critical point of binary systems are also discussed.展开更多
The Bohr Hamiltonian with axially deformed shape confined in a quasi-exactly solvable decaticβ-part potential is studied.It is shown that the decatic model can well reproduce the X(5)model results as far as the energ...The Bohr Hamiltonian with axially deformed shape confined in a quasi-exactly solvable decaticβ-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
Nitrogen injection under conditions close vicinity of the liquid-gas critical point is studied numerically. The fluid thermodynamic and transport properties vary drasti- cally and exhibit anomalies in the near-critica...Nitrogen injection under conditions close vicinity of the liquid-gas critical point is studied numerically. The fluid thermodynamic and transport properties vary drasti- cally and exhibit anomalies in the near-critical regime. These anomalies can cause distinctive effects on heat-transfer and fluid-flow characteristics. To focus on the influence of ther- modynamics on the flow field, a relatively low injection Reynolds number of 1 750 is adopted. For comparisons, a reference case with the same configuration and Reynolds number is simulated in the ideal gas regime. The model accommodates full conservation laws, real-fluid thermody- namic and transport phenomena. Results reveal that the flow features of the near-critical fluid jet are significantly differ- ent from their counterpart. The near-critical fluid jet spreads faster and mixes more efficiently with the ambient fluid along with a more rapidly development of the vortex pairing pro- cess. Detailed analysis at different streamwise locations in- cluding both the flat shear-layer region and fully developed vortex region reveals the important effect of volume dilata- tion and baroclinic torque in the near-critical fluid case. The former disturbs the shear layer and makes it more unstable. The volume dilatation and baroclinic effects strengthen the vorticity and stimulate the vortex rolling up and pairing pro- cess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
This paper deals with the existence of solutions to the elliptic equation-△u-μ/|x|2=λu +|u|2*-2u + f(x,u) in Ω,u = 0 on (?)Ω, where Ω is a bounded domain in RN(N≥3), 0 ∈ Ω 2*=2N/N-2,λ> 0, λ (?) σμ,σμ...This paper deals with the existence of solutions to the elliptic equation-△u-μ/|x|2=λu +|u|2*-2u + f(x,u) in Ω,u = 0 on (?)Ω, where Ω is a bounded domain in RN(N≥3), 0 ∈ Ω 2*=2N/N-2,λ> 0, λ (?) σμ,σμ is the spectrum of the operator -△-μI/|x|2 with zero Dirichlet boundary condition, 0 <μ< μ-,μ-=(N-2)2/4, f(x,u)is an asymmetric lower order perturbation of |u|2* -1 at infinity. Using the dual variational methods, the existence of nontrivial solutions is proved.展开更多
文摘In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.
基金Supported by National Natural Science Foundation of China
文摘In order to generalize Hadamard's theory of fundamental solutions to the case of degenerate holomorphic PDE,this paper studies the asymptotic expansion of Dirac-type distribution associated with a class of hypersurfaces F(x)with degenerate critical points and proves that[F(x)](+)(lambda)is a distribution-valued meromorphic of lambda is an element of C under some assumptions on F(x).Next,the authors use the Normal form theory of Arnold and prove that for a hypersurface F(x)=0 with A(mu)type degenerate critical point at x=0,F-+(lambda)is a distribution-valued meromorphic function of lambda.
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.
文摘In this paper foe bifurcation of critical points for the quadratic systems of type(II)and (III) is investigated. and an answer to the problem given in[1] is given.
文摘Suppose A,B and C are the bounded linear operators on a Hilbert space H, when A has a generalized inverse A - such that (AA -) *=AA - and B has a generalized inverse B - such that (B -B) *=B -B,the general characteristic forms for the critical points of the map F p:X→‖ A X B-C ‖ p p (1<p<∞), have been obtained, it is a generalization for P J Maher's result about p=2. Similarly, the same question has been discussed for several operators.
基金supported by the National Natural Science Foundation of China(Grant Nos.12134020 and 12374156)the National Key Research and Development Program of China(Grant No.2023YFA1406500)。
文摘Deconfined quantum critical points(DQCPs)have been proposed as a class of continuous quantum phase transitions occurring between two ordered phases with distinct symmetry-breaking patterns,beyond the conventional framework of Landau-Ginzburg-Wilson(LGW)theory.At the DQCP,the system exhibits emergent gauge fields,fractionalized excitations,and enhanced symmetries.
基金supported by the National Natural Science Foundation of China(Grant Nos.12222515,12075324 for S.Yin,and 12347107,1257-4160 for Y.F.Jiang)the National Key R&D Program of China(Grant No.2022YFA1402703 for Y.F.Jiang)+1 种基金the Science and Technology Projects in Guangdong Province(Grant No.2021QN02X561 for S.Yin)the Science and Technology Projects in Guangzhou City(Grant No.2025A04J5408 for S.Yin)。
文摘The conventional Kibble–Zurek mechanism,describing driven dynamics across critical points based on the adiabatic-impulse scenario(AIS),has attracted broad attention.However,the driven dynamics at the tricritical point with two independent relevant directions have not been adequately studied.Here,we employ the time-dependent variational principle to study the driven critical dynamics at a one-dimensional supersymmetric Ising tricritical point.For the relevant direction along the Ising critical line,the AIS apparently breaks down.Nevertheless,we find that the critical dynamics can still be described by finite-time scaling in which the driving rate has a dimension of r_(μ)=z+1/v_(μ)with z and v_(μ)being the dynamic exponent and correlation length exponent in this direction,respectively.For driven dynamics along another direction,the driving rate has a dimension of r_(p)=z+1/v_(p)with v_(p)being another correlation length exponent.Our work brings a new fundamental perspective into nonequilibrium critical dynamics near the tricritical point,which could be realized in programmable quantum processors in Rydberg atomic systems.
基金Project supported by the Natural Science Foundation of China.
文摘We study the global qualitative properties of the well-known Kukles systems (1) below. Firstly, the number of critical points in case (1) has a center or a fine focus.
文摘In order to provide a reference for the further study of microbial contamination in the pork production process. Microbial contamination of pigs came from three slaughterhouses were detected, and critical control points in the progress of hog slaughter and processing were analyzed. The results showed that microbial con- taminatian existed in the entire slaughter and processing progress, including shower and assassination bloodletting, separation of the internal organs, chopping boards, workshop environment, personal hygiene of the operators, etc. , which should be paid more attention to. The results indicated that reasonable protection measures should be carried out, disinfection awareness of the operators should be improved, and regular disinfection should be ruled under the condition of continu- ous operation.
基金supported by the National Natural Science Foundation of China (Grant No.40874052)the Key Laboratory of Geo-detection (China University of Geosciences,Beijing),Ministry of Education
文摘Up to now, the primary method for studying critical porosity and porous media are experimental measurements and data analysis. There are few references on how to numerically calculate porosity at the critical point, pore fluid-related parameters, or framework-related parameters. So in this article, we provide a method for calculating these elastic parameters and use this method to analyze gas-bearing samples. We first derive three linear equations for numerical calculations. They are the equation of density p versus porosity Ф, density times the square of compressional wave velocity p Vp^2 versus porosity, and density times the square of shear wave velocity pVs^2 versus porosity. Here porosity is viewed as an independent variable and the other parameters are dependent variables. We elaborate on the calculation steps and provide some notes. Then we use our method to analyze gas-bearing sandstone samples. In the calculations, density and P- and S-velocities are input data and we calculate eleven relative parameters for porous fluid, framework, and critical point. In the end, by comparing our results with experiment measurements, we prove the viability of the method.
文摘In this paper, we consider the problem of existence as well as multiplicity results for a bi-harmonic equation under the Navier boundary conditions： △2 u = K（x）u p , u 〉 0 in Ω , △u = u = 0 on Ω , where Ω is a smooth domain in R n , n 5, and p ＋ 1 = 2 n n 4 is the critical Sobolev exponent. We obtain highlightly a new criterion of existence, which provides existence results for a dense subset of positive functions, and generalizes Bahri-Coron type criterion in dimension six. Our argument gives also estimates on the Morse index of the obtained solutions and extends some known results. Moreover, it provides, for generic K, Morse inequalities at infinity, which delivers lower bounds for the number of solutions. As further applications of this Morse theoretical approach, we prove more existence results.
基金the Deanship of Scientific Research at Taibah University on material and moral support in the financing of this research project
文摘This paper is concerned with the harmonic equation(P;) : ?u = 0, u > 0 in B;and ?u/?ν+(（n-2）/2)u =(（n-2）/2) Ku;on S;where B;is the unit ball in R;, n ≥ 4 with Euclidean metric g;, ?B;= S;is its boundary, K is a function on S;and ε is a small positive parameter. We construct solutions of the subcritical equation(P;) which blow up at one critical point of K. We give also a sufficient condition on the function K to ensure the nonexistence of solutions for(P;) which blow up at one point. Finally, we prove a nonexistence result of single peaked solutions for the supercritical equation(P;).
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Supported by NSFC(11326127,11101335)NWNULKQN-11-23the Fundamental Research Funds for the Gansu Universities
文摘In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.
基金supported by NSF of China(11201488),supported by NSF of China(11371146)Hunan Provincial Natural Science Foundation of China(14JJ4002)
文摘In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear SchrSdinger equations with negative parameter which arose from the study of self-channeling of high-power ultrashort laser in matter.
基金Supported by the National Natural Science Foundation of China (No. 20076004) and the Doctoral Program Foundation of the Institution of Higher Education of China (No. 2000001005).
文摘The performance of supercritical fluid (SCF) as a solvent can be greatly affected by addition of anentrainer to the system. In this study, a constant volume visual method is used to measure the critical point ofCO2+n-butyraldehyde, CO2+ i-butyraldehyde and CO2+alcohol binary systems and CO2+entrainer+trisodiumsalt of tri-(m-sulfonphenyl)phosphine (TPPTS) ternary systems, which provides us good theoretical basis for super-critical extraction and chemical reaction. The relationship between critical point and concentration of the entrainerare discussed. The phase behavior of binary system and that of ternary system are compared. The relationshipbetween the concentration of TPPTS and critical point of binary systems are also discussed.
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 decaticβ-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 in part by the National Natural Science Foundation of China (11132010 and 11072236)
文摘Nitrogen injection under conditions close vicinity of the liquid-gas critical point is studied numerically. The fluid thermodynamic and transport properties vary drasti- cally and exhibit anomalies in the near-critical regime. These anomalies can cause distinctive effects on heat-transfer and fluid-flow characteristics. To focus on the influence of ther- modynamics on the flow field, a relatively low injection Reynolds number of 1 750 is adopted. For comparisons, a reference case with the same configuration and Reynolds number is simulated in the ideal gas regime. The model accommodates full conservation laws, real-fluid thermody- namic and transport phenomena. Results reveal that the flow features of the near-critical fluid jet are significantly differ- ent from their counterpart. The near-critical fluid jet spreads faster and mixes more efficiently with the ambient fluid along with a more rapidly development of the vortex pairing pro- cess. Detailed analysis at different streamwise locations in- cluding both the flat shear-layer region and fully developed vortex region reveals the important effect of volume dilata- tion and baroclinic torque in the near-critical fluid case. The former disturbs the shear layer and makes it more unstable. The volume dilatation and baroclinic effects strengthen the vorticity and stimulate the vortex rolling up and pairing pro- cess
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.
文摘This paper deals with the existence of solutions to the elliptic equation-△u-μ/|x|2=λu +|u|2*-2u + f(x,u) in Ω,u = 0 on (?)Ω, where Ω is a bounded domain in RN(N≥3), 0 ∈ Ω 2*=2N/N-2,λ> 0, λ (?) σμ,σμ is the spectrum of the operator -△-μI/|x|2 with zero Dirichlet boundary condition, 0 <μ< μ-,μ-=(N-2)2/4, f(x,u)is an asymmetric lower order perturbation of |u|2* -1 at infinity. Using the dual variational methods, the existence of nontrivial solutions is proved.
