The Cauchy problem in Rn of (i) ut = Δuα+1+uβ and (ii) with non-negative initial value is studied. Here α>0, β>1. It is proved that for (i) with β = α+2/n being the critical case every non-trivial solutio...The Cauchy problem in Rn of (i) ut = Δuα+1+uβ and (ii) with non-negative initial value is studied. Here α>0, β>1. It is proved that for (i) with β = α+2/n being the critical case every non-trivial solution blows up in finite time. A similar result is proved for (ii).展开更多
The magnetic properties of inverse ferrite Fe_(3+) Fe_(3+)Co_(2+) O^(2-)_4, Fe^(3+) Fe^(3+)Cu^(2+) O^2_(-4), Fe^(3+) Fe^(3+)Fe^(2+) O^2_(-4),and Fe^(3+) Fe^(3+)Ni^(2+) O^(2-)_4spinels have been studied using Monte Car...The magnetic properties of inverse ferrite Fe_(3+) Fe_(3+)Co_(2+) O^(2-)_4, Fe^(3+) Fe^(3+)Cu^(2+) O^2_(-4), Fe^(3+) Fe^(3+)Fe^(2+) O^2_(-4),and Fe^(3+) Fe^(3+)Ni^(2+) O^(2-)_4spinels have been studied using Monte Carlo simulation. We have also calculated the critical and Curie Weiss temperatures from the thermal magnetizations and inverse of magnetic susceptibilities for each system.Magnetic hysteresis cycles have been found for the four systems. Finally, we found the critical exponents associated with magnetization, magnetic susceptibility, and external magnetic field. Our results of critical and Curie Weiss temperatures are similar to those obtained by experiment results. The critical exponents are similar to those of known 3 D-Ising model.展开更多
In this paper, we deal with the following problem：By variational method, we prove the existenceof a nontrivial weak solution whenand the existence of a cylindricalweak solution when
In this paper a semilinear biharmonic problem involving nearly critical growth with Navier boundary condition is considered on an any bounded smooth domain. It is proved that positive solutions concentrate on a point ...In this paper a semilinear biharmonic problem involving nearly critical growth with Navier boundary condition is considered on an any bounded smooth domain. It is proved that positive solutions concentrate on a point in the domain, which is also a critical point of the Robin’s function corresponding to the Green’s function of biharmonic operator with the same boundary condition. Similar conclusion has been obtained in [6] under the condition that the domain is strictly convex.展开更多
The purpose of this work is to identify the universality class of the nonequilibrium phase transition in the two-dimensional kinetic Ising ferromagnet driven by propagating magnetic field wave. To address this issue, ...The purpose of this work is to identify the universality class of the nonequilibrium phase transition in the two-dimensional kinetic Ising ferromagnet driven by propagating magnetic field wave. To address this issue, the finite size analysis of the nonequilibrium phase transition, in two-dimensional Ising ferromagnet driven by plane propagating magnetic wave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium dynamic phase transition from a high temperature dynamically symmetric (propagating) phase to a low temperature dynamically symmetry-broken (pinned) phase as the system is cooled below the transition temperature. This transition temperature is determined precisely by studying the fourth-order Binder Cumulant of the dynamic order parameter as a function of temperature for different system sizes (L). From the finite size analysis of dynamic order parameter ?and the dynamic susceptibility , we have estimated the critical exponents and ?(measured from the data read at the critical temperature obtained from Binder cumulant), and (measured from the peak positions of dynamic susceptibility). Our results indicate that such driven Ising ferromagnet belongs to the same universality class of the two-dimensional equilibrium Ising ferromagnet (where and ), within the limits of statistical errors.展开更多
A general weighted second order elliptic equation involving critical growth is considered on bounded smooth. domain in n-dimension space. There is the singular point for the weighted coefficients in the domain. With g...A general weighted second order elliptic equation involving critical growth is considered on bounded smooth. domain in n-dimension space. There is the singular point for the weighted coefficients in the domain. With generalized blow up method, some results are obtained for asymptotic behavior of positive solutions. This problem includes Laplacian operators as special cases.展开更多
In this paper, we are concerned with the following problem：{（-△）ku=λf（x）｜u｜q-2u＋g（x）｜u｜k＊-2u, x∈Ω, u∈H k0 （Ω）, where Ωis a bounded domain in RN with N ≥2k＋1, 1〈q〈2,λ〉0, f, g are continuous ...In this paper, we are concerned with the following problem：{（-△）ku=λf（x）｜u｜q-2u＋g（x）｜u｜k＊-2u, x∈Ω, u∈H k0 （Ω）, where Ωis a bounded domain in RN with N ≥2k＋1, 1〈q〈2,λ〉0, f, g are continuous functions on Ω which are somewhere positive but which may change sign on Ω. k＊ = N2/N-2k is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple nontrivial solutions to this equation is verified.展开更多
The Blume-Capel model in the presence of external magnetic field H has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton in three-dimension lattice. The field critical exp...The Blume-Capel model in the presence of external magnetic field H has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton in three-dimension lattice. The field critical exponent 5 is estimated using the power law relations and the finite size scaling functions for the magnetization and the susceptibility in the range -0.1≤ h = H/J ≤0. The estimated value of the field critical exponent 5 is in good agreement with the universal value （δ = 5） in three dimensions. The simulations are carried out on a simple cubic lattice under periodic boundary conditions.展开更多
The ferroelectric transitions of several SrTiO3-based ferroelectrics are investigated experimentally and theoretically, with special attention to the critical scaling exponents associated with the phase transitions, i...The ferroelectric transitions of several SrTiO3-based ferroelectrics are investigated experimentally and theoretically, with special attention to the critical scaling exponents associated with the phase transitions, in order to understand the competition among quantum fluctuations （QFs）, quenched disorder, and ferroelectric ordering. Two representative systems with sufficiently strong QFs and quenched disorders in competition with the ferroelectric ordering are investigated. We start from non-stoichiometric SrTiO3（STO） with the Sr/Ti ratio deviating slightly from one, which is believed to maintain strong QFs. Then, we address Ba/Ca co-doped Sr1-x（Ca0.6389Ba0.3611）xTiO3（SCBT） with the averaged Sr-site ionic radius identical to the Sr2＋ ionic radius, which is believed to offer remarkable quenched disorder associated with the Sr-site ionic mismatch. The critical exponents associated with polarization P and dielectric susceptibility ε, respectively, as functions of temperature T close to the critical point Tc, are evaluated. It is revealed that both non-stoichiometric SrTiO3 and SCBT exhibit much bigger critical exponents than the Landau mean-field theory predictions. These critical exponents then decrease gradually with increasing doping level or deviation of Sr/Ti ratio from one. A transverse Ising model applicable to the Sr-site doped STO （e.g., Sr1-xCaxTiO3） at low level is used to explain the observed experimental data. It is suggested that the serious deviation of these critical exponents from the Landau theory predictions in these STO-based systems is ascribed to the significant QFs and quenched disorder by partially suppressing the long-range spatial correlation of electric dipoles around the transitions. The present work thus sheds light on our understanding of the critical behaviors of ferroelectric transitions in STO in the presence of quantum fluctuations and quenched disorder, whose effects have been demonstrated to be remarkable.展开更多
In this paper a general weighted p-Laplacian equation involving critical growth and singular coefficients is considered on the unit ball, rather complete results are obtained for asymptotic behavio...In this paper a general weighted p-Laplacian equation involving critical growth and singular coefficients is considered on the unit ball, rather complete results are obtained for asymptotic behavior of positive solutions as λ→0+. This problem includes p- Laplacian, weighted Laplacian, and the Hessian operators which are special cases of our result.展开更多
The thermodynamics of strongly interacting matter near the critical end point are investigated in a holographic QCD model, which can describe the QCD phase diagram in T-μ plane qualitatively. Critical exponents along...The thermodynamics of strongly interacting matter near the critical end point are investigated in a holographic QCD model, which can describe the QCD phase diagram in T-μ plane qualitatively. Critical exponents along different axes(α,β,γ,δ) are extracted numerically. It is given that α≈0,β≈0.54,γ≈1.04, and δ≈2.97,which is similar to the three-dimensional Ising mean-field approximation and previous holographic QCD model calculations. We also discuss the possibilities to go beyond the mean field approximation by including the full back-reaction of the chiral dynamics in the holographic framework.展开更多
I investigate the ferromagnetic phase transition inside strong quark matter (SQM) with one gluon exchange interaction between strong quarks. I use a variational method and the Landau-Fermi liquid theory and obtain the...I investigate the ferromagnetic phase transition inside strong quark matter (SQM) with one gluon exchange interaction between strong quarks. I use a variational method and the Landau-Fermi liquid theory and obtain the thermodynamics quantities of SQM. In the low temperature limit, the equation of state (EOS) and critical exponents for the second-order phase transition (ferromagnetic phase transition) in SQM are analytically calculated. The results are in agreement with the Ginzberg-Landau theory.展开更多
文摘The Cauchy problem in Rn of (i) ut = Δuα+1+uβ and (ii) with non-negative initial value is studied. Here α>0, β>1. It is proved that for (i) with β = α+2/n being the critical case every non-trivial solution blows up in finite time. A similar result is proved for (ii).
文摘The magnetic properties of inverse ferrite Fe_(3+) Fe_(3+)Co_(2+) O^(2-)_4, Fe^(3+) Fe^(3+)Cu^(2+) O^2_(-4), Fe^(3+) Fe^(3+)Fe^(2+) O^2_(-4),and Fe^(3+) Fe^(3+)Ni^(2+) O^(2-)_4spinels have been studied using Monte Carlo simulation. We have also calculated the critical and Curie Weiss temperatures from the thermal magnetizations and inverse of magnetic susceptibilities for each system.Magnetic hysteresis cycles have been found for the four systems. Finally, we found the critical exponents associated with magnetization, magnetic susceptibility, and external magnetic field. Our results of critical and Curie Weiss temperatures are similar to those obtained by experiment results. The critical exponents are similar to those of known 3 D-Ising model.
基金Supported by the National Science Foundation of China(11071245 and 11101418)
文摘In this paper, we deal with the following problem：By variational method, we prove the existenceof a nontrivial weak solution whenand the existence of a cylindricalweak solution when
基金The research work was supported by the National Natural Foundation of China (10371045)Guangdong Provincial Natural Science Foundation of China (000671).
文摘In this paper a semilinear biharmonic problem involving nearly critical growth with Navier boundary condition is considered on an any bounded smooth domain. It is proved that positive solutions concentrate on a point in the domain, which is also a critical point of the Robin’s function corresponding to the Green’s function of biharmonic operator with the same boundary condition. Similar conclusion has been obtained in [6] under the condition that the domain is strictly convex.
文摘The purpose of this work is to identify the universality class of the nonequilibrium phase transition in the two-dimensional kinetic Ising ferromagnet driven by propagating magnetic field wave. To address this issue, the finite size analysis of the nonequilibrium phase transition, in two-dimensional Ising ferromagnet driven by plane propagating magnetic wave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium dynamic phase transition from a high temperature dynamically symmetric (propagating) phase to a low temperature dynamically symmetry-broken (pinned) phase as the system is cooled below the transition temperature. This transition temperature is determined precisely by studying the fourth-order Binder Cumulant of the dynamic order parameter as a function of temperature for different system sizes (L). From the finite size analysis of dynamic order parameter ?and the dynamic susceptibility , we have estimated the critical exponents and ?(measured from the data read at the critical temperature obtained from Binder cumulant), and (measured from the peak positions of dynamic susceptibility). Our results indicate that such driven Ising ferromagnet belongs to the same universality class of the two-dimensional equilibrium Ising ferromagnet (where and ), within the limits of statistical errors.
文摘A general weighted second order elliptic equation involving critical growth is considered on bounded smooth. domain in n-dimension space. There is the singular point for the weighted coefficients in the domain. With generalized blow up method, some results are obtained for asymptotic behavior of positive solutions. This problem includes Laplacian operators as special cases.
基金supported by the National Natural Science Foundation of China(11326139,11326145)Tian Yuan Foundation(KJLD12067)+1 种基金Central Specialized Fundation of SCUEC(CZQ13013)the Project of Jiangxi Province Technology Hall(2014BAB211010)
文摘In this paper, we are concerned with the following problem：{（-△）ku=λf（x）｜u｜q-2u＋g（x）｜u｜k＊-2u, x∈Ω, u∈H k0 （Ω）, where Ωis a bounded domain in RN with N ≥2k＋1, 1〈q〈2,λ〉0, f, g are continuous functions on Ω which are somewhere positive but which may change sign on Ω. k＊ = N2/N-2k is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple nontrivial solutions to this equation is verified.
文摘The Blume-Capel model in the presence of external magnetic field H has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton in three-dimension lattice. The field critical exponent 5 is estimated using the power law relations and the finite size scaling functions for the magnetization and the susceptibility in the range -0.1≤ h = H/J ≤0. The estimated value of the field critical exponent 5 is in good agreement with the universal value （δ = 5） in three dimensions. The simulations are carried out on a simple cubic lattice under periodic boundary conditions.
基金the National Basic Research Program of China(Grant Nos.2011CB922101 and 2009CB623303)the National Natural Science Foundation of China(Grant Nos.11234005 and 11074113)the Priority Academic Development Program of Jiangsu Higher Education Institutions,China
文摘The ferroelectric transitions of several SrTiO3-based ferroelectrics are investigated experimentally and theoretically, with special attention to the critical scaling exponents associated with the phase transitions, in order to understand the competition among quantum fluctuations （QFs）, quenched disorder, and ferroelectric ordering. Two representative systems with sufficiently strong QFs and quenched disorders in competition with the ferroelectric ordering are investigated. We start from non-stoichiometric SrTiO3（STO） with the Sr/Ti ratio deviating slightly from one, which is believed to maintain strong QFs. Then, we address Ba/Ca co-doped Sr1-x（Ca0.6389Ba0.3611）xTiO3（SCBT） with the averaged Sr-site ionic radius identical to the Sr2＋ ionic radius, which is believed to offer remarkable quenched disorder associated with the Sr-site ionic mismatch. The critical exponents associated with polarization P and dielectric susceptibility ε, respectively, as functions of temperature T close to the critical point Tc, are evaluated. It is revealed that both non-stoichiometric SrTiO3 and SCBT exhibit much bigger critical exponents than the Landau mean-field theory predictions. These critical exponents then decrease gradually with increasing doping level or deviation of Sr/Ti ratio from one. A transverse Ising model applicable to the Sr-site doped STO （e.g., Sr1-xCaxTiO3） at low level is used to explain the observed experimental data. It is suggested that the serious deviation of these critical exponents from the Landau theory predictions in these STO-based systems is ascribed to the significant QFs and quenched disorder by partially suppressing the long-range spatial correlation of electric dipoles around the transitions. The present work thus sheds light on our understanding of the critical behaviors of ferroelectric transitions in STO in the presence of quantum fluctuations and quenched disorder, whose effects have been demonstrated to be remarkable.
基金The research work was supported by the National Natural Science Foundation of China (No. 10071024)the Guangdong Provincial N
文摘In this paper a general weighted p-Laplacian equation involving critical growth and singular coefficients is considered on the unit ball, rather complete results are obtained for asymptotic behavior of positive solutions as λ→0+. This problem includes p- Laplacian, weighted Laplacian, and the Hessian operators which are special cases of our result.
基金Supported by the NSFC(11725523,11735007,11805084 and 11261130311)(CRC110 by DFG and NSFC)
文摘The thermodynamics of strongly interacting matter near the critical end point are investigated in a holographic QCD model, which can describe the QCD phase diagram in T-μ plane qualitatively. Critical exponents along different axes(α,β,γ,δ) are extracted numerically. It is given that α≈0,β≈0.54,γ≈1.04, and δ≈2.97,which is similar to the three-dimensional Ising mean-field approximation and previous holographic QCD model calculations. We also discuss the possibilities to go beyond the mean field approximation by including the full back-reaction of the chiral dynamics in the holographic framework.
文摘I investigate the ferromagnetic phase transition inside strong quark matter (SQM) with one gluon exchange interaction between strong quarks. I use a variational method and the Landau-Fermi liquid theory and obtain the thermodynamics quantities of SQM. In the low temperature limit, the equation of state (EOS) and critical exponents for the second-order phase transition (ferromagnetic phase transition) in SQM are analytically calculated. The results are in agreement with the Ginzberg-Landau theory.
