Quantitative determination of the critical points of Mott metal–insulator transition in strongly correlated systems

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.

Linear numerical calculation method for obtaining critical point,pore fluid,and framework parameters of gas-bearing media

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.

Influence of Different Equations of State on Simulation Results of Supercritical CO_(2) Centrifugal Compressor

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.

NONSMOOTH CRITICAL POINT THEOREMS AND ITS APPLICATIONS TO QUASILINEAR SCHRDINGER EQUATIONS

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.

An Analytic Equation of State Based on SAFT-CP for Binary Non-Polar Alkane Mixtures Across the Critical Point

The description using an analytic equation of state of thermodynamic properties near the critical points of fluids and their mixtures remains a challenging problem in the area of chemical engineering. Based on the statistical associating fluid theory across the critical point (SAFT-CP), an analytic equation of state is established in this work for non-polar mixtures. With two binary parameters, this equation of state can be used to calculate not only vapor-liquid equilibria but also critical properties of binary non-polar alkane mixtures with acceptable deviations.

Fluid phases of argon: A debate on the absence of van der Waals’ “critical point”

A phase diagram of argon based upon percolation transition loci determined from literature experimental p-V isotherms, and simulation values using a Lennard-Jones model shows three fluid phases. The liquid phase spans all temperatures, from a metastable amorphous ground state at 0K, to ultra-high T. There is a supercritical mesophase bounded by percolation transition loci, and a gas phase. Intersection of two percolation loci in the p-T plane thermodynamically defines a critical line between two coexisting gas and liquid critical states at T = Tc, and the single mesophase for T > Tc. A debate on the absence of a van der Waals critical point in the Gibbs p-T density surface is appended.

CALCULATIONS OF THE PHASE EQUILIBRIA AND CRITICAL CURVES WITH THE EQUATION OF STATE FOR BINARY MIXTURES

A rational equation of state of the perturbation type with a repulsion and attraction term has been applied to reproduce critical curves of six different binary systems up to high temperatures and pressures. A square well potential for intermolecular interaction is used. With pairwise combination rules for these potentials three adjustable parameters are needed. The experimental critical point and phase equilibrium data are compared with the values predicted using the equation of state. Good agreement is obtained for the analysis of the critical pressure composition data and molar volumes.

A numerical study of fluid injection and mixing under near-critical conditions

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

The Existence of Ground State Solutions for Schrödinger-Kirchhoff Equations Involving the Potential without a Positive Lower Bound

In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R2 and f has critical exponential growth. By using a version of Trudinger-Moser inequality and variational methods, we obtain the existence of ground state solutions for this problem.

Ground states for asymptotically periodic quasilinear Schrdinger equations with critical growth

For a class of asymptotically periodic quasilinear Schr？dinger equations with critical growth the existence of ground states is proved.First applying a change of variables the quasilinear Schr？dinger equations are reduced to semilinear Schr？dinger equations in which the corresponding functional is well defined in H1 RN .Moreover there is a one-to-one correspondence between ground states of the semilinear Schr？dinger equations and the quasilinear Schr？dinger equations.Then the mountain-pass theorem is used to find nontrivial solutions for the semilinear Schr？dinger equations. Finally under certain monotonicity conditions using the Nehari manifold method and the concentration compactness principle the nontrivial solutions are found to be exactly the same as the ground states of the semilinear Schr？dinger equations.

CORRELATION OF CRITICAL LOCI FOR FLUID MIXTURES

The hard-sphere three-parameter equation of state proposed in our previous investigation was applied to correlate binary critical loci of alkane-alkane, aromatic-aromatic, hydrocarbon-inorganic gas and systems containing oxygenated hydrocarbons including those exhibiting type Ⅲ behaviors as classified by van Konynenberg and Scott. A new procedure was also presented which simplified mathematical manipulations and permitted the reduction of the computation time.Results were compared with those obtained by Patel-Teja equation with temperature-dependent binary interaction parameters. Significant improvements were achieved by the proposed equation with temperature-dependent parameters.In addition parameters obtained from the critical locus calculations were used to predict vapor-liquid equilibria of hydrogen-carbon monoxide and hydrogen-carbon dioxide systems. Prediction accuracies were found to be very satisfactory.

EXISTENCE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS AND HARDY TERMS

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.

THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF TYPE EQUATIONS

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.

EXISTENCE OF A GROUND STATE SOLUTION FOR THE CHOQUARD EQUATION WITH NONPERIODIC POTENTIALS

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.

一类Kirchhoff型方程边值问题多重解的存在性研究

本文讨论了一类Kirchhoff型方程{-(a+b‖u‖^(2))Δu=bμu^(3)+f(x,u),x∈Ωu=0,x∈∂Ω多重解的存在性,其中:Ω⊂R^(N)是有界区域(N=1,2,3),a,b>0,μ∈R为参数,μ小于非线性特征值问题{-‖u‖^(2)Δu=μu^(3),x∈Ωu=0,x∈∂Ω{的主特征值,即μ<μ1,f∈C(Ω×R,R)在无穷远处满足次四次条件。利用临界点理论及Clark定理可以证明上述Kirchhoff型方程多重解的存在性。

EXISTENCE AND NONEXISTENCE OF SOLUTIONS FOR A HARMONIC EQUATION WITH CRITICAL NONLINEARITY

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;).

具有无界势能的Kirchhoff-型差分方程多个同宿轨的存在性

该文运用临界点理论研究了具有无界势能的Kirchhoff-型差分方程多个同宿轨的存在性.特别地,文中借助于非线性项次线性增长条件和一些技巧证明了能量泛函满足Palais-Smale紧性条件.最后举例说明主要结论.

Infinitely Many Solutions and a Ground-State Solution for Klein-Gordon Equation Coupled with Born-Infeld Theory

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.

Existence of Multiple Equilibrium Points in Global Attractor for the Strongly Damped Wave Equations

The aim of this paper is to study the long-term behavior of strongly damped wave equations with a Lyapunov function. Using the theory established by estimating the Z2 index of some sets and the idea of invariant sets of semi-flow,the properties of the global attractor for strongly damped wave equation are discussed. The existence of multiple equilibrium points in global attractor for strongly damped wave equations with critical growth of nonlinearity is obtained. And under some additional condition, the infinite dimension of the attractor is proven.

Study on Critical Properties for CO_2+Cosolvent Binary System and Ternary System

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.