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Experimental study on the size effect on the equation of state of concretes under shock loading
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作者 Mei Li Jian Cui +2 位作者 Yanchao Shi Baijian Tang Xin Chen 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2024年第3期160-167,共8页
Adopting the classical theory of hydrocodes,the constitutive relations of concretes are separated into an equation of state(EoS)which describes the volumetric behavior of concrete material and a strength model which d... Adopting the classical theory of hydrocodes,the constitutive relations of concretes are separated into an equation of state(EoS)which describes the volumetric behavior of concrete material and a strength model which depicts the shear properties of concrete.The experiments on the EoS of concrete is always challenging due to the technical difficulties and equipment limitations,especially for the specimen size effect on the EoS.Although some researchers investigate the shock properties of concretes by fly-plate impact tests,the specimens used in their tests are usually in one size.In this paper,the fly-plate impact tests on concrete specimens with different sizes are performed to investigate the size effect on the shock properties of concrete materials.The mechanical background of the size effect on the shock properties are revealed,which is related to the lateral rarefaction effect and the deviatoric stress produced in the specimen.According to the tests results,the modified EoS considering the size effect on the shock properties of concrete are proposed,which the bulk modulus of concrete is unpredicted by up to 20% if size effects are not accounted for. 展开更多
关键词 CONCRETE equation of state Size effect Shock wave Fly-plate impact test
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Normalized Ground State Solutions of Nonlinear Choquard Equations with Nonconstant Potential
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作者 LI Nan ZHAO Hui-yan XU Li-ping 《Chinese Quarterly Journal of Mathematics》 2024年第3期250-261,共12页
In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/... In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/N Under appropriate hypotheses on V(x),we prove that the above Choquard equation has a normalized ground state solution by utilizing variational methods. 展开更多
关键词 Choquard equation Nonconstant potential function Normalized ground state solutions Variational methods
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Infinitely Many Solutions and a Ground-State Solution for Klein-Gordon Equation Coupled with Born-Infeld Theory
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作者 Fangfang Huang Qiongfen Zhang 《Journal of Applied Mathematics and Physics》 2024年第4期1441-1458,共18页
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
关键词 Klein-Gordon equation Born-Infeld Theory Infinitely Many Solutions Ground-state Solution Critical Point Theory
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Bayesian analysis of nuclear equation of state at high baryon density 被引量:1
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作者 Long‑Gang Pang Xin‑Nian Wang 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2023年第12期156-158,共3页
Bayesian analysis was employed to constrain the equation of state(EoS)of nuclear matter with a baryon density of up to six times the nuclear saturation density,using data from heavy-ion collisions at beam energies√S_... Bayesian analysis was employed to constrain the equation of state(EoS)of nuclear matter with a baryon density of up to six times the nuclear saturation density,using data from heavy-ion collisions at beam energies√S_(NN)=2-10GeV.The resulting EoS excellently agrees with that constrained by astrophysical observations. 展开更多
关键词 OBSERVATIONS equation state
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THE EXISTENCE AND CONCENTRATION OF GROUND STATE SIGN-CHANGING SOLUTIONS FOR KIRCHHOFF-TYPE EQUATIONS WITH A STEEP POTENTIAL WELL 被引量:1
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作者 吴梦慧 唐春雷 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1781-1799,共19页
In this paper,we consider the nonlinear Kirchhoff type equation with a steep potential well−(a+b∫_(R)^(3)|∇u|^(2 )dx)Δu+λV(x)u=f(u)in R^(3),where a,b>0 are constants,λ is a positive parameter,V∈C(R3,R)is a ste... In this paper,we consider the nonlinear Kirchhoff type equation with a steep potential well−(a+b∫_(R)^(3)|∇u|^(2 )dx)Δu+λV(x)u=f(u)in R^(3),where a,b>0 are constants,λ is a positive parameter,V∈C(R3,R)is a steep potential well and the nonlinearity f∈C(R,R)satisfies certain assumptions.By applying a signchanging Nehari manifold combined with the method of constructing a sign-changing(PS)C sequence,we obtain the existence of ground state sign-changing solutions with precisely two nodal domains when λ is large enough,and find that its energy is strictly larger than twice that of the ground state solutions.In addition,we also prove the concentration of ground state sign-changing solutions. 展开更多
关键词 Kirchhoff-type equation ground state sign-changing solutions steep potential well
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Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients
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作者 Hiroshi Uechi Lisa Uechi Schun T. Uechi 《Journal of Applied Mathematics and Physics》 2024年第5期1733-1743,共11页
The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple ba... The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general. 展开更多
关键词 The Nonlinear Differential equation with Time-Dependent Coefficients The Bifurcation-Integration Solution Nonequilibrium Irreversible states Thermomechanical Dynamics (TMD)
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EXISTENCE OF A GROUND STATE SOLUTION FOR THE CHOQUARD EQUATION WITH NONPERIODIC POTENTIALS
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作者 罗缘圆 高冬梅 王俊 《Acta Mathematica Scientia》 SCIE CSCD 2023年第1期303-323,共21页
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
关键词 Choquard equation ground state solution critical points variational methods
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The Existence of Ground State Solutions for Schrödinger-Kirchhoff Equations Involving the Potential without a Positive Lower Bound
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作者 Yuqi Wang Die Wang Shaoxiong Chen 《Journal of Applied Mathematics and Physics》 2023年第3期790-803,共14页
In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R<sup>2</sup> and f has critical exponential growth. By using a version of Trudinger... In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R<sup>2</sup> 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. 展开更多
关键词 Schrödinger-Kirchhoff equations Critical Exponential Growth Ground state Solution Degenerate Potential
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Long-Time Behavior of Solution for Autonomous Suspension Bridge Equations with State-Dependent Delay
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作者 Suping Wang Qiaozhen Ma Xukui Shao 《Engineering(科研)》 2023年第10期632-646,共15页
This work is devoted to the following suspension bridge with state-dependent delay: . The main goal of this paper is to investigate the long-time behavior of the system. Under suitable hypothesis, the quasi-stability ... This work is devoted to the following suspension bridge with state-dependent delay: . The main goal of this paper is to investigate the long-time behavior of the system. Under suitable hypothesis, the quasi-stability estimates of the system are established, based on which the existence of global attractor with finite fractal dimension is obtained. Furthermore, the existence of exponential attractor is proved. 展开更多
关键词 Suspension Bridge equation state-Dependent Delay Global Attractor Exponential Attractor Quasi-Stability
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THRESHOLD RESULT FOR SEMILINEAR PARABOLIC EQUATIONS WITH INDEFINITE NON-HOMOGENEOUS TERM
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作者 谢君辉 戴求亿 刘芳 《Acta Mathematica Scientia》 SCIE CSCD 2012年第6期2302-2314,共13页
In this paper, we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations {μt-△μ=g(μ)+λf(x),(x,t)∈Ω×(0,T),μ=0,(x,t)∈ Ω×[0,T)... In this paper, we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations {μt-△μ=g(μ)+λf(x),(x,t)∈Ω×(0,T),μ=0,(x,t)∈ Ω×[0,T),μ(x,0)=μ0(x)≥0,x∈Ω.By combining a priori estimate of global solution with property of stationary solution set of problem (P), we prove that the minimal stationary solution Uλ(x) of problem (P) is stable, whereas, any other stationary solution is an initial datum threshold for the existence and nonexistence of global solution to problem (P). 展开更多
关键词 parabolic equations initial boundary value problem global solution thresh-old result non-homogenous tern:
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An Elliptic Gradient Estimate for A Non-homogeneous Heat Equation on Complete Noncompact Manifolds
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作者 JI Xiang 《Chinese Quarterly Journal of Mathematics》 2018年第1期61-67,共7页
Let M be an n-dimensional complete noncompact Riemannian manifold. In this paper, we will give the elliptic gradient estimate for positive smooth solutions to the non-homogeneous heat equation(?_t-△)u(x, t) = A(x, t)... Let M be an n-dimensional complete noncompact Riemannian manifold. In this paper, we will give the elliptic gradient estimate for positive smooth solutions to the non-homogeneous heat equation(?_t-△)u(x, t) = A(x, t)when the metric evolves under the Ricci flow. As applications, we get Harnack inequalities to compare solutions at the same time. 展开更多
关键词 non-homogeneous heat equation Ricci flow Bochner formula elliptic type gradient estimate Harnack inequality
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CALCULATIONS OF THE PHASE EQUILIBRIA AND CRITICAL CURVES WITH THE EQUATION OF STATE FOR BINARY MIXTURES
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作者 田宜灵 乔瑞平 +1 位作者 宋瑛 任晓文 《Transactions of Tianjin University》 EI CAS 1998年第1期62-67,共6页
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 ... 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. 展开更多
关键词 equation of state binary system critical curve phase equilibrium high temperature and high pressure
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Modeling and simulation of JWL equation of state for reactive Al/PTFE mixture 被引量:13
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作者 蒋建伟 王树有 +1 位作者 张谋 魏强 《Journal of Beijing Institute of Technology》 EI CAS 2012年第2期150-156,共7页
An analytical method is presented to fit parameters of Jones-Wilkins-Lee (JWL) equation of state (EOS) for the chemical process of aluminum-polytetrafluoroethylene ( AI/PTFE ) mixture. Subroutine codes for both ... An analytical method is presented to fit parameters of Jones-Wilkins-Lee (JWL) equation of state (EOS) for the chemical process of aluminum-polytetrafluoroethylene ( AI/PTFE ) mixture. Subroutine codes for both strength model and EOS were developed in explicit-FE code AUTODYN. Firstly, the shock Hugoniot data of reactive A1/PTFE mixture was analytically derived by implemen- ting this methodology. The JWL EOS was verified to fit shock Hugoniot data of both reacted and un- reacted A1/PTFE mixture, which gives reasonable results. Furthermore, to numerically ascertain the reaction phases of ignition and growth and quasi detonation of A1/PTFE mixture, characterized ex- periment was setup to validate the reaction phases and coefficients of JWL EOS for A1/PTFE mix- ture. From the test, a promising example of reactive mixture A1/PTFE is capable to enhance lethality of weapons, the status computation in clude quasi-detonation pressure and temperature of A1/PTFE mixture in different chemical reaction phases is validated. 展开更多
关键词 A1/PTFE JWL equation of states quasi detonation numerical simulation
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EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY 被引量:4
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作者 Sanjukta DAS Dwijendra PANDEY N. SUKAVANAM 《Acta Mathematica Scientia》 SCIE CSCD 2016年第5期1509-1523,共15页
This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained b... This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam’s novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory. 展开更多
关键词 approximate controllability cosine family state dependent delay neutral stochastic differential equation measure of noncompactness
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EQUATION OF STATE BASED HYDRATE MODEL FOR NATURAL GAS SYSTEMS CONTAINING BRINE AND POLAR INHIBITOR 被引量:2
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作者 左有祥 郭天民 Sφren Gommesen 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 1996年第3期4-17,共14页
A new thermodynamic model for gas hydrates was established by combining the modified Patel-Teja equation of state proposed for aqueous electrolyte systems and the simplified Holder -John multi -shell hydrate model. Th... A new thermodynamic model for gas hydrates was established by combining the modified Patel-Teja equation of state proposed for aqueous electrolyte systems and the simplified Holder -John multi -shell hydrate model. The new hydrate model is capable of predicting the hydrate formation/dissociation conditions of natural gas systems containing pure water/formation water (brine) and polar inhibitor without using activity coefficient model. Extensive test results indicate very encouraging results. 展开更多
关键词 HYDRATE model equation of state BRINE natural gas
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Strangeness to increase the density of finite nuclear systems in constraining the high-density nuclear equation of state 被引量:2
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作者 Wei-Zhou Jiang Rong-Yong Yang Si-Na Wei 《Nuclear Science and Techniques》 SCIE CAS CSCD 2017年第12期244-247,共4页
As the high-density nuclear equation of state(EOS) is not very well constrained, we suggest that the structural properties from the finite systems can be used to extract a more accurate constraint. By including the st... As the high-density nuclear equation of state(EOS) is not very well constrained, we suggest that the structural properties from the finite systems can be used to extract a more accurate constraint. By including the strangeness degrees of freedom, the hyperon or anti-kaon, the finite systems can then have a rather high-density core which is relevant to the nuclear EOS at high densities directly. It is found that the density dependence of the symmetry energy is sensitive to the properties of multi-K hypernuclei, while the high-density EOS of symmetric matter correlates sensitively to the properties of kaonic nuclei. 展开更多
关键词 NUCLEAR equation of state RELATIVISTIC meanfield theory STRANGENESS
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Basic quantities of the equation of state in isospin asymmetric nuclear matter 被引量:6
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作者 Jie Liu Chao Gao +1 位作者 Niu Wan Chang Xu 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2021年第11期1-12,共12页
Based on the Hugenholtz-Van Hove theorem six basic quantities of the EoS in isospin asymmetric nuclear matter are expressed in terms of the nucleon kinetic energy t(k),the isospin symmetric and asymmetric parts of the... Based on the Hugenholtz-Van Hove theorem six basic quantities of the EoS in isospin asymmetric nuclear matter are expressed in terms of the nucleon kinetic energy t(k),the isospin symmetric and asymmetric parts of the single-nucleon potentials U_(0)(ρ,k)and U_(sym,i)(ρ,k).The six basic quantities include the quadratic symmetry energy E_(sym,2)(ρ),the quartic symmetry energy E_(sym,4)(ρ),their corresponding density slopes L_(2)(ρ)and L_(4)(ρ),and the incompressibility coefficients K_(2)(ρ)and K_(4)(ρ).By using four types of well-known effective nucleon-nucleon interaction models,namely the BGBD,MDI,Skyrme,and Gogny forces,the density-and isospin-dependent properties of these basic quantities are systematically calculated and their values at the saturation density q_(0)are explicitly given.The contributions to these quantities from t(k)U_(0)(ρ,k),and U_(sym,i)(ρ,k)are also analyzed at the norma nuclear density q_(0).It is clearly shown that the first-order asymmetric term U_(sym,1)(ρ,k)(also known as the symmetry potential in the Lane potential)plays a vital role in determining the density dependence of the quadratic symmetry energy E_(sym,2)(ρ).It is also shown that the contributions from the high-order asymmetric parts of the single-nucleon potentials(U_(sym,i)(ρ,k)with i>1)cannot be neglected in the calculations of the other five basic quantities Moreover,by analyzing the properties of asymmetric nuclear matter at the exact saturation densityρ_(sat)(δ),the corresponding quadratic incompressibility coefficient is found to have a simple empirical relation K_(sat,2)=K_(2)(ρ_(0))-4.14L_(2)(ρ_(0)) 展开更多
关键词 equation of state Symmetry energy HVH theorem Single-nucleon potential
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Representation of Phase Behavior of Ionic Liquids Using the Equation of State for Square-well Chain Fluids with Variable Range 被引量:5
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作者 李进龙 何清 +2 位作者 何昌春 彭昌军 刘洪来 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2009年第6期983-989,共7页
An equation of state (EOS) for square-well chain fluids with variable range (SWCF-VR) developed based on statistical mechanics for chemical association was employed for the calculations of pressure-volume-temperat... An equation of state (EOS) for square-well chain fluids with variable range (SWCF-VR) developed based on statistical mechanics for chemical association was employed for the calculations of pressure-volume-temperature (pVT) and phase equilibrium of pure ionic liquids (ILs) and their mixtures. The new molecular parameters for 23 ILs were obtained by fitting their experimental density data over a wide temperature and pressure ranges. The mo- lecular parameters of ILs composed of homologous organic cation and an identical anion such as [Cxmim][NTf2] are good linear with respect to their molecular weight, indicating that the molecular parameters of homologous substances, subsequently p VT and vapor-liquid equilibria vapor-liquid equilibria (VLE) can be predicted using the generalized parameter when no experimental data were available. The new set of parameters were satisfactorily used for calculations of the property of solvent and ILs mixture and the solubility of gas in various ILs at low pressure only using one temperature-independent binary interaction parameter. 展开更多
关键词 equation of state ionic liquids square-well chain phase behavior
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New Approach for Solving Master Equations in Quantum Optics and Quantum Statistics by Virtue of Thermo-Entangled State Representation 被引量:11
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作者 FAN Hong-Yi HU Li-Yun 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第4期729-742,共14页
By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation (η|, which can arrange master equations of density operators p(t) in quant... By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation (η|, which can arrange master equations of density operators p(t) in quantum statistics as state-vector evolution equations due to the elegant properties of (η|. In this way many master equations (respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators) can be concisely solved. Specially, for a damping process characteristic of the decay constant k we find that the matrix element of p(t) at time t in 〈η| representation is proportional to that of the initial po in the decayed entangled state (ηe^-kt| representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ = f(d^2η/π)(η|ρ〉D(η), which is different from all the previous known representations. 展开更多
关键词 master equation fictitious mode thermo-entangled state representation damping oscillator and laser phase sensitive and phase diffusion processes
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The pressure compensation technology of deep-sea sampling based on the real gas state equation 被引量:5
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作者 Shuo Wang Shijun Wu Canjun Yang 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2020年第8期88-95,共8页
Compressed gas is usually used for the pressure compensation of the deep-sea pressure-maintaining sampler.The pressure and volume of the recovered fluid sample are highly related to the precharged gas. To better under... Compressed gas is usually used for the pressure compensation of the deep-sea pressure-maintaining sampler.The pressure and volume of the recovered fluid sample are highly related to the precharged gas. To better understand the behavior of the gas under high pressure, we present a new real gas state equation based on the compression factor Z which was derived from experimental data. Then theoretical calculation method of the pressure and volume of the sample was introduced based on this empirical gas state equation. Finally, the proposed calculation method was well verified by the high-pressure vessel experiment of the sampler under 115 MPa. 展开更多
关键词 gas state equation deep-sea sampler pressure compensation sample pressure sample volume
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