This article summarized systematically the previous investigations on t he dielectric relaxation of wood, the main substances and extractives in wood at oven-dry state, and the dielectric relaxation based on the adso...This article summarized systematically the previous investigations on t he dielectric relaxation of wood, the main substances and extractives in wood at oven-dry state, and the dielectric relaxation based on the adsorbed water in w o od cell wall under equilibrium and non-equilibrium state. Moreover, some expect a tions for future research were proposed on this basis. The purpose of this artic le is to provide other researchers an overall understanding about the research i n this region, and further to promote the research onto a new and higher level.展开更多
Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the general...Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.展开更多
On the basis of Karman's theory of thin plates with large deflection, the Boltzmann law on linear viscoelastic materials and the mathematical model of dynamic analysis on viscoelastic thin plates, a set of nonline...On the basis of Karman's theory of thin plates with large deflection, the Boltzmann law on linear viscoelastic materials and the mathematical model of dynamic analysis on viscoelastic thin plates, a set of nonlinear integro partial differential equations is first presented by means of a structural function introduced in this paper. Then, by using the Galerkin technique in spatial field and a backward difference scheme in temporal field, the set of nonlinear integro partial differential equations reduces to a system of nonlinear algebraic equations. After solving the algebraic equations, the buckling behavior and multiple equilibrium states can be obtained.展开更多
1,3,5-Triazine molecules represent a class of molecules that may have been prebiotic information carriers in a primordial soup in early Earth and their excited state dynamics has received attention in recent years.In ...1,3,5-Triazine molecules represent a class of molecules that may have been prebiotic information carriers in a primordial soup in early Earth and their excited state dynamics has received attention in recent years.In our previous study,one component with lifetime longer than100 ps was discovered in 2-amino-1,3,5-trainzine(2-AT),but its nature has not been revealed.In this study,excited state dynamics of 2-AT is studied in different solvents by using femtosecond time-resolved transient absorption and fluorescence upconversion spectroscopy.Interestingly,an equilibrium state consisting of the brightππ^(*)and dark nπ^(*)states in 2-AT is directly observed in aqueous solution and its dynamics is solvent sensitive.The whole picture of the excited state deactivation mechanism of 2-AT is proposed based on our spectroscopy results.展开更多
A calculation of the energy loss due to a transition from non-equilibrium to equilibrium state is given. Three different physical systems are considered in this study: connecting an uncharged capacitor to a charged ca...A calculation of the energy loss due to a transition from non-equilibrium to equilibrium state is given. Three different physical systems are considered in this study: connecting an uncharged capacitor to a charged capacitor, emission of a photon from an excited atom, and releasing an object from a compressed spring. In this study, it is shown that a specific fraction of the total energy stored in a non-equilibrium system should be consumed to reach the equilibrium state.展开更多
The principle of increasing entropy （PIE） is commonly considered as a universal physical law tbr natural systems. It also means that a non-equilibrium steady state （NESS） must not appear in any isolated natural sy...The principle of increasing entropy （PIE） is commonly considered as a universal physical law tbr natural systems. It also means that a non-equilibrium steady state （NESS） must not appear in any isolated natural systems. Here we experimentally investigate an isolated human social system with a clustering effect. We report that the PIE cannot always hold, and that NESSs can come to appear. Our study highlights the role of human adaptability in the PIE, and makes it possible to study human social systems by using some laws originating from traditional physics.展开更多
1 Equilibrium and inequilibrium of tidal mud flat The general dynamical state of tidal flat is usually measured by silting rate of mudflat surface in vertical direction and by prograding rate of outer edge of the tida...1 Equilibrium and inequilibrium of tidal mud flat The general dynamical state of tidal flat is usually measured by silting rate of mudflat surface in vertical direction and by prograding rate of outer edge of the tidal flat to-展开更多
For characteristics of open and far from thermodynamic equilibrium in welding chemical reaction, a new kind of quantitative method, which is used to analyze direction and extent for chemical reaction of SiO2/Fe during...For characteristics of open and far from thermodynamic equilibrium in welding chemical reaction, a new kind of quantitative method, which is used to analyze direction and extent for chemical reaction of SiO2/Fe during quasi-steady state period, is introduced with the concept of non-equilibrium stationary state. The main idea is based on thermodynamic driving forces, which result in non-zero thermodynamic fluxes and lead to chemical reaction far away from thermodynamic equilibrium. There exists certain dynamic equilibrium relationship between rates of diffusion fluxes in liquid phase of reactants or products and the rate equation of chemical reaction when welding is in quasi-steady state. As result of this, a group of non-linear equations containing concentrations of all substances at interface of slag/liquid-metal may be established. Moreover the stability of this non-equilibrium stationary state is discussed using dissipative structure theory and it is concluded theoretically that this non-equilibrium stationary state for welding chemical reaction is of stability.展开更多
A new non-cubic equation of state is proposed for calculation of the thermodynamic properties ofnonpolar and polar fluids and their mixtures,including,saturated vapor pressure,saturated liquid volume,saturated vapor v...A new non-cubic equation of state is proposed for calculation of the thermodynamic properties ofnonpolar and polar fluids and their mixtures,including,saturated vapor pressure,saturated liquid volume,saturated vapor volume,heats of vaporization and vapor-liquid equilibria.The new equation is derived from thegeneralized van der Waals partition function in which the repulsive terms are expressed with the Carnahan andStarling equation for hard spheres,and the attractive terms are made up of the dispersive energy and theChemical association energy. The rules of dependence of parameters α and σ and on temperature are considered broadly so that the newequation yields good agreement with experimental saturated properties of 20 nonpolar and 27 polar fluids in therange of reduced temperatures of 0.5 to 1.0 The new equation with parameters group-contributed generally givessatisfactory predictions on saturated properties. Correlations of vapor-liquid equilibrium data for alcohol-containing systems by using van展开更多
Here we review a new class of mixing rules (hat have extended range of mixtures and conditions that can now be described by equation of state models. One characteristic of these mixing rules is that they simultaneousl...Here we review a new class of mixing rules (hat have extended range of mixtures and conditions that can now be described by equation of state models. One characteristic of these mixing rules is that they simultaneously satisfy the boundary conditions of producing a second virial coefficient that is quadratic in mole fraction, and a free energy of mixing like that of an activity coefficient model at high density, though the mixing rule is itself independent of density. We show that using this mixing rule, various asymmetric, highly nonideal mixtures can be accurately described. One serendipitous result is that the parameters in this mixing rule model are almost independent of temperature, which allows accurate extrapolations of phase behavior to be made over large ranges of temperature and pressure.展开更多
Based on suitable choice of states, this paper studies the stability of the equilibrium state of the EZ model by regarding the evolution of the EZ model as a Markov chain and by showing that the Markov chain is ergodi...Based on suitable choice of states, this paper studies the stability of the equilibrium state of the EZ model by regarding the evolution of the EZ model as a Markov chain and by showing that the Markov chain is ergodic. The Markov analysis is applied to the EZ model with small number of agents, the exact equilibrium state for N = 5 and numerical results for N = 18 are obtained.展开更多
This article presents a mathematical model for the medium-term scheduling of the operating states of electric power systems.The scheduling period is divided into several time intervals.The model can be used to determi...This article presents a mathematical model for the medium-term scheduling of the operating states of electric power systems.The scheduling period is divided into several time intervals.The model can be used to determine the equilibrium state in which each supplier earns maximum profit from supplying electricity to the wholesale market.We estimated the maximum value of public welfare,which indicates the total financial gains of suppliers and consumers,to determine the prices at the nodes of the power system.This was done by considering the balance constraints at the nodes of the power system and constraints on the allowable values of generation,power flows,and volumes of energy resources consumed over several time intervals.This problem belongs to the class of bi-level Stackelberg game-theoretic models with several leaders.The market equilibrium is modeled simultaneously in several intervals,given the multiplicity and duration of interactions.We considered two approaches for solving the multi-interval equilibrium state problem.The first approach involved directly solving a system of joint optimality conditions for electricity suppliers and consumers.The second approach involved iterative searches until the equilibrium state was reached.This article presents the results of medium-term scheduling using a case study of a simplified real-world power system.展开更多
The phase equilibrium data of CO2 hydrocarbon binary mixtures are important for the design and operation of CO 2 ood- ing, coal liquefaction, and supercritical extraction processes. Numerous pieces of binary phase equ...The phase equilibrium data of CO2 hydrocarbon binary mixtures are important for the design and operation of CO 2 ood- ing, coal liquefaction, and supercritical extraction processes. Numerous pieces of binary phase equilibrium data have been obtained. Thus, models for the accurate calculation of binary and multicomponent mixtures must be developed on the basis of existing data. In this work, 3578 vapor liquid phase equilibrium data points for 10 CO 2 hydrocarbon binary mixtures, including CO2 butane, CO 2 pentane, CO 2 isopentane, C O 2 hexane, CO 2 benzene, CO 2 heptane, CO 2 octane, C O 2 non- ane, CO 2 decane, and C O 2 undecane, were collected. The PR and PR-BM equations of state (EOS) in combination with relevant mixing rules were used to calculate the phase equilibrium data of the CO 2 hydrocarbon binary mixtures. The binary interaction parameter k ij in the PR EOS was temperature independent, whereas parameters in the PR-BM EOS were functions of temperature. Thus, the phase equilibrium data and other thermodynamic properties of the binary and multicomponent mixtures at di erent temperatures and pressures can be calculated by using the parameters obtained in this work. The PR-BM EOS performed better than the PR EOS, and the average absolute deviations over the temperature range of 255.98 408.15 K calculated by the PR EOS and PR-BM EOS were less than 5.74% and 3.36%, respectively. The results calculated by the two EOS were compared with those calculated by other models, such as PPR78, PR + LCVM + UNIFAC, KIE + PR EOS + HV, and PSRK. The phase equilibrium data of CO 2 butane decane, CO 2 hexane decane, and C O 2 octane decane ternary mixtures were calculated by the two EOS. The average overall deviations for the CO 2 mole fractions calculated by the two EOS were less than 7.66%.展开更多
Not so much had been talked about equilibrium in control area. On the basis of the phenomenon of balance, the concept of control-equilibrium and control-equilibrium of a control system is proposed. According to this t...Not so much had been talked about equilibrium in control area. On the basis of the phenomenon of balance, the concept of control-equilibrium and control-equilibrium of a control system is proposed. According to this theory, a perfect control method should not only guarantee stability of the system, but also ensure the control-equilibrium of the system. To achieve the control-equilibrium, feed-forward control is required.展开更多
文摘This article summarized systematically the previous investigations on t he dielectric relaxation of wood, the main substances and extractives in wood at oven-dry state, and the dielectric relaxation based on the adsorbed water in w o od cell wall under equilibrium and non-equilibrium state. Moreover, some expect a tions for future research were proposed on this basis. The purpose of this artic le is to provide other researchers an overall understanding about the research i n this region, and further to promote the research onto a new and higher level.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10772025,10932002 and 10972127)the Natural Science Foundation of Henan Province,China(Grant No.102300410144)the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics,China
文摘Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.
文摘On the basis of Karman's theory of thin plates with large deflection, the Boltzmann law on linear viscoelastic materials and the mathematical model of dynamic analysis on viscoelastic thin plates, a set of nonlinear integro partial differential equations is first presented by means of a structural function introduced in this paper. Then, by using the Galerkin technique in spatial field and a backward difference scheme in temporal field, the set of nonlinear integro partial differential equations reduces to a system of nonlinear algebraic equations. After solving the algebraic equations, the buckling behavior and multiple equilibrium states can be obtained.
基金supported by Shanghai Rising-Star Program(No.19QA1402800)。
文摘1,3,5-Triazine molecules represent a class of molecules that may have been prebiotic information carriers in a primordial soup in early Earth and their excited state dynamics has received attention in recent years.In our previous study,one component with lifetime longer than100 ps was discovered in 2-amino-1,3,5-trainzine(2-AT),but its nature has not been revealed.In this study,excited state dynamics of 2-AT is studied in different solvents by using femtosecond time-resolved transient absorption and fluorescence upconversion spectroscopy.Interestingly,an equilibrium state consisting of the brightππ^(*)and dark nπ^(*)states in 2-AT is directly observed in aqueous solution and its dynamics is solvent sensitive.The whole picture of the excited state deactivation mechanism of 2-AT is proposed based on our spectroscopy results.
文摘A calculation of the energy loss due to a transition from non-equilibrium to equilibrium state is given. Three different physical systems are considered in this study: connecting an uncharged capacitor to a charged capacitor, emission of a photon from an excited atom, and releasing an object from a compressed spring. In this study, it is shown that a specific fraction of the total energy stored in a non-equilibrium system should be consumed to reach the equilibrium state.
文摘The principle of increasing entropy （PIE） is commonly considered as a universal physical law tbr natural systems. It also means that a non-equilibrium steady state （NESS） must not appear in any isolated natural systems. Here we experimentally investigate an isolated human social system with a clustering effect. We report that the PIE cannot always hold, and that NESSs can come to appear. Our study highlights the role of human adaptability in the PIE, and makes it possible to study human social systems by using some laws originating from traditional physics.
文摘1 Equilibrium and inequilibrium of tidal mud flat The general dynamical state of tidal flat is usually measured by silting rate of mudflat surface in vertical direction and by prograding rate of outer edge of the tidal flat to-
基金This project is supported by National Natural Science Foundation of China(No. 50544025)Natural Science Foundation of High Education of Jiangsu Province, China (No. 05KJB460030)
文摘For characteristics of open and far from thermodynamic equilibrium in welding chemical reaction, a new kind of quantitative method, which is used to analyze direction and extent for chemical reaction of SiO2/Fe during quasi-steady state period, is introduced with the concept of non-equilibrium stationary state. The main idea is based on thermodynamic driving forces, which result in non-zero thermodynamic fluxes and lead to chemical reaction far away from thermodynamic equilibrium. There exists certain dynamic equilibrium relationship between rates of diffusion fluxes in liquid phase of reactants or products and the rate equation of chemical reaction when welding is in quasi-steady state. As result of this, a group of non-linear equations containing concentrations of all substances at interface of slag/liquid-metal may be established. Moreover the stability of this non-equilibrium stationary state is discussed using dissipative structure theory and it is concluded theoretically that this non-equilibrium stationary state for welding chemical reaction is of stability.
文摘A new non-cubic equation of state is proposed for calculation of the thermodynamic properties ofnonpolar and polar fluids and their mixtures,including,saturated vapor pressure,saturated liquid volume,saturated vapor volume,heats of vaporization and vapor-liquid equilibria.The new equation is derived from thegeneralized van der Waals partition function in which the repulsive terms are expressed with the Carnahan andStarling equation for hard spheres,and the attractive terms are made up of the dispersive energy and theChemical association energy. The rules of dependence of parameters α and σ and on temperature are considered broadly so that the newequation yields good agreement with experimental saturated properties of 20 nonpolar and 27 polar fluids in therange of reduced temperatures of 0.5 to 1.0 The new equation with parameters group-contributed generally givessatisfactory predictions on saturated properties. Correlations of vapor-liquid equilibrium data for alcohol-containing systems by using van
文摘Here we review a new class of mixing rules (hat have extended range of mixtures and conditions that can now be described by equation of state models. One characteristic of these mixing rules is that they simultaneously satisfy the boundary conditions of producing a second virial coefficient that is quadratic in mole fraction, and a free energy of mixing like that of an activity coefficient model at high density, though the mixing rule is itself independent of density. We show that using this mixing rule, various asymmetric, highly nonideal mixtures can be accurately described. One serendipitous result is that the parameters in this mixing rule model are almost independent of temperature, which allows accurate extrapolations of phase behavior to be made over large ranges of temperature and pressure.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60534080, 60774085, and 70771012)
文摘Based on suitable choice of states, this paper studies the stability of the equilibrium state of the EZ model by regarding the evolution of the EZ model as a Markov chain and by showing that the Markov chain is ergodic. The Markov analysis is applied to the EZ model with small number of agents, the exact equilibrium state for N = 5 and numerical results for N = 18 are obtained.
基金the State Assignment Project (No. FWEU-754 2021-0001) of the Basic Research Program of the Russian Federation 2021-2030
文摘This article presents a mathematical model for the medium-term scheduling of the operating states of electric power systems.The scheduling period is divided into several time intervals.The model can be used to determine the equilibrium state in which each supplier earns maximum profit from supplying electricity to the wholesale market.We estimated the maximum value of public welfare,which indicates the total financial gains of suppliers and consumers,to determine the prices at the nodes of the power system.This was done by considering the balance constraints at the nodes of the power system and constraints on the allowable values of generation,power flows,and volumes of energy resources consumed over several time intervals.This problem belongs to the class of bi-level Stackelberg game-theoretic models with several leaders.The market equilibrium is modeled simultaneously in several intervals,given the multiplicity and duration of interactions.We considered two approaches for solving the multi-interval equilibrium state problem.The first approach involved directly solving a system of joint optimality conditions for electricity suppliers and consumers.The second approach involved iterative searches until the equilibrium state was reached.This article presents the results of medium-term scheduling using a case study of a simplified real-world power system.
基金supported by the National Key Research and Development Program of China (2016YFB0600804-3)Shandong Natural Science Foundation (ZR2017BB076)
文摘The phase equilibrium data of CO2 hydrocarbon binary mixtures are important for the design and operation of CO 2 ood- ing, coal liquefaction, and supercritical extraction processes. Numerous pieces of binary phase equilibrium data have been obtained. Thus, models for the accurate calculation of binary and multicomponent mixtures must be developed on the basis of existing data. In this work, 3578 vapor liquid phase equilibrium data points for 10 CO 2 hydrocarbon binary mixtures, including CO2 butane, CO 2 pentane, CO 2 isopentane, C O 2 hexane, CO 2 benzene, CO 2 heptane, CO 2 octane, C O 2 non- ane, CO 2 decane, and C O 2 undecane, were collected. The PR and PR-BM equations of state (EOS) in combination with relevant mixing rules were used to calculate the phase equilibrium data of the CO 2 hydrocarbon binary mixtures. The binary interaction parameter k ij in the PR EOS was temperature independent, whereas parameters in the PR-BM EOS were functions of temperature. Thus, the phase equilibrium data and other thermodynamic properties of the binary and multicomponent mixtures at di erent temperatures and pressures can be calculated by using the parameters obtained in this work. The PR-BM EOS performed better than the PR EOS, and the average absolute deviations over the temperature range of 255.98 408.15 K calculated by the PR EOS and PR-BM EOS were less than 5.74% and 3.36%, respectively. The results calculated by the two EOS were compared with those calculated by other models, such as PPR78, PR + LCVM + UNIFAC, KIE + PR EOS + HV, and PSRK. The phase equilibrium data of CO 2 butane decane, CO 2 hexane decane, and C O 2 octane decane ternary mixtures were calculated by the two EOS. The average overall deviations for the CO 2 mole fractions calculated by the two EOS were less than 7.66%.
文摘Not so much had been talked about equilibrium in control area. On the basis of the phenomenon of balance, the concept of control-equilibrium and control-equilibrium of a control system is proposed. According to this theory, a perfect control method should not only guarantee stability of the system, but also ensure the control-equilibrium of the system. To achieve the control-equilibrium, feed-forward control is required.
