The Tolman length δ 0 of a liquid with a plane surface has attracted increasing theoretical attention in recent years,but the expression of Tolman length in terms of observable quantities is still not very clear.In 2...The Tolman length δ 0 of a liquid with a plane surface has attracted increasing theoretical attention in recent years,but the expression of Tolman length in terms of observable quantities is still not very clear.In 2001,Bartell gave a simple expression of Tolman length δ 0 in terms of isothermal compressibility.However,this expression predicts that Tolman length is always negative,which is contrary to the results of molecular dynamics simulations（MDS） for simple liquids.In this paper,this contradiction is analyzed and the reason for the discrepancy in the sign is found.In addition,we introduce a new expression of Tolman length in terms of isothermal compressibility for simple fluids not near the critical points under some weak restrictions.The Tolman length of simple liquids calculated by using this formula is consistent with that obtained using MDS regarding the sign.展开更多
There still exists controversy on the sign and magnitude of the Tolman＇s length and the Tolman＇s gap. Further experimental, computational and theoretical investigations on them are needed to solve this problem. In 2...There still exists controversy on the sign and magnitude of the Tolman＇s length and the Tolman＇s gap. Further experimental, computational and theoretical investigations on them are needed to solve this problem. In 2006, Blokhuis and Kuipers obtained a rigorous relationship between the Tolman＇s length and other thermodynamic quantities for the single-component liquid-vapour system. In the present paper, we derive two general relationships between the Tolman＇s length and other thermodynamic quantities for the single-component liquid vapour system. The relationship derived by Blokhuis and Kuipers and an earlier result turn out to be two special cases of our results.展开更多
In 1949, Tolman found the relation between the surface tension and Tolman length, which determines the dimensional effect of the surface tension. Tolman length is the difference between the equimolar surface and the s...In 1949, Tolman found the relation between the surface tension and Tolman length, which determines the dimensional effect of the surface tension. Tolman length is the difference between the equimolar surface and the surface of tension. In recent years, the magnitude, expression, and sign of the Tolman length remain an open question. An incompressible and homogeneous liquid droplet model is proposed and the approximate expression and sign for Tolman length are derived in this paper. We obtain the relation between Tolman length and the radius of the surface of tension(R_(s)) and found that they increase with the Rs decreasing. The Tolman length of plane surface tends to zero. Taking argon for example, molecular dynamics simulation is carried out by using the Lennard–Jones(LJ) potential between atoms at a temperature of 90 K. Five simulated systems are used, with numbers of argon atoms being 10140, 10935, 11760, 13500, and 15360, respectively. By methods of theoretical study and molecular dynamics simulation, we find that the calculated value of Tolman length is more than zero, and it decreases as the size is increased among the whole size range. The value of surface tension increases with the radius of the surface of tension increasing, which is consistent with Tolman’s theory. These conclusions are significant for studying the size dependence of the surface tension.展开更多
The Tolman-Oppenheimer-Volkov (TOV) equation is solved with a new ansatz: the external boundary condition with mass M<sub>0</sub> and radius R<sub>1</sub> is dual to the internal boundary condi...The Tolman-Oppenheimer-Volkov (TOV) equation is solved with a new ansatz: the external boundary condition with mass M<sub>0</sub> and radius R<sub>1</sub> is dual to the internal boundary condition with density ρ<sub>bc</sub> and inner radius r<sub>i</sub>, and the two boundary conditions yield the same result. The inner boundary condition is imposed with a density ρ<sub>bc</sub> and an inner radius r<sub>i</sub>, which is zero for the compact neutron stars, but non-zero for the shell-stars: stellar shell-star and galactic (supermassive) shell-star. Parametric solutions are calculated for neutron stars, stellar shell-stars, and galactic shell-stars. From the results, an M-R-relation and mass limits for these star models can be extracted. A new method is found for solving the Einstein equations for Kerr space-time with matter (extended Kerr space-time), i.e. rotating matter distribution in its own gravitational field. Then numerical solutions are calculated for several astrophysical models: white dwarf, neutron star, stellar shell-star, and galactic shell-star. The results are that shell-star star models closely resemble the behaviour of abstract black holes, including the Bekenstein-Hawking entropy, but have finite redshifts and escape velocity v c and no singularity.展开更多
This study examines the effect of charge on physical features of a gravastar model in the framework of Rastall gravity.A gravastar is an alternative model to a black hole consisting of three separate regions:the inner...This study examines the effect of charge on physical features of a gravastar model in the framework of Rastall gravity.A gravastar is an alternative model to a black hole consisting of three separate regions:the inner sector,the intermediate shell and the outer sector.Different values of the barotropic equation of state(EoS)parameter provide the mathematical basis for these regions.Field equations(FEs)are initially developed for a spherically symmetric spacetime coupled with charged matter distribution.We then use the temporal component of TolmanⅣspacetime to formulate the radial metric potential for both the inner region and intermediate shell.We also apply the matching criteria to ensure smooth matching of exterior and interior spacetimes so that the constants resulting from integrations can be determined.Afterwards,we explore various physical properties of the developed gravastar model such as the proper length,entropy,energy,and others to analyze how shell thickness and charge affect them.It is concluded that,in the background of Rastall theory,a gravastar model exists and serves as a viable alternative to the black hole.展开更多
针对移动机器人环境认知问题,受老鼠海马体位置细胞在特定位置放电的启发,构建动态增减位置细胞认知地图模型(Dynamic growing and pruning place cells-based cognitive map model,DGP-PCCMM),使机器人在与环境交互的过程中自组织构建...针对移动机器人环境认知问题,受老鼠海马体位置细胞在特定位置放电的启发,构建动态增减位置细胞认知地图模型(Dynamic growing and pruning place cells-based cognitive map model,DGP-PCCMM),使机器人在与环境交互的过程中自组织构建认知地图,进行环境认知.初始时刻,认知地图由初始点处激活的位置细胞构成;随着与环境的交互,逐渐得到不同位置点处激活的位置细胞,并建立其之间的连接关系,实现认知地图的动态增长;如果机器人在已访问区域发现新的障碍物,利用动态缩减机制对认知地图进行更新.此外,提出一种位置细胞序列规划算法,该算法以所构建的认知地图作为输入,进行位置细胞序列规划,实现机器人导航.为验证模型的正确性和有效性,对Tolman的经典老鼠绕道实验进行再现.实验结果表明,本文模型能使机器人在与环境交互的过程中动态构建并更新认知地图,能初步完成对Tolman老鼠绕道实验的再现.此外,进行了与四叉树栅格地图、动态窗口法的对比实验和与其他认知地图模型的讨论分析.结果表明了本文方法在所构建地图的简洁性、完整性和对动态障碍适应性方面的优势.展开更多
In view of the continued disputes on the fundamental question of whether the surface tension of a vapour bubble in liquid argon increases, or decreases, or remains unchanged with the increase of curvature radius, a cy...In view of the continued disputes on the fundamental question of whether the surface tension of a vapour bubble in liquid argon increases, or decreases, or remains unchanged with the increase of curvature radius, a cylindrical vapour bubble of argon is studied by molecular dynamics simulation in this paper instead of spherical vapour bubble so as to reduce the statistical error. So far, the surface tension of the cylindrical vapour bubble has not been studied by molecular dynamics simulation in the literature. Our results show that the surface tension decreases with radius increasing. By fitting the Tolman equation with our data, the Tolman length σ = -0.6225 sigma is given under cut-off radius 2.5σ, where σ = 0.3405 nm is the diameter of an argon atom. The Tolman length of Ar being negative is affirmed and the Tolman length of Ar being approximately zero given in the literature is negated, and it is pointed out that this error is attributed to the application of the inapplicable empirical equation of state and the neglect of the difference between surface tension and an equimolar surface.展开更多
The no-evolution, concordance expanding universe cosmology and no-evolution, static universe tired light model are compared against observational data on eight cosmology tests. The no-evolution tired light model is fo...The no-evolution, concordance expanding universe cosmology and no-evolution, static universe tired light model are compared against observational data on eight cosmology tests. The no-evolution tired light model is found to make a superior fit on all tests. Any attempts to introduce evolutionary corrections to improve the concordance cosmology fit on one test often worsen its fit on other tests. Light curve data of high redshift gamma ray bursts and quasars fail to support claims for cosmological time dilation due to expansion. Also, the SCP supernova light curve test results are considered to be flawed by selection effect biases. The big bang theory also has difficulty accounting for redshift quantization, for the multi-megaparsec periodicity seen in the distribution of galaxy superclusters, and for the discovery of galaxies at redshifts as high as <em>z</em> ~11.9. In overview, it is concluded that a static universe cosmology must be sought to explain the origin of the universe. One possible choice is a cosmology that predicts nonconservative tired-light redshifting in intergalactic space, the continuous creation of neutrons in space, the rate of matter creation scaling with both celestial body mass and temperature, galaxies growing progressively in size, and changing their morphology in the manner suggested by Jeans and Hubble.展开更多
The Bach equations are a version of higher-order gravitational field equations, exactly they are of fourth-order. In 4-dimensions the Bach-Einstein gravitational field equations are treated here as a perturbation of E...The Bach equations are a version of higher-order gravitational field equations, exactly they are of fourth-order. In 4-dimensions the Bach-Einstein gravitational field equations are treated here as a perturbation of Einstein’s gravity. An approximate inversion formula is derived which admits a comparison of the two field theories. An application to these theories is given where the gravitational Lagrangian is expressed linearly in terms of R, R<sup>2</sup>, |Ric|<sup>2</sup>, where the Ricci tensor Ric = R<sub>αβ</sub>dx<sup>α</sup>dx<sup>β</sup> is inserted in some formulas which are of geometrical or physical importance, such as;Raychaudhuri equation and Tolman’s formula.展开更多
We analyze in this work anisotropic heat conduction induced by a harmonically oscillating laser source incident on rotating conductors, exploiting an analogy with an effect discovered long ago, called the Zel’dovich ...We analyze in this work anisotropic heat conduction induced by a harmonically oscillating laser source incident on rotating conductors, exploiting an analogy with an effect discovered long ago, called the Zel’dovich effect. We re-covered the main results of a recently published paper that predicts the translational Doppler frequency shift of a thermal wave induced on a sample moving with uniform rectilinear motion. We extend then this framework to take into account the frequency shift of a thermal field propagating on a rotating platform. We show that it coincides with the rotational frequency shift which has been recently observed on surface acoustic waves and hydrodynamic surface waves, called rotational superradiance. Finally, we use an analogy with the Tolman effect to deduce a simple estimate of the average temperature gradient induced by rotation, showing the existence of a new cooling effect associated with heat torque transfer.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 11072242)
文摘The Tolman length δ 0 of a liquid with a plane surface has attracted increasing theoretical attention in recent years,but the expression of Tolman length in terms of observable quantities is still not very clear.In 2001,Bartell gave a simple expression of Tolman length δ 0 in terms of isothermal compressibility.However,this expression predicts that Tolman length is always negative,which is contrary to the results of molecular dynamics simulations（MDS） for simple liquids.In this paper,this contradiction is analyzed and the reason for the discrepancy in the sign is found.In addition,we introduce a new expression of Tolman length in terms of isothermal compressibility for simple fluids not near the critical points under some weak restrictions.The Tolman length of simple liquids calculated by using this formula is consistent with that obtained using MDS regarding the sign.
基金supported by the National Natural Science Foundation of China(Grant No.10772189)the Knowledge Innovation Program of Chinese Academy of Sciences
文摘There still exists controversy on the sign and magnitude of the Tolman＇s length and the Tolman＇s gap. Further experimental, computational and theoretical investigations on them are needed to solve this problem. In 2006, Blokhuis and Kuipers obtained a rigorous relationship between the Tolman＇s length and other thermodynamic quantities for the single-component liquid-vapour system. In the present paper, we derive two general relationships between the Tolman＇s length and other thermodynamic quantities for the single-component liquid vapour system. The relationship derived by Blokhuis and Kuipers and an earlier result turn out to be two special cases of our results.
基金Project supported by the National Key Research and Development Program of China(Grant No.2016YFB0700500)the Scientific Research and Innovation Team of Cangzhou Normal University,China(Grant No.cxtdl1907)+2 种基金the Key Scientific Study Program of Hebei Provincial Higher Education Institution,China(Grant No.ZD2020410)the Cangzhou Natural Science Foundation,China(Grant No.197000001)the General Scientific Research Fund Project of Cangzhou Normal University,China(Grant No.xnjjl1906)。
文摘In 1949, Tolman found the relation between the surface tension and Tolman length, which determines the dimensional effect of the surface tension. Tolman length is the difference between the equimolar surface and the surface of tension. In recent years, the magnitude, expression, and sign of the Tolman length remain an open question. An incompressible and homogeneous liquid droplet model is proposed and the approximate expression and sign for Tolman length are derived in this paper. We obtain the relation between Tolman length and the radius of the surface of tension(R_(s)) and found that they increase with the Rs decreasing. The Tolman length of plane surface tends to zero. Taking argon for example, molecular dynamics simulation is carried out by using the Lennard–Jones(LJ) potential between atoms at a temperature of 90 K. Five simulated systems are used, with numbers of argon atoms being 10140, 10935, 11760, 13500, and 15360, respectively. By methods of theoretical study and molecular dynamics simulation, we find that the calculated value of Tolman length is more than zero, and it decreases as the size is increased among the whole size range. The value of surface tension increases with the radius of the surface of tension increasing, which is consistent with Tolman’s theory. These conclusions are significant for studying the size dependence of the surface tension.
文摘The Tolman-Oppenheimer-Volkov (TOV) equation is solved with a new ansatz: the external boundary condition with mass M<sub>0</sub> and radius R<sub>1</sub> is dual to the internal boundary condition with density ρ<sub>bc</sub> and inner radius r<sub>i</sub>, and the two boundary conditions yield the same result. The inner boundary condition is imposed with a density ρ<sub>bc</sub> and an inner radius r<sub>i</sub>, which is zero for the compact neutron stars, but non-zero for the shell-stars: stellar shell-star and galactic (supermassive) shell-star. Parametric solutions are calculated for neutron stars, stellar shell-stars, and galactic shell-stars. From the results, an M-R-relation and mass limits for these star models can be extracted. A new method is found for solving the Einstein equations for Kerr space-time with matter (extended Kerr space-time), i.e. rotating matter distribution in its own gravitational field. Then numerical solutions are calculated for several astrophysical models: white dwarf, neutron star, stellar shell-star, and galactic shell-star. The results are that shell-star star models closely resemble the behaviour of abstract black holes, including the Bekenstein-Hawking entropy, but have finite redshifts and escape velocity v c and no singularity.
文摘This study examines the effect of charge on physical features of a gravastar model in the framework of Rastall gravity.A gravastar is an alternative model to a black hole consisting of three separate regions:the inner sector,the intermediate shell and the outer sector.Different values of the barotropic equation of state(EoS)parameter provide the mathematical basis for these regions.Field equations(FEs)are initially developed for a spherically symmetric spacetime coupled with charged matter distribution.We then use the temporal component of TolmanⅣspacetime to formulate the radial metric potential for both the inner region and intermediate shell.We also apply the matching criteria to ensure smooth matching of exterior and interior spacetimes so that the constants resulting from integrations can be determined.Afterwards,we explore various physical properties of the developed gravastar model such as the proper length,entropy,energy,and others to analyze how shell thickness and charge affect them.It is concluded that,in the background of Rastall theory,a gravastar model exists and serves as a viable alternative to the black hole.
文摘针对移动机器人环境认知问题,受老鼠海马体位置细胞在特定位置放电的启发,构建动态增减位置细胞认知地图模型(Dynamic growing and pruning place cells-based cognitive map model,DGP-PCCMM),使机器人在与环境交互的过程中自组织构建认知地图,进行环境认知.初始时刻,认知地图由初始点处激活的位置细胞构成;随着与环境的交互,逐渐得到不同位置点处激活的位置细胞,并建立其之间的连接关系,实现认知地图的动态增长;如果机器人在已访问区域发现新的障碍物,利用动态缩减机制对认知地图进行更新.此外,提出一种位置细胞序列规划算法,该算法以所构建的认知地图作为输入,进行位置细胞序列规划,实现机器人导航.为验证模型的正确性和有效性,对Tolman的经典老鼠绕道实验进行再现.实验结果表明,本文模型能使机器人在与环境交互的过程中动态构建并更新认知地图,能初步完成对Tolman老鼠绕道实验的再现.此外,进行了与四叉树栅格地图、动态窗口法的对比实验和与其他认知地图模型的讨论分析.结果表明了本文方法在所构建地图的简洁性、完整性和对动态障碍适应性方面的优势.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11072242)
文摘In view of the continued disputes on the fundamental question of whether the surface tension of a vapour bubble in liquid argon increases, or decreases, or remains unchanged with the increase of curvature radius, a cylindrical vapour bubble of argon is studied by molecular dynamics simulation in this paper instead of spherical vapour bubble so as to reduce the statistical error. So far, the surface tension of the cylindrical vapour bubble has not been studied by molecular dynamics simulation in the literature. Our results show that the surface tension decreases with radius increasing. By fitting the Tolman equation with our data, the Tolman length σ = -0.6225 sigma is given under cut-off radius 2.5σ, where σ = 0.3405 nm is the diameter of an argon atom. The Tolman length of Ar being negative is affirmed and the Tolman length of Ar being approximately zero given in the literature is negated, and it is pointed out that this error is attributed to the application of the inapplicable empirical equation of state and the neglect of the difference between surface tension and an equimolar surface.
文摘The no-evolution, concordance expanding universe cosmology and no-evolution, static universe tired light model are compared against observational data on eight cosmology tests. The no-evolution tired light model is found to make a superior fit on all tests. Any attempts to introduce evolutionary corrections to improve the concordance cosmology fit on one test often worsen its fit on other tests. Light curve data of high redshift gamma ray bursts and quasars fail to support claims for cosmological time dilation due to expansion. Also, the SCP supernova light curve test results are considered to be flawed by selection effect biases. The big bang theory also has difficulty accounting for redshift quantization, for the multi-megaparsec periodicity seen in the distribution of galaxy superclusters, and for the discovery of galaxies at redshifts as high as <em>z</em> ~11.9. In overview, it is concluded that a static universe cosmology must be sought to explain the origin of the universe. One possible choice is a cosmology that predicts nonconservative tired-light redshifting in intergalactic space, the continuous creation of neutrons in space, the rate of matter creation scaling with both celestial body mass and temperature, galaxies growing progressively in size, and changing their morphology in the manner suggested by Jeans and Hubble.
文摘The Bach equations are a version of higher-order gravitational field equations, exactly they are of fourth-order. In 4-dimensions the Bach-Einstein gravitational field equations are treated here as a perturbation of Einstein’s gravity. An approximate inversion formula is derived which admits a comparison of the two field theories. An application to these theories is given where the gravitational Lagrangian is expressed linearly in terms of R, R<sup>2</sup>, |Ric|<sup>2</sup>, where the Ricci tensor Ric = R<sub>αβ</sub>dx<sup>α</sup>dx<sup>β</sup> is inserted in some formulas which are of geometrical or physical importance, such as;Raychaudhuri equation and Tolman’s formula.
文摘We analyze in this work anisotropic heat conduction induced by a harmonically oscillating laser source incident on rotating conductors, exploiting an analogy with an effect discovered long ago, called the Zel’dovich effect. We re-covered the main results of a recently published paper that predicts the translational Doppler frequency shift of a thermal wave induced on a sample moving with uniform rectilinear motion. We extend then this framework to take into account the frequency shift of a thermal field propagating on a rotating platform. We show that it coincides with the rotational frequency shift which has been recently observed on surface acoustic waves and hydrodynamic surface waves, called rotational superradiance. Finally, we use an analogy with the Tolman effect to deduce a simple estimate of the average temperature gradient induced by rotation, showing the existence of a new cooling effect associated with heat torque transfer.
