By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechan...By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.展开更多
A mobile Coulomb gas permeating a fixed background crystalline lattice of charged colloidal crystals is subject to an electrostatic-elastic coupling,which we study on the continuum level by introducing a minimal coupl...A mobile Coulomb gas permeating a fixed background crystalline lattice of charged colloidal crystals is subject to an electrostatic-elastic coupling,which we study on the continuum level by introducing a minimal coupling between electrostatic and displacement fields.We derive linearized,Debye–Hückel-like mean-field equations that can be analytically solved,incorporating the minimal coupling between electrostatic and displacement fields leading to an additional effective attractive interaction between mobile charges that depends in general on the strength of the coupling between the electrostatic and displacement fields.By analyzing the Gaussian fluctuations around the mean-field solution we also identify and quantify the region of its stability in terms of the electrostatic-elastic screening length.This detailed continuum theory incorporating the standard lattice elasticity and electrostatics of mobile charges provides a baseline to investigate the electrostatic-elastic coupling for microscopic models in colloid science and materials science.展开更多
The Maxwell-Boltzmann (MB) distribution for velocities in ideal gases is usually defined between zero and infinity. A double truncated MB distribution is here introduced and the probability density function, the distr...The Maxwell-Boltzmann (MB) distribution for velocities in ideal gases is usually defined between zero and infinity. A double truncated MB distribution is here introduced and the probability density function, the distribution function, the average value, the rth moment about the origin, the root-mean-square speed and the variance are evaluated. Two applications are presented: 1) a numerical relationship between root-mean-square speed and temperature, and 2) a modification of the formula for the Jeans escape flux of molecules from an atmosphere.展开更多
Two relativistic distributions which generalize the Maxwell Boltzman (MB) distribution are analyzed: the relativistic MB and the Maxwell-Jüttner (MJ) distribution. For the two distributions, we derived in terms o...Two relativistic distributions which generalize the Maxwell Boltzman (MB) distribution are analyzed: the relativistic MB and the Maxwell-Jüttner (MJ) distribution. For the two distributions, we derived in terms of special functions the constant of normalization, the average value, the second moment about the origin, the variance, the mode, the asymptotic behavior, approximate expressions for the average value as function of the temperature and the connected inverted expressions for the temperature as function of the average value. Two astrophysical applications to the synchrotron emission in presence of the magnetic field and the relativistic electrons are presented.展开更多
On the basis of the entropy of incomplete statistics （IS） and the joint probability factorization condition, two controversial problems existing in IS are investigated： one is what expression of the internal energy...On the basis of the entropy of incomplete statistics （IS） and the joint probability factorization condition, two controversial problems existing in IS are investigated： one is what expression of the internal energy is reasonable for a composite system and the other is whether the traditional zeroth law of thermodynamics is suitable for IS. Some new equivalent expressions of the internal energy of a composite system are derived through accurate mathematical calculation. Moreover, a self-consistent calculation is used to expound that the zeroth law of thermodynamics is also suitable for IS, but it cannot be proven theoretically. Finally, it is pointed out that the generalized zeroth law of thermodynamics for incomplete nonextensive statistics is unnecessary and the nonextensive assumptions for the composite internal energy will lead to mathematical contradiction.展开更多
A multi-relaxation-time discrete Boltzmann model for compressible non-ideal gases with adjustable specific heat ratio is proposed,and the impact of surface tension on Rayleigh-Taylor instability(RTI)is investigated fr...A multi-relaxation-time discrete Boltzmann model for compressible non-ideal gases with adjustable specific heat ratio is proposed,and the impact of surface tension on Rayleigh-Taylor instability(RTI)is investigated from two perspectives:macroscopic and non-equilibrium characteristics.In terms of physical cognition,(1)it is found that there are two critical surface tensions:the upper critical value and the lower critical value.When the surface tension is below the lower critical value,the RTI evolution aligns qualitatively with the case without surface tension.As the surface tension coefficient increases,the inhibitory effect on RTI evolution gradually strengthens.When the surface tension is greater than the upper critical value,the disturbance interface tends to be stable after multiple oscillations.When the surface tension is in between,the perturbation interface first reverses,or even multiple reverses,and then destabilizes and develops rapidly.(2)A series of new kinetic behavior characteristics are given,and it is found that some behavior characteristics have important reference value for the control of system behavior.For example,the first peak in the growth rate of the global average non-organized momentum flux strength D_(2)corresponds to the onset of the regular nonlinear stage.The peak in the growth rate of the global average non-organized energy flux strength D_(3,1)marks the beginning of the re-acceleration stage.The onset of the uniform acceleration stage in the growth rate of the global average nonequilibrium strength D_(T NE)corresponds to the system transitioning into the regular nonlinear stage,while its terminal point(also the peak)corresponds to the system entering the re-acceleration stage.These insights enhance understanding of RTI mechanisms in complex fluids kinetically.展开更多
文摘By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.
基金HW is partially supported by the open research fund of Songshan Lake Materials Laboratory No.2023SLABFN20the General Program of National Natural Science Foundation of China(NSFC)under Grant No.12374210+2 种基金the startup fund under Grant No.WIUCASQD2022005 from Wenzhou Institute University of Chinese Academy of Sciences(WIU-CAS)Z-CO-Y was supported by the Major Program of the NSFC under Grant No.22193032RP acknowledges the support of UCAS and funding from the Key Program of NSFC under Grant No.12034019.
文摘A mobile Coulomb gas permeating a fixed background crystalline lattice of charged colloidal crystals is subject to an electrostatic-elastic coupling,which we study on the continuum level by introducing a minimal coupling between electrostatic and displacement fields.We derive linearized,Debye–Hückel-like mean-field equations that can be analytically solved,incorporating the minimal coupling between electrostatic and displacement fields leading to an additional effective attractive interaction between mobile charges that depends in general on the strength of the coupling between the electrostatic and displacement fields.By analyzing the Gaussian fluctuations around the mean-field solution we also identify and quantify the region of its stability in terms of the electrostatic-elastic screening length.This detailed continuum theory incorporating the standard lattice elasticity and electrostatics of mobile charges provides a baseline to investigate the electrostatic-elastic coupling for microscopic models in colloid science and materials science.
文摘The Maxwell-Boltzmann (MB) distribution for velocities in ideal gases is usually defined between zero and infinity. A double truncated MB distribution is here introduced and the probability density function, the distribution function, the average value, the rth moment about the origin, the root-mean-square speed and the variance are evaluated. Two applications are presented: 1) a numerical relationship between root-mean-square speed and temperature, and 2) a modification of the formula for the Jeans escape flux of molecules from an atmosphere.
文摘Two relativistic distributions which generalize the Maxwell Boltzman (MB) distribution are analyzed: the relativistic MB and the Maxwell-Jüttner (MJ) distribution. For the two distributions, we derived in terms of special functions the constant of normalization, the average value, the second moment about the origin, the variance, the mode, the asymptotic behavior, approximate expressions for the average value as function of the temperature and the connected inverted expressions for the temperature as function of the average value. Two astrophysical applications to the synchrotron emission in presence of the magnetic field and the relativistic electrons are presented.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11005041)the Natural Science Foundation of Fujian Province, China (Grant No. 2010J05007)+2 种基金the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, China (Grant No. 2010-1561)the Basic Science Research Foundation, China (Grant No. JB-SJ1005)the Science Research Fund of Huaqiao University, China (including the support forHuang (Grant No. 11BS207))
文摘On the basis of the entropy of incomplete statistics （IS） and the joint probability factorization condition, two controversial problems existing in IS are investigated： one is what expression of the internal energy is reasonable for a composite system and the other is whether the traditional zeroth law of thermodynamics is suitable for IS. Some new equivalent expressions of the internal energy of a composite system are derived through accurate mathematical calculation. Moreover, a self-consistent calculation is used to expound that the zeroth law of thermodynamics is also suitable for IS, but it cannot be proven theoretically. Finally, it is pointed out that the generalized zeroth law of thermodynamics for incomplete nonextensive statistics is unnecessary and the nonextensive assumptions for the composite internal energy will lead to mathematical contradiction.
基金supported by the National Natural Science Foundation of China(Grant Nos.11875001,and 12172061)the Shandong Province Higher Educational Youth Innovation Science and Technology Program(Grant No.2019KJJ009)+6 种基金the Natural Science Foundation of Shandong Province(Grant Nos.ZR2020MA061,and ZR2022MA075)the Foundation of National Key Laboratory of Shock Wave and Detonation Physics(Grant No.JCKYS2023212003)the opening project of State Key Laboratory of Explosion Science and Technology(Beijing Institute of Technology)(Grant No.KFJJ2023-02M)the Hebei Outstanding Youth Science Foundation(Grant No.A2023409003)the Central Guidance on Local Science and Technology Development Fund of Hebei Province(Grant No.226Z7601G)the 2023 Computational Physics Key Laboratory Youth Fund Sponsored Project(Grant No.6142A05QN23001)the science foundation of NCIAE(Grant No.GFCXJJ-2023-01)。
文摘A multi-relaxation-time discrete Boltzmann model for compressible non-ideal gases with adjustable specific heat ratio is proposed,and the impact of surface tension on Rayleigh-Taylor instability(RTI)is investigated from two perspectives:macroscopic and non-equilibrium characteristics.In terms of physical cognition,(1)it is found that there are two critical surface tensions:the upper critical value and the lower critical value.When the surface tension is below the lower critical value,the RTI evolution aligns qualitatively with the case without surface tension.As the surface tension coefficient increases,the inhibitory effect on RTI evolution gradually strengthens.When the surface tension is greater than the upper critical value,the disturbance interface tends to be stable after multiple oscillations.When the surface tension is in between,the perturbation interface first reverses,or even multiple reverses,and then destabilizes and develops rapidly.(2)A series of new kinetic behavior characteristics are given,and it is found that some behavior characteristics have important reference value for the control of system behavior.For example,the first peak in the growth rate of the global average non-organized momentum flux strength D_(2)corresponds to the onset of the regular nonlinear stage.The peak in the growth rate of the global average non-organized energy flux strength D_(3,1)marks the beginning of the re-acceleration stage.The onset of the uniform acceleration stage in the growth rate of the global average nonequilibrium strength D_(T NE)corresponds to the system transitioning into the regular nonlinear stage,while its terminal point(also the peak)corresponds to the system entering the re-acceleration stage.These insights enhance understanding of RTI mechanisms in complex fluids kinetically.
