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
Human living would be impossible without air quality. Consistent advancements in practically every aspect of contemporary human life have harmed air quality. Everyday industrial, transportation, and home activities tu...Human living would be impossible without air quality. Consistent advancements in practically every aspect of contemporary human life have harmed air quality. Everyday industrial, transportation, and home activities turn up dangerous contaminants in our surroundings. This study investigated two years’ worth of air quality and outlier detection data from two Indian cities. Studies on air pollution have used numerous types of methodologies, with various gases being seen as a vector whose components include gas concentration values for each observation per-formed. We use curves to represent the monthly average of daily gas emissions in our technique. The approach, which is based on functional depth, was used to find outliers in the city of Delhi and Kolkata’s gas emissions, and the outcomes were compared to those from the traditional method. In the evaluation and comparison of these models’ performances, the functional approach model studied well.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
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
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
In this paper, we study the age and spatial distributions of Cepheids in the Small Magellanic Cloud （SMC） as a function of their ages using data from the OGLE III photometric catalogue. A period - age relation deriv...In this paper, we study the age and spatial distributions of Cepheids in the Small Magellanic Cloud （SMC） as a function of their ages using data from the OGLE III photometric catalogue. A period - age relation derived for Classical Cepheids in the Large Magellanic Cloud （LMC） has been used to find the ages of Cepheids. The age distribution of the SMC Classical Cepheids is found to have a peak at log（Age） ： 8.40 ± 0.10 which suggests that a major star formation event might have occurred in the SMC about 250 4- 50 Myr ago. It is believed that this star forming burst had been triggered by close interactions of the SMC with the LMC and/or the Milky Way. A comparison of the observed spatial distributions of the Cepheids and open star clusters has also been carried out to study the star formation scenario in the SMC.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
The Babao River Basin is the "water tower" of the Heihe River Basin.The combination of vulnerable ecosystems and inhospitable natural environments substantially restricts the existence of humans and the sust...The Babao River Basin is the "water tower" of the Heihe River Basin.The combination of vulnerable ecosystems and inhospitable natural environments substantially restricts the existence of humans and the sustainable development of society and environment in the Heihe River Basin.Soil temperature(ST) is a critical soil variable that could affect a series of physical,chemical and biological soil processes,which is the guarantee of water conservation and vegetation growth in this region.To measure the temporal variation and spatial pattern of ST fluctuation in the Babao River Basin,fluctuation of ST at various depths were analyzed with ST data at depths of 4,10 and 20 cm using classical statistical methods and permutation entropy.The study results show the following: 1) There are variations of ST at different depths,although ST followed an obvious seasonal law.ST at shallower depths is higher than at deeper depths in summer,and vice versa in winter.The difference of ST between different depths is close to zero when ST is near 5℃ in March or –5℃ in September.2) In spring,ST at the shallower depths becomes higher than at deeper depths as soon as ST is above –5℃;this is reversed in autumn when ST is below 5℃.ST at a soil depth of 4 cm is the first to change,followed by ST at 10 and 20 cm,and the time that ST reaches the same level is delayed for 10–15 days.In chilling and warming seasons,September and February are,respectively,the months when ST at various depths are similar.3) The average PE values of ST for 17 sites at 4 cm are 0.765 in spring > 0.764 in summer > 0.735 in autumn > 0.723 in winter,which implies the complicated degree of fluctuations of ST.4) For the variation of ST at different depths,it appears that Max,Ranges,Average and the Standard Deviation of ST decrease by depth increments in soil.Surface soil is more complicated because ST fluctuation at shallower depths is more pronounced and random.The average PE value of ST for 17sites are 0.863 at a depth of 4 cm > 0.818 at 10 cm > 0.744 at 20 cm.5) For the variation of ST at different elevations,it appears that Max,Ranges,Average,Standard Deviation and ST fluctuation decrease with increasing elevation at the same soil depth.And with the increase of elevation,the decrease rates of Max,Range,Average,Standard Deviation at 4 cm are –0.89℃/100 m,–0.94℃/100 m,–0.43℃/100 m,and –0.25℃/100 m,respectively.In addition,this correlation decreased with the increase of soil depth.6) Significant correlation between PE values of ST at depths of 4,10 and 20 cm can easily be found.This finding implies that temperature can easily be transmitted within soil at depths between 4 and 20 cm.7) For the variation of ST on shady slope and sunny slope sides,it appears that the PE values of ST at 4,10 and 20 cm for 8 sites located on shady slope side are 0.868,0.824 and 0.776,respectively,whereas they are 0.858,0.810 and 0.716 for 9 sites located on sunny slope side.展开更多
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.
文摘Human living would be impossible without air quality. Consistent advancements in practically every aspect of contemporary human life have harmed air quality. Everyday industrial, transportation, and home activities turn up dangerous contaminants in our surroundings. This study investigated two years’ worth of air quality and outlier detection data from two Indian cities. Studies on air pollution have used numerous types of methodologies, with various gases being seen as a vector whose components include gas concentration values for each observation per-formed. We use curves to represent the monthly average of daily gas emissions in our technique. The approach, which is based on functional depth, was used to find outliers in the city of Delhi and Kolkata’s gas emissions, and the outcomes were compared to those from the traditional method. In the evaluation and comparison of these models’ performances, the functional approach model studied well.
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.
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Indian Academy of Sciences(IASc),Bangalore for the financial assistance provided through the IAS-SRFP 2014the grant received under the Indo-Russian project INT/RUS/RFBR/P-219 funded by Department of Science and Technology,New Delhi
文摘In this paper, we study the age and spatial distributions of Cepheids in the Small Magellanic Cloud （SMC） as a function of their ages using data from the OGLE III photometric catalogue. A period - age relation derived for Classical Cepheids in the Large Magellanic Cloud （LMC） has been used to find the ages of Cepheids. The age distribution of the SMC Classical Cepheids is found to have a peak at log（Age） ： 8.40 ± 0.10 which suggests that a major star formation event might have occurred in the SMC about 250 4- 50 Myr ago. It is believed that this star forming burst had been triggered by close interactions of the SMC with the LMC and/or the Milky Way. A comparison of the observed spatial distributions of the Cepheids and open star clusters has also been carried out to study the star formation scenario in the SMC.
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.
基金National Key R&D Program of China,No.2017YFB0504102National Natural Science Foundation of China,No.41771537
文摘The Babao River Basin is the "water tower" of the Heihe River Basin.The combination of vulnerable ecosystems and inhospitable natural environments substantially restricts the existence of humans and the sustainable development of society and environment in the Heihe River Basin.Soil temperature(ST) is a critical soil variable that could affect a series of physical,chemical and biological soil processes,which is the guarantee of water conservation and vegetation growth in this region.To measure the temporal variation and spatial pattern of ST fluctuation in the Babao River Basin,fluctuation of ST at various depths were analyzed with ST data at depths of 4,10 and 20 cm using classical statistical methods and permutation entropy.The study results show the following: 1) There are variations of ST at different depths,although ST followed an obvious seasonal law.ST at shallower depths is higher than at deeper depths in summer,and vice versa in winter.The difference of ST between different depths is close to zero when ST is near 5℃ in March or –5℃ in September.2) In spring,ST at the shallower depths becomes higher than at deeper depths as soon as ST is above –5℃;this is reversed in autumn when ST is below 5℃.ST at a soil depth of 4 cm is the first to change,followed by ST at 10 and 20 cm,and the time that ST reaches the same level is delayed for 10–15 days.In chilling and warming seasons,September and February are,respectively,the months when ST at various depths are similar.3) The average PE values of ST for 17 sites at 4 cm are 0.765 in spring > 0.764 in summer > 0.735 in autumn > 0.723 in winter,which implies the complicated degree of fluctuations of ST.4) For the variation of ST at different depths,it appears that Max,Ranges,Average and the Standard Deviation of ST decrease by depth increments in soil.Surface soil is more complicated because ST fluctuation at shallower depths is more pronounced and random.The average PE value of ST for 17sites are 0.863 at a depth of 4 cm > 0.818 at 10 cm > 0.744 at 20 cm.5) For the variation of ST at different elevations,it appears that Max,Ranges,Average,Standard Deviation and ST fluctuation decrease with increasing elevation at the same soil depth.And with the increase of elevation,the decrease rates of Max,Range,Average,Standard Deviation at 4 cm are –0.89℃/100 m,–0.94℃/100 m,–0.43℃/100 m,and –0.25℃/100 m,respectively.In addition,this correlation decreased with the increase of soil depth.6) Significant correlation between PE values of ST at depths of 4,10 and 20 cm can easily be found.This finding implies that temperature can easily be transmitted within soil at depths between 4 and 20 cm.7) For the variation of ST on shady slope and sunny slope sides,it appears that the PE values of ST at 4,10 and 20 cm for 8 sites located on shady slope side are 0.868,0.824 and 0.776,respectively,whereas they are 0.858,0.810 and 0.716 for 9 sites located on sunny slope side.
