The shear viscosity （7） and entropy density （s） are studied for the central Au＋Au collisions with the help of a microscopic transport model, namely the isospin-dependent quantum molecular dynamic model （IQMD）. ...The shear viscosity （7） and entropy density （s） are studied for the central Au＋Au collisions with the help of a microscopic transport model, namely the isospin-dependent quantum molecular dynamic model （IQMD）. Employ the formula given in Ref. [1],η is calculated as a time dependent variable for different incident energies from 40 MeV/u to 120 MeV/u and the energy dependence of η/s of nuclear matter in the most compressed stage in collision process is displayed.展开更多
Estimating the Probability Density Function（PDF） of the performance function is a direct way for structural reliability analysis,and the failure probability can be easily obtained by integration in the failure domai...Estimating the Probability Density Function（PDF） of the performance function is a direct way for structural reliability analysis,and the failure probability can be easily obtained by integration in the failure domain.However,efficiently estimating the PDF is still an urgent problem to be solved.The existing fractional moment based maximum entropy has provided a very advanced method for the PDF estimation,whereas the main shortcoming is that it limits the application of the reliability analysis method only to structures with independent inputs.While in fact,structures with correlated inputs always exist in engineering,thus this paper improves the maximum entropy method,and applies the Unscented Transformation（UT） technique to compute the fractional moments of the performance function for structures with correlations,which is a very efficient moment estimation method for models with any inputs.The proposed method can precisely estimate the probability distributions of performance functions for structures with correlations.Besides,the number of function evaluations of the proposed method in reliability analysis,which is determined by UT,is really small.Several examples are employed to illustrate the accuracy and advantages of the proposed method.展开更多
An approach of limit state equation for surrounding rock was put forward based on deformation criterion. A method of symmetrical sampling of basic random variables adopted by classical response surface method was mend...An approach of limit state equation for surrounding rock was put forward based on deformation criterion. A method of symmetrical sampling of basic random variables adopted by classical response surface method was mended, and peak value and deflection degree of basic random variables distribution curve were took into account in the mended sampling method. A calculation way of probability moment, based on mended Rosenbluth method, suitable for non-explicit performance function was put forward. The first, second, third and fourth order moments of functional function value were calculated by mended Rosenbluth method through the first, second, third and fourth order moments of basic random variable. A probability density the function（PDF） of functional function was deduced through its first, second, third and fourth moments, the PDF in the new method took the place of the method of quadratic polynomial to approximate real functional function and reliability probability was calculated through integral by the PDF for random variable of functional function value in the new method. The result shows that the improved response surface method can adapt to various statistic distribution types of basic random variables, its calculation process is legible and need not itemtive circulation. In addition, a stability probability of surrounding rock for a tunnel was calculated by the improved method, whose workload is only 30% of classical method and its accuracy is comparative.展开更多
The thermodynamic properties of charged particles,such as the energy density,pressure,entropy density,particle density,and squared speed of sound at the kinetic freeze-out in the Au+Au collisions from the relativistic...The thermodynamic properties of charged particles,such as the energy density,pressure,entropy density,particle density,and squared speed of sound at the kinetic freeze-out in the Au+Au collisions from the relativistic heavy ion collider (RHIC)beam energy scan program √S_(NN) and in the Cu+Cu collisions at √S_(NN),200 GeV are studied using the thermodynamically consistent Tsallis distribution.The energy density,pressure,and particle density decrease monotonically with the collision energy for the same collision centrality;These properties also decrease monotonically from the central to peripheral collisions at the same collision energy.While the scaled energy densityε∕T^(4) and scaled entropy density s∕T^(3) demonstrate the opposite trend with the collision energy for the same collision centrality.There is a correlation betweenε∕T^(4) and s∕T^(3) at the same centrality.In addition,the squared speed of sound was calculated to determine that all the collision energies share nearly the same value at different collision centralities.展开更多
Using entropy density of Dirac field near the event horizon of a rectilinear non-uniformly accelerating Kinnersley black hole, the law for the thermal radiation of black hole is studied and the instantaneous radiation...Using entropy density of Dirac field near the event horizon of a rectilinear non-uniformly accelerating Kinnersley black hole, the law for the thermal radiation of black hole is studied and the instantaneous radiation energy density is obtained. It is found that the instantaneous radiation energy density of a black hole is always proportional to the quartic of the temperature on event horizon in the same direction. That is to say, the thermal radiation of a black hole always satisfies the generalized Stefan-Boltzmann law. In addition, the derived generalized Stefan Boltzmann coefficient is no longer a constant, but a dynamic coefficient related to the space-time metric near the event horizon and the changing rate of the event horizon in black holes.展开更多
In this paper,the quadratic program problem and minimum discrimination information (MDI) problem with a set of quadratic inequality constraints and entropy constraints of density are considered.Based on the properties...In this paper,the quadratic program problem and minimum discrimination information (MDI) problem with a set of quadratic inequality constraints and entropy constraints of density are considered.Based on the properties of the generalized geometric programming,the dual programs of these two problems are derived.Furthermore,the duality theorems and related Kuhn-Tucker conditions for two pairs of the prime-dual programs are also established by the duality theory.展开更多
We first study the Shannon information entropies of constant total length multiple quantum well systems and then explore the effects of the number of wells and confining potential depth on position and momentum inform...We first study the Shannon information entropies of constant total length multiple quantum well systems and then explore the effects of the number of wells and confining potential depth on position and momentum information entropy density as well as the corresponding Shannon entropy.We find that for small full width at half maximum（FWHM） of the position entropy density,the FWHM of the momentum entropy density is large and vice versa.By increasing the confined potential depth,the FWHM of the position entropy density decreases while the FWHM of the momentum entropy density increases.By increasing the potential depth,the frequency of the position entropy density oscillation within the quantum barrier decreases while that of the position entropy density oscillation within the quantum well increases.By increasing the number of wells,the frequency of the position entropy density oscillation decreases inside the barriers while it increases inside the quantum well.As an example,we might localize the ground state as well as the position entropy densities of the1 st,2 nd,and 6 th excited states for a four-well quantum system.Also,we verify the Bialynicki–Birula–Mycieslki（BBM）inequality.展开更多
The thermodynamic properties of Zn Se are obtained by using quasi-harmonic Debye model embedded in Gibbscode for pressure range 0–10 GPa and for temperature range 0–1000 K. Helmholtz free energy, internal energy, en...The thermodynamic properties of Zn Se are obtained by using quasi-harmonic Debye model embedded in Gibbscode for pressure range 0–10 GPa and for temperature range 0–1000 K. Helmholtz free energy, internal energy, entropy,Debye temperature, and specific heat are calculated. The thermal expansion coefficient along with Gruneisen parameter are also calculated at room temperature for the pressure range. It is found that internal energy is pressure dependent at low temperature, whereas entropy and Helmholtz free energy are pressure sensitive at high temperature. At ambient conditions,the obtained results are found to be in close agreement to available theoretical and experimental data.展开更多
Background Finding methods to judge the quality of X-ray crystallographic information is an active research topic.The quality of electron density maps reconstructed by Fourier transform is always limited by the finite...Background Finding methods to judge the quality of X-ray crystallographic information is an active research topic.The quality of electron density maps reconstructed by Fourier transform is always limited by the finite resolution,the amplitude/phase error and the completeness of diffraction data.At present,the R value and effective resolution are common ways of evaluating the quality of electron density maps.Unfortunately,the current evaluation methods are only dependent on diffraction amplitude,without any phase information.Methods Advanced evaluation functions in real space are designed to estimate the electron density map quality.The electron density map definition evaluation function relies on the atomicity of the electron density distribution.We use the power spectrum electron density entropy in protein crystallography for the first time.These two functions include both structure factor amplitudes and phases via the Fourier transform of electron density map.Results We carry out tests on synthetic data sets of known structures,varying the resolution and error,and draw the quality curves of electron density maps with theoretical,noisy and experimental diffraction data by two evaluation functions at different resolutions.The curves reveal the optimum structure and resolution of proteins clearly.Conclusions The work presented here offers new methods to evaluate the qualities of the electron density maps of proteins with slight differences,and brand new indicators to select the optimum diffraction resolution of protein structures.展开更多
Using the related formula of dynamic black holes, the instantaneous radiation energy density of the general spherically symmetric charged dynamic black hole and the arbitrarily accelerating charged dynamic black hole ...Using the related formula of dynamic black holes, the instantaneous radiation energy density of the general spherically symmetric charged dynamic black hole and the arbitrarily accelerating charged dynamic black hole is calculated. It is found that the instantaneous radiation energy density of black hole is always proportional to the quartic of the temperature of event horizon in the same direction. The proportional coefficient of generalized Stefan-Boltzmann is no longer a constant, and it becomes a dynamic coefficient that is related to the event horizon changing rate, space-time structure near event horizon and the radiation absorption coefficient of the black hole. It is shown that there should be an internal relation between the gravitational field around black hole and its thermal radiation.展开更多
We calculate the shear viscosity（η） and bulk viscosity（ζ） to entropy density（s） ratios η/s and ζ/s of a gluon plasma system in kinetic theory, including both the elastic gg←→gg forward scattering and the i...We calculate the shear viscosity（η） and bulk viscosity（ζ） to entropy density（s） ratios η/s and ζ/s of a gluon plasma system in kinetic theory, including both the elastic gg←→gg forward scattering and the inelastic soft gluon bremsstrahlung gg←→ggg processes. Due to the suppressed contribution to η and ζ in the gg←→gg forward scattering and the effective g←→gg gluon splitting, Arnold, Moore and Yaffe（AMY） and Arnold, Dogan and Moore（ADM） have got the leading order computations for η and ζ in high-temperature QCD matter. In this paper, we calculate the correction to η and ζ in the soft gluon bremsstrahlung gg←→ggg process with an analytic method.We find that the contribution of the collision term from the gg←→ggg soft gluon bremsstrahlung process is just a small perturbation to the gg←→gg scattering process and that the correction is at～ 5% level. Then, we obtain the bulk viscosity of the gluon plasma for the number-changing process. Furthermore, our leading-order result for bulk viscosity is the formula ζ∝（αs^2 T^3）/（lnαs^-1） in high-temperature gluon plasma.展开更多
In this paper,the authors first introduce the tree-indexed Markov chains in random environment,which takes values on a general state space.Then,they prove the existence of this stochastic process,and develop a class o...In this paper,the authors first introduce the tree-indexed Markov chains in random environment,which takes values on a general state space.Then,they prove the existence of this stochastic process,and develop a class of its equivalent forms.Based on this property,some strong limit theorems including conditional entropy density are studied for the tree-indexed Markov chains in random environment.展开更多
Let(ξ_n)_(n=0)~∞ be a Markov chain with the state space X = {1, 2, · · ·, b},(g_n(x, y))_(n=1)~∞ be functions defined on X × X, and F_(m_n,b_n)(ω) =1 /b_n sum from k=m_n+1 to m_n+b_n g_k(ξ_(k-...Let(ξ_n)_(n=0)~∞ be a Markov chain with the state space X = {1, 2, · · ·, b},(g_n(x, y))_(n=1)~∞ be functions defined on X × X, and F_(m_n,b_n)(ω) =1 /b_n sum from k=m_n+1 to m_n+b_n g_k(ξ_(k-1), ξ_k).In this paper the limit properties of F_(m_n,b_n)(ω) and the generalized relative entropy density f_(m_n,b_n)(ω) =-(1/b_n) log p(ξ_(m_n,m_n+b_n)) are discussed, and some theorems on a.s. convergence for(ξ_n)_n=0~∞ and the generalized Shannon-McMillan(AEP) theorem on finite nonhomogeneous Markov chains are obtained.展开更多
基金supported by National Natural Science Foundation of China(Nos.11035009,10979074,10775167,10775168)the Major State Basic Research Development Program in China(No.2007CB815004)+1 种基金the Shanghai Development Foundation for Science and Technology(No.09JC1416800)the Knowledge Innovation Project of Chinese Academy of Sciences of China(No.KJCX2-EW-N01)
文摘The shear viscosity （7） and entropy density （s） are studied for the central Au＋Au collisions with the help of a microscopic transport model, namely the isospin-dependent quantum molecular dynamic model （IQMD）. Employ the formula given in Ref. [1],η is calculated as a time dependent variable for different incident energies from 40 MeV/u to 120 MeV/u and the energy dependence of η/s of nuclear matter in the most compressed stage in collision process is displayed.
基金supported by the Equipment Development Department ‘‘13th Five-year” Equipment Research Field Foundation of China Central Military Commission(No.6140244010216HT15001)
文摘Estimating the Probability Density Function（PDF） of the performance function is a direct way for structural reliability analysis,and the failure probability can be easily obtained by integration in the failure domain.However,efficiently estimating the PDF is still an urgent problem to be solved.The existing fractional moment based maximum entropy has provided a very advanced method for the PDF estimation,whereas the main shortcoming is that it limits the application of the reliability analysis method only to structures with independent inputs.While in fact,structures with correlated inputs always exist in engineering,thus this paper improves the maximum entropy method,and applies the Unscented Transformation（UT） technique to compute the fractional moments of the performance function for structures with correlations,which is a very efficient moment estimation method for models with any inputs.The proposed method can precisely estimate the probability distributions of performance functions for structures with correlations.Besides,the number of function evaluations of the proposed method in reliability analysis,which is determined by UT,is really small.Several examples are employed to illustrate the accuracy and advantages of the proposed method.
基金Project(50378036) supported by the National Natural Science Foundation of China Project (200503) supported by the Foundation ofCommunications Department of Hunan Province, China
文摘An approach of limit state equation for surrounding rock was put forward based on deformation criterion. A method of symmetrical sampling of basic random variables adopted by classical response surface method was mended, and peak value and deflection degree of basic random variables distribution curve were took into account in the mended sampling method. A calculation way of probability moment, based on mended Rosenbluth method, suitable for non-explicit performance function was put forward. The first, second, third and fourth order moments of functional function value were calculated by mended Rosenbluth method through the first, second, third and fourth order moments of basic random variable. A probability density the function（PDF） of functional function was deduced through its first, second, third and fourth moments, the PDF in the new method took the place of the method of quadratic polynomial to approximate real functional function and reliability probability was calculated through integral by the PDF for random variable of functional function value in the new method. The result shows that the improved response surface method can adapt to various statistic distribution types of basic random variables, its calculation process is legible and need not itemtive circulation. In addition, a stability probability of surrounding rock for a tunnel was calculated by the improved method, whose workload is only 30% of classical method and its accuracy is comparative.
基金supported in part by the National Natural Science Foundation of China (Nos. 11905120 and 11947416)the Natural Science Foundation of the Sichuan Province (No. 2023NSFSC1322)+1 种基金the United States Department of Energy (#DE-FG02-93ER40773)the NNSA (No. DENA0003841 (CENTAUR))。
文摘The thermodynamic properties of charged particles,such as the energy density,pressure,entropy density,particle density,and squared speed of sound at the kinetic freeze-out in the Au+Au collisions from the relativistic heavy ion collider (RHIC)beam energy scan program √S_(NN) and in the Cu+Cu collisions at √S_(NN),200 GeV are studied using the thermodynamically consistent Tsallis distribution.The energy density,pressure,and particle density decrease monotonically with the collision energy for the same collision centrality;These properties also decrease monotonically from the central to peripheral collisions at the same collision energy.While the scaled energy densityε∕T^(4) and scaled entropy density s∕T^(3) demonstrate the opposite trend with the collision energy for the same collision centrality.There is a correlation betweenε∕T^(4) and s∕T^(3) at the same centrality.In addition,the squared speed of sound was calculated to determine that all the collision energies share nearly the same value at different collision centralities.
基金supported by the National Natural Science Foundation of China (Grant No 10773002)the Technology Planning Project of Education Bureau of Shandong Province, China (Grant No J07WJ49)
文摘Using entropy density of Dirac field near the event horizon of a rectilinear non-uniformly accelerating Kinnersley black hole, the law for the thermal radiation of black hole is studied and the instantaneous radiation energy density is obtained. It is found that the instantaneous radiation energy density of a black hole is always proportional to the quartic of the temperature on event horizon in the same direction. That is to say, the thermal radiation of a black hole always satisfies the generalized Stefan-Boltzmann law. In addition, the derived generalized Stefan Boltzmann coefficient is no longer a constant, but a dynamic coefficient related to the space-time metric near the event horizon and the changing rate of the event horizon in black holes.
文摘In this paper,the quadratic program problem and minimum discrimination information (MDI) problem with a set of quadratic inequality constraints and entropy constraints of density are considered.Based on the properties of the generalized geometric programming,the dual programs of these two problems are derived.Furthermore,the duality theorems and related Kuhn-Tucker conditions for two pairs of the prime-dual programs are also established by the duality theory.
基金Project supported by the Iranian Nanotechnology Initiative Council(INIC)the 20180677-SIP-IPN,Mexicothe CONACYT 288856-CB-2016,Mexico
文摘We first study the Shannon information entropies of constant total length multiple quantum well systems and then explore the effects of the number of wells and confining potential depth on position and momentum information entropy density as well as the corresponding Shannon entropy.We find that for small full width at half maximum（FWHM） of the position entropy density,the FWHM of the momentum entropy density is large and vice versa.By increasing the confined potential depth,the FWHM of the position entropy density decreases while the FWHM of the momentum entropy density increases.By increasing the potential depth,the frequency of the position entropy density oscillation within the quantum barrier decreases while that of the position entropy density oscillation within the quantum well increases.By increasing the number of wells,the frequency of the position entropy density oscillation decreases inside the barriers while it increases inside the quantum well.As an example,we might localize the ground state as well as the position entropy densities of the1 st,2 nd,and 6 th excited states for a four-well quantum system.Also,we verify the Bialynicki–Birula–Mycieslki（BBM）inequality.
文摘The thermodynamic properties of Zn Se are obtained by using quasi-harmonic Debye model embedded in Gibbscode for pressure range 0–10 GPa and for temperature range 0–1000 K. Helmholtz free energy, internal energy, entropy,Debye temperature, and specific heat are calculated. The thermal expansion coefficient along with Gruneisen parameter are also calculated at room temperature for the pressure range. It is found that internal energy is pressure dependent at low temperature, whereas entropy and Helmholtz free energy are pressure sensitive at high temperature. At ambient conditions,the obtained results are found to be in close agreement to available theoretical and experimental data.
基金This work was financially supported by grants from the Strategic Priority Research Program of the Chinese Academy of Sciences(XDB08030103)the National Natural Science Foundation of China(31570744)the National Key Research and Development Project(2017YFA0504900).
文摘Background Finding methods to judge the quality of X-ray crystallographic information is an active research topic.The quality of electron density maps reconstructed by Fourier transform is always limited by the finite resolution,the amplitude/phase error and the completeness of diffraction data.At present,the R value and effective resolution are common ways of evaluating the quality of electron density maps.Unfortunately,the current evaluation methods are only dependent on diffraction amplitude,without any phase information.Methods Advanced evaluation functions in real space are designed to estimate the electron density map quality.The electron density map definition evaluation function relies on the atomicity of the electron density distribution.We use the power spectrum electron density entropy in protein crystallography for the first time.These two functions include both structure factor amplitudes and phases via the Fourier transform of electron density map.Results We carry out tests on synthetic data sets of known structures,varying the resolution and error,and draw the quality curves of electron density maps with theoretical,noisy and experimental diffraction data by two evaluation functions at different resolutions.The curves reveal the optimum structure and resolution of proteins clearly.Conclusions The work presented here offers new methods to evaluate the qualities of the electron density maps of proteins with slight differences,and brand new indicators to select the optimum diffraction resolution of protein structures.
基金the Science Foundation of Heze University (Grant No. XY06WL01)
文摘Using the related formula of dynamic black holes, the instantaneous radiation energy density of the general spherically symmetric charged dynamic black hole and the arbitrarily accelerating charged dynamic black hole is calculated. It is found that the instantaneous radiation energy density of black hole is always proportional to the quartic of the temperature of event horizon in the same direction. The proportional coefficient of generalized Stefan-Boltzmann is no longer a constant, and it becomes a dynamic coefficient that is related to the event horizon changing rate, space-time structure near event horizon and the radiation absorption coefficient of the black hole. It is shown that there should be an internal relation between the gravitational field around black hole and its thermal radiation.
基金Supported by Ministry of Science and Technology of China(MSTC)under the"973"Project(2015CB856904(4))National Natural Science Foundation of China(11735007,11521064)
文摘We calculate the shear viscosity（η） and bulk viscosity（ζ） to entropy density（s） ratios η/s and ζ/s of a gluon plasma system in kinetic theory, including both the elastic gg←→gg forward scattering and the inelastic soft gluon bremsstrahlung gg←→ggg processes. Due to the suppressed contribution to η and ζ in the gg←→gg forward scattering and the effective g←→gg gluon splitting, Arnold, Moore and Yaffe（AMY） and Arnold, Dogan and Moore（ADM） have got the leading order computations for η and ζ in high-temperature QCD matter. In this paper, we calculate the correction to η and ζ in the soft gluon bremsstrahlung gg←→ggg process with an analytic method.We find that the contribution of the collision term from the gg←→ggg soft gluon bremsstrahlung process is just a small perturbation to the gg←→gg scattering process and that the correction is at～ 5% level. Then, we obtain the bulk viscosity of the gluon plasma for the number-changing process. Furthermore, our leading-order result for bulk viscosity is the formula ζ∝（αs^2 T^3）/（lnαs^-1） in high-temperature gluon plasma.
基金supported by the National Natural Science Foundation of China(Nos.11571142,11971197,11601191)。
文摘In this paper,the authors first introduce the tree-indexed Markov chains in random environment,which takes values on a general state space.Then,they prove the existence of this stochastic process,and develop a class of its equivalent forms.Based on this property,some strong limit theorems including conditional entropy density are studied for the tree-indexed Markov chains in random environment.
基金supported in part by the NNSF of China(No.11571142)the RP of Anhui Provincial Department of Education(No.KJ2017A851)
文摘Let(ξ_n)_(n=0)~∞ be a Markov chain with the state space X = {1, 2, · · ·, b},(g_n(x, y))_(n=1)~∞ be functions defined on X × X, and F_(m_n,b_n)(ω) =1 /b_n sum from k=m_n+1 to m_n+b_n g_k(ξ_(k-1), ξ_k).In this paper the limit properties of F_(m_n,b_n)(ω) and the generalized relative entropy density f_(m_n,b_n)(ω) =-(1/b_n) log p(ξ_(m_n,m_n+b_n)) are discussed, and some theorems on a.s. convergence for(ξ_n)_n=0~∞ and the generalized Shannon-McMillan(AEP) theorem on finite nonhomogeneous Markov chains are obtained.
