Two calculation methods on the partition functions for diatomic molecules in plas- mas out of thermal equilibrium are reported. A Boltzmann distribution for the electronic, vi- brational and rotational quantum levels ...Two calculation methods on the partition functions for diatomic molecules in plas- mas out of thermal equilibrium are reported. A Boltzmann distribution for the electronic, vi- brational and rotational quantum levels is assumed in the two calculation methods. The results obtained by two methods are displayed for four sorts of diatomic molecules, 02, N2, OH and NO, that are present in humid air plasmas. The calculation method of density for the electronically excited states is developed. Finally, a method to calculate the partition functions for simulating the non-normalized diatomic spectra is discussed.展开更多
It has remained an open problem to accurately compute the partition function of macroscopic systems since the establishment of statistical physics. A rapid method approaching this problem was presented and was strictl...It has remained an open problem to accurately compute the partition function of macroscopic systems since the establishment of statistical physics. A rapid method approaching this problem was presented and was strictly tested by molecular dynamic (MD) simulations on Ar atoms in both dense gaseous and liquid states. The outcomes from the method on the internal energy and the work of isothermal expansion (and therefore the free energy) are in good agreement with the MD simulations, suggesting the method would be immediately applied in vast areas.展开更多
In this paper, we study a certain partition function a(n) defined by ∑n≥0 a(n)qn := ∏n=1(1- qn)-1(1 -2n)-1. We prove that given a positive integer j 〉 1 and a prime m _〉 5, there are infinitely many cong...In this paper, we study a certain partition function a(n) defined by ∑n≥0 a(n)qn := ∏n=1(1- qn)-1(1 -2n)-1. We prove that given a positive integer j 〉 1 and a prime m _〉 5, there are infinitely many congruences of the type a(An + B) ≡ 0 (rood m3). This work is inspired by Ono's ground breaking result in the study of the distribution of the partition function p(n).展开更多
We use the work of de Vega, Sanchez, and Comes (1997), to approximate the “particle density” of a “graviton gas”. This “particle density” derivation is compared with Dolgov’s (1997) expression of the Vacuum ene...We use the work of de Vega, Sanchez, and Comes (1997), to approximate the “particle density” of a “graviton gas”. This “particle density” derivation is compared with Dolgov’s (1997) expression of the Vacuum energy in terms of a phase transition. The idea is to have a quartic potential, and then to utilize the Bogomol’nyi inequality to refine what the phase transition states. We utilize Ng, Infinite quantum information procedures to link our work with initial entropy and other issues and close with a variation in the HUP: at the start of the expansion of the universe.展开更多
The total internal partition sums were calculated in the product approximation at temperatures up to 5000 K for the asymptotic asymmetric-top HO2 molecule. The calculations of the rotational partition function and the...The total internal partition sums were calculated in the product approximation at temperatures up to 5000 K for the asymptotic asymmetric-top HO2 molecule. The calculations of the rotational partition function and the vibrational partition function were carried out with the rigid-top model and in the harmonic oscillator approximation, respectively. Our values of the total internal partition sums are consistent with the data of HITRAN database with -0.14% at 296 K. Using the calculated partition functions, we have calculated the line intensities of υ2 band of HO2 at several high temperatures. The results showed that the calculated line intensities are in very good agreement with those of HITRAN database at temperatures up to 3000 K, which provides a strong support for the calculations of partition functions and line intensities at high temperatures. Then we have extended the calculation to higher temperatures. The simulated spectra of υ2 band of the asymptotic asymmetric-top HO2 molecule at 4000 and 5000 K are also obtained.展开更多
Total internal partition sums are calculated in the product approximation at temperatures up to 6000K for the asymptotic asymmetric-top SiO2 molecule. The rotational partition function and the vibrational partition fu...Total internal partition sums are calculated in the product approximation at temperatures up to 6000K for the asymptotic asymmetric-top SiO2 molecule. The rotational partition function and the vibrational partition function are calculated with the rigid-top model and in the harmonic oscillator approximation, respectively. Our values of the total internal partition sums are consistent with the calculated value in the Gaussian program within $-0.137$% at 296K. Using the calculated partition functions and the rotationless transition dipole moment squared as a constant, we calculate the line intensities of 001--000 band of SiO2 at normal, medium and high temperatures. Simulated spectra of the 001--000 band of the asymptotic asymmetric-top SiO2 molecule at 2000, 5000 and 6000K are also obtained.展开更多
A polymer filament consisting of many similar molecules linked in a one-dimensional array is very flexible. As a result, shapes with a relatively large curvature can be accommodated elastically. When loosely confined ...A polymer filament consisting of many similar molecules linked in a one-dimensional array is very flexible. As a result, shapes with a relatively large curvature can be accommodated elastically. When loosely confined in a thermal environment, such a flexible strand may become tangled owing to its flexibility. When confined within a narrow "tube" over its full length, a flexible molecule may behave quite differently. Here, we consider the qualitative nature of deformation of an individual filament when confined within a tube. Commonly the tube is formed within the cluster by a large number of surrounding filaments of the same type.展开更多
A second-order dynamic phase transition in a non-equilibrium Eggers urn model for the separation of sand is studied. The order parameter, the susceptibility and the stationary probability distribution have been calcul...A second-order dynamic phase transition in a non-equilibrium Eggers urn model for the separation of sand is studied. The order parameter, the susceptibility and the stationary probability distribution have been calculated. By applying the Lee-Yang zeros method of equilibrium phase transitions, we study the distributions of the effective partition function zeros and obtain the same result for the model. Thus, the Lee-Yang theory can be applied to a more general non-equilibrium system.展开更多
1. Introduction In quantum optics, optical frequency conversion is a typical nonlinear process and is worth studying, for example, a second harmonic frequency generation will generate a squeezed state.[1'2l In this ...1. Introduction In quantum optics, optical frequency conversion is a typical nonlinear process and is worth studying, for example, a second harmonic frequency generation will generate a squeezed state.[1'2l In this work, we tackle the evolution of an initial coherent state in a Raman dispersion process which is also a nonlinear process. The process involves the inelastic scattering of a pho- ton when it is incident on a molecule. The photon loses some of its energy to the molecule or gains some from it, and so leaves the molecule with a lower or a higher frequency. The lower frequency components of the scattered radiation are called the Stokes lines and the higher frequency components are called the anti- Stokes lines. The Hamiltonian governing its dynamics is[3]展开更多
A path-integral representation of central spin system immersed in an antiferromagnetic environment was investigated. To carry out this study, we made use of the discrete-time propagator method associated with a basic ...A path-integral representation of central spin system immersed in an antiferromagnetic environment was investigated. To carry out this study, we made use of the discrete-time propagator method associated with a basic set involving coherent states of Grassmann variables which made it possible to obtain the analytical propagator which is the centerpiece of the study. In this study, we considered that the environment was in the low-temperature and low-excitation limit and was split into 2 subnets that do not interact with each other. The evaluation of our system was made by considering the first neighbor approximation. From the formalism of the path integrals, it is easy to evaluate the partition function and thermodynamic properties followed from an appropriate tracing over Grassmann variables in the imaginary time domain. We show that the energy of the system depends on the number of sites <em>n</em> when <em>β </em><em></em><span></span>→ 0.展开更多
In many interesting physical examples, the partition function is divergent, as first pointed out in 1924 by Fermi (for the hydrogen-atom case). Thus, the usual toolbox of statistical mechanics becomes unavailable, not...In many interesting physical examples, the partition function is divergent, as first pointed out in 1924 by Fermi (for the hydrogen-atom case). Thus, the usual toolbox of statistical mechanics becomes unavailable, notwithstanding the well-known fact that the pertinent system may appear to be in a thermal steady state. We tackle and overcome these difficulties hereby appeal to firmly established but not too well-known mathematical recipes and obtain finite values for a typical divergent partition function, that of a Brownian particle in an external field. This allows not only for calculating thermodynamic observables of interest, but for also instantiating other kinds of statistical mechanics’ novelties.展开更多
Traditionally, fractal image compression suffers from lengthy encoding time in measure ofhours. In this paper, combined with characteristlcs of human visual system, a flexible classification technique is proposed. Thi...Traditionally, fractal image compression suffers from lengthy encoding time in measure ofhours. In this paper, combined with characteristlcs of human visual system, a flexible classification technique is proposed. This yields a corresponding adaptive algorithm which can cut down the encoding timeinto second's magnitude. Experiment results suggest that the algorithm can balance the overall encodingperformance efficiently, that is, with a higher speed and a better PSNR gain.展开更多
The modular design technology is of importance increasingly,as product structure is more and more complex.Modular design systems face challenging problems as the design information tends to be dynamic,redundant,and ve...The modular design technology is of importance increasingly,as product structure is more and more complex.Modular design systems face challenging problems as the design information tends to be dynamic,redundant,and very large.This paper describes a novel approach for handling them.In this approach,a partition is firstly performed for the complex structural components by mapping functions to the structures layer by layer.Based on this partition,a comprehensive design matrix is then developed to identify the key design mode which is driven by a special function.The design process is also programmed by analyzing the coupled information on both the functional and structural hierarchies.Then,the integrated knowledge model based on object-oriented method and hybrid inference method is constructed.In this model,knowledge can be organized at hierarchical classification and expressed with different forms.Finally,the methodology developed has been applied to a real application in automobile cylinder block design and the results are presented.展开更多
The asymptotic expansion of the heat kernel Θ(t)=sum from ∞ to j=1 exp(-tλ_j) where {λ_j}_(j=1)~∞ are the eigen-values of the negative Laplacian -Δ_n=-sum from n to k=1((?))~2 in R^n(n=2 or 3) is studied for sho...The asymptotic expansion of the heat kernel Θ(t)=sum from ∞ to j=1 exp(-tλ_j) where {λ_j}_(j=1)~∞ are the eigen-values of the negative Laplacian -Δ_n=-sum from n to k=1((?))~2 in R^n(n=2 or 3) is studied for short-time t for a generalbounded domain Ω with a smooth boundary (?)Ω.In this paper,we consider the case of a finite number of theDirichlet conditions φ=0 on Γ_i (i=1,...,J) and the Neumann conditions (?)=0 on Γ_i (i=J+1,...,k) andthe Robin conditions ((?)+γ_i)φ=0 on Γ_i (i=k+1,...,m) where γ_i are piecewise smooth positive impedancefunctions,such that (?)Ω consists of a finite number of piecewise smooth components Γ_i(i=1,...,m) where(?)Ω=(?)Γ_i.We construct the required asymptotics in the form of a power series over t.The senior coefficients inthis series are specified as functionals of the geometric shape of the domain Ω.This result is applied to calculatethe one-particle partition function of a“special ideal gas”,i.e.,the set of non-interacting particles set up in abox with Dirichlet,Neumann and Robin boundary conditions for the appropriate wave function.Calculationof the thermodynamic quantities for the ideal gas such as the internal energy,pressure and specific heat revealsthat these quantities alone are incapable of distinguishing between two different shapes of the domain.Thisconclusion seems to be intuitively clear because it is based on a limited information given by a one-particlepartition function;nevertheless,its formal theoretical motivation is of some interest.展开更多
文摘Two calculation methods on the partition functions for diatomic molecules in plas- mas out of thermal equilibrium are reported. A Boltzmann distribution for the electronic, vi- brational and rotational quantum levels is assumed in the two calculation methods. The results obtained by two methods are displayed for four sorts of diatomic molecules, 02, N2, OH and NO, that are present in humid air plasmas. The calculation method of density for the electronically excited states is developed. Finally, a method to calculate the partition functions for simulating the non-normalized diatomic spectra is discussed.
基金Project supported by the Specialized Research Fund for the Doctoral Program of Higher Education,China(Grant No.20130071110018)the National Natural Science Foundation of China(Grant No.11274073)
文摘It has remained an open problem to accurately compute the partition function of macroscopic systems since the establishment of statistical physics. A rapid method approaching this problem was presented and was strictly tested by molecular dynamic (MD) simulations on Ar atoms in both dense gaseous and liquid states. The outcomes from the method on the internal energy and the work of isothermal expansion (and therefore the free energy) are in good agreement with the MD simulations, suggesting the method would be immediately applied in vast areas.
文摘In this paper, we study a certain partition function a(n) defined by ∑n≥0 a(n)qn := ∏n=1(1- qn)-1(1 -2n)-1. We prove that given a positive integer j 〉 1 and a prime m _〉 5, there are infinitely many congruences of the type a(An + B) ≡ 0 (rood m3). This work is inspired by Ono's ground breaking result in the study of the distribution of the partition function p(n).
文摘We use the work of de Vega, Sanchez, and Comes (1997), to approximate the “particle density” of a “graviton gas”. This “particle density” derivation is compared with Dolgov’s (1997) expression of the Vacuum energy in terms of a phase transition. The idea is to have a quartic potential, and then to utilize the Bogomol’nyi inequality to refine what the phase transition states. We utilize Ng, Infinite quantum information procedures to link our work with initial entropy and other issues and close with a variation in the HUP: at the start of the expansion of the universe.
基金Project supported by the Major Program for Basic Research of National Security, China (Grant No 5134202-04)the National Natural Science Foundation of China (Grant No 10574096)the Natural Science Foundation of the Bureau of Education of Guizhou Province, China (Grant No 2006204)
文摘The total internal partition sums were calculated in the product approximation at temperatures up to 5000 K for the asymptotic asymmetric-top HO2 molecule. The calculations of the rotational partition function and the vibrational partition function were carried out with the rigid-top model and in the harmonic oscillator approximation, respectively. Our values of the total internal partition sums are consistent with the data of HITRAN database with -0.14% at 296 K. Using the calculated partition functions, we have calculated the line intensities of υ2 band of HO2 at several high temperatures. The results showed that the calculated line intensities are in very good agreement with those of HITRAN database at temperatures up to 3000 K, which provides a strong support for the calculations of partition functions and line intensities at high temperatures. Then we have extended the calculation to higher temperatures. The simulated spectra of υ2 band of the asymptotic asymmetric-top HO2 molecule at 4000 and 5000 K are also obtained.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10965002)the Scientific Research Program of the Education Bureau of Jiangxi Province,China (Grant No. 2007326)the Scientific Research Program of the Science and Technology Bureau of Jiangxi Province,China (Grant No. 200621)
文摘Total internal partition sums are calculated in the product approximation at temperatures up to 6000K for the asymptotic asymmetric-top SiO2 molecule. The rotational partition function and the vibrational partition function are calculated with the rigid-top model and in the harmonic oscillator approximation, respectively. Our values of the total internal partition sums are consistent with the calculated value in the Gaussian program within $-0.137$% at 296K. Using the calculated partition functions and the rotationless transition dipole moment squared as a constant, we calculate the line intensities of 001--000 band of SiO2 at normal, medium and high temperatures. Simulated spectra of the 001--000 band of the asymptotic asymmetric-top SiO2 molecule at 2000, 5000 and 6000K are also obtained.
文摘A polymer filament consisting of many similar molecules linked in a one-dimensional array is very flexible. As a result, shapes with a relatively large curvature can be accommodated elastically. When loosely confined in a thermal environment, such a flexible strand may become tangled owing to its flexibility. When confined within a narrow "tube" over its full length, a flexible molecule may behave quite differently. Here, we consider the qualitative nature of deformation of an individual filament when confined within a tube. Commonly the tube is formed within the cluster by a large number of surrounding filaments of the same type.
基金Project supported by the National Natural Science Foundation of China (Grant No 10175035)the Foundation for Outstanding Young Teacher of Ministry of Education of China
文摘A second-order dynamic phase transition in a non-equilibrium Eggers urn model for the separation of sand is studied. The order parameter, the susceptibility and the stationary probability distribution have been calculated. By applying the Lee-Yang zeros method of equilibrium phase transitions, we study the distributions of the effective partition function zeros and obtain the same result for the model. Thus, the Lee-Yang theory can be applied to a more general non-equilibrium system.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10775097 and 10475056)
文摘1. Introduction In quantum optics, optical frequency conversion is a typical nonlinear process and is worth studying, for example, a second harmonic frequency generation will generate a squeezed state.[1'2l In this work, we tackle the evolution of an initial coherent state in a Raman dispersion process which is also a nonlinear process. The process involves the inelastic scattering of a pho- ton when it is incident on a molecule. The photon loses some of its energy to the molecule or gains some from it, and so leaves the molecule with a lower or a higher frequency. The lower frequency components of the scattered radiation are called the Stokes lines and the higher frequency components are called the anti- Stokes lines. The Hamiltonian governing its dynamics is[3]
文摘A path-integral representation of central spin system immersed in an antiferromagnetic environment was investigated. To carry out this study, we made use of the discrete-time propagator method associated with a basic set involving coherent states of Grassmann variables which made it possible to obtain the analytical propagator which is the centerpiece of the study. In this study, we considered that the environment was in the low-temperature and low-excitation limit and was split into 2 subnets that do not interact with each other. The evaluation of our system was made by considering the first neighbor approximation. From the formalism of the path integrals, it is easy to evaluate the partition function and thermodynamic properties followed from an appropriate tracing over Grassmann variables in the imaginary time domain. We show that the energy of the system depends on the number of sites <em>n</em> when <em>β </em><em></em><span></span>→ 0.
文摘In many interesting physical examples, the partition function is divergent, as first pointed out in 1924 by Fermi (for the hydrogen-atom case). Thus, the usual toolbox of statistical mechanics becomes unavailable, notwithstanding the well-known fact that the pertinent system may appear to be in a thermal steady state. We tackle and overcome these difficulties hereby appeal to firmly established but not too well-known mathematical recipes and obtain finite values for a typical divergent partition function, that of a Brownian particle in an external field. This allows not only for calculating thermodynamic observables of interest, but for also instantiating other kinds of statistical mechanics’ novelties.
文摘Traditionally, fractal image compression suffers from lengthy encoding time in measure ofhours. In this paper, combined with characteristlcs of human visual system, a flexible classification technique is proposed. This yields a corresponding adaptive algorithm which can cut down the encoding timeinto second's magnitude. Experiment results suggest that the algorithm can balance the overall encodingperformance efficiently, that is, with a higher speed and a better PSNR gain.
基金the National Natural Science Foundation of China (No. 50935006); the National High Technology Research and Development Program (863) of China (No. 2009AA04Z147);the Science- Technology Research and Development Program of Shaanxi Province (No. 2008KW-07)
文摘The modular design technology is of importance increasingly,as product structure is more and more complex.Modular design systems face challenging problems as the design information tends to be dynamic,redundant,and very large.This paper describes a novel approach for handling them.In this approach,a partition is firstly performed for the complex structural components by mapping functions to the structures layer by layer.Based on this partition,a comprehensive design matrix is then developed to identify the key design mode which is driven by a special function.The design process is also programmed by analyzing the coupled information on both the functional and structural hierarchies.Then,the integrated knowledge model based on object-oriented method and hybrid inference method is constructed.In this model,knowledge can be organized at hierarchical classification and expressed with different forms.Finally,the methodology developed has been applied to a real application in automobile cylinder block design and the results are presented.
文摘The asymptotic expansion of the heat kernel Θ(t)=sum from ∞ to j=1 exp(-tλ_j) where {λ_j}_(j=1)~∞ are the eigen-values of the negative Laplacian -Δ_n=-sum from n to k=1((?))~2 in R^n(n=2 or 3) is studied for short-time t for a generalbounded domain Ω with a smooth boundary (?)Ω.In this paper,we consider the case of a finite number of theDirichlet conditions φ=0 on Γ_i (i=1,...,J) and the Neumann conditions (?)=0 on Γ_i (i=J+1,...,k) andthe Robin conditions ((?)+γ_i)φ=0 on Γ_i (i=k+1,...,m) where γ_i are piecewise smooth positive impedancefunctions,such that (?)Ω consists of a finite number of piecewise smooth components Γ_i(i=1,...,m) where(?)Ω=(?)Γ_i.We construct the required asymptotics in the form of a power series over t.The senior coefficients inthis series are specified as functionals of the geometric shape of the domain Ω.This result is applied to calculatethe one-particle partition function of a“special ideal gas”,i.e.,the set of non-interacting particles set up in abox with Dirichlet,Neumann and Robin boundary conditions for the appropriate wave function.Calculationof the thermodynamic quantities for the ideal gas such as the internal energy,pressure and specific heat revealsthat these quantities alone are incapable of distinguishing between two different shapes of the domain.Thisconclusion seems to be intuitively clear because it is based on a limited information given by a one-particlepartition function;nevertheless,its formal theoretical motivation is of some interest.