Taking Au3Cu-type sublattice system as an example, three discoveries have been presented. First, the fourth barrier to hinder the progress of metal materials science is that today’s researchers do not understand that...Taking Au3Cu-type sublattice system as an example, three discoveries have been presented. First, the fourth barrier to hinder the progress of metal materials science is that today’s researchers do not understand that the Gibbs energy function of an alloy phase should be derived from Gibbs energy partition function constructed of alloy gene sequence and their Gibbs energy sequence. Second, the six rules for establishing alloy gene Gibbs energy partition function have been discovered, and it has been specially proved that the probabilities of structure units occupied at the Gibbs energy levels in the degeneracy factor for calculating configuration entropy should be degenerated as ones of component atoms occupied at the lattice points. Third, the main characteristics unexpected by today’s researchers are as follows. There exists a single-phase boundary curve without two-phase region coexisting by the ordered and disordered phases. The composition and temperature of the top point on the phase-boundary curve are far away from those of the critical point of the Au3Cu compound; At 0 K, the composition of the lowest point on the composition-dependent Gibbs energy curve is notably deviated from that of the Au3Cu compounds. The theoretical limit composition range of long range ordered Au3Cu-type alloys is determined by the first jumping order degree.展开更多
Taking AuCu3-type sublattice system as an example, three discoveries have been presented: First, the third barrier hindering the progress in metal materials science is that researchers have got used to recognizing exp...Taking AuCu3-type sublattice system as an example, three discoveries have been presented: First, the third barrier hindering the progress in metal materials science is that researchers have got used to recognizing experimental phenomena of alloy phase transitions during extremely slow variation in temperature by equilibrium thinking mode and then taking erroneous knowledge of experimental phenomena as selected information for establishing Gibbs energy function and so-called equilibrium phase diagram. Second, the equilibrium holographic network phase diagrams of AuCu3-type sublattice system may be used to describe systematic correlativity of the composition?temperature-dependent alloy gene arranging structures and complete thermodynamic properties, and to be a standard for studying experimental subequilibrium order-disorder transition. Third, the equilibrium transition of each alloy is a homogeneous single-phase rather than a heterogeneous two-phase, and there exists a single-phase boundary curve without two-phase region of the ordered and disordered phases; the composition and temperature of the top point on the phase-boundary curve are far away from the ones of the critical point of the AuCu3 compound.展开更多
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
Using the bosonic coherent state representation and the Schwinger bosonic operator realization of angular momentum we find the formula for the quantum Hamiltonian H =iaiUijUjl a1 for SU（2） rotation U, in this way w...Using the bosonic coherent state representation and the Schwinger bosonic operator realization of angular momentum we find the formula for the quantum Hamiltonian H =iaiUijUjl a1 for SU（2） rotation U, in this way we further specify the angular velocity w, iUU = （1/2）σ·ω, where σ is the Pauli matrix. Though the spin as a quantum observable has no classical correspondence, we may still mimic it as a rigid body rotation characterized by 3 Euler angles, and calculate its Pseudo-classical rotational partition function of spin one-half.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 equilibrium statistical field theory,the partition function has fundamental importance.In this paper we propose a direct and general method for calculating the partition function and equation of state of QCD at fin...In equilibrium statistical field theory,the partition function has fundamental importance.In this paper we propose a direct and general method for calculating the partition function and equation of state of QCD at finite chemical potential.It is found that the partition function is totally determined by the dressed quark propagator at finite chemical potential up to a multiplicative constant.From this a criterion for the phase transition between the Nambu and the Wigner phases is obtained.This general method is applied to two specific cases:the free quark theory and QCD with a model dressed quark propagator having confinement features.In the first case,the standard Fermi distribution at T=0 is reproduced.In the second case,we apply the conclusion in previous works to obtain the dressed quark propagator at finite chemical potential and find the unphysical result that the baryon number density vanishes for all values of chemical potential.The reason for this result is discussed.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
Following the approach of our previous paper we continue to study the asymptotic solution of periodic Schrodinger operators. Using the eigenvalues obtained earlier the corresponding asymptotic wave functions are deriv...Following the approach of our previous paper we continue to study the asymptotic solution of periodic Schrodinger operators. Using the eigenvalues obtained earlier the corresponding asymptotic wave functions are derived. This gives further evidence in favor of the monodromy relations for the Floquet exponent proposed in the previous paper. In particular, the large energy asymptotic wave functions are related to the instanton partition function of N = 2 supersymmetric gauge theory with surface operator. A relevant number theoretic dessert is appended.展开更多
The gl（1/1） supersymmetric vertex model with domain wall boundary conditions （DWBC） on an N × N square lattice is considered. We derive the reduction formulae for the one-point boundary correlation functions ...The gl（1/1） supersymmetric vertex model with domain wall boundary conditions （DWBC） on an N × N square lattice is considered. We derive the reduction formulae for the one-point boundary correlation functions of the model. The determinant representation for the boundary correlation functions is also obtained.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 total internal partition sums （TIPS） are calculated at the temperature up to 6000 K for 12 C16 02. Using the calculated partition functions, we produce the line intensities of v3 band of 12C1602 at several high ...The total internal partition sums （TIPS） are calculated at the temperature up to 6000 K for 12 C16 02. Using the calculated partition functions, we produce the line intensities of v3 band of 12C1602 at several high temperatures. The results show that the calculated line intensities are in very good agreement with those of HITRAN database at the temperature up to 3000 K, which provides a strong support for the calculations of TIPS and line intensities at high temperature. Then the calculation is extended to further high temperature, and the simulated spectra of u3 band of 12C1602 at 5000 and 6000 K are reported.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
The line intensities of 001-000 transition of the asymptotic asymmetric-top Oa molecule at several temperatures are calculated by directly calculating the partition functions and regarding the rotationless transition ...The line intensities of 001-000 transition of the asymptotic asymmetric-top Oa molecule at several temperatures are calculated by directly calculating the partition functions and regarding the rotationless transition dipole moment squared as a constant. The calculated values of the total internM partition sums （TIPS） are consistent with the data of HITRAN database with -0.61% at 296 K. The calculated line intensity data at 500 K and 3000 K are also in excellent agreement with the data in HITRAN database with less than 0.659% and 5.458% at 500 K and 3000 K, which provide a strong support for the calculations of partition function and fine intensity at high temperature. Then we extend the calculation to higher temperatures. The line intensities and simulated spectra of v3 band of the asymptotic asymmetric-top O3 molecule at 4000 and 5000 K are reported. The results are of significance for the studying of the molecular high-temperature spectrum including experimental measurements and theoretical calculations.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
In this study, we reveal the difference between Woods-Saxon(WS) and Generalized Symmetric WoodsSaxon(GSWS) potentials in order to describe the physical properties of a nucleon, by means of solving Schr¨odinger eq...In this study, we reveal the difference between Woods-Saxon(WS) and Generalized Symmetric WoodsSaxon(GSWS) potentials in order to describe the physical properties of a nucleon, by means of solving Schr¨odinger equation for the two potentials. The additional term squeezes the WS potential well, which leads an upward shift in the spectrum, resulting in a more realistic picture. The resulting GSWS potential does not merely accommodate extra quasi bound states, but also has modified bound state spectrum. As an application, we apply the formalism to a real problem,an α particle confined in Bohrium-270 nucleus. The thermodynamic functions Helmholtz energy, entropy, internal energy,specific heat of the system are calculated and compared for both wells. The internal energy and the specific heat capacity increase as a result of upward shift in the spectrum. The shift of the Helmholtz free energy is a direct consequence of the shift of the spectrum. The entropy decreases because of a decrement in the number of available states.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
The path-integral quantization of thermal scalar, vector, and spinor fields is performed newly in the coherent-state representation. In doing this, we choose the thermal electrodynamics and psi(4) theory as,examples. ...The path-integral quantization of thermal scalar, vector, and spinor fields is performed newly in the coherent-state representation. In doing this, we choose the thermal electrodynamics and psi(4) theory as,examples. By this quantization, correct expressions of the partition functions and the generating functionals for the quantum thermal electrodynamics and psi(4) theory are obtained in the coherent-state representation. These expressions allow us to perform analytical calculations of the partition functions and generating functionals and therefore are useful in practical applications. Especially, the perturbative expansions of the generating functionals are derived specifically by virtue of the stationary-phase method. The generating functionals formulated in the position space are re-derived from the ones given in the coherent-state representation.展开更多
The imaginary time path integral formalism offers a powerful numerical tool for simulating thermodynamic properties of realistic systems.We show that,when second-order and fourth-order decompositions are employed,they...The imaginary time path integral formalism offers a powerful numerical tool for simulating thermodynamic properties of realistic systems.We show that,when second-order and fourth-order decompositions are employed,they share a remarkable unified analytic form for the partition function of the harmonic oscillator.We are then able to obtain the expression of the thermodynamic property and the leading error terms as well.In order to obtain reasonably optimal values of the free parameters in the generalized symmetric fourth-order decomposition scheme,we eliminate the leading error terms to achieve the accuracy of desired order for the thermodynamic property of the harmonic system.Such a strategy leads to an efficient fourth-order decomposition that produces thirdorder accurate thermodynamic properties for general systems.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
基金Project(51071181)supported by the National Natural Science Foundation of ChinaProject(2013FJ4043)supported by the Natural Science Foundation of Hunan Province,China
文摘Taking Au3Cu-type sublattice system as an example, three discoveries have been presented. First, the fourth barrier to hinder the progress of metal materials science is that today’s researchers do not understand that the Gibbs energy function of an alloy phase should be derived from Gibbs energy partition function constructed of alloy gene sequence and their Gibbs energy sequence. Second, the six rules for establishing alloy gene Gibbs energy partition function have been discovered, and it has been specially proved that the probabilities of structure units occupied at the Gibbs energy levels in the degeneracy factor for calculating configuration entropy should be degenerated as ones of component atoms occupied at the lattice points. Third, the main characteristics unexpected by today’s researchers are as follows. There exists a single-phase boundary curve without two-phase region coexisting by the ordered and disordered phases. The composition and temperature of the top point on the phase-boundary curve are far away from those of the critical point of the Au3Cu compound; At 0 K, the composition of the lowest point on the composition-dependent Gibbs energy curve is notably deviated from that of the Au3Cu compounds. The theoretical limit composition range of long range ordered Au3Cu-type alloys is determined by the first jumping order degree.
基金Project(51071181)supported by the National Natural Science Foundation of ChinaProject(2013FJ4043)supported by the Natural Science Foundation of Hunan Province,China
文摘Taking AuCu3-type sublattice system as an example, three discoveries have been presented: First, the third barrier hindering the progress in metal materials science is that researchers have got used to recognizing experimental phenomena of alloy phase transitions during extremely slow variation in temperature by equilibrium thinking mode and then taking erroneous knowledge of experimental phenomena as selected information for establishing Gibbs energy function and so-called equilibrium phase diagram. Second, the equilibrium holographic network phase diagrams of AuCu3-type sublattice system may be used to describe systematic correlativity of the composition?temperature-dependent alloy gene arranging structures and complete thermodynamic properties, and to be a standard for studying experimental subequilibrium order-disorder transition. Third, the equilibrium transition of each alloy is a homogeneous single-phase rather than a heterogeneous two-phase, and there exists a single-phase boundary curve without two-phase region of the ordered and disordered phases; the composition and temperature of the top point on the phase-boundary curve are far away from the ones of the critical point of the AuCu3 compound.
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Supported by National Natural Science Foundation of China under Grant Nos.10874174 and 90203002
文摘Using the bosonic coherent state representation and the Schwinger bosonic operator realization of angular momentum we find the formula for the quantum Hamiltonian H =iaiUijUjl a1 for SU（2） rotation U, in this way we further specify the angular velocity w, iUU = （1/2）σ·ω, where σ is the Pauli matrix. Though the spin as a quantum observable has no classical correspondence, we may still mimic it as a rigid body rotation characterized by 3 Euler angles, and calculate its Pseudo-classical rotational partition function of spin one-half.
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.
基金National Natural Science Foundation of China under Grant No.10575050the Research Fund for the Doctoral Program of Higher Education under Grant No.20060284020
文摘In equilibrium statistical field theory,the partition function has fundamental importance.In this paper we propose a direct and general method for calculating the partition function and equation of state of QCD at finite chemical potential.It is found that the partition function is totally determined by the dressed quark propagator at finite chemical potential up to a multiplicative constant.From this a criterion for the phase transition between the Nambu and the Wigner phases is obtained.This general method is applied to two specific cases:the free quark theory and QCD with a model dressed quark propagator having confinement features.In the first case,the standard Fermi distribution at T=0 is reproduced.In the second case,we apply the conclusion in previous works to obtain the dressed quark propagator at finite chemical potential and find the unphysical result that the baryon number density vanishes for all values of chemical potential.The reason for this result is discussed.
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）.
基金supported by the FAPESP No.2011/21812-8,through IFT-UNESP
文摘Following the approach of our previous paper we continue to study the asymptotic solution of periodic Schrodinger operators. Using the eigenvalues obtained earlier the corresponding asymptotic wave functions are derived. This gives further evidence in favor of the monodromy relations for the Floquet exponent proposed in the previous paper. In particular, the large energy asymptotic wave functions are related to the instanton partition function of N = 2 supersymmetric gauge theory with surface operator. A relevant number theoretic dessert is appended.
基金National Natural Science Foundation of China under Grant No.90403019
文摘The gl（1/1） supersymmetric vertex model with domain wall boundary conditions （DWBC） on an N × N square lattice is considered. We derive the reduction formulae for the one-point boundary correlation functions of the model. The determinant representation for the boundary correlation functions is also obtained.
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.
基金The project supported by National Natural Science Foundation of China under Grant No. 10676025, and the Research Fund for the Doctoral Program of High Education of China under Grant No. 20050610010
文摘The total internal partition sums （TIPS） are calculated at the temperature up to 6000 K for 12 C16 02. Using the calculated partition functions, we produce the line intensities of v3 band of 12C1602 at several high temperatures. The results show that the calculated line intensities are in very good agreement with those of HITRAN database at the temperature up to 3000 K, which provides a strong support for the calculations of TIPS and line intensities at high temperature. Then the calculation is extended to further high temperature, and the simulated spectra of u3 band of 12C1602 at 5000 and 6000 K are reported.
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supported by National Natural Science Foundation of China under Grant No.10574096the Major Program for Basic Research of National Security of China under Grant No.5134202-04the Natural Science Foundation of the Bureau of Education of Guizhou Province under Grant No.2006204
文摘The line intensities of 001-000 transition of the asymptotic asymmetric-top Oa molecule at several temperatures are calculated by directly calculating the partition functions and regarding the rotationless transition dipole moment squared as a constant. The calculated values of the total internM partition sums （TIPS） are consistent with the data of HITRAN database with -0.61% at 296 K. The calculated line intensity data at 500 K and 3000 K are also in excellent agreement with the data in HITRAN database with less than 0.659% and 5.458% at 500 K and 3000 K, which provide a strong support for the calculations of partition function and fine intensity at high temperature. Then we extend the calculation to higher temperatures. The line intensities and simulated spectra of v3 band of the asymptotic asymmetric-top O3 molecule at 4000 and 5000 K are reported. The results are of significance for the studying of the molecular high-temperature spectrum including experimental measurements and theoretical calculations.
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Supported by the Turkish Science and Research Council(TBTAK)Akdeniz University
文摘In this study, we reveal the difference between Woods-Saxon(WS) and Generalized Symmetric WoodsSaxon(GSWS) potentials in order to describe the physical properties of a nucleon, by means of solving Schr¨odinger equation for the two potentials. The additional term squeezes the WS potential well, which leads an upward shift in the spectrum, resulting in a more realistic picture. The resulting GSWS potential does not merely accommodate extra quasi bound states, but also has modified bound state spectrum. As an application, we apply the formalism to a real problem,an α particle confined in Bohrium-270 nucleus. The thermodynamic functions Helmholtz energy, entropy, internal energy,specific heat of the system are calculated and compared for both wells. The internal energy and the specific heat capacity increase as a result of upward shift in the spectrum. The shift of the Helmholtz free energy is a direct consequence of the shift of the spectrum. The entropy decreases because of a decrement in the number of available states.
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.
文摘The path-integral quantization of thermal scalar, vector, and spinor fields is performed newly in the coherent-state representation. In doing this, we choose the thermal electrodynamics and psi(4) theory as,examples. By this quantization, correct expressions of the partition functions and the generating functionals for the quantum thermal electrodynamics and psi(4) theory are obtained in the coherent-state representation. These expressions allow us to perform analytical calculations of the partition functions and generating functionals and therefore are useful in practical applications. Especially, the perturbative expansions of the generating functionals are derived specifically by virtue of the stationary-phase method. The generating functionals formulated in the position space are re-derived from the ones given in the coherent-state representation.
基金supported by the National Natural Science Foundation of China(No.21961142017,No.22073009 and No.21421003)the Ministry of Science and Technology of China(No.2017YFA0204901)。
文摘The imaginary time path integral formalism offers a powerful numerical tool for simulating thermodynamic properties of realistic systems.We show that,when second-order and fourth-order decompositions are employed,they share a remarkable unified analytic form for the partition function of the harmonic oscillator.We are then able to obtain the expression of the thermodynamic property and the leading error terms as well.In order to obtain reasonably optimal values of the free parameters in the generalized symmetric fourth-order decomposition scheme,we eliminate the leading error terms to achieve the accuracy of desired order for the thermodynamic property of the harmonic system.Such a strategy leads to an efficient fourth-order decomposition that produces thirdorder accurate thermodynamic properties for general systems.
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]
