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Alloy gene Gibbs energy partition function and equilibrium holographic network phase diagrams of AuCu_3-type sublattice system 认领 引用 被引量：5
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作者 谢佑卿 李小波 +2 位作者 刘心笔 聂耀庄 彭红建 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2014年第11期3585-3610,共26页
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
关键词 AuCu3 compound AuCu3-type sublattice system alloy gene Gibbs energy partition function equilibrium holographic network phase diagram systematic metal materials science
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Alloy gene Gibbs energy partition function and equilibrium holographic network phase diagrams of Au_3Cu-type sublattice system 认领 引用 被引量：4
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作者 谢佑卿 聂耀庄 +2 位作者 李小波 彭红建 刘心笔 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2015年第1期211-240,共30页
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
关键词 Au3Cu compound Au3Cu-type sublattice system alloy gene Gibbs energy partition function equilibrium holographic network phase diagrams systematic metal materials science
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Calculation of Partition Function of QCD at Finite Chemical Potential 认领 引用
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作者 SUN Wei-Min ZONG Hong-Shi 《Communications in Theoretical Physics》 SCIE CAS 2008年第2期435-438,共4页
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
关键词 partition function of QCD phase transition
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Rapidly calculating the partition function of macroscopic systems 认领 引用
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作者 李菁田 宁博元 +2 位作者 龚乐诚 庄军 宁西京 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第3期236-241,共6页
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
关键词 partition function statistical physics free energy calculation
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Pseudo-Classical Partition Function of Spin One-Half Derived by Coherent State Method 认领 引用
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作者 许业军 范洪义 《Communications in Theoretical Physics》 SCIE CAS 2010年第6期1046-1048,共3页
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... 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
关键词 partition function coherent state angular velocity the IWOP technique
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Partition Functions for Diatomic Molecules in Plasmas out of Thermal Equilibrium 认领 引用 被引量：1
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作者 Graldine FAURE 《Plasma Science and Technology》 SCIE EI CAS CSCD 2012年第3期192-200,共9页
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
关键词 partition function Boltzmann distribution diatomic molecule
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Distribution of a Certain Partition Function Modulo Powers of Primes 认领 引用 被引量：1
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作者 Hei-Chi CHAN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第4期625-634,共10页
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
关键词 Distribution of partition function Ono＇s theorem Ramanujan＇s congruences
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Grassmann corner transfer-matrix renormalization group approach to one-dimensional fermionic models 认领 引用
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作者 Jian-Gang Kong Zhi-Yuan Xie 《Chinese Physics B》 SCIE EI CAS CSCD 2026年第6期478-489,共12页
The strongly correlated fermions play a vital role in modern physics.For a given fermionic Hamiltonian system,the most widely used approach to exploring the underlying physics is to study the wave function that incorp... The strongly correlated fermions play a vital role in modern physics.For a given fermionic Hamiltonian system,the most widely used approach to exploring the underlying physics is to study the wave function that incorporates Fermi–Dirac statistics,which can be obtained variationally by energy minimization or by imaginary-time evolution.In this work,we develop an accurate tensor network method for one-dimensional interacting fermionic models based on the coherentstate path-integral representation of the fermionic partition function.Employing the coherent-state representation,the partition function is effectively represented as a(1+1)-dimensional anisotropic Grassmann-valued tensor network,and the Grassmann version of the corner transfer-matrix renormalization group algorithm is developed to contract the tensor network and evaluate physical quantities.We validate our method on the one-dimensional fermionic Hubbard model with a magnetic field,where the essential features of the phase diagram in the(µ,B)plane are quantitatively captured.Our work offers a promising approach to interacting fermionic models within the framework of tensor networks. 展开更多
关键词 Grassmann tensor network fermionic path integral partition function
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Boundary Correlation Functions of the gl(1|1)Supersymmetric Vertex Model 认领 引用 被引量：1
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作者 ZHANG Chen-Jun ZHOU Jian-Hua YUE Rui-Hong 《Communications in Theoretical Physics》 SCIE CAS 2008年第7期17-22,共6页
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 mod... 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
关键词 domain wall boundary conditions partition function boundary correlation function
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Modular Design of Complex Product Based on the Triple Fusion of Function/Feature/Knowledge 认领 引用 被引量：2
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作者 李宝童 洪军 +2 位作者 李婷 邱志惠 陈玉宝 《Journal of Shanghai Jiaotong university(Science)》 EI 2010年第5期563-570,共8页
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
关键词 modular design functional feature partition comprehensive design matrix knowledge model
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A New Treatment for Some Periodic Schr?dinger Operators Ⅱ: The Wave Function 认领 引用
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作者 Wei H 《Communications in Theoretical Physics》 SCIE CAS CSCD 2018年第6期645-654,共10页
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
关键词 spectral theory periodic differential operators Seiberg-Witten duality instanton partition function
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3D holographic metasurface design by deep learning with partitioned loss function 认领 引用 被引量：1
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作者 YUNXIN GUO YI YANG +4 位作者 FAN HUANG JIANQIANG GU CHUNMEI OUYANG QUAN XU XUEQIAN ZHANG 《Photonics Research》 SCIE EI CAS CSCD 2025年第12期3383-3398,共16页
Deep learning has significantly accelerated the automation of metasurface design and reduced its dependence on empirical approaches.However,it still has not fully demonstrated its capabilities in the most challenging ... Deep learning has significantly accelerated the automation of metasurface design and reduced its dependence on empirical approaches.However,it still has not fully demonstrated its capabilities in the most challenging light field manipulation:3D holography.In this paper,we present a framework that integrates a fully connected forward prediction network with a 3D convolutional inverse design network to design terahertz 3D holographic metasurfaces. 展开更多
关键词 light field manipulation d holographyin deep learning d holographic metasurface partitioned loss function d convolutional inverse design network empirical approacheshoweverit terahertz d holographic metasurfaces forward prediction network
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High Temperature Spectrum for v3 Band of Carbon Dioxide 认领 引用 被引量：9
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作者 SONG Xiao-Shu YANG Xiang-Dong +3 位作者 GUO Yun-Dong WANG Jun CHENG Xin-Lu LING-HURong-Feng 《Communications in Theoretical Physics》 SCIE CAS 2007年第5期892-896,共5页
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
关键词 partition functions carbon dioxide line intensities high temperature
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Line intensities of the asymptotic asymmetric-top radical HO_2 at high temperatures 认领 引用 被引量：7
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作者 宋晓书 程新路 +2 位作者 杨向东 令狐荣锋 吕兵 《Chinese Physics B》 SCIE EI CAS 2008年第1期158-163,共6页
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
关键词 asymptotic asymmetric-top molecule line intensities partition functions high temperature
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Study on High-Temperature Spectra of Asymptotic Asymmetric-Top Molecule O_3 认领 引用 被引量：2
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作者 SONG Xiao-Shu GUO Yun-Dong +3 位作者 LING-HU Rong-Feng Lv Bing CHENG Xin-Lu YANG Xiang-Dong 《Communications in Theoretical Physics》 SCIE CAS 2008年第8期481-485,共5页
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
关键词 asymptotic asymmetric-top molecule line intensities partition functions high temperature spectrum
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Study on high-temperature spectra of asymptotic asymmetric-top radical SiO_2 认领 引用 被引量：2
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作者 伍冬兰 曾学锋 +1 位作者 谢安东 万慧军 《Chinese Physics B》 SCIE EI CAS 2010年第4期208-212,共5页
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
关键词 asymptotic asymmetric-top molecule line intensities partition functions high temperature spectra
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Coherent state evolution in a Raman dispersion process 认领 引用 被引量：1
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作者 杜建明 任刚 范洪义 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第9期1-4,共4页
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 w... 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
关键词 Raman dispersion process integration within an ordered products of operators three-mode coherent state partition function
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The second-order dynamic phase transition and Lee-Yang zeros in Eggers urn model 认领 引用 被引量：1
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作者 刘小贤 童培庆 《Chinese Physics B》 SCIE EI CAS 2008年第11期3930-3935,共6页
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
关键词 urn model non-equilibrium system Lee-Yang theory partition function
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Forced motion of an elastic filament through a narrow tube 认领 引用 被引量：1
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作者 L.B.Freund 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2015年第6期789-790,共2页
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
关键词 Statistical mechanics. Biofilament. Reptation Partition function
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Comparative Effect of an Addition of a Surface Term to Woods-Saxon Potential on Thermodynamics of a Nucleon 认领 引用
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作者 B.C.Lütfüoglu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2018年第1期23-27,共5页
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
关键词 Woods-Saxon potential generalized symmetric Woods-Saxon potential bound states analytical solutions partition function thermodynamic functions
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