Partition Functions for Diatomic Molecules in Plasmas out of Thermal Equilibrium

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.

Rapidly calculating the partition function of macroscopic systems

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.

Using “Particle Density” of “Graviton Gas”, to Obtain Value of Cosmological Constant

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.

Line intensities of the asymptotic asymmetric-top radical HO_2 at high temperatures

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.

Study on high-temperature spectra of asymptotic asymmetric-top radical SiO_2

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.

Forced motion of an elastic filament through a narrow tube

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.

The second-order dynamic phase transition and Lee-Yang zeros in Eggers urn model

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.

分子阻障内旋转配分函数的二点pade’逼近

一、分子阻障内旋转配分函数的计算在理论化学中一直为人们所研究,早在五十年代Pitzer就用数值方法进行了计算,但求得这一配分函数的近似解析表示式仍有重要意义,在文献中作者曾用Wigner-Kirkwood微扰展开法求得阻障内旋转配分函数的近似解析表示式,根据此式所作的数值计算结果表明:在温度较高,内旋转动惯量较大时和Pitzer的数值计算结果符合得甚好,但随着温度的降低偏离也就增大,计算Wigner-Kirkwood展开式的的高次项固然可以改善所得之配分函数,但此时计算烦杂,困难较大,本文则采用二点Pade’逼近法将Wigner-Kirkwood微扰展开式（包括一级量子改正项）作为高温展开式,并选用配分函数Q=Σe-tEi的前三项作为其低温展开式,然后用二点Pade’逼近进行内插,求得阻障内旋转配分函数的[5/5]Pade’逼近式,它在整个温度范围内均能给出良好的数值结果。

Coherent state evolution in a Raman dispersion process

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]

Distribution of a Certain Partition Function Modulo Powers of Primes

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）.

A HIGH SPEED ADAPTIVE FRACTAL IMAGE CODING ALGORITHM USING FLEXIBLE CLASSIFICATION TECHNIQUE

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.

Thermodynamic Parameters of Central Spin Coupled to an Antiferromagnetic Bath: Path Integral Formalism

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 n when β → 0.

Brownian Motion in an External Field Revisited

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.

Modular Design of Complex Product Based on the Triple Fusion of Function/Feature/Knowledge

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.

Short-time Asymptotics of the Heat Kernel on Bounded Domain with Piecewise Smooth Boundary Conditions and Its Applications to an Ideal Gas

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.