在激波波面中氧分子的非平衡离解

对强激波作用下双原子分子振动与离解耦合的非平衡离解过程进行了理论计算.本工作的特点是将计算起点建立在分子基本参数上,采用主方程理论处理振动与离解的耦合,振动跃迁几率用SSH理论计算,在离解限附近考虑多量子数跃迁并计及原子复合的影响.对O2-Ar体系,计算给出了在正激波后O2分子振动能级分布、振动弛豫时间、离解孕育时间、离解产物浓度、离解速率系数等物理量随时间的演化.计算结果分别与Camac和Wray的实验相符.计算显示,在激波作用的后期,有准稳态的振动能级布居分布.计算结果显示,Park模型低估了非平衡离解速率系数,Hansen模型则高估了非平衡离解速率系数.

Forward-looking Pairwise Stability in Networks with Externalities

We consider cooperation situations where players have network relations. Networks evolve according to a stationary transition probability matrix and at each moment in time players receive payoffs from a stationary allocation rule. Players discount the future by a common factor. The pair formed by an allocation rule and a transition probability matrix is called a forward-looking network formation scheme if, first, the probability that a link is created is positive if the discounted, expected gains to its two participants are positive, and if, second, the probability that a link is eliminated is positive if the discounted, expected gains to at least one of its two participants are positive. The main result is the existence, for all discount factors and all value functions, of a forward-looking network formation scheme. Furthermore, we can always nd a forward-looking network formation scheme such that (i) the allocation rule is component balanced and (ii) the transition probabilities increase in the di erence in payo s for the corresponding players responsible for the transition. We use this dynamic solution concept to explore the tension between e ciency and stability.

Stationary absolute distributions for chains of infinite order

Let {Ƶ_n}^∞_{n = -∞} be a stochastic process with state space S₁ = {0, 1, …, D – 1}. Such a process is called a chain of infinite order. The transitions of the chain are described by the functions

Q_i(i⁽⁰⁾) = Ƥ(Ƶ_n = i | Ƶ_{n - 1} = i ⁽⁰⁾₁, Ƶ_{n - 2} = i ⁽⁰⁾₂, …) (i ɛ S₁), where i⁽⁰⁾ = (i⁽⁰⁾₁, i⁽⁰⁾₂, …) ranges over infinite sequences from S₁. If i⁽ⁿ⁾ = (i⁽ⁿ⁾₁, i⁽ⁿ⁾₂, …) for n = 1, 2,…, then i⁽ⁿ⁾ → i⁽⁰⁾ means that for each k, i⁽ⁿ⁾_k = i⁽⁰⁾_k for all n sufficiently large.

Given functions Q_i(i⁽⁰⁾) such that

(i) 0 ≤ Q_i(i⁽⁰) ≤ ξ ˂ 1

(ii)D – 1/Ʃ/i = 0 Q_i(i⁽⁰⁾) Ξ 1

(iii) Q_i(i⁽ⁿ⁾) → Q_i(i⁽⁰⁾) whenever i⁽ⁿ⁾ → i⁽⁰⁾,

we prove the existence of a stationary chain of infinite order {Ƶ_n} whose transitions are given by

Ƥ (Ƶ_n = i | Ƶ_{n - 1}, Ƶ_{n - 2}, …) = Q_i(Ƶ_{n - 1}, Ƶ_{n - 2}, …)

With probability 1. The method also yields stationary chains {Ƶ_n} for which (iii) does not hold but whose transition probabilities are, in a sense, “locally Markovian.” These and similar results extend a paper by T.E. Harris [Pac. J. Math., 5 (1955), 707-724].

Included is a new proof of the existence and uniqueness of a stationary absolute distribution for an Nth order Markov chain in which all transitions are possible. This proof allows us to achieve our main results without the use of limit theorem techniques.

I. Quantum mechanics of one-dimensional two-particle models. II. A quantum mechanical treatment of inelastic collisions

Part I

Solutions of Schrödinger’s equation for system of two particles bound in various stationary one-dimensional potential wells and repelling each other with a Coulomb force are obtained by the method of finite differences. The general properties of such systems are worked out in detail for the case of two electrons in an infinite square well. For small well widths (1-10 a.u.) the energy levels lie above those of the noninteresting particle model by as much as a factor of 4, although excitation energies are only half again as great. The analytical form of the solutions is obtained and it is shown that every eigenstate is doubly degenerate due to the “pathological” nature of the one-dimensional Coulomb potential. This degeneracy is verified numerically by the finite-difference method. The properties of the square-well system are compared with those of the free-electron and hard-sphere models; perturbation and variational treatments are also carried out using the hard-sphere Hamiltonian as a zeroth-order approximation. The lowest several finite-difference eigenvalues converge from below with decreasing mesh size to energies below those of the “best” linear variational function consisting of hard-sphere eigenfunctions. The finite-difference solutions in general yield expectation values and matrix elements as accurate as those obtained using the “best” variational function.

The system of two electrons in a parabolic well is also treated by finite differences. In this system it is possible to separate the center-of-mass motion and hence to effect a considerable numerical simplification. It is shown that the pathological one-dimensional Coulomb potential gives rise to doubly degenerate eigenstates for the parabolic well in exactly the same manner as for the infinite square well.

Part II

A general method of treating inelastic collisions quantum mechanically is developed and applied to several one-dimensional models. The formalism is first developed for nonreactive “vibrational” excitations of a bound system by an incident free particle. It is then extended to treat simple exchange reactions of the form A + BC →AB + C. The method consists essentially of finding a set of linearly independent solutions of the Schrödinger equation such that each solution of the set satisfies a distinct, yet arbitrary boundary condition specified in the asymptotic region. These linearly independent solutions are then combined to form a total scattering wavefunction having the correct asymptotic form. The method of finite differences is used to determine the linearly independent functions.

The theory is applied to the impulsive collision of a free particle with a particle bound in (1) an infinite square well and (2) a parabolic well. Calculated transition probabilities agree well with previously obtained values.

Several models for the exchange reaction involving three identical particles are also treated: (1) infinite-square-well potential surface, in which all three particles interact as hard spheres and each two-particle subsystem (i.e. BC and AB) is bound by an attractive infinite-square-well potential; (2) truncated parabolic potential surface, in which the two-particle subsystems are bound by a harmonic oscillator potential which becomes infinite for interparticle separations greater than a certain value; (3) parabolic (untruncated) surface. Although there are no published values with which to compare our reaction probabilities, several independent checks on internal consistency indicate that the results are reliable.

Energy transfer in molecular collisions

Two general, numerically exact, quantum mechanical methods have been developed for the calculation of energy transfer in molecular collisions. The methods do not treat electronic transitions because of the exchange symmetry of the electrons. All interactions between the atoms in the system are written as potential energies.

The first method is a matrix generalization of the invariant imbedding procedure, ^{17, 20} adapted for multi-channel collision processes. The second method is based on a direct integration of the matrix Schrödinger equation, with a re-orthogonalization transform applied during the integration.

Both methods have been applied to a collinear collision model for two diatoms, interacting via a repulsive exponential potential. Two major studies were performed. The first was to determine the energy dependence of the transition probabilities for an H₂ on the H₂ model system. Transitions are possible between translational energy and vibrational energy, and from vibrational modes of one H₂ to the other H₂. The second study was to determine the variation of vibrational energy transfer probability with differences in natural frequency of two diatoms similar to N₂.

Comparisons were made to previous approximate analytical solutions of this same problem. For translational to vibrational energy transfer, the previous approximations were not adequate. For vibrational to vibrational energy transfer of one vibrational quantum, the approximations were quite good.

Thermodynamic and kinetic behavior of an argon plasma jet. Decomposition of nitric oxide between 1300 - 1750 degrees K in an argon plasma

In the first part of the study, an RF coupled, atmospheric pressure, laminar plasma jet of argon was investigated for thermodynamic equilibrium and some rate processes.

Improved values of transition probabilities for 17 lines of argon I were developed from known values for 7 lines. The effect of inhomogeneity of the source was pointed out.

The temperatures, T, and the electron densities, n_e , were determined spectroscopically from the population densities of the higher excited states assuming the Saha-Boltzmann relationship to be valid for these states. The axial velocities, v_z, were measured by tracing the paths of particles of boron nitride using a three-dimentional mapping technique. The above quantities varied in the following ranges: 10¹² ˂ n_e ˂ 10¹⁵ particles/cm³, 3500 ˂ T ˂ 11000 °K, and 200 ˂ v_z ˂ 1200 cm/sec.

The absence of excitation equilibrium for the lower excitation population including the ground state under certain conditions of T and n_e was established and the departure from equilibrium was examined quantitatively. The ground state was shown to be highly underpopulated for the decaying plasma.

Rates of recombination between electrons and ions were obtained by solving the steady-state equation of continuity for electrons. The observed rates were consistent with a dissociative-molecular ion mechanism with a steady-state assumption for the molecular ions.

In the second part of the study, decomposition of NO was studied in the plasma at lower temperatures. The mole fractions of NO denoted by x_NO were determined gas-chromatographically and varied between 0.0012 ˂ x_NO ˂ 0.0055. The temperatures were measured pyrometrically and varied between 1300 ˂ T ˂ 1750°K. The observed rates of decomposition were orders of magnitude greater than those obtained by the previous workers under purely thermal reaction conditions. The overall activation energy was about 9 kcal/g mol which was considerably lower than the value under thermal conditions. The effect of excess nitrogen was to reduce the rate of decomposition of NO and to increase the order of the reaction with respect to NO from 1.33 to 1.85. The observed rates were consistent with a chain mechanism in which atomic nitrogen and oxygen act as chain carriers. The increased rates of decomposition and the reduced activation energy in the presence of the plasma could be explained on the basis of the observed large amount of atomic nitrogen which was probably formed as the result of reactions between excited atoms and ions of argon and the molecular nitrogen.

970nm抽运下Tm^3／Yb^3＋共掺氧氟玻璃的频率上转换发光

稀土离子掺杂的氧氟玻璃是一种新型上转换发光材料。制备了Tm^3／Yb^3＋单掺、共掺的摩尔分数为n（SiO2）-0．30，n（PbF2）-0．50，n=（Al2O3）=0．15，n（AlF3）=（0．049-x），n（TmF3）=y，n（YbF3）=x（x=0，0．001，0．010，0．015，0．020，y=0，0．001）系统氧氟玻璃，研究了其上转换发光特性、分析了其上转换发光机理。研究发现，在970nm抽运光源激发下，Tm^3＋单掺时没有可见光上转换发射；而加入Yb^3＋后产生了强的蓝光（452n

980 nm 抽运下Yb-Tm-Ho 三掺氟磷酸盐玻璃的2 μm 荧光性质

The thermal stability, 2 μm fluorescence properties and energy transfer mechanism in Ho³⁺ doped fluorophosphate glass sensitized by Yb³⁺ and Tm³⁺ were investigated. The characteristic temperatures, absorption spectrum and fluorescence spectrum of the glass sample were measured. ΔT calculated from the characteristic temperatures shows that the thermal stability of fluorophosphate glass is better than fluoride glass. According to the absorption spectrum, several spectroscopic parameters of the glass sample, such as Judd-Ofelt parameters and spontaneous transition probability were calculated and compared with other glass hosts. The largest spontaneous transition probability for Ho³⁺:⁵ I7&rarr⁵I8 transition in fluorophosphate glass which is 78.48 s^-1 indicates that fluorophosphate glass is an appropriate base glass to achieve 2 m fluorescence. From the fluorescence spectrum of the glass sample, the extremely strong 2.0 μm fluorescence intensity is observed, which is higher than the intensity of 1.8 μm fluorescence, showing that Ho³⁺ ions sensitized by Yb³⁺ and Tm³⁺ is efficient. Meanwhile, the absorption sections and emission sections of Yb³⁺, Tm³⁺ and Ho³⁺ were calculated and the pumping scheme and energy transfer mechanism among Yb³⁺, Tm³⁺ and Ho³⁺ are discussed. The study indicates that Yb-Tm-Ho tri-doped fluorophosphate glass is a significant sensitization glass system under 980 nm excitation for 2 μm applications.

808 nm 抽运的Ho3+，Tm3+及Er3+掺杂的氟磷酸盐 玻璃的2.0 μm 光谱性质研究

2.0 μm spectroscopic properties of Er³⁺/Tm³⁺/Ho³⁺ triply-doped fluorophosphate glasses pumped by 808 nm and the energy transfer mechanisms between the three rare earth ions were investigated. J-O theory was used to calculate the parameters of Ho³⁺ in fluorophosphate glasses. Absorption and emission cross-sections and the gain coefficients were calculated. The obtained lifetime r and spontaneous transition probability Ar of Ho³⁺:⁵I7 level were 10.64 ms and 93.95 s^-1 respectively. The calculated maximum emission cross-section of 2.0 μm was 9.26×10^-21 cm². The energy transfer analysis indicated that the cross-relaxation of Tm³⁺ was important and the resonent energy transfer in Er³⁺&rarrHo³⁺, Tm³⁺&rarrHo³⁺, Er³⁺&rarrTm³⁺&rarrHo³⁺ process was the main channel. The study revealed that the Er³⁺/Tm³⁺/Ho³⁺ triply-doped fluorophosphate glass would be a potential material for 2.0 μm emission because of the efficient sensitization of Er³⁺ and Tm³⁺ to Ho³⁺.

Optical transitions and upconversion luminescence of Er3+/Yb3+-codoped halide modified tellurite glasses

Er3+-doped halide modified tellurite glasses were synthesized by conventional melting and quenching method. The Judd-Ofelt analysis was performed on the absorption spectra and the transition probabilities, excited state lifetimes, and the branching ratios were calculated and discussed. The intense infrared and visible fluorescence spectra under 980 nm excitation were obtained. Strong upconversion signal was observed at pumping power as low as 30 mW in the glasses with halide ions. The upconversion mechanisms and power dependent intensities were discussed, which showed two-photon process are involved for the green and red emissions. The decay times of the emitting states and the corresponding quantum efficiency were determined and explained. (C) 2004 American Institute of Physics.

Spectroscopic properties and thermal stability of Er3+/Yb3+-codoped fluorophosphate glasses

A comprehensive study on the thermal stability and spectroscopic properties of Er3+/Yb3+-codoped Al(PO3)(3)-based fluorophosphate glasses is reported of the 1.5μ m fibre amplifiers in this paper. From optical absorption spectra, the Judd-Ofelt parameters of Er3+ in the glasses and several important optical properties, such as the radiative transition probability, the branching ratio and the spontaneous emission probability, have been calculated by using Judd-Ofelt theory. The fluorophosphate glass exhibits broadband near-infrared emission at 1.53μ m with a full width at half-maximum over 63nm, and a large calculated stimulated-emission cross-section of 6.85 x 10(-21)cm(2).

Upconversion emission in Er3+ doped novel bismuthate glass

Novel Er3+-doped bismuth lead strontiam glass was fabricated and characterized, and the absorption spectrum and upconversion spectrum of the glass were studied. The Judd-Ofelt intensity parameters Omega(t)(t = 2, 4, 6) were found to be Omega(2) = 3.27 x 10(-20) cm(2), Omega(4) = 1.15 x 10(-20) cm(2), and Omega(6) = 0.38 x 10(-20) cm(2). The oscillator strength, the spontaneous transition probabilities, the fluorescence branching ratios, and excited state lifetimes were also measured and calculated. The upconversion emission intensity varies with the power of infrared excitation intensity. A plot of log I-up vs log I-IR yields a straight line with slope 1.86, 1.88 and 1.85, corresponding to 525, 546, and 657 nm emission bands, respectively, which indicates that a two-photon process for the red and green emission.

铒掺杂钠铝硅玻璃成分对其光谱性质的影响

研究了Na2O含量对Na2O-Al2O3-SiO2(NAS)玻璃的光谱性质的影响。利用Judd-Ofelt(J-O)理论和吸收光谱计算了Er^3+掺杂的铝硅酸盐玻璃的Ωt参数、自发辐射几率和自发辐射寿命，分析了Ωt参数与Na2O含量的关系以及与吸收截面，Er^3+离子^4I13 2能级的自发辐射几率和荧光半峰全宽(FWHM)等性质的关系。随Na2O含量的增加．J-O参数Ωt(t=2，4，6)减小，Er^3+离子1533nm的吸收截面和荧光半峰全宽．Er^3+离子^4I13 2能级的自发辐射几率也减小，而E

高浓度掺Er^3＋铌酸锂晶体的光谱参数计算

用提拉法成功地生长了6mol％的高浓度掺铒铌酸锂晶体。测量了晶体的两个非偏振方向（X和Z）以及两个偏振方向（π和δ）的吸收光谱。高浓度掺铒铌酸锂晶体的吸收系数高，有利于提高泵浦效率。根据所测的吸收光谱用Judd-Ofelt理论拟合出了Er^3＋离子的强度参数Ωλ。所得的均方差结果显示偏振拟合的误差要小于非偏振拟合。利用偏振吸收数据计算了各能级跃迁的自发辐射跃迁几率（AJJ’）、辐射寿命（τ）、荧光分支比（β）和积分发射截面（σp）等参数，对计算结果进行了讨论并与其他文献的报道结果进行了比较。

Spectroscopic properties of Nd3+:(La,Sr)(Al,Ta)O-3 crystal

A new laser crystal Nd3+:(La, Sr)(Al, Ta)O-3 (abbreviated as Nd3+:LSAT) has been grown by the conventional Czochralski method. The absorption and luminescence spectra of trivalent neodymium in Nd3+:LSAT crystal were measured at room temperature. The value of absorption and emission cross-section was calculated. The Judd-Ofelt analysis was applied to the crystal to get the phenomenological parameters (Omega(i), i = 2,4,6), the line strengths, the radiative transition rates, the branching ratios and the radiative lifetime. (C) 2006 Elsevier B.V. All rights reserved.