Use of anisotropic atom-atom potential functions in lattice-dynamical calculations for solid nitrogen

For solid nitrogen, a set of ‘anisotropic’ atom-atom semi-empirical potential functions, which are easily derived from the usual ‘6-exp’ or ‘12-6’, eliminates the difficulties encountered in demonstrating the stability of the γ-phase in lattice-dynamical calculations according to the Born-von Karman procedure.

Negative eigenvalues of the dynamical matrices in certain regions of the Brillouin zone disappear, the agreement with experimental data improves and the α-γ transition is foreseen.     

Temporal autocorrelation functions of solar speckle pattern

A study of day-time temporal autocorrelation functions of speckles was performed on the solar granulation with the McMath telescope of the Kitt Peak National Observatory. In the space of only a few minutes, rapid variations of time constants are observed. For some observations, a single and high value T of time-constant is obtained: average = 170 ms, standard deviation = 80 ms. The temporal autocorrelation functions are consistent with theoretical curves obtained from a single layer atmospheric turbulence model. For other observations, a super-imposed short time-constant τ, showing little variations around 5.5 ms (standard deviation 1 ms), is also present. It is shown that T depends on the diameter of the telescope D and that the value τ of the short time scale, when it occurs, is correlated with the Fried parameter r₀.     

On the validity and properties of the atom-atom potential as a function of intermolecular separation,configuration, and partial wave order

The intermolecular partial wave expansion of the atom-atom potential U is reviewed briefly and developed, by using results due to Sack, so that the radial components of the expansion can be evaluated to arbitrary accuracy for all relevant partial wave orders and values of the intermolecular distance r. These results are used to study the convergence of the partial wave expansion of U as a function of partial wave order, r, intermolecular orientation, and the anisotropy of the interacting molecules. In marked contrast to previous work it is found that many of the higher order partial wave components of U are important relative to the isotropic term even for the interaction of relatively spherical molecules and that the results obtained from a truncated partial wave expansion depend significantly upon the method of summation due to the generally poor convergence of the expansion. The validity of the atom-atom potential as a representation of the correct attractive intermolecular potential is also discussed in some detail. There are basic problems associated with the representations furnished by both the isotropic and the anisotropic parts of the atom-atom potential at intermediate and large r. The different convergence properties of the r ^-1 expansions of the partial wave expansions of U and of the correct potential for these values of r is illustrated by using model interactions. While it appears that it may be possible to obtain a qualitatively reasonable representation of the attractive part of an intermolecular potential over a useful range of r from atom-atom results, this apparently cannot be achieved for wider ranges of r or for the purely anisotropic part of the potential.     

Inverse moment analysis of time dependent autocorrelation functions

We apply inverse moment techniques to analyse certain time dependent autocorrelation functions. The experimentally measured values are interpreted as moments of a probability distributionf(x) which is calculated numerically. For this purpose we use Chebychev's algorithm. By means of the inverse algorithm we can reproduce the original data within numerical precision. The ill-conditioning of the inverse moment problem is circumvented by making an ansatz for the unknown higher order moments. We discuss in particular exponentially and algebraically decaying correlation functions.     

Structures and autocorrelation functions of liquid Al and Mg modelled via Lennard-Jones potential from molecular dynamics simulation

The structures and autocorrelation functions of Al and Mg in the liquid state are investigated through the pair distribution functiong(r), the diffusion coefficients as well as the shear viscosity via the Green-Kubo and Einstein relations. From the structure and the Enskog relation we determined the frequency of collisions of atoms in the first shell ofg(r) in the systems. We also discovered that the packing fraction of Lennard-Jones liquids should be approximately half the reduced density value. This approximation is accurate to within 99%. The temperature dependence of the pair distribution function and the atomic mean square displacement are investigated by performing simulations at various experimental temperatures and corresponding densities. The structures of the systems are affected by temperature via movements of atoms in the first minimum ofg(r). The Lennard-Jones model shows that density dependence of the shear viscosity is in agreement with what is expected of simple liquids in the range of investigated temperatures and densities. In the gas limit, the Stoke-Einstein relationDη =K _BT /2πσ is grossly overestimated by Lennard-Jones model. This could not be attributed to deficiencies in the model, as other investigators using first principle method could not obtain the gas limit of the Stoke-Einstein relation.     

On some positivity properties of the interquark potential in QCD

We argue that the Fourier transform of the exponential e(-betaV(R)) of the static interquark potential in QCD is positive. It has been shown by Lieb some time ago that this property allows in the same limit of static, spin independent potential, to prove a certain mass relation between baryons with different quark flavors.     

The effects of random noise on optically determined autocorrelation and chord functions

Global chord functions are good candidates for use in an autonomous shape recognition system because not only do they possess the valuable attributes of being practically invariant to scaling, translation and rotation but it is possible to determine them very rapidly, by the autocorrelation method, in a hybrid optical-digital system. A further aspect must however be examined before implementation in an operational system is considered; the robustness of the complete processing to random noise. In this paper the effects of additive uncorrelated noise in the input image on the autocorrelation and the resulting chord functions are addressed. It is shown that the whole process is quite robust. Most of the chord function structure is retained for signal to noise ratios of 2:1 and some is still present at 1:1.     

N维势箱函数量子特性的可视化研究

运用量子理论推导和数值计算相结合的方法,本文首先得到了一维势箱函数的示意图及其模型.接着,全面、系统地研究了量子理论中N维势箱函数的波函数、能级和概率密度.最后,运用MATLAB软件对势箱函数的所有特性进行了仿真模拟.我们发现:N维势箱中粒子的能量是量子化的、不连续;量子数n不能为零,且n越大对应的能级越高,而质量m越大,对应的能级越低.一般条件下,一维势箱长度a越大(粒子运动范围越大),对应的能级越低;节点数为n-1,节点越多,波长越短,频率越高,能级越高.二维势箱函数波函数的峰值个数为n x 0x0E?SymboltB@0x0Fn y,且与Ψ=0平面的交线数也为n x 0x0E?SymboltB@0x0Fn y;概率密度分布的极大值个数也为n x 0x0E?SymboltB@0x0Fn y.对于简并度,一般情况下,二维势箱模型下的粒子的简并度是不确定的;但对于二维正方势箱函数模型,其箱内微观粒子的能级简并度分为特殊和一般两种情况.三维势箱函数的简并度为n x+n y+n z.最后,首次借助MATLAB软件的色彩实现了四维表现,得到了三维势箱函数的四维空间切片图.这种可视化的结果与理论结果完全一致,这对于抽象性概念的理解具有重要意义.     

The effect of steepness of soft-core square-well potential model on some fluid properties

The effect of repulsive steepness of the soft-core square well (SCSW) potential model on the second virial coefficient, critical behaviour (two- phase region and the position of critical point), and coordination number are investigated. The soft-core thermodynamic perturbation theory (TPT) presented by Weeks-Chandler-Anderson (WCA) recently developed by Ben-Amotz and Stell (BAS) has been used for the reference system, and the Barker-Henderson TPT for the perturbed system. The Barker-Henderson macroscopic compressibility approximation has been used for all order perturbation terms in which the second-order one is improved by assuming that the molecules in every two neighbouring shells are correlated upon the original assumption. By using the hard-sphere isothermal compressibility consistency for the radial distribution function (RDF), an analytical closed expression has been derived for the Helmholtz free energy function contained effective hard-sphere diameter. The accuracy of the model has been examined for the hard-core system, and an appropriate range found for the attractive width of the potential well (R), then the effect of steepness parameter on the critical quantities, coordination number, and the inversion temperature of the second virial coefficient, has been investigated qualitatively. The predicted results are in good agreement with the computer simulation data for the critical constants, and coordination number at the limit of the hard-core square-well potential model at least qualitatively, and for the attractive range 1.55 ≤ R ≤ 1.7, quantitatively. It was found that the steepness of the potential model has a marginal effect on the critical behaviour, and also every thermodynamic quantity at low and medium temperatures for which the molecular penetration is negligible, but since the penetration at high temperatures is significant, the role of the steepness of potential on the inversion temperature of the second virial coefficient and coordination number is highlighted.     

Analytical potential energy functions for the ground and some excited states of N2

The analytical potential energy functions have been calculated for the ground state X¹Σ⁺_g and four excited electronic states a¹Π_g, A³Σ⁺_u, B′³Σ^?_u and B³Π_g of N₂ molecule using the algebraic and energy-consistent methods (AM-ECM). Based on our previously published full AM vibrational energies and spectroscopic constants, the low-lying force constants f_n, the expansion coefficients a_n and the variational parameters λ in the AM–ECM potentials are determined for these states. The computed AM–ECM potential energy curve of each state is in excellent agreement with the experimental data and better than other analytical potentials.     

Long-time tails of the velocity autocorrelation functions for the triangular periodic Lorentz gas

We present numrical results on the velocity autocorrelation function (VACF)C(t)=<ν(t)·ν(0)> for the periodic Lorentz gas on a two-dimensional triangular lattice as a function of the radiusR of the hard disk scatterers on the lattice. Our results for the unbounded horizon case confirm 1/t decay of the VACF for long times (out to 100 times the mean free time between collisions) and provide strong support for the conjecture by Friedman and Martin that the 1/t decay is due to long free paths along which a moving particle does not scatter up to timet. Even after new sets of long free paths become available forR<1/4, we continue to find good agreement between numerical results and an analytically estimated 1/t decay. For the bounded horizon case , our numerical VACFs decay exponentially, although it is difficult to discriminate among pure exponential decay, exponential decay with prefactor, and stretched exponential decay.     

Refractive indices and related properties of some potential mixed crystals

The high frequency refractive indices of some binary, ternary and quaternary mixed crystals have been evaluated from the knowledge of plasmon energy and the lowest gap energy of the crystals for their applications in heterojunctionled and solar cells. The Fermi energy screening factor correction has been applied to effect accuracy in prediction. The model has been used to study the temperature and pressure dependence of refractive index. The calculated value agrees with experiment (within a few percent) justifying the validity of the model.     

Free energy and some sample path properties of a random walk with random potential

We study the asymptotic behavior of the free energy for a model (defined by Sinai) of one-dimensional random walk with random potential. In particular, we obtain a central limit theorem and a strong law of large numbers for this free energy. We use some results on the free energy to study some sample path properties of this random walk which are related respectively to its recurrence and localization. Some exponents describing the recurrence and localization are found.     

Quarkonium spectral functions with complex potential

We study quarkonium spectral functions at high temperatures using a potential model with complex potential. The real part of the potential is constrained by the lattice QCD data on static quark anti-quark correlation functions, while the imaginary part of the potential is taken from perturbative calculations. We find that the imaginary part of the potential has significant effect on quarkonium spectral functions, in particular, it leads to the dissolution of the 1S charmonium and excited bottomonium states at temperatures about 250 MeV and melting of the ground state bottomonium at temperatures slightly above 450 MeV.     

Suppression of dephasing due to a trapping potential and atom-atom interactions in a trapped-condensate interferometer

We propose and demonstrate a novel trapped-condensate interferometer using optical Bragg diffractions in a harmonic magnetic potential, which can realize a long coherence time with low dephasing. Dephasing of wave packets due to the magnetic potential is canceled by setting the interrogation time equal to the oscillation period of the harmonic potential. The harmonic potential also helps to suppress dephasing due to condensate atom-atom interactions. An interference signal with a fringe contrast of 30% is observed at an interrogation time of 58 ms. For a longer interrogation time about 100 ms, the spatial coherence of the condensate is still maintained with low dephasing, although the interference fringe is washed out by external vibrational noise.     

Wannier functions with a simple model potential

Wannier functions for the two lowest bands are calculated for a one-dimensional two Fourier component potential. These functions show the general behavior predicted by Kohn.     

含苯乙烯桥侧链三枝分子的二阶非线性光学性质

采用密度泛函理论B3LYP/6-311+g(d,p)方法对含苯乙烯桥侧链均三嗪类衍生物的8个分子(Y1-Y8)进行几何构型优化,对其最优构型采用TD-DFT(TDB3LYP/6-311+g(d,p)),计算电子吸收光谱,用有限场FF方法及自编程序计算二阶非线性光学（NLO）性质。结果表明,8个分子的μ（或0）值为104数量级个原子单位(10-29 esu),显示出良好的二阶非线性光学性能。在其三支链的末端引入强供电子基团（如-N(CH3)2或-N(CH2CH3)2）比引入弱供电子基团及吸电子基团,更有利于改善体系的二阶非线性光学性质,从而可获得良好的非线性光学材料。     

Ringing non-Gaussianity from inflation with a step in the second derivative of the potential

Pramana - This paper deals with the nonlinear generalised advection–diffusion–reaction (GADR) equation subject to some initial and boundary conditions (BCs). Some exact finite...     

The symmetry properties of correlated wave functions

The resolution of a correlated wave function Ψ about an orbital approximation Ψ₀ for any state of an N-electron system is discussed with particular reference to the symmetry conditions which the n-electron correlation functions of X_n must satisfy in order that Ψ have the correct symmetry properties for the state in question. It is shown how for a closed-shell state the symmetry properties of the correlation functions are determined by those of the spin-orbital products which they replace in Ψ₀, and how this is not in general true for an open-shell state. It is shown how the symmetry properties of an n-electron correlation function can always be uniquely defined by those of the (N-n)-electron spin-orbital product to which it is coupled in X_n , and the general symmetry conditions which the correlation functions must satisfy are derived.