Dec 2008, Volume 3 Issue 4

    

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• Accurate vibrational energy spectra and dissociation energies of some diatomic electronic states

  SUN Wei-guo, LIU Xiu-ying, WANG Yu-jie, ZHAN Yan, FAN Qun-chao

  2008, 3(4): 382-413. https://doi.org/10.1007/s11467-008-0032-0

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  An algebraic method (AM) used to study the full vibrational spectra of diatomic systems, and an analytical formula used to calculate accurate molecular dissociation energies are applied to study the full vibrational spectra and molecular dissociation energies of some electronic states of homonuclear and heteronuclear diatomic molecules and diatomic ions. Studies show that the AM method and the analytical expression are reliable and economical physical methods for studying full vibrational spectra and molecular dissociation energies of diatomic electronic systems theoretically. They are particularly useful for those diatomic systems whose highlying vibrational energies may not be available.
• Calculation of the escape probabilities of Fe XVII resonance lines for the Voigt profile

  HE Jian, ZHANG Qing-guo

  2008, 3(4): 414-417. https://doi.org/10.1007/s11467-008-0035-x

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  Using the Voigt profile we obtained, we calculate the escape probabilities of Fe XVII resonance lines at 15.02, 13.28, 12.12, 11.13, 11.02 and 10.12 Å for optically thick plasma, both for slab and cylindrical geometry. The oscillator strength, the number density of the absorbing atoms in the ground state, and the optical depth in the line center are discussed in this calculation. Results show that the escape probabilities for the slab geometry are larger than that for the cylindrical geometry. This calculation is useful for the study of the Fe XVII resonance lines.
• Steady needle growth with 3-D anisotropic surface tension

  CHEN Xiao-jun, CHEN Yong-qiang, XU Jian-pu, XU Jian-jun

  2008, 3(4): 418-435. https://doi.org/10.1007/s11467-008-0040-0

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  The effect of the anisotropic interfacial energy on dendritic growth has been an important subject, and has preoccupied many researchers in the field of materials science and condensed matter physics. The present paper is dedicated to the study of the effect of full 3-D anisotropic surface tension on the steady state solution of dendritic growth. We obtain the analytical form of the first order approximation solution in the regular asymptotic expansion around the Ivantsov’s needle growth solution, which extends the steady needle growth solution of the system with isotropic surface tension obtained by Xu and Yu (J. J. Xu and D. S. Yu, J. Cryst. Growth, 1998, 187: 314; J. J. Xu, Interfacial Wave Theory of Pattern Formation: Selection of Dendrite Growth and Viscous Fingering in a Hele-Shaw Flow, Berlin: Springer-Verlag, 1997).The solution is expanded in the general Laguerre series in any finite region around the needle-tip, and it is also expanded in a power series in the far field behind the tip. Both solutions are then numerically matched in the intermediate region. Based on this global valid solution, the dependence of Peclet number Pe and the interface’s morphology on the anisotropy parameter of surface tension as well as other physical parameters involved are determined. On the basis of this global valid solution, we explore the effect of the anisotropy parameter on the Peclet number of growth, as well as the morphology of the interface.
• Ajellium model analysis on quantum growth of metal nanowires and nanomesas

  HAN Yong

  2008, 3(4): 436-443. https://doi.org/10.1007/s11467-008-0037-8

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  A simple jellium model is used to investigate the stability of a metal nanowire as a function of its size. The theoretical results from the model indicate the quantum selectivity of preferable radii of nanowires, in apparent agreement with the experimental observations. It is consequently suggested that a series of stable “magic numbers” and “instability gaps” observed in the synthesis experiments of Au nanowires is mainly attributed to the quantum-mechanical behavior. These stable radii can be achieved by rearranging atoms during the formation of nanowires. The model is also used to analyze the growth of Au nanomesas on a graphite surface, and the puzzling growth behavior of Au nanomesas can be reasonably explained.
• Influence of structure disorders and temperatures of systems on the bio-energy transport in protein molecules (II)

  PANG Xiao-feng

  2008, 3(4): 457-488. https://doi.org/10.1007/s11467-008-0039-6

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  The influence of molecular structure disorders and physiological temperature on the states and properties of solitons as transporters of bio-energy are numerically studied through the fourth-order Runge-Kutta method and a new theory based on my paper [Front. Phys. China, 2007, 2(4): 469]. The structure disorders include fluctuations in the characteristic parameters of the spring constant, dipole-dipole interaction constant and exciton-phonon coupling constant, as well as the chain-chain interaction coefficient among the three channels and ground state energy resulting from the disorder distributions of masses of amino acid residues and impurities. In this paper, we investigate the behaviors and states of solitons in a single protein molecular chain, and in ?-Helix protein molecules with three channels. In the former we prove first that the new solitons can move without dispersion, retaining its shape, velocity and energy in a uniform and periodic protein molecule. In this case of structure disorder, the fluctuations of the spring constant, dipole-dipole interaction constant and exciton-phonon coupling constant, as well as the ground state energy and the disorder distributions of masses of amino acid residues of the proteins influence the states and properties of motion of solitons. However, they are still quite stable and are very robust against these structure disorders, even in the presence of larger disorders in the sequence of masses, spring con-stants and coupling constants. Still, the solitons may disperse or be destroyed when the disorder distribution of the masses and fluctuations of structure parameters are quite great. If the effect of thermal perturbation of the environment on the soliton in nonuniform proteins is considered again, it is still thermally stable at the biological temperature of 300 K, and at the longer time period of 300 ps and larger spacing of 400 amino acids. The new soliton is also thermally stable in the case of motion over a long time period of 300 ps in the region of 300–320 K under the influence of the above structure disorders. However, the soliton disperses in the case of a higher temperature of 325 K and in larger structure disorders. Thus, we determine that the soliton’s lifetime and critical temperature are 300 ps and 300–320 K, respectively. These results are also consistent with analytical data obtained via quantum perturbed theory. In ?-helix protein molecules with three channels, results obtained show that these structure disorders and quantum fluctuations can change the states and features of solitons, decrease their amplitudes, energies and velocities, but they still cannot destroy the solitons, which can still transport steadily along the molecular chains while retaining energy and momentum when the quantum fluctuations are small, such as in structure disorders and quantum fluctuations of 0.67 < ?_k < 2,

  

  Long-term memory of the returns in the Chinese stock indices

  WAN Wei, ZHANG Jian-Wei

  2008, 3(4): 489-494. https://doi.org/10.1007/s11467-008-0038-7

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  The modified R/S statistic (MRS) and the local Whittle method (LWM) are used to analyze the long-range dependence on various indices of the Chinese stock markets. The MRS accepts the null hypothesis of no long-range dependence while the LWM rejects it. We also find that the long-range dependence phenomena presented in these markets depend on the time in which they are measured.