Approximate wφ - Ωφ Relations in Quintessence Models

Quintessence field is a widely-studied candidate of dark energy. There is ＂tracker solution＂ in quintessence models, in which evolution of the field φ at present times is not sensitive to its initial conditions. When the energy density of dark energy is negleetable （Ωφ 〈〈 1）, evolution of the tracker solution can be well analysed from ＂tracker equation＂. In this paper, we try to study evolution of the quintessence field from ＂full tracker equation＂, which is valid for all spans of Ωφ. We get stable fixed points of we and wφ （noted as wφ and Ωφ） from the ＂full tracker equation＂, i.e., we and ωφ will always approach ωφ and Ωφ respectively. Since wφ and Ωφ are analytic functions of φ, analytic relation of φ can be obtained, which is a good approximation for the we φ relation and can be obtained for the most type of quintessence potentials. By using this approximation, we find that inequalities ωφ 〈 we and 〈ωφ are statisfied if the we （or ωφ） decreases with time. In this way, the potentiai U（φ） can be constrained directly from observations, by no need of solving the equations of motion numerically.     

Optimization of extinction efficiency of gold‐coated polystyrene bead substrates improves surface‐enhanced Raman scattering effects by post‐growth microwave heating treatment

We report a novel post‐growth microwave treatment approach to selectively modify the surface morphologies of gold (Au) films coated on the polystyrene (PS) bead substrates for effectively improving the surface‐enhanced Raman scattering (SERS) effect on the analytes. The discrete dipole approximation (DDA) model was introduced to evaluate the enhancement effects by calculating the localized electromagnetic field distribution and extinction efficiency based on the sizes of the trenches and voids, and the surface roughness of the modified Au–PS bead substrates. The SERS performance of microwave‐modified Au–PS substrates on rhodamine 6G (Rh 6G) and saliva yields at least 10‐fold improvements in SERS intensities compared to the as‐grown substrates, which is also in agreement with theoretical predictions by DDA modeling. This work demonstrates both experimentally and theoretically the efficacy of the microwave heating treatment on modifying the Au–PS bead substrates for the realization of high SERS performance in biomedical applications. Copyright © 2009 John Wiley & Sons, Ltd.     

Comparative study between dispersive and non-dispersive dielectric permittivity in spectral remittances of chiral sculptured zirconia thin films

The transmission and reflection spectra from a right-handed chiral sculptured zirconia thin film are calculated using the piecewise homogeneity approximation method and the Bruggeman homogenization formalism using both dispersive and non-dispersive functions for axial and non-axial states. The comparison of spectral results shows that the dispersion of the dielectric function has a considerable effect on the results. In axial excitation of cross-polarized reflectances and co-polarized transmittances the dispersion effect becomes more pronounced at wavelengths further away from the homogenization wavelength. This is also true in the case of non-axial excitation of circular transmittances, while there are considerable differences for cross-polarized reflectances where (wavelength) the first Bragg peak occurs. At wavelengths in the vicinity of the homogenization wavelength the dispersion effect of the dielectric function in R_RR becomes more significant.     

用A238U超核聚变检验裂变机制的可行性探讨

超核_A²³⁸U的裂变的剪断过程,用不断上升的势垒模拟,对不同的剪断过程(恒速或加速),对A末态激发几率(布居于轻裂块的几率)作了计算,分别为27%或31%。有待实验检验。     

1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators

Let (P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let D_A be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote T_ω:= (D_A(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (T_ω · e^-t(D_A−f)2) near t=0 define 1-forms a^(k)_f, K=0, 1, 2, … on (P). In this paper we calculate aa⁽⁰⁾_f, a⁽¹⁾_f, a⁽²⁾_f and study some of their properties. For instance using the 1-form a⁽²⁾_f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S⁴.     

Upper bounds on correlation decay for one-dimensional long-range spin-glass models

Some recent results on one-dimensional spin-glass models with polynomially decreasing interactions are described.     

Asymptotic infiltration into a soil which contains cracks or holes but whose surface is otherwise impermeable

An asymptotic, one-dimensional Green-Ampt model is derived for infiltration into a soil whose surface is impermeable except for regularly spaced vertical cracks, and infiltration into a cylindrical soil column whose top surface is also impermeable except for a central hole. The model is valid at times when the wetting front has become horizontal and corresponds to one-dimensional infiltration initiated from a plane lying above or below the soil surface, depending on the crack spacing/depth ratio (or column radius/hole depth ratio). When applicable, asymptotic Green-Ampt solutions are shown to agree well, in selected cases, with corresponding finite difference solutions of the saturated-unsaturated flow equations.     

损伤材料裂纹尖端附近的应力场

本文导出了损伤材料的全量理论,导出了全量公式中H的渐近表达式;最后得到损伤材料平面应变条件下的裂纹尖端的应力应变场。     

On the summation of the Brillouin-Wigner type perturbation series

It is shown that if the ‘mean excitation energy’ assumption is introduced in the Brillouin-Wigner perturbation series, then the resulting series can be exactly summed. The implications of the result for calculating energy shift and for constructing trial functions are examined with special reference to the ground state of the helium atom.