Infrared reflectivity and dielectric permeability of ultra-thin Cu and Al films

In this report we present an experimental investigation of the reflectivity (R) and the dielectric permeability () for Cu and Al ultra-thin films ranging in thickness from a few monolayers to 12 nm at infrared and visible wavelengths. The metal films were prepared by RF-sputtering on SiO₂ (glass) and Si substrates. IR reflectivity was measured at 9.2 μm, while was measured with the help of laser ellipsometer at a wavelength of 632.8 nm. Two types of oscillations on R(d) and (d) were discovered for two thickness regions determined by the critical thickness value d*. Oscillations at d<d* with periods near 0.3 nm for Al and Cu films were observed on R(d) and (d) due to quantum sized effects (QSEs). At d>d* (thickness between 6–12 nm) we discover a new type of strong oscillation of R(d) and (d) with an oscillating period of 0.2 nm. For thickness larger than 12 nm all the oscillations tend to disappear and R and behave almost as their volume values. A possible explanation for the appearance of these two kinds of oscillations is based on the introduction of the critical film thickness d*.     

Response of line focus acoustic microscope to specimen containing a subsurface crack

A numerical model is presented to calculate V(z) and V(x, z) curves for a line focus acoustic microscope and a specimen containing a subsurface crack. In this model, a Gaussian beam which is tracked through the lens into the coupling fluid and into the specimen, interacts with the crack. The numerical approach is based on the solution of singular integral equations by the boundary element method. The system of singular integral equations follows from the conditions at the interface of the coupling fluid and the specimen and on the faces of the crack. An electromechanical reciprocity relation is used to express the voltage at the terminals of the microscope's transducer in terms of the calculated incident and back-scattered fields. V(z) and V(x, z) curves are presented for various locations and orientations of the crack. The characteristic features of the V(z) and particularly the V(x, z) curves, as they relate to crack configuration, are discussed in some detail.     

Binding energy of an exciton bound to ionized donors in quantum dots

Binding energies for an exciton (X) trapped in the two-dimensional quantum dot by a positive ion located on the z axis at a distance d from the dot plane are calculated by using the method of few-body physics. This configuration is called a barrier (D⁺,X) center. The dependence of the binding energy of the ground state of the barrier (D⁺,X) center on the dot radius for a few values of the distance d between the fixed positive ion on the z axis and the dot plane is obtained. We find that when d<0.2nm the barrier (D⁺,X) center does not form a bound state.     

Joule–Thomson expansion of higher dimensional nonlinearly AdS black hole with power Maxwell invariant source

In this paper, the Joule–Thomson expansion of the higher dimensional nonlinearly anti-de Sitter(Ad S) black hole with power Maxwell invariant source is investigated. The results show the Joule–Thomson coefficient has a zero point and a divergent point, which coincide with the inversion temperature Tiand the zero point of the Hawking temperature, respectively. The inversion temperature increases monotonously with inversion pressure. For the high-pressure region, the inversion temperature decreases with the dimensionality D and the nonlinearity parameter s, whereas it increases with the charge Q. However, Tifor the low-pressure region increase with D and s, while it decreases with Q. The ratio ηBHbetween the minimum inversion temperature and the critical temperature does not depend on Q, it recovers the higher dimensional Reissner–N?rdstrom Ad S black hole case when s = 1. However, for s 1, it becomes smaller and smaller as D increases and approaches a constant when D →∞. Finally, we found that an increase of mass M and s, or reducing the charge Q and D can enhance the isenthalpic curve, and the effect of s on the isenthalpic curve is much greater than other parameters.     

不同硅晶面指数上的类倒金字塔结构研究与分析

晶体硅作为一种重要的半导体材料,在集成电路、太阳能电池等方面具有广泛的应用.基于各向异性的刻蚀方法,不同晶面指数的硅都可以在表面形成由{111}晶面族组成的正/倒金字塔.本文基于{111}晶面族与（abc）晶面相交构成类倒金字塔结构的特性,建立了硅的晶面指数（abc）与所形成的类倒金字塔结构的数学模型.将硅的晶面指数（abc）分成0≤a≤b<c,0≤a<b=c,a=b=c三种情况进行讨论,分别得到不同晶面指数的类倒金字塔结构.实验结果的扫描电子显微镜图证实了理论计算的准确性.晶面指数与类倒金字塔结构具有一一对应的关系,因此可以根据各向异性刻蚀后的类倒金字塔结构,进行硅的晶面指数进行检测.     

Scaling probability, key to the equilibrium statistical volume distribution in foams

The equilibrium statistical volume distribution in foams, which has been previously demonstrated to be the so-called log-normal, is accounted on probability grounds by a scaling law on the bubble's volume time-evolution. This law states that the conditional probability for a given bubble to have the volume v(t + Δt), he assumption that it was v(t), to depend solely on the relationship v(t + Δt)/v(t), and in particular, to be independent of the time t. The theoretical results, however, allow to go further. Indeed, since the time dependece of its parameters (expectation and variance) are given functions of time, only two parameters are necessary to describe completely the foam.     

晶体离子质量差异对激活离子声子参助能量传递几率的影响

在已有理论模型的基础上讨论了基质晶体离子质量差异对激活离子声子参助能量传递几率的影响。结果表明基质离子的质量差异除了导致声子频率的变化从而影响其声子参助能量传递几率,还直接改变其传递几率的显式。对单声子参助能量传递过程,其传递几率必须乘以质量差异因子D²,对双声子参助能量传递过程其传递几率则乘以因子D⁴。文中给出了两种不同质量离子组成的晶体的因子D的表示式和p种不同质量的离子组成的晶体的因子D的一般表达式。     

Non-abelian vortices on surfaces and their statistics

We discuss the physics of topological vortices moving on an arbitrary surface M in a YangMills-Higgs theory in which the gauge group G breaks to a finite subgroup H. We concentrate on the case where M is compact and/or non-orientable. Interesting new features arise which have no analog on the plane. The consequences for the quantum statistics of vortices are discussed, particularly when H is non-abelian.     

糖的原子电距矢量表达及其核磁共振碳谱模拟

提出以原子电性距离矢量(VAED),描述上百种糖分子中数百个不同等价碳原子的化学环境;并结合γ效应校正,建立核磁共振碳谱(¹³C NMR)化学位移(CS)的五参数线性模型.用于糖分子中四类不同的等价碳原子化学位移的估计,复相关系数R和均方根误差RMS及标准偏差SD和F-统计量F分别为:伯碳n=62,R=0.991 0,RMS=1.960 2(SD=1.9762,F=5 0 2.32 94,EV=0.980 5);仲碳n=79,R=0.9886,RMS=2.5 40 5(SD=2.5 5 67,F=5 1 5.60 4 6,EV=0.975 7);叔碳n=30 2,R=0.95 1 4,RMS=3.6884(SD=3.694 5,F=4 68.82 76,EV=0.90 35)及季碳n=1 4,R=0.5 772,RMS=8.862 6(SD=9.1 972,F=0.5 82 8,EV=-0.0 837).经交互校验,伯仲叔碳的化学位移模型稳定性较好.并综合几种处理方法,找到一种较好的建模方法,将它用于几个外部样本的定量预测,结果良好.     

色散介质电磁特性时域有限差分分析的Newmark方法

根据Debye模型、Drude模型和Lorentz模型3种常见色散介质模型频域极化率的特点,利用频域到时域的转换关系jω→?/?t,将极化矢量P与电场强度E的频域关系转换成时域内关于P的二阶微分方程,其对3种色散介质模型皆适用,具有统一的形式.然后采用相比于中心差分具有更高精度的Newmark两步算法(Newmark-β-γ法)求解该方程,进而得到E→P的递推公式,再结合本构关系得到D→E的时域递推式.实现了色散介质电磁场量的时域有限差分迭代计算.数值计算结果表明该方法是适用于3种色散介质模型的通用算法,并且相比于移位算子时域有限差分方法等以中心差分为基础的离散方案具有更高的计算精度.     

Impurity effect as a probe for the pairing symmetry of graphene-based superconductors

We study theoretically the single impurity effect on graphene-based superconductors. Four different pairing symmetries are discussed. Sharp in-gap resonant peaks are found near the impurity site for the d+id pairing symmetry and the p+ip pairing symmetry when the chemical potential is large. As the chemical potential decreases, the in-gap states are robust for the d + id pairing symmetry while they disappear for the p + ip pairing symmetry. Such in-gap peaks are absent for the fully gapped extended s-wave pairing symmetry and the nodal f-wave pairing symmetry. The existence of the ingap resonant peaks can be explained well based on the sign-reversal of the superconducting gap along different Fermi pockets and by analyzing the denominator of the T-matrix. All of the features may be checked by the experiments, providing a useful probe for the pairing symmetry of graphene-based superconductors.     

On matching conditions in the WKB method

The modified matching conditions for quasiclassical wave functions on both sides of a turning point for the radial Schrödinger equation have been obtained. They differ significantly from the usual Kramers condition which holds for the one-dimensional case. Namely, the ratio C₂/C₁ in the subbarrier and the classical allowed regions is not a universal constant ( , as usual), but depends on the values of the orbital angular momentum l, energy E and on the behaviour of the potential V(r) at r → 0. The comparison with exact and numerical solutions of the Schrödinger equation shows that the modified matching conditions not only make the quasiclassical approximation in the subbarrier region asymptotically exact within the n → ∞ limit, but also considerably enhances its accuracy even in the case of small quantum numbers, n 1. The power-law, funnel and short-range potentials are considered in detail.     

Finite-size scaling properties of the damage distance and dynamical critical exponent for the Ising model

With the damage spreading method, scaling properties of the damage distance on the Ising model with heat bath dynamics are studied numerically. With the parallel flipping scheme, the scaling curves fall on two curves, which depend on the odd or even lattice sizes. The both scaling curves give the consistent dynamical exponent as z = 2.16±0.04 for d = 2 and z = 2.09±0.05 for d = 3, respectively. By shifting one of them, two curves overlap each other perfectly. Meanwhile, all the scaling curves obtained by single-spin flipping processes (with different odd or even lattice sizes) fall on a single curve, from which the consistent dynamical critical exponent with the parallel scheme is obtained z = 2.18±0.02 for d = 2 and z = 2.08±0.04 for d = 3.     

Generalized Einstein manifolds

A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F⁰(M, g_t) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g₀ F⁰(g_t) of the integral I(g_t) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (g_t) for G = g₀, then for a CID we show that for certain Finslerian manifolds, I″(g₀) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs.     

块多分裂方法与预条件子空间迭代方法

提出一种块多分裂并行PE迭代算法(MPPE),可以克服M^-1r^(s)并行化处理的困难。这种算法格式简单明了,收敛速度快。并证明了当矩阵A是M-阵和H-阵时,该算法是收敛的。同时把这种分裂作为预处理矩阵,对子空间方法类进行了预处理,并给出的计算实例显示该算法很有效,对子空间方法类的余量光滑和加速都起到了比较好的作用。     

Numerical calculation of current density distributions in high temperature superconducting tapes with finite thickness in self field and external field

The current density distribution of high temperature superconducting (HTS) tapes is modeled for the combined case of an alternating self and applied magnetic field. This numerical analysis is based on the two-dimensional Poisson equation for the vector potential. A one-dimensional current (z-direction) and a one-dimensional applied field (y-direction) are assumed. The vector potential is rewritten into an equation of motion for the current density J(x,y,t). The model covers the finite thickness of the conductor and an n-power E–J relation. The magnetic field dependence of J_c is also included in this E–J relation. A time-dependent two-dimensional current distribution that is influenced by the aspect ratio of the conductor and the material properties in E=f(J,B) is calculated numerically. The numerical results are compared with the experimental results for the AC loss of a tape driven by a transport current. Finally, a total AC loss factor is given for two cases in magnetic field direction, perpendicular and parallel to the conductor broad side.     

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.     

Specific heat and spin susceptibility of dilute alloys*

The change in the specific heat and spin susceptibility of a metal of valence Z due to the introduction of a small number of impurity atoms with valence (Z + q) is calculated by the Thomas-Fermi method. It is shown that in the case of copper an exact Thomas-Fermi calculation accounts approximately for the seemingly linear behaviour of the change in C_v and X from q = 1 to q = 3 observed in recent experiments by Rayne. It does not, however, account for absolute values. In an appendix a check on the validity of the Thomas-Fermi theory is made for q < 1 by recalculating the specific heat and spin susceptibility by means of the techniques of many-body perturbation theory. The different methods give essentially the same results.     

Preferential attachment network model with aging and initial attractiveness

In this paper, we generalize the growing network model with preferential attachment for new links to simultaneously include aging and initial attractiveness of nodes. The network evolves with the addition of a new node per unit time, and each new node has m new links that with probability Π_i are connected to nodes i already present in the network. In our model, the preferential attachment probability Π_i is proportional not only to k_i + A, the sum of the old node i's degree k_i and its initial attractiveness A, but also to the aging factor ${\tau }_{i}^{-\alpha }$, where τ_i is the age of the old node i. That is, ${{\rm{\Pi }}}_{i}\propto ({k}_{i}+A){\tau }_{i}^{-\alpha }$. Based on the continuum approximation, we present a mean-field analysis that predicts the degree dynamics of the network structure. We show that depending on the aging parameter α two different network topologies can emerge. For α < 1, the network exhibits scaling behavior with a power-law degree distribution P(k) ∝ k^−γ for large k where the scaling exponent γ increases with the aging parameter α and is linearly correlated with the ratio A/m. Moreover, the average degree k(t_i, t) at time t for any node i that is added into the network at time t_i scales as $k({t}_{i},t)\propto {t}_{i}^{-\beta }$ where 1/β is a linear function of A/m. For α > 1, such scaling behavior disappears and the degree distribution is exponential.