不同晶体取向下纳米压痕的多尺度模拟

采用准连续介质多尺度方法模拟面心立方金属铝单晶薄膜的纳米压痕变形过程.对薄膜分别采用三种不同的晶体取向(分别为x［1 1 1］,y［1 1 0］,z［1 1 2］; x［1 1 2］,y［1 1 1］,z［1 1 0］;x［1 1 0］,y［0 0 1］,x［1 1 0］),得到载荷-位移响应曲线.加载过程中,对晶体内部变形比较剧烈的部分画出原子图,并从微观角度分析产生剧烈变形的原 关键词： 纳米压痕 准连续介质方法 晶体取向 位错成核     

Stress and morphology of a nonpolar a-plane GaN layer on r-plane sapphire substrate

The anisotropic strain of a nonpolar (1120) a-plane GaN epilayer on an r-plane (1102) sapphire substrate, grown by low-pressure metal-organic vapour deposition is investigated by Raman spectroscopy. The room-temperature Raman scattering spectra of nonpolar a-plane GaN are measured in surface and edge backscattering geometries. The lattice is contracted in both the c- and the m-axis directions, and the stress in the m-axis direction is larger than that in the c-axis direction. On the surface of this sample, a number of cracks appear only along the m-axis, which is confirmed by the scanning electron micrograph. Atomic force microscopy images reveal a significant decrease in the root-mean-square roughness and the density of submicron pits after the stress relief.     

Noncommutative Geometry¶and Gauge Theory on Fuzzy Sphere

The differential algebra on the fuzzy sphere is constructed by applying Connes' scheme. The U(1) gauge theory on the fuzzy sphere based on this differential algebra is defined. The local U(1) gauge transformation on the fuzzy sphere is identified with the left U(N+1) transformation of the field, where a field is a bimodule over the quantized algebra . The interaction with a complex scalar field is also given. Received: 21 January 1998 / Accepted: 4 February 2000     

Investigation on bainite transformation and metastable omega/orthorhombic martensite phases in as-quenched Cu-bearing ferrite steel

Abstract

The as-quenched microstructures of low-carbon Cu-bearing ferrite steel are investigated by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). It is found that the granular bainite formation in Cu-bearing ferrite steel is attributed to a mixed mode of diffusional and displacive mechanisms. Besides, the particle-like or plate-shaped ω phases, along with thin-plate martensites consist of twin, are observed in the Mn1.4Cu-bearing steel, and the orientation relationship is determined as: [2 ?1 ?10]_ω // [0 1 1]_α and (0 1 ?1 0)_ω // (2 ?1 1)_α. The ultra-fine or ellipsoidal shaped nanoscale orthorhombic martensite phases, along with laths martensites consist of a high density of dislocations, are observed in the Mn0.66Cu-bearing steel, and the orientation relationship is determined as: [0 1 ?1]o//[?1 1 1]α and (?1 1 1)o//(1 0 1) α. A model is proposed to describe the overall martensite transformation kinetics by taking into account the Mn content, heterogeneity of C content and dislocation reactions play a major role in the subsequent martensite transformation.     

Optical-to-microwave frequency chain utilizing a two-laser-based optical parametric oscillator network

A method for building an optical-to-microwave frequency chain and for measuring optical frequencies relative to the cesium primary frequency standard is described. Based on optical frequency division via parametric oscillators, the concept is to generate two known ratios (1/2 and 4/9) of an optical calibration frequencyf ₁ whose frequency difference is measured relative to the cesium clock. The (1/2) ratio is obtained by either a 2:1 frequency division off ₁ or second-harmonic generation of (l/2)f ₁. The (4/9) ratio off ₁ can be generated with a 3:1 frequency divider driven by a second laser atf ₂ that is chosen to be near (2/3)f ₁, which in turn is obtained with af ₁-pumped 3:1 frequency divider. A set of auxiliary Optical Parametric Oscillators (OPOs) with outputs centered at (1/2)f ₁ is used to facilitate the difference-frequency measurement between the two ratios. A practical configuration utilizing a YAG and a Ti: Al₂O₃ laser and its application to a number of precision measurements of interest are presented.     

Twisted Diff S 1-action on loop groups and representations of the virasoro algebra

A modified Hamiltonian action of Diff S ¹on the phase space LG ^C /G^C, where LG is a loop group, is defined by twisting the usual action by a left translation in LG. This twisted action is shown to be generated by a nonequivariant moment map, thereby defining a classical Poisson bracket realization of a central extension of the Lie algebra diff_C S ¹. The resulting formula expresses the Diff S ¹generators in terms of the left LG translation generators, giving a shifted modification of both the classical and quantum versions of the Sugawara formula.Research supported in part by the Natural Sciences and Engineering Research Council of Canada and the National Science Foundation.     

Photoconductivity derived from an exact modelling of the uncompensated one-donor model. III—problem of fitting the exact model with approximate models

Abstract

The paper is essentially devoted to a quantitative comparison of the exact (1D) model developed in Part I, with two approximate models indicated by Kittel (1D_a1) and by Van der Ziel (1D_a2). And this is made for identical values of their common parameters. This allows to show that models 1D and 1D_a1 generally present no suitable intervals for fitting. The model of Van der Ziel is more suited, for, a good fitting with the 1D model can be obtained, for relatively reduced G values, and for temperatures bounded upward by the characteristic temperature T ₀ defined previously. The role played by the sub-models, obtained after simplifying the 1D_ai model equations, is studied also.     

Automatic Regularization by Quantization in Reducible Representations of CCR: Point-Form Quantum Optics with Classical Sources

Electromagnetic fields are quantized in a manifestly covariant way by means of a class of reducible “center-of-mass N-representations” of the algebra of canonical commutation relations (CCR). The four-potential A _a (x) transforms in these representations as a Hermitian four-vector field in Minkowski four-position space (without change of gauge), but in momentum space it splits into spin-1 massless photons and two massless scalars. What we call quantum optics is the spin-1 sector of the theory. The scalar fields have physical status similar to that of dark matter (spin-1 and spin-0 particle numbers are separately conserved). There are no negative-norm or zero-norm states. Unitary dynamics is given by the point-form interaction picture, with minimal-coupling Hamiltonian constructed from fields that are free on the null-cone boundary of the Milne universe. SL(2,C) transformations as well as the dynamics are represented unitarily in the Hilbert space corresponding to N four-dimensional oscillators. Vacuum is a Bose-Einstein condensate of the N-oscillator gas and is given by any N-oscillator product state annihilated by all annihilation operators. The form of A _a (x) is determined by an analogue of the twistor equation. The same equation guarantees that the set of vacuum states is Poincaré invariant. The formalism is tested on quantum fields produced by pointlike classical sources. Photon statistics is well defined even for pointlike charges, with ultraviolet and infrared regularizations occurring automatically as a consequence of the formalism. The probabilities are not Poissonian but of a Rényi type with α=1−1/N; the Shannon limit N→∞ is an ultraviolet/infrared-regularized Poisson distribution. The average number of photons occurring in Bremsstrahlung splits into two parts: The one due to acceleration, and the one that remains nonvanishing even for inertially moving charges. Classical Maxwell electrodynamics is reconstructed from coherent-state averaged solutions of Heisenberg equations. We show in particular that static pointlike charges polarize vacuum and produce effective charge densities and fields whose form is sensitive to both the choice of representation of CCR and the corresponding vacuum state.     

Complexified Gravity in Noncommutative Spaces

The presence of a constant background antisymmetric tensor for open strings or D-branes forces the space-time coordinates to be noncommutative. This effect is equivalent to replacing ordinary products in the effective theory by the deformed star product. An immediate consequence of this is that all fields get complexified. The only possible noncommutative Yang–Mills theory is the one with U(N) gauge symmetry. By applying this idea to gravity one discovers that the metric becomes complex. We show in this article that this procedure is completely consistent and one can obtain complexified gravity by gauging the symmetry U(1,D−1) instead of the usual SO(1,D−1). The final theory depends on a Hermitian tensor containing both the symmetric metric and antisymmetric tensor. In contrast to other theories of nonsymmetric gravity the action is both unique and gauge invariant. The results are then generalized to noncommutative spaces. Received: 1 June 2000 / Accepted: 27 November 2000     

Hypergeometric series in a series expansion of the directed-bond percolation probability on the square lattice

The asymmetric directed-bond percolation (ADBP) problem with an asymmetry parameterk is introduced and some rigorous results are given concerning a series expansion of the percolation probability on the square lattice. It is shown that the first correction term,d _n,1 (k) is expressed by Gauss' hypergeometric series with a variablek. Since the ADBP includes the ordinary directed bond percolation as a special case withk=1, our results give another proof for the Baxter-Guttmann's conjecture thatd _n,1(1) is given by the Catalan number, which was recently proved by Bousquet-Mélou. Direct calculations on finite lattices are performed and combining them with the present results determines the first 14 terms of the series expansion for percolation probability of the ADBP on the square lattice. The analysis byDlog Padé approximations suggests that the critical value depends onk, while asymmetry does not change the critical exponent of percolation probability.     

Master Analytic Representations and unified representation theory of certain orthogonal and pseudo-orthogonal groups

The representation theory of the groupsSO(5),SO(4, 1),SO(6) andSO(5, 1) is studied using the method of Master Analytic Representations (MAR). It is shown that a single analytic expression for the matrix elements of the generators ofSO(n+1) andSO(n, 1) in anSO(n) basis yields all the unitary representations (forn=4,5); and that the compact and non-compact groups have essentially the same analytic representation. Once the MAR of a group is worked out, the search for the unitary irreducible representations is reduced to a purely arithmetic operation. The utmost care has been exercised to conduct the discussions at an elementary level: knowledge of simple angular momentum theory is the only prerequisite.Work supported in part by the National Science Foundation.Work supported in part by the U.S. Atomic Energy Commission.     

A note on the solution of a spinor equation

An equation of spinor algebra, which is specified by two positive integers,M andN, is solved by relating it to the problem of integrating a two-dimensional Hamiltonian homogeneous polynomial system of ordinary differential equations, whose degree isN}-1. The case in whichN=1 reduces to a well-known result of spinor algebra. The caseM=N=4 is of relevance in the study of symmetry operators of Maxwell's equations on a curved space-time. It is also shown, using spinor notation, that the first integral for a general two-dimensional Hamiltonian system of ordinary differential equations (whether polynomial or analytic) is determinable in a purely algebraic manner, i.e., by using no integration.     

基于小波变换和维纳滤波的半导体器件1/f噪声滤波

针对半导体器件中普遍存在的1/f噪声提出了一种结合了提升小波变换和维纳滤波器的处理方法.首先利用重新加权迭代最小二乘法拟合1/f噪声的功率谱曲线得到噪声参数的估计,从而选择恰当的小波.其次,对包含了1/f噪声的信号进行提升小波变换.考虑到小波变换对1/f噪声的白化作用,利用维纳滤波器对每一层小波系数进行处理.设计了最优全通滤波器以校正维纳滤波器的相频特性,使得小波系数经滤波后相位不变.最后利用提升小波逆变换获得被1/f噪声淹没的信号.利用实验检验了提出方法的有效性,实验数据采自用于微创外科手术机器人的力传感器.结果表明提出的方法能够有效抑制1/f噪声,并使传感器的分辨力提高了25%. 关键词： 半导体器件 f噪声')" href="#">1/f噪声 提升小波变换 维纳滤波     

The Moduli of Flat PGL(2,ℝ) Connections on¶Riemann Surfaces

Suppose X is a compact Riemann surface with genus g>1. Each class [σ] ∈ Hom(π₁(X),PGL(2,ℝ))/PGL(2,ℝ) is associated with the first and second Stiefel–Whitney classes w ₁([σ]) and w ₂([σ]). The set of representation classes with a fixed w ₁≠ 0 has two connected components. These two connected components are characterized by w ₂ being 0 or 1. For each fixed w ₁≠ 0, we prove that the component, characterized by w ₂= 0, contains an open dense set diffeomorphic to the total space of a vector bundle of rank 2g−2 over a once punctured algebraic torus of dimension g−1. The other component, characterized by w ₂= 1, contains an open dense set diffeomorphic to the total space of a vector bundle of rank 2g−2 over an algebraic torus of dimension g−1. Received: 2 January 1997 / Accepted: 28 November 1998     

Intersubband transitions in Al0.82In0.18N/GaN single quantum well

The influence of the width of a lattice-matched Al_0.82In_0.18N/GaN single quantum well (SQW) on the absorption coefficients and wavelength of the intersubband transition (ISBT) has been investigated by solving the Schrödinger and Poisson equations self-consistently. The wavelength of 1—2 ISBT increases with L, the thickness of the single quantum well, ranging from 2.88 μm to 3.59 μm. The absorption coefficients of 1—2 ISBT increase with L at first and then decrease with L, with a maximum when L is equal to 2.6 nm. The wavelength of 1—3 ISBT decreases with L at first and then increases with L, with a minimum when L is equal to 4 nm, ranging from approximately 2.03 μm to near 2.11 μm. The absorption coefficients of 1—3 ISBT decrease with L. The results indicate that mid-infrared can be realized by the Al_0.82In_0.18N/GaN SQW. In addition, the wavelength and absorption coefficients of ISBT can be adjusted by changing the width of the SQW.     

Radiation from a Circular Waveguide Flush-mounted to a Ground Plane covered by a Plasma or a Dielectric Slab

A theory of the radiation from the open end of a circular waveguide fed in the dominant TE₁₁ mode and flush-mounted to an infinite, perfectly conducting flat ground plane covered by a plasma or a dielectric sheath is developed. In this analysis, the contributions to the aperture admittance and the excited fields from the higher order TE_1n (n ≥ 1) and TM_1l(l ≥ 1) modes are included. The aperture admittance for which the higher order modes are considered, has been calculated by two methods: 1. variational technique and 2. successive iteration method. It is shown that for any desired order of accuracy the results of these approaches are identical. Expressions for radiated fields, surface waves for all radial values of r, and the fields which represent glancing incident fields inside the slab are derived. The contribution of the surface waves to the aperture admittance is also presented.     

Drinfeld twist for two-parametric deformation of gl(2) and sl(1/2)

Drinfeld twist is applied to the Lie algebra gl(2) so that a two-parametric deformation of it is obtained, which is identical to the Jordanian deformation of the gl(2) obtained by Aneva et al. The same twist element is applied to deform the Lie superalgebra sl(1/2), since the gl(2) is embedded into the sl(1/2). By making use of the FRT-formalism, we construct a deformation of the Lie supergroup SL(1/2).     

Joint distributions and local realism in the higher-spin Einstein-Podolsky-Rosen experiment

A method is given to determine whether or not the distribution functions describing the two spin measurements in the spin-s Einstein-Podolsky-Rosen experiment are compatible with the existence of distributions describing three spin measurements (not all of which can actually be performed). When applied to the spin-1/2 case the method gives the results of Wigner, or of Clauser, Holt, Horne, and Shimony, depending on whether or not the two-spin distributions are assumed to have the forms given by the quantum theory. Generalizations of the conditions of Wigner or of Clauser et al. to the spin-1 case are explicitly calculated. The spin-3/2 case is examined in some simple geometries to show that an apparently monotonic trend toward local realism as s increases from1/2 to1 is, in fact, violated when s increases from1 to3/2. The analysis is based on a novel representation of the modulus squared of a rotation matrix element. The structure of that matrix element responsible for the restoration of local realism in the classical (large s) limit is identified, but a rigorous treatment of the classical limit is not attempted. The higher-spin results are significantly stronger than those given by Mermin's spin-s Bell inequality.     

Modeling 1/f noise using moving averages

A model of 1/f noise is considered, based on moving averages of ordern. The coefficientsα _k defining the model are calculated numerically using Seidel iteration which turns out to converge rapidly. The convergence is independent ofn which seems to be caused by the fact that the nonlinear problem solved is defined by a self-similar matrix. The coefficientsα _k appear to approach, with indefinitely growingn, valuesα _k =1/√k and thus the model has a kind of Fourier invariance. Physical interpretation of the invariance is suggested as well as of coefficientsα _k describing long-range correlations. Fractal sets of dimensiond=2.5 are proposed to play certain role in explaining the latter. This work was partly supported by the Scientific Grant Agency of the Ministry of Education of Slovak Republic (VEGA) under the Grant No. 1/3143/96 and by the Slovak Literary Fund.     

A proof of part of Haldane's conjecture on spin chains

It has been argued that the spectra of infinite length, translation and U(1) invariant, anisotropic, antiferromagnetic spin s chains differ according to whether s is integral or 1/2 integral: There is a range of parameters for which there is a unique ground state with a gap above it in the integral case, but no such range exists for the 1/2 integral case. We prove the above statement for 1/2 integral spin. We also prove that for all s, finite length chains have a unique ground state for a wide range of parameters. The argument was extended to SU(n) chains, and we prove analogous results in that case as well.Work partially supported by U.S. National Science Foundation grant PHY80-19754 and by the A.P. Sloan Foundation.Work partially supported by U.S. National Science Foundation grant PHY-85-15288.