利用密度泛函理论研究BnNi(n≤5)小团簇的结构和磁性

基于第一性原理，用密度泛函理论中的广义梯度近似方法，获得了B_nNi(n≤5)小团簇在不同自旋多重度下的几何构型，确定了最低能量结构，并计算了相应的频率、平均结合能和磁性. 结果表明：B_nNi(n≤5)小团簇最低能量结构的自旋多重度分别为2，1，2，1，2；Ni掺入B团簇后增大了其结合能；Ni原子磁矩和团簇总磁矩随团簇尺寸增大而呈现振荡趋势. 关键词： nNi小团簇')" href="#">B_nNi小团簇 自旋多重度 磁性     

The Spin-Statistics Theorem in Arbitrary Dimensions

We investigate the spin-statistics connection in arbitrary dimensions for hermitian spinor or tensor quantum fields with a rotationally invariant bilinear Lagrangian density. We use essentially the same simple method as for space dimension D=3. We find the usual connection (tensors as bosons and spinors as fermions) for D=8n+3,8n+4,8n+5, but only bosons for spinors and tensors in dimensions 8n±1 and 8n. In dimensions 4n+2 the spinors may be chosen as bosons or fermions. The argument hinges on finding the identity representation of the rotation group either on the symmetric or the antisymmetric part of the square of the field representation. Permanent address of L.J. Boya: Departamento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain     

Existence,uniqueness, and nondegeneracy of positive solutions of semilinear elliptic equations

We study positive solutions of the Dirichlet problem: u(x)+f(u(x))=0,xD ⁿ ,u(x)=0,xD ⁿ , whereD ⁿ is ann-ball. We find necessary and sufficient conditions for solutions to be nondegenerate. We also give some new existence and uniqueness theorems.Research supported in part by NSF Contract Number MCS 80-02337     

Theoretical investigation of selected hydrogenated germanium clusters (Ge5Hn,n = 0–12) from density functional theory calculations

ABSTRACT

We reported the selected hydrogen absorption of Ge₅H_n isomers and their Ge₅H_n^? anions in the size range of n?=?0–12 for the first time by B3LYP, BPW91, BHandHLYP and BP86 methods in combination with 6-311++G** basis sets. The optimum geometrical structure, relative stability, electronic properties and dissociation behaviour of Ge₅H_n (n?=?0–12) cluster and their Ge₅H_n^? anions were systematically analysed by a series of methods and can be applied to the study of more complex cluster systems. H bridged structure and double H bridged structures were found in the size range of n?=?1–6 in neutral clusters and corresponding anion with triangular bipyramidal framework of Ge₅. The visible odd-even oscillations were observed in the study of change rules with increasing size from the Δ₂E(n), H-dissociation energy (De), HOMO–LUMO band-gap (E_gap) and electron affinity (EA) energy. This conclusion indicated that Ge₅H_n clusters with even H atoms were more stable than clusters with odd H atoms. The infrared spectra of the Ge₅H_n (n?=?0–12) clusters were also simulated which will further stimulate study on germanium-based nanomaterials.     

Energies,Landé <Emphasis Type="Italic">g</Emphasis>-factors,and lifetimes for some excited levels of doubly ionized lanthanum

Using the relativistic Hartree-Fock (HFR) method developed by Cowan, we calculated the energy levels, Landé g-factors, and lifetimes for nd (n = 5–25), ns (n = 6–24), ng (n = 5–25), nf (n = 4–22), and np (n = 6–25) excited levels of doubly ionized lanthanum (La III, Z = 57). We compared the results with previously reported calculations and experiments.     

Structural and magnetic properties of bimetallic Con ? 1Cr clusters with density functional theory

We have investigated the structural and magnetic properties of small bimetallic Co _{n − 1}Cr (n = 2 − 9) clusters by means of spin-polarized density functional theory approach. We found the ground state structures of Co _{n − 1}Cr were very similar to those of pure Co _n except n = 3,6. The clusters were of high stability at n = 6. Magnetic moments showed an interesting size-dependent variation: the magnetic moments of Co _{n − 1}Cr can be obtained by minus 7μB for n = 2, 4, 6–9 or by plus 1μB for n = 5 from those of the Co _n counterparts. The different magnetic behavior stems from ferromagnetic alignment or ferrimagnetic alignment of Co and Cr atoms in Co _{n − 1}Cr, associated with their longer or shorter interatomic distances.      

Laser-Induced Diffraction Rings from an Absorbing Solution

We observed multiple diffraction rings of a cw Ar⁺ laser beam from a nitrobenzene solution of saturable absorber BDN (bis-(4-dimethylaminodithiobenzil)-nickel) caused by the spatial self-phase modulation at low incident optical intensities. We obtained 37 rings for a 200-μm thick sample at an optical intensity of 38 W/mm². The refractive-index change Δ;n and effective nonlinear refractive index n₂ were determined from the number of observed rings and by the z-scan technique. We obtained large values of Δ;n∼0.1 and n₂ = -2.9×;10^-5 cm²/W. This large nonlinearity is attributed to a thermal effect resulting from linear absorption.     

Dynamic hyperpolarizabilities of excited states of hydrogen

On the basis of the generalized Sturm expansion of the radial part of the Coulomb Green function, a computational method is proposed and numerical results are presented for the dynamic hyperpolarizability γ and the corrections E ⁽⁴⁾ (quadratic in the light intensity) to the quasi-energy of the ground and excited states of hydrogen with principal quantum numbers n≤5 in a monochromatic light field. In this approach, the problem is reduced to the summation of well-convergent double series of the hypergeometric kind, which ensures reliable numerical results both for states with a large n, and in a wide range of field frequencies ω, including the above-threshold frequency range of ?ω?|E _n | (|E _n | is the ionization potential of the state |nlm〉 under investigation). We consider the frequency dependence of γ and E ⁽⁴⁾, their differences for the cases of linear and circular polarizations of the field, and the relation between their real and imaginary parts, which determine the laser field-induced corrections to the position and width of energy levels. For n=5, the significant role of mixing the |nlm〉 states with different values of l by a laser field in the region of resonances on intermediate bound states is demonstrated. The linear (in intensity) corrections to the photoionization cross section for excited states are analyzed and the threshold intensity corresponding to the onset of atomic level stabilization is estimated for a number of states with n=3 and n=5.

     

<Emphasis Type="Italic">xPert</Emphasis>: computer algebra for metric perturbation theory

We present the tensor computer algebra package xPert for fast construction and manipulation of the equations of metric perturbation theory, around arbitrary backgrounds. It is based on the combination of explicit combinatorial formulas for the nth order perturbation of curvature tensors and their gauge changes, and the use of highly efficient techniques of index canonicalization, provided by the underlying tensor system xAct, for Mathematica. We give examples of use and show the efficiency of the system with timings plots: it is possible to handle orders n = 4 or n = 5 within seconds, or reach n = 10 with timings below 1 h.     

Branching rules for conformal embeddings

We give explicit formulas for the branching rules of the conformal embeddingssu(n(n+1)/2)₁su(n) _n+2,su(n(n–1)/2)₁su(n) _n–2,sp(n)₁so(n)₄su(2) _n , andso(m+n)₁so(m)₁ so(n)₁ withm andn odd.This research was supported in part by CONICET, CONICOR and SECYT.     

Global Regularity of Wave Maps¶II. Small Energy in Two Dimensions

We show that wave maps from Minkowski space ℝ^{1+ n} to a sphere S ^{m −1} are globally smooth if the initial data is smooth and has small norm in the critical Sobolev space , in all dimensions n≥ 5. This generalizes the results in the prequel [40] of this paper, which addressed the high-dimensional case n≥ 5. In particular, in two dimensions we have global regularity whenever the energy is small, and global regularity for large data is thus reduced to demonstrating non-concentration of energy. Received: 14 December 2000 / Accepted: 18 June 2001     

On the Equivalence¶of Certain Coset Conformal Field Theories

We demonstrate the equivalence of Kazama–Suzuki cosets G(m, n, k) and G(k, n, m) based on complex Grassmannians by proving that the corresponding conformal precosheaves are isomorphic. We also determine all the irreducible representations of the conformal precosheaves. Received: 24 August 2001 / Accepted: 5 December 2001     

Gauss Decomposition of the Yangian $$Y({\mathfrak{gl}}_{m|n})$$

We describe a Gauss decomposition for the Yangian of the general linear Lie superalgebra. This gives a connection between this Yangian and the Yangian of the classical Lie superalgebra Y(A(m − 1, n − 1)) (for m ≠ n) defined and studied in papers by Stukopin, and suggests natural definitions for the Yangians and Y(A(n, n)). We also show that the coefficients of the quantum Berezinian generate the centre of the Yangian . This was conjectured by Nazarov in 1991.     

Lattice instantons in the large dimension limit

We give a lattice construction of the discretizations of the topologically nontrivial maps S ^2n–1S ⁿ . For n=1, 2, 4, 8, these are the Hopf maps. The construction, based on Barnes-Wall lattices, Reed-Muller error-correcting codes, and Hadamard matrices, generalizes to n=2 ⁱ for i any integer. Manton's result for the cases n=2 and 4 (i.e., the monopole and instanton) are included. We argue that discrete harmonic analysis will be exact in the infinite dimension limit.Work supported in part by the DOE contract #DE-ACO2-87ER-40325.B.Department of Energy Outstanding Junior Investigator supported in part by DOE contract number DE-FGO5-85ER-40226.     

355 nm激光光电离甲醛飞行时间质谱的研究

利用脉宽为5 ns脉冲Nd: YAG 355 nm激光在功率密度为10¹¹–10¹² W/cm²条件下实现了甲醛含水团簇多光子电离, 并用飞行时间质谱对其电离产物和电离过程进行了研究. 实验中观测到了甲醛的质子化团簇系列 (CH₂O)_nH⁺(n=1–4), 甲醛的去质子化团簇系列(CH₂O)_nCHO⁺ (n=1–3), 以及两个起源于H₂CO去质子和质子化的含水团簇系列HCO⁺(H₂O)_n(n=1,3,5)和H₃CO⁺(H₂O)_n(n=1,3,5), 并对其中的一些团簇结构构型进行了猜测. 研究在不同的激光功率密度下甲醛团簇质谱峰的变换情况, 当激光密度达到9.3× 10¹¹ W/cm², 开始出现CH₂O和H₂O本体及其光致碎片的信号, 但对应的各质量峰没有明显地分辨开, 而是以包络的形式出现, 这是激光电离产生高能离子释放的一种表现, 提出认等离子体动力学鞘层加速机制(模型)来解释高能离子形成的物理机制. 关键词： 甲醛 团簇 飞行时间质谱 激光电离     

Structure and magnetism on iron oxide clusters Fe nO m ( n = 1-5): Calculation from first principles

We have studied structural and magnetic properties in small iron oxide clusters, Fe_nO_m (n = 1-5), by means of the first-principles calculation based on the density functional theory. We have used not only the usual spin polarized scheme, but also the scheme for noncollinear magnetism to carry out efficient optimization in magnetic structure. The result of FeO_m (m = 1-4) is in good agreement with the previous work. We found the stable adduct clusters in FeO₅ and FeO₆. The bridge site of oxygen atom is more favorable in energy than any other site for the clusters of Fe_nO (n = 2-5). As increasing the number of oxygen atoms, the alignment of Fe magnetic moments changes from ferromagnetic configuration to antiferromagnetic one at Fe_nO_n (n = 2-4). Received 10 September 2002 Published online 3 July 2003     

On Spherically Symmetric Solutions¶of the Compressible Isentropic Navier–Stokes Equations

We prove the global existence of weak solutions to the Cauchy problem for the compressible isentropic Navier–Stokes equations in ℝ ⁿ (n= 2, 3) when the Cauchy data are spherically symmetric. The proof is based on the exploitation of the one-dimensional feature of symmetric solutions and use of a new (multidimensional) property induced by the viscous flux. The present paper extends Lions' existence theorem [15] to the case 1< γ <γ _n for spherically symmetric initial data, where γ is the specific heat ratio in the pressure, γ _n = 3/2 for n= 2 and γ _n = 9/5 for n= 3. Dedicated to Professor Rolf Leis on the occasion of his 70th birthday Received: 17 January 2000 / Accepted: 3 July 2000     

ConCm±(n=1-5; m=1,2)团簇的密度泛函理论研究

本文采用基于自旋极化的密度泛函理论系统研究了Co_nC_m^± (n=1-5; m=1,2)团簇的几何结构和电子结构特性. 将Co_nC^± (n=2-5)团簇中的一个Co替换为C原子, 个体的基态几何结构发生明显变化; 在Co_nC₂^± (n=1-5)团簇的生长序列中, 发现从n=3开始团簇中的两个C原子有彼此分离分布的趋势, 我们分析, 这是Co金属能够维持单壁碳纳米管(SCNTs)保持开口生长, 成为非常有效的一种催化剂的重要原因. 同时, 将Co_nC^± (n=2-5)团簇中添加一个Co原子后系统的总磁矩出现大幅下降的趋势, 但仍保持奇偶交替的规律. 通过比较中性及带电的Co_nC以及Co_nC₂ (n=1-5)团簇的碎裂能, 本工作发现: 由实验获取的SCNTs应均为带正电的体系, 这一结论与已有的实验模型拟合得很好.     

On Some Mean Matrix Inequalites of Dynamical Interest

Let A SL(n,). We show that for all n>2 there exist dimensional strictly positive constants C_n such thatwhere ||A|| denotes the operator norm of A (which equals the largest singular value of A), denotes the spectral radius, and the integral is with respect to the Haar measure on O_n, normalized to be a probability measure. The same result (with essentially the same proof) holds for the unitary group U_n in place of the orthogonal group. The result does not hold in dimension 2. This answers questions asked in [3, 5, 4]. We also discuss what happens when the integral above is taken with respect to measure other than the Haar measure.The author is supported by the NSF DMS.Acknowledgement The author would like to thank Amie Wilkinson for bringing the question to his attention.     

Symmetry-breaking transitions and dissociation of two-dimensional Plateau borders

We have experimentally studied the dissociation/coalescence of internal Plateau borders (PBs) in simple monolayer bubble clusters, as a result of changing the liquid fraction. At large liquid content, the clusters consist of n bubbles of the same size, symmetrically placed around an internal n-sided PB (n-PB). On decreasing the liquid fraction we observed symmetry-breaking transitions in the 4- and 5-bubble clusters (but not in the 3-bubble cluster), followed by dissociation of the PBs. We used the Surface Evolver to determine the various equilibrium configurations of the corresponding two-dimensional wet clusters and their surface energies. The sequence of 4-bubble cluster configurations observed on varying the liquid fraction correlates qualitatively with that predicted on the basis of Surface Evolver calculations. The same is not true of the 5-bubble cluster.