A note on differentiability of the cluster density for independent percolation in high dimensions

The cluster density function of independent percolation in ad-dimensional lattice is considered. For eachn, it is shown that(p) has finitenth leftderivative at critical probabilityp _c ifd is sufficiently large. This result agrees with the Bethe lattice approximation, where thenth one-sided derivative of(p) is bounded atp _c for alln.     

选择理论生成幂律的扩展性研究

应用选择理论可以解释人类行为导致的幂律分布现象.通过对选择理论合理而简单的扩展,发现了更多幂律生成机制.研究表明选择理论对于单调的门限分布规律体现出生成机制的一般性;此类机制的扩展对幂律成因的深入研究具有较强的理论意义. 关键词： 选择理论 幂律分布 门限规律     

Tree graph inequalities and critical behavior in percolation models

Various inequalities are derived and used for the study of the critical behavior in independent percolation models. In particular, we consider the critical exponent associated with the expected cluster sizex and the structure of then-site connection probabilities =_n(x₁,..., x_n). It is shown that quite generally 1. The upper critical dimension, above which attains the Bethe lattice value 1, is characterized both in terms of the geometry of incipient clusters and a diagramatic convergence condition. For homogeneousd-dimensional lattices with (x, y)=O(¦x -y¦^–(d–2+), atp=p _c, our criterion shows that =1 if > (6-d)/3. The connectivity functions _n are generally bounded by tree diagrams which involve the two-point function. We conjecture that above the critical dimension the asymptotic behavior of _n, in the critical regime, is actually given by such tree diagrams modified by a nonsingular vertex factor. Other results deal with the exponential decay of the cluster-size distribution and the function ₂ (x, y). A. P. Sloan Foundation Research Fellow. Research supported in part by the National Science Foundation Grant No. PHY-8301493.Research supported in part by the National Science Foundation Grant No. MCS80-19384.     

Essential singularity in percolation problems and asymptotic behavior of cluster size distribution

It is rigorously proved that the analog of the free energy for the bond and site percolation problem on in arbitrary dimension (> 1) has a singularity at zero external field as soon as percolation appears, whereas it is analytic for small concentrations. For large concentrations at least, it remains, however, infinitely differentiable and Borel-summable. Results on the asymptotic behavior of the cluster size distribution and its moments, and on the average surface-to-size ratio, are also obtained. Analogous results hold for the cluster generating function of any equilibrium state of a lattice model, including, for example, the Ising model, but infinite-range andn-body interactions are also allowed.Supported by the Fonds National Suisse de la Recherche Scientifique (to HK).     

Si_4N_4团簇结构与性质的密度泛函理论研究(英文)

用密度泛函理论(DFT)中的杂化密度泛函B3LYP方法,在6-31G(d)的水平上对Si4N4团簇的可能结构进行了几何结构优化和电子结构计算,得到了可能的17个异构体.Si4N4团簇的最稳定结构是有8个Si-N键的平面结构.用自然键轨道(NBO)方法分析了成键性质.计算结果表明,Si-N键中Si原子向N原子有较大的电荷转移,因此Si-N原子间有较强的电相互作用;最强的IR和Raman谱峰分别位于1387.64cm-1和1415.05cm-1处;并计算了Si4N4团簇的最稳定结构的极化率和超极化率.     

Si3N4团簇结构与性质的密度泛函理论研究

用杂化密度泛函B3LYP在6-31G*的水平上研究了Si3N4团簇可能结构的平衡几何构型和电子结构,得到了24个可能的异构体.Si3N4团簇的最稳定结构是由7个Si—N键和2个N—N键形成的3个四边形构成的三维结构.用自然键轨道方法(NBO)分析了成键性质,结果表明,Si—N键中的Si、N原子的净电荷较大,说明Si—N键中Si、N原子的相互作用主要是电相互作用.最强的IR和Raman峰分别位于1033.40 cm-1,473.63 cm-1处.并且讨论了最稳定结构的极化率和超极化率.     

Density functional theory study on the structure and properties of Si3N4clusters

The hybrid density functional theory B3LYP with basis sets 6-31G· has been used to study on the equilibrium geometries and electronic structures of possible isomers of Si3N4 clusters. 24 possible isomers are obtained. The most stable isomer of Si3N4 is a 3D structure with 7 Si-N bonds and 2 N-N bonds that could be formed by 3 quadrangles. The bond properties of the most stable isomer was analyzed by using natural bond orbital method (NBO), the results suggest that the charges on Si and N atoms in Si-N bonds are quite large, so the interaction of N-Si atoms in Si3N4 cluster is of strongly electric interaction. The primary IR and Raman vibrational frequency located at 1033.40 cm-1, 473.63 cm-1 respectively. The polarizabilities and hyperpolarizabilities of the most stable isomer are also analyzed.     

Density functional theory study on the structure and properties of Si3N4 clusters

The hybrid density functional theory B3LYP with basis sets 6-31G＊ has been used to study on the equilibrium geometries and electronic structures of possible isomers of Si3N4 clusters. 24 possible isomers are obtained. The most stable isomer of Si3N4 is a 3D structure with 7 Si-N bonds and 2 N-N bonds that could beformed by 3 quadrangles. The bond properties of the most stable isomer was analyzed by using natural bond orbital method （NBO）, the results suggest that the charges on Si and N atoms in Si-N bonds are quite large, so theinteraction of N-Si atoms in Si3N4 cluster is of strongly electric interaction. The primary IR and Raman vibrational frequency located at 1033.40 cm^-1, 473.63 cm^-1 respectively. The polarizabilities and hyperpolarizabilities of the most stable isomer are also analyzed.     

Structures and electronic properties of SimN8-m（0 〈 m 〈 8） clusters： a density functional theory study

The geometries, electronic structures and related properties of SimN8-m（0 〈 m 〈 8） clusters are studied using density functional theory （DFT） with hybrid functional B3LYP. The calculated results reveal several trends. For any stoichiometric clusters, the lowest energy isomers with an alteration of N and Si atoms are favourable in energy if the numbers of Si and N atoms are large enough to form ... Si N-Si-N... alternative chains. The bond lengths of single Si-N bonds are very close to the corresponding values of the bulk and other SiN clusters. The geometries for N-rich and Si4N4 clusters are planar structures, but three-dimensional structures are favourable in energy for Si-rich clusters. With the increase of m, the isotropic polarizability and average polarizability increase, the total binding energies generally decrease, the HOMO-LUMO gap and vertical ionization potential oscillate with increasing number of valence electrons, and their values with even valence electrons are larger than those with odd valence electrons. The atomic charges, IR and Raman properties are also reported.     

价键优选法：二、三周期小团簇的理论研究

使用价键优选法，在较小的计算量下，系统地得到了二、三周期元素团簇体系(直到四原子为止)关键结构的性质.还能得到团簇从双原子到四原子的演化过程.对所有团簇的电子结构进行分析，可以理解特定元素的四原子团簇出现T_d立体结构的原因.更加有趣的是，通过较小团簇结合能和对应元素单质宏观性质( 熔点、沸点等)的相应变化关系，能够理解在熔解、沸腾过程中关键结构的作用. 关键词： 价键优选法 团簇关键结构 团簇 第一原理分子动力学 物质性质     

MgmBn(m=1,2;n=1—4)团簇结构与性质的密度泛函理论研究

用密度泛函理论(DFT)的杂化密度泛函B3LYP方法在6-31G基组水平上对Mg_mB_n(m=1,2;n=1-4)团簇各种可能的构型进行几何结构优化，预测了各团簇的最稳定结构.并对最稳定结构的振动特性、电离势、成键特性、极化率和超极化率等性质进行了理论研究.结果表明，团簇的最稳定结构大多是平面结构，团簇的稳定结构中通常是几个呈负电性的B原子形成一个负电中心，而其他B原子和Mg原子通常处在端位，且显正电性；团簇中通常是B-B键和B-Mg键共存，极少出现Mg-Mg键， 关键词： mB_n(m=1')" href="#">Mg_mB_n(m=1 n=1-4)团簇 密度泛函理论 结构与性质     

(HMgN3)n(n=1–5)团簇结构与性质的密度泛函理论研究

利用密度泛函理论在B3LYP/6-311G^*水平上对叠氮化合物(HMgN₃)_n(n=1–5)团簇各种可能构型进行了几何优化,预测了各团簇的最稳定结构. 并对最稳定结构的成键特性、电荷分布、振动特性及稳定性进行理论研究. 结果表明:HMgN₃团簇最稳定结构为直线型;(HMgN₃)_n(n=2,5)团簇最稳定结构为叠氮基中N原子和金属原子相连构成Mg–N–Mg结构;(HMgN₃)_n(n=3,4)团簇最稳定结构为叠氮基与Mg原子相互链接形成的环状结构. 团簇最稳定结构中金属Mg原子均显示正电性,H原子均显示负电性,叠氮基中间的N原子显示正电性、两端的N原子显示负电性,且与Mg原子直接作用的N原子负电性更强. Mg–N键和Mg–H键为典型的离子键,叠氮基内N原子之间是共价键. 团簇最稳定结构的红外光谱分为三部分,其最强振动峰均位于2258–2347 cm^-1,振动模式为叠氮基中N–N键的反对称伸缩振动. 叠氮基在团簇和晶体中结构不变,始终以直线型存在. 稳定性分析显示,(HMgN₃)₃团簇相对于其他团簇更为稳定. 关键词： 3)_n(n=1–5)团簇')" href="#">(HMgN₃)_n(n=1–5)团簇 叠氮基 密度泛函理论 结构与性质     

Linear and nonlinear optical properties of semiconductor nanorings with magnetic field and disorder - Influence on excitons and biexcitons

Linear and nonlinear optical absorption spectra are studied theoretically for semiconductor nanorings penetrated by a magnetic field. Due to the Aharanov-Bohm effect the spectral position as well as the oscillator strength of the exciton change periodically as function of the magnetic flux enclosed by the ring. In the nonlinear differential absorption spectra it is found that the magnetic field strongly modifies Coulomb many-body correlations. In particular, the magnetic-field-induced increase of the exciton binding energy is accompanied by a decrease of the biexciton binding energy. The persistence of these effects in the presence of energetic disorder is analyzed. Received 31 January 2001     

Size and concentration effects in the optical properties of alloyed ( Au x Ag 1 - x ) n and core-shell ( Ni x Ag 1 - x ) n embedded clusters

Optical properties of mixed clusters (Au_xAg _{1 - x} ) _n and (Ni_xAg _{1 - x} ) _n , produced by laser vaporization and embedded in an alumina matrix, are reported. The size effects are investigated for different concentrations (x = 0.25, 0.5 and 0.75) in the diameter range 2-4 nm. For alloyed clusters (Au_xAg _{1 - x} ) _n of a given size an almost linear evolution of the surface plasmon frequency ω _s with the concentration is observed (between those of pure gold and pure silver clusters). Moreover the blue-shift and the damping of the resonance with decreasing size is all the more important as the gold concentration in the particles increases. Such results are in agreement with theoretical calculations carried out in the frame of the time-dependent local-density-approximation (TDLDA) including an inner skin of ineffective screening and the porosity of the matrix. The optical response of (Ni_xAg _{1 - x} ) _n clusters exhibits a surface plasmon resonance in the same spectral range as the one observed for pure silver clusters, but considerably damped and broadened. For a given mean cluster size 3.0 nm, a blue-shift of the resonance is observed when increasing the nickel concentration (between x = 0.25 and x = 0.75). The results are in good qualitative agreement with classical predictions in the dipolar approximation, assuming a core-shell geometry. Received 21 November 2000     

Momentum transfer theory of ion transport under the influence of resonant charge transfer collisions: the case of argon and neon ions in parent gases

Transport properties of ion swarms in presence of Resonant Charge Transfer (RCT) collisions are studied using Momentum Transfer Theory (MTT). It was shown that, not surprisingly, RCT collisions may be represented as a special case of elastic scattering. Using the developed MTT we tested a previously available anisotropic set of cross-sections for Ar+Ar ⁺ collisions by making the comparisons with the available data for the transverse diffusion coefficient. We also developed an anisotropic set of Ne+Ne ⁺ integral cross-sections based on the available data for mobility, longitudinal and transverse diffusion. Anisotropic sets of cross-sections are needed for Monte Carlo simulations of ion transport and plasma models. Received 16 June 2002 / Received in final form 2nd August 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: vrhovac@phy.bg.ac.yu RID="b" ID="b"e-mail: zoran@phy.bg.ac.yu     

Cross sections and transport properties of Cl<Superscript>-</Superscript> ions in noble gases

We have used a simple semi-analytic — momentum transfer theory (MTT) to develop negative halogen ions/noble gases momentum transfer integral cross sections based on the available data for reduced mobility at 300 K as a function of E/N. The unfolded cross sections were validated or further improved by assuring a good agreement between our Monte Carlo (MC) calculated transport data and the available experimental results. The data are produced with an aim to provide plasma modellers with cross section data and transport coefficients. We have also calculated the net rates of elastic scattering and detachment.