On the Euler characteristics of random surfaces

In a Monte Carlo computer experiment, we simulate the Gibbs distribution of nonconnected two-dimensional surfaces isometrically embedded in three-dimensional Euclidean space with fixed boundary and the action given by the area. The simulation involves surfaces built out of plaquettes in a cubical lattice. The foam structure is analyzed in terms of correlations of the local fluctuations in the Euler characteristic and the area. The scaling behavior of the area and the Euler characteristic is discussed by varying the boundary. We show evidence of a phase transition point which is independent of the choice of the boundary. An existence proof is given of the thermodynamic limit for the models considered.Supported in part by the Deutsche Forschungsgemeinschaft and NSF grant No. Phy 81 09110A 01.     

关于自由能的一些讨论

给出了自由能函数的完整表达式,并说明了自由能展开式中各项的物理意义．指出了自由能展开式系数及自变量的共轭变量的意义,吉布斯自由能的一阶偏导数都是热力学变量;吉布斯自由能的二阶偏导数一律都是物性张量．讨论了相变过程中的自由能函数展开式应保留的项数等,还给出了相稳定性条件．     

用赝势方法研究铅的结构相变

 本文用赝势方法计算了铅的面心立方结构和金刚石结构的晶体总能，讨论了两种结构在高压下的稳定性。     

Monte Carlo study of self-avoiding surfaces

Two models of self-avoiding surfaces on the cubic lattice are studied by Monte Carlo simulations. Both the first model with fluctuating boundary and the second one with a fixed boundary are found to belong to the universality class of branched polymers. The algorithms as well as the methods used to extract the critical exponents are described in detail. The results are compared to other recent estimates in the literature.     

Structural and elastic properties of barium chalcogenides (BaX,X=O,Se, Te) under high pressure

In the present paper we have investigated the high-pressure, structural phase transition of Barium chalcogenides (BaO, BaSe and BaTe) using a three-body interaction potential (MTBIP) approach, modified by incorporating covalency effects. Phase transition pressures are associated with a sudden collapse in volume. The phase transition pressures and associated volume collapses obtained from TBIP show a reasonably good agreement with experimental data. Here, the transition pressure, NaCl-CsCl structure increases with decreasing cation-to-anion radii ratio. In addition, the elastic constants and their combinations with pressure are also reported. It is found that TBP incorporating a covalency effect may predict the phase transition pressure, the elastic constants and the pressure derivatives of other chalcogenides as well.      

Symmetrical adhesion of two cylindrical colloids to a tubular membrane

With the full treatment of the Helfrich model we theoretically study the symmetrical adhesion of two cylindrical colloids to a tubular membrane. The adhesion of the rigid cylinders with different radius from the membrane tube surface can produce both shallow wrapping with relatively small wrapping angle and deep wrapping with big wrapping angle. These significant structural behaviors can be obtained by analyzing the system energy. A second order adhesion transition from the desorbed to weakly adhered states is found, and a first order phase transition where the cylindrical colloids undergo an abrupt transition from weakly adhered to strongly adhered states can be obtained as well.     

双柱胶体粒子与管状生物膜的相互作用

本文采用Helfrich理论模型研究双柱胶体粒子与管状生物膜的相互作用.通过对柱状粒子与不同半径的管状膜吸附时的自由能分析发现,该体系存在具有较小包络角的弱吸附相以及具有较大包络角的深度吸附相.进一步研究发现体系从解吸附相到弱吸附相的相变是二级相变,而从弱吸附相到深度吸附相的相变是一级相变.双柱粒子与管状膜相对位置的不同会影响体系相变和结构.     

Multiple phase transitions in the generalized Curie-Weiss model

The generalized Curie-Weiss model is an extension of the classical Curie-Weiss model in which the quadratic interaction function of the mean spin value is replaced by a more general interaction function. It is shown that the generalized Curie-Weiss model can have a sequence of phase transitions at different critical temperatures. Both first-order and second-order phase transitions can occur, and explicit criteria for the two types are given. Three examples of generalized Curie-Weiss models are worked out in detail, including one example with infinitely many phase transitions. A number of results are derived using large-deviation techniques.     

Elastic wave surfaces for the (111) plane of cubic crystals

The nature of inverse velocity surfaces as well as energy surfaces for elastic wave propagation in the (111) plane have been studied for a number of cubic crystals. The sections of inverse velocity surfaces by the (111) plane exhibit six-fold symmetry in all cases. Cuspidal edges are exhibited with a six-fold symmetry by both the slow transverse and fast transverse shear modes in the (111) plane, unlike the case of the (100) and (110) planes for which only the slow transverse shear mode exhibits cuspidal edges. The slow transverse mode energy surface exhibits cuspidal edges along direction or an equivalent symmetry direction. The inverse velocity surfaces of the A-15 compounds exhibit unusually large inflexions for the slow transverse mode, whereas their energy surfaces have large cuspidal edges which intersect each other resulting in common regions of cusps.     

模拟退火算法在化学自由能模型中的应用

对化学自由能模型进行系统性的研究，着重分析化学反应动态平衡条件下粒子组分的求解方案，提出应用模拟退火算法寻找自由能密度函数极小值点的求解方案.该方案同时解决了两个难题：1）在一级相变区化学势平衡方程组可能遇到多个解而无法甄别其物理意义.通过模拟退火算法定位到自由能密度函数曲面的最低点，因而可从多个解中甄别出稳定的热力学平衡态.2）模拟退火算法用随机的"热涨落"消除初值敏感性，因而可采用同一套初值计算不同的温度密度点，为实现宽区域上大量温度密度点的连续快速计算奠定基础.作为该平衡态求解方案的应用，计算氦流体在"等离子相变"区的物态方程，揭示了丰富的"等离子相变"现象，并与第一性原理计算揭示的氢流体"液液相变"现象进行类比.     

Structural properties of silver iodide and copper iodide

The structural changes within the Silver iodide (AgI) and Copper iodide (CuI) induced by pressure have been investigated using an effective interaction potential. CuI and AgI in their parent zinc blende (ZnS) to rock salt (NaCl) through an intermediate structure have been reported. The calculated values for the phase transition pressures and associate volume collapses are generally in good agreement with measured data.      

Structural phase transitions and elastic properties of zirconia

The structural phase transformations in various phases (monoclinic, ortho I, ortho II, and tetragonal) of zirconia (ZrO₂) have been investigated using an effective interionic interaction potential. The cohesive energy, the equation of state, and the elastic properties of these phases have also been studied and found to reproduce well the experimentally observed data for almost all the phases of zirconia ceramics.     

The calculation of the surface energy of high-index surfaces in metals at zero temperature

We used the molecular dynamics simulation with interatomic potentials of the embedded atom method to calculate the high-index surface energies of the surfaces containing the 〈0 0 1〉 axis or 〈−1 1 0〉 axis in f.c.c. metal Al, Cu and Ni at zero temperature. We generalized an empirical formula based on structural unit model for high-index surfaces and present some new formulas that can be used to estimate the surface energy and structural feature of high-index surfaces very well. The results show that the closest surfaces have the lowest surface energy and the surface energies of the closest (1 1 1) surface and the next closest (1 1 0), (1 0 0) surfaces are the extremum on the curve of surface energy versus orientation angle. We also calculated the b.c.c. metal Fe and obtained a similar result. The difference is that in the b.c.c. metal the surface energies of the closest (1 1 0) surface and the next closest (1 0 0), (1 1 2) surfaces are the extremum on the curve of surface energy versus orientation angle. The results of theoretical simulation and the empirical formula consist well with the experiment data.     

稀土区奇A核晕带存在从转动到振动形状演化的直接证据(英文)

原子核的形状演化效应是核结构研究的重要基础问题之一。通常认为,A=160质量区的奇A核位于大形变核区域,它们的激发态能谱将呈现出典型的转动激发特征。然而,基于E-GOS曲线方法,发现随着角动量的增加,该质量区奇A核的晕带具有显著地从转动激发演化成为振动激发的形状演化现象。此外,为深入理解原子核形状演化的微观机制,采用Total-Routhian-Surface（TRS）方法针对稀土区的奇A核进行了理论计算,结果表明,165Yb和157Dy同位素在低激发态时具有稳定的长椭形变,当角动量大于0.50 MeV后,核芯的四极形变显著减小并开始产生三轴形变。The phase transition of nuclei with increasing angular momentum (or spin) and excitation energy is one of the most fundamental topics of nuclear structure research. The odd-N nuclei with A ≈160 are widely considered belonging to the well-deformed region, and their excitation spectra are energetically favored to exhibit the rotational characteristics. In this work, however, the evidence suggesting that the nuclei changes from rotation to vibration along the yrast lines as a function of spin was found. The simple method, named as E-Gamma Over Spin (E-GOS) curves, would be used to discern the evolution from rotational to vibrational structure in nuclei for various spin ranges. Meanwhile, in order to understand the band structure properties of nuclei, theoretical calculations have been performed for the yrast bands of the odd-A rare-earth nuclei within the framework of the total routhian surface (TRS) model. The TRS plots predict that the 165Yb and 157Dy isotopes have large quadrupole shapes at low spin states. At higher rotational frequency (hω~ >0.50 MeV), a clear reduction of the quadrupole deformation is indicated by the present results, and the isotopes become rigid in the γ deformation.     

半导体硅重构表面及其相变动力学的研究进展

简单介绍了文章作者在半导体硅重构表面及其相变动力学研究方面的进展.近期Si(111) (7×7)-(1×1)相变的实验研究发现,将温度升高到相变温度以上时,7×7岛面积以恒定的衰减速率随时间减小至零,且初始面积越大的岛这个衰减速率就越大.文章作者分析了大量的实验事实,由此提出了一个双速相场模型来解释这个重要而令人困惑的现象.模型重点是：在相变过程中,7×7关键结构变化较快,随后的层错消解过程要慢得多.这个模型完美地解释了相关实验现象,说明该模型抓住了关键物理要素,这种相场方法也可以用于其他半导体表面相变研究.     

Representation surfaces of Young''s modulus and Poisson''s ratio for BCC transition metals

 The general expressions for the compliance , Young's modulus E(h k l) and Poisson's ratio υ(h k l) along an arbitrary direction [h k l] are given for cubic crystals. The representation surfaces, for which the length of the radius vector in the [h k l] direction equals to E(h k l) or υ(h k l), are constructed for seven BCC transition metals Cr, Fe, Mo, Nb, Ta, V and W. Neglecting W, which is isotropic, both representation surfaces of Young's modulus and Poisson's ratio are spherical surfaces. The remaining BCC transition metals may be grouped into two classes. In the first group (Cr, Mo, Nb and V) with negative values of s_A, Young's modulus surface has eight depressed corners and six rounded protuberances at the centers of the faces. In the second group (Fe and Ta) with positive values of s_A, on the contrary, Young's modulus surface has eight rounded protuberance corners and six depressions at the centers of the faces. The contrary conclusions are obtained for Poisson's ratio.     

Structural stability of TiO and TiN under high pressure

The high pressure phase transition and elastic behavior of Transition Metal Compounds (TiO and TiN) which crystallize in NaCl-structure have been investigated using the three body potential model (TBPM) approach. These interactions arise due to the electron-shell deformation of the overlapping ions in crystals. The TBP model consists of a long range Coulomb, three body interactions, and the short-range overlap repulsive forces operative up to the second neighboring ions. The authors of this paper estimated the values of the phase transition pressures, associated volume collapses, and elastic constants, all of which were found to be closer to available experimental data than other calculations. Thus, the TBPM approach promises to predict the phase transition pressure and pressure variations of elastic constants of Transition Metal compounds.