IONIZATION POTENTIALS OF NICKEL CLUSTERS

The mean coordination numbers of some nickel clusters have been calculated for some proposed geometric structures for them, and their ionization potentials are obtained using an effective coordination-number model. It is shown that the mean effective-coordination number of all atoms of a cluster should be taken as a parameter to describe the d-band width of the cluster instead of mean effective coordination number of surface atoms.     

固溶体的位形配分函数

这篇短文分二节,第一节是将王德懋,许永焕及作者所合写的一篇论文中的求固溶体的配分函数的方法,应用到各种固溶体上。我们处理了二种不同晶体结构的情形,处理了有长程秩及无长程秩的情形,处理了只有最近邻作用而无其他邻作用的情形及既有最近邻作用又有次最近邻作用的情形。在各种不同情形下,这个方法都被证明是合用的。第二节是用同一方法讨论准化学公式。我们证明了在保留了这个方法中所谓结构常数中的最低一个时,准化学公式是成立的,不论固溶体中有多少种原子。其次,我们指出,在保留较高级的结构常数后,寻常的准化学公式应如何的改进。最后我们直接写下三个互为近邻的原子所构成的各种不同的集团的数目的准化学公式,讨论了与此相应的组合数,并指出这样的理论与我们的理论是不同的。     

Coordination number of percolating clusters

The coordination number of percolating clusters and their backbones, on the square and simple cubic lattices, is investigated numerically. At the percolation threshold, the average coordination number of the clusters is 2.239 ± 0.012 and 2.079 ± 0.016 for d = 2 and d = 3, respectively. The corresponding numbers for the backbones are 2.402 ± 0.016 and 2.246 ± 0.034.     

Über die Interpretation der Röntgenbeugungsdiagramme von mehrkomponentigen Schmelzen

The final results of x-ray diffraction experiments in molten alloys are electron distribution curves. These are used to get a decision between statistical distribution of the atoms of different kinds in the melt, between ordering of the atoms or between segregation. The according equations are deduced and finally a simple graphical method for the evaluation of the results is given. Important fact for the evaluation of molten alloys with a great difference between the atomic numbers of the two components is the number of scattering electrons in the first coordination sphere. With molten alloys which show little difference between the atomic numbers of the components the radius of the first coordination sphere is deciding. Finally it is shown, that the short range order parameter, which until now only was used in regard to the ordering in solid solutions, also can be used to get valuable results of the degree of ordering in molten alloys.     

Discrete modeling of the mechanics of entangled materials

We employ a discrete computational model to study the entanglement transition of non-cross-linked semiflexible fibers during isostatic compressions. We determine, as a function of the fiber aspect ratio, packing densities and caging numbers, i.e., the density and number of contacts per fiber at the entanglement transition. The caging number is found to be 8 for short fibers and to drop down to 4 for longer fibers. Compressions beyond the entanglement transition allow us to determine, for these networks that deform primarily by bending, the scaling exponents of the pressure and of the bulk modulus (=3), as well as of the number of contacts per fiber (=1).     

The kinetics of adsorption on fractals: A numerical experiment

An approach similar to the “random rain” model was used to simulate the formation of a three-dimensional cluster from identical particles. The cluster had a fractal structure with the mean fractal number that increased as the number of constituting “atoms” grew. We simulated adsorption on this cluster and considered the relation between the structure of the cluster and the number of vacant centers on which adsorption could occur. By analogy with the coordination number of an atom, the notion of the coordination number of a fractal particle was introduced. The fractal and coordination numbers were shown to be interrelated. An equation for the kinetics of irreversible adsorption on fractals was suggested.     

Chaos from turbulence: stochastic-chaotic equilibrium in turbulent convection at high Rayleigh numbers

It is shown that the correlation function of the mean wind velocity generated by a turbulent thermal convection (Rayleigh number Ra ～ 10(11)) exhibits exponential decay with a very long correlation time, while the corresponding largest Lyapunov exponent is certainly positive. These results together with the reconstructed phase portrait indicate the possible presence of chaotic component in the examined mean wind. Telegraph approximation is also used to study the relative contribution of the chaotic and stochastic components to the mean wind fluctuations and an equilibrium between these components has been studied in detail.     

A Two-Surface Problem of the Electron Flow in a Semiconductor on the Basis of Kinetic Theory

A steady flow of electrons in a semiconductor between two parallel plane Ohmic contacts is studied on the basis of the semiconductor Boltzmann equation, assuming a relaxation-time collision term, and the Poisson equation for the electrostatic potential. A systematic asymptotic analysis of the Boltzmann–Poisson system for small Knudsen numbers (scaled mean free paths) is carried out in the case where the Debye length is of the same order as the distance between the contacts and where the applied potential is of the same order as the thermal potential. A system of drift-diffusion-type equations and their boundary conditions is obtained up to second order in the Knudsen number. A numerical comparison is made between the obtained system and the original Boltzmann–Poisson system.     

Maximum entropy approach for deducing amino Acid interactions in proteins

We present a maximum entropy approach for inferring amino acid interactions in proteins subject to constraints pertaining to the mean numbers of various types of equilibrium contacts for a given sequence or a set of sequences. We have carried out several kinds of tests for a two-dimensional lattice model with just two types of amino acids with very promising results. We also show that the method works very well even when the mean numbers of contacts are not known and therefore can be applied to real proteins.     

Continuum model of bimetallic nanoparticles for calculating partial coordination numbers

A way of calculating partial coordination numbers is proposed for bimetallic nanoparticles with different radial distributions of atoms relative to a selected center. It is based on a continuum approximation for the atomic density distribution in the volume of nanoparticles (continuum model) and does not require the use of cluster-based models of nanoparticles to obtain information on the distribution of components in nanoparticles. The results obtained in this manner are compared to those from directly calculating the partial coordination numbers in atomic clusters.     

Water characteristics depend on the ionic environment. Thermodynamics and modelisation of the aquo ions

We have characterized the aquo ion in solution by five parameters: the charge q and the corresponding crystallographic radius R_c of the ion with the coordination number N, the radius R_w of the water molecule in the aquo complex and the number H of water molecules in the second hydration shell. A consistent set of these parameters has been derived from literature data. From an analysis of experimental determinations of the cation-oxygen distance and evaluation of electrostriction phenomena, we have concluded that the radius R_w of the water molecule depends on the charge of the central ion and on its crystallographic radius.

The different ion-water interactions and previous models are discussed, and we propose an ionic model and a general relation which gives the free hydration energy, ΔG(hyd), of a monatomic ion with ionic character. It depends on the five fundamental characteristics of the aquo ion and reproduces the experimental data with standard deviation less than 0.3%. In the case of lanthanides, it is shown that the model including average values of the oxygen-cation distance, or different distances, taking into account the local structure of the aquo ion, gives similar thermodynamic data. The proposed model gives also the possibility to deduce properties of the ions such as consistent values of the coordination numbers.     

Observation of a parity oscillation in the conductance of atomic wires

Using a scanning tunnel microscope or mechanically controllable break junctions atomic contacts for Au, Pt, and Ir are pulled to form chains of atoms. We have recorded traces of conductance during the pulling process and averaged these for a large number of contacts. An oscillatory evolution of conductance is observed during the formation of the monoatomic chain suggesting a dependence on the numbers of atoms forming the chain being even or odd. This behavior is not only observed for the monovalent metal Au, as was predicted, but is also found for the other chain-forming metals, suggesting it to be a universal feature of atomic wires.     

Sound Attenuation in a Circular Duct of a Viscous Medium in the Absence of Mean Flow

Abstract

An analytical method to study the effect of viscosity of a medium and the wave number on sound propagation and sound attenuation numbers in circular ducts has been presented. The method is based on the variation of parameters of the solution corresponding to the case of inviscid acoustic waves in circular ducts and axisymmetric modes. A mathematical model is constructed to describe the physical problem in general. Three basic assumptions have been considered, namely, each flow quantity has been written as the sum of a steady mean flow and an unsteady acoustic flow quantity. The effect of thermal conductivity of the gas has been neglected as well as no mean flow. The results for a wide range of wave numbers and Reynolds numbers show that for a viscous medium, the propagation number is a weak function of the Reynolds number, and as the Reynolds number increases, the propagation number approaches its inviscid value. Also the propagation number is independent of the wave number. For the attenuation number, it decreases monotonically with the increase of the Reynolds number and it vanishes when Reynolds number exceeds 10⁴.     

Local structure analysis of YSZ by Y-89 MAS-NMR

The local coordination structure around Yttrium ions in yttria stabilized zirconia (YSZ) has been investigated by ⁸⁹Y MAS-NMR. The NMR spectrum showed multiple peaks corresponding to yttrium ions in different coordination numbers. The compositional dependence of spectra was observed. Yttrium ions of different oxygen coordination number were quantified. The oxygen vacancy concentration around the cations was determined. It was found that the vacancies were distributed around Zirconium ions in lower Y₂O₃ concentrations, and the vacancy concentration located to Yttrium began increasing at concentrations above 10 mol% Y₂O₃. The local structure change was able to be directly observed by ⁸⁹Y NMR measurements.     

直接模拟离散颗粒对湍流射流的影响

发展了一种基于双向耦合的直接数值模拟方法,研究了两相湍流射流中离散颗粒对气相射流的影响。流场采用高分辨率的算法直接耦合求解,颗粒相采用拉格朗日方法跟踪。结果表明不同Stokes数的颗粒对射流的影响不同。所有的颗粒都降低了射流速度半宽,但对流向平均速度剖面的影响比较复杂.Stokes数为0.01和50的颗粒降低了横向平均速度,使得湍流强度剖面变的更宽更低;而Stokes数为1的颗粒则增加了横向平均速度,降低了湍流强度。     

Shell evolution in neutron-rich nuclei: the single particle perspective

The isospin dependence of spin-orbit(SO)splitting becomes increasingly important as N/Z increases in neutron-rich nuclei.Following the initial independent-particle strategy toward explaining the occurrence of magic numbers,we systematically investigated the isospin effect on the shell evolution in neutron-rich nuclei within the Woods-Saxon mean-field potential and the SO term.It is found that new magic numbers N=14 and N=16 may emerge in neutron-rich nuclei if one changes the sign of the isospin-dependent term in the SO coupling,whereas the traditional magic number,N=20,may disappear.The magic number N=28 is expected to be destroyed despite the sign choice of the isospin part in the SO splitting,corresponding to the strength of the SO coupling term.Meanwhile,the N=50 and 82 shells may persist within the single particle scheme,although there is a decreasing trend of their gaps toward extreme proton-deficient nuclei.Besides,an appreciable energy gap appears at N=32 and 34 in neutron-rich Ca isotopes.All these results are more consistent with those of the interacting shell model when enhancing the strength of the SO potential in the independent particle model.The present study may provide a more reasonable starting point than the existing one for not only the interacting shell model but also other nuclear many-body calculations toward the neutron-dripline of the Segrèchart.     

Linking numbers for self-avoiding loops and percolation: application to the spin quantum hall transition

Nonlocal twist operators are introduced for the O(n) and Q-state Potts models in two dimensions which count the numbers of self-avoiding loops (respectively, percolation clusters) surrounding a given point. Their scaling dimensions are computed exactly. This yields many results: for example, the number of percolation clusters which must be crossed to connect a given point to an infinitely distant boundary. Its mean behaves as (1/3sqrt[3] pi) |ln( p(c)-p)| as p-->p(c)-. As an application we compute the exact value sqrt[3]/2 for the conductivity at the spin Hall transition, as well as the shape dependence of the mean conductance in an arbitrary simply connected geometry with two extended edge contacts.     

Character expansion methods for matrix models of dually weighted graphs

We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally due to Itzykson and Di Francesco, and then demonstrate how to take the largeN limit of this expansion. The relationship to the usual matrix model resolvent is elucidated. Our methods give as a by-product an extremely simple derivation of the Migdal integral equation describing the largeN limit of the Itzykson-Zuber formula. We illustrate and check our methods by analysing a number of models solvable by traditional means. We then proceed to solve a new model: a sum over planar graphys possessing even coordination numbers on both the original and the dual lattice. We conclude by formulating the equations for the case of arbitrary sets of even, self-dual coupling constants. This opens the way for studying the deep problems of phase transitions from random to flat lattices. January 1995     

Role of rigidity in the fluid-solid transition

We examine the fluid-solid transition for a hard-disk system. By counting the near neighbors in the average configurations of a grand-canonical Monte Carlo simulation, this enables us to relate the thermodynamic transition with the rigidity theory, since we find that the coordination number in the fluid-solid transition is close to the coordination number predicted by a mean field rigidity theory, due to dynamical jamming of particles, where the contact region between disks is the radial ring outside a disk with a maximum allowed coordination number that is not bigger than six. Using these ideas, we were able to produce a continuous glass-like transition when nucleation of rigidity is suppressed.     

On the properties of cycles of simple Boolean networks

We study two types of simple Boolean networks, namely two loops with a cross-link and one loop with an additional internal link. Such networks occur as relevant components of critical K=2 Kauffman networks. We determine mostly analytically the numbers and lengths of cycles of these networks and find many of the features that have been observed in Kauffman networks. In particular, the mean number and length of cycles can diverge faster than any power law.