A note on the cluster variation method

Kikuchi's cluster variation method (CVM) is reformulated as the truncation of a Möbius inversion. An attempt is made to explicate and simplify the various approaches to the CVM. This formulation makes apparent the connection of the method with other types of cluster approximation. An illustration of the procedure is provided.     

Superposition approximations from a variation principle

A variation principle is introduced involving then-particle molecular distribution function (where 1 n N) for a fluid containingN molecules. An integral involving any approximaten-particle distribution function proves to define aleast upper bound to the true system free energy. This integral can, therefore, be minimized with respect to the form of a trial distribution function to provide a best estimate to the exact distribution function. When no other constraints, save the requirement of normalization, are applied to the trial function, the extremum corresponds to the exact function. Using this variation principle, it is possible to demonstrate that the optimum triplet superposition approximation is the Krikwood approximation, and that the optimum quadruplet approximation is the form suggested by Fisher and Kopeliovich. Furthermore, all higher-order optimum superposition approximations are specified.Research supported under NSF Grant GP-20884.     

A method of computational flow imaging applied to better comparison between theory and experiments

Computational flow imaging (CFI) is a prediction of transmission of optical waves through theoretical flow fields. In this paper, it is introduced to perform flow visualization for measurements of thermal parameters. A new method to achieve better plan of experiments and better comparison between theory and experiment was proposed. The influence of solved theoretical flow fields on quality of Computational Flow Imaging is also studied. It is found that the grid density of numerical analogue should satisfy the Nyquist-Shannon sampling principle to ensure the CFI can be correctly expressed.     

The comparison of the CPU time between SO-FDTD method and PLCDRC method for dispersive media

The precision and computational efficiency of the shift operator finite-difference time-domain (SO-FDTD) method are compared with those of the piecewise linear current density recursive convolution (PLCDRC) method by simulating the electromagnetic wave at different frequency propagation in homogeneous unmagnetized plasma in this paper. The results show that the two methods almost have the same precision, but the CPU time of the SO-FDTD method is less than that of the PLCDRC method, this is because the SO-FDTD method eliminates many convolution operations of the PLCDRC method.     

Reconciliation between the Mach principle and the principle of equality of the inertial and gravitational masses

A study of kinematics of a 2-body system is used to show that the Mach principle, previously rejected by general relativity, can still serve as an alternative to the concept of absolute space, if one assumes that the background of distant stars determines both the inertial and the gravitational masses of a body.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 10–13, June, 1990.     

非同步的多普勒水声跟踪定位原理

提出了一种新的水声跟踪定位方法,它仅测量目标非同步声信标到达各测量基元的接收信号和频率,来对目标声学跟踪定位,称之为非同步多普勒定位方法,本文介绍其原理,处和仿真结果。     

The principle of the maximum entropy method

Abstract

The theoretical background of the maximum entropy method (MEM) when it is applied to restore the electron or nuclear densities from diffraction data is described. In MEM, the concept of “entropy” is introduced to deal with any incompleteness in an observation in a proper way. An incompleteness causes some ambiguities in the results to some extent. The essence of the method is to find a solution which necessarily agrees with the observation, leaving the measure of ambiguities (entropy) maximum. A few results for simple structures with typical types of chemical bonding are also presented.     

A comparison between Lanczos and moment methods

A simple procedure is suggested for generating the 2n - 1 Lanczos tridiagonal elements from the 2n - 1 moments of any hamiltonian with regard to a given starting vector. The numerical feasibility is studied in the quartic oscillator example.     

A comparison of vowel normalization procedures for language variation research

An evaluation of vowel normalization procedures for the purpose of studying language variation is presented. The procedures were compared on how effectively they (a) preserve phonemic information, (b) preserve information about the talker's regional background (or sociolinguistic information), and (c) minimize anatomical/physiological variation in acoustic representations of vowels. Recordings were made for 80 female talkers and 80 male talkers of Dutch. These talkers were stratified according to their gender and regional background. The normalization procedures were applied to measurements of the fundamental frequency and the first three formant frequencies for a large set of vowel tokens. The normalization procedures were evaluated through statistical pattern analysis. The results show that normalization procedures that use information across multiple vowels ("vowel-extrinsic" information) to normalize a single vowel token performed better than those that include only information contained in the vowel token itself ("vowel-intrinsic" information). Furthermore, the results show that normalization procedures that operate on individual formants performed better than those that use information across multiple formants (e.g., "formant-extrinsic" F2-F1).     

Dislocation modeling in bcc lithium: A comparison between continuum and atomistic predictions in the modified embedded atoms method

In this study, the modified embedded-atom method (MEAM) was applied to compare the predictions of dislocation core properties obtained by molecular statics with the continuum predictions obtained in the framework of the simplified 1D-Peierls–Nabarro model. To this end, a set of four fictive Li potentials in the MEAM framework was proposed with the condition that all four potentials reproduce the same elastic constants, the same transition energies between bcc and fcc crystal structures, and between bcc and hcp crystal structures, while the unstable stacking fault energy on the plane {110} in the direction <111> was varied around the value predicted by first-principles. Within these potentials, direct atomistic calculations were performed to evaluate dislocation core properties such as dislocation half width and Peierls stress and the results were compared with continuum predictions. We found that the trends predicted by the Peierls–Nabarro model, i.e. (i) a decrease of the dislocation half width with increasing unstable stacking fault energy, and (ii) an increase of the Peierls stress with increasing the magnitude of the unstable stacking fault energy, were recovered using atomic calculations in the MEAM framework. Moreover, the magnitude of the dislocation half width and the Peierls stress calculated in the MEAM framework are in good agreement with the Peierls–Nabarro predictions when the dislocation half width is determined using a generic strategy. Specifically, the dislocation half width is defined as the distance for which the disregistery is included between b/4 and 3b/4. It was, therefore, demonstrated herein that the set of fictive potentials could be parameterized in the MEAM framework to validate or to disprove the continuum theory using atomistic methods.     

A deterministic method study of the impact of the Pauli principle in double-gate MOSFETs

The Pauli principle is included in a multisubband deterministic solver for two-dimensional devices without approximations.The nonlinear Boltzmann equations are treated properly without compromising on accuracy,convergence,or CPU time.The simulation results indicate the significant impact of the Pauli principle on the transport properties of the quasi-2D electron gas,especially for the on state.     

A cluster variation method for lattice gas models

Czechoslovak Journal of Physics -     

A comparison between shake-up and UV charge-transfer transitions

The He(II) spectra of the unsubstituted metallocenes {M(η-C₅H₅)₂}, M  V, Cr, Mn, Fe, Co, Ni and Ru, and of {Mn(η-C₅H₄Me)₂} are reported; both He(I) and He(II) spectra of some decamethylmetallocenes {M(η-C₅Me₅)₂}, where M  Mg, V, Cr, Mn, Fe, Co and Ni, are also given. Intensity changes between the He(I) and He(II) spectra are shown to provide a reliable guide to band assignment. A ligand field treatment of the decamethylmanganocene cation, including limited configuration interaction, gives values for Δ₂, B and C; these values are also in good agreement with the photoelectron spectra of {M(η-C₅Me₅)₂} where M  V, Cr and Fe. Overlap between the ligand and metal “d” band structures prevents complete assignment in the cases of Co and Ni.     

一种基于互易原理的超声功率新测量方法

本文从换能器的互易原理出发，利用平面波自易校准法获得换能器的自由场发送电流响应．根据平面活塞型换能器的衍射规律，推导出发射声功率的表达式．由此计算互易换能器在给定驱动电流（或电压）作用下的辐射超声功率．基于上述原理，使用自易校准装置测量了互易换能器的声功率一频率曲线．估计的测量不确定优于±20％．     

A comparison between optical properties of TiO2 nanowires obtained by EMA method and experiment

Optical properties of TiO₂ nanowires, synthesized by two-step thermal evaporation process, have been studied experimentally and theoretically. Based on the theoretical method optical constants of nanowires have been calculated with the use of the effective medium approximation (EMA). As evidenced by X-ray diffraction patterns our synthesized nanowires, whose diameters and lengths were within the ranges of 50-90 nm and 500-1500 nm, respectively, were found to be crystalline rutile TiO₂ with the major refraction being along the (1 1 0) direction. The experimental data of the reflectance of TiO₂ nanowires has been obtained using spectrometer in wavelength 250-800 nm, and then, compared with the spectrum of reflectance predicted by the EMA theoretical model. Our measured experimental optical data has been found to be in good accord with our predicted results spectrum with the use of the EMA modeling; this agreement indicates that our estimation of the volume fraction from atomic force microscopy (AFM) data was accurate.     

A comparison between electron and ion damage in quartz

Abstract

The effects of in-situ electron and ion bombardment in quartz are compared. Both types of irradiation readily induce the metamict transformation and, furthermore, do so in linear proportion over the entire range of their combination. The results suggest that the creation of oxygen vacancies is responsible for the metamict transformation in both cases.     

The correspondence principle between classical and quantum quantities

Questions of the reestablishment of a classical quantity from the known quantum operator are investigated in this article, in that case when the operators are constructed according to the rule proposed in article [15]. The existence of a twofold limiting transition is proved, in which the investigated rule satisfies the requirements of the correspondence principle.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 18–23, June, 1974.The author expresses his deep gratitude to V. V. Kuryshkin for suggesting the topic and for systematic aid in the work.     

Tiling problems and undecidability in the cluster variation method

In cluster approximations for lattice systems the thermodynamic behavior of the infinite system is inferred from that of a relatively small, finite subsystem (cluster), approximations being made for the influence of the surrounding system. In this context we study, for translation-invariant classical lattice systems, the conditions under which a state for a cluster admits an extension to a global translation-invariant state. This extension problem is related to undecidable tiling problems. The implication is that restrictions of global translation-invariant states cannot be characterized purely locally in general. This means that there is an unavoidable element of uncertainty in the application of a cluster approximation.