实验验证肥皂膜与肥皂泡的两个物理特性

为了验证对称双漏斗肥皂膜实验在肥皂膜腰部半径自动变细之前的整个过程中肥皂膜的形状始终满足最小表面能原理,采用了四对半径不同的漏斗分别进行验证,利用FastStone Capture[1]软件对每种情况下的腰部半径随漏斗间距变化关系进行测量。通过拟合理论曲线与构建四种情况下分别对应的离散点,从而验证了这样一个结论：肥皂膜的形状在稳定区以内均满足最小表面能原理。此外,为了验证大小肥皂泡连通前后的半径关系,使用简易三通管,并使用FastStone Capture软件,测量了五次独立重复实验的数据。最后得到与理论计算相比较低误差的实验结果,从而验证了大小肥皂泡连通前后满足体积相加性。     

A statistical‐mechanical analysis of group additivity. Calculation of thermochemical values from frequency distributions

Molecular vibrational frequencies of homologous series plotted as cumulative frequency distributions are very similar, and the fine structure of the distributions exhibit identical features. An obvious explanation is that the changes in the molecular frequency distributions (MFDs) from one homologue to the next is independent of the chain length and of the functional groups in the molecule. Since group additivity is valid for the chosen homologous series there is here an explanation for the linearity of thermochemical values expressed by group additivity. For these properties the following hypothesis is proposed: group additivity is observed when the MFD is a sum of group frequency distributions (GFDs). This leads to additivity for the zero‐point vibrational energy which is confirmed by analysis of the frequencies of 126 organic molecules from 11 homologous series. The frequency distribution for a methylene group is estimated from that of octadecane. From this GFD combined with 11 different MFD it is possible to calculate model frequencies for the homologous series which are in good agreement with frequencies from ab initio calculations. For three thermochemical parameters (the logarithm of the vibrational partition function, the vibrational excitation energy and the vibrational heat capacity), the combination of the estimated methylene GFD with 11 different MFDs lead to group additivity values for a methylene group which are identical over a wide temperature range. The derivation of Benson additivity for thermochemical functions from frequency distributions is at step towards a better understanding of Benson additivity. Copyright © 2008 John Wiley & Sons, Ltd.     

Large Deviations in Weakly Interacting Boundary Driven Lattice Gases

One-dimensional, boundary-driven lattice gases with local interactions are studied in the weakly interacting limit. The density profiles and the correlation functions are calculated to first order in the interaction strength for zero-range and short-range processes differing only in the specifics of the detailed-balance dynamics. Furthermore, the effective free-energy (large-deviation function) and the integrated current distribution are also found to this order. From the former, we find that the boundary drive generates long-range correlations only for the short-range dynamics while the latter provides support to an additivity principle recently proposed by Bodineau and Derrida.     

基于BRDF理论的散射光谱加和性研究

依据双向反射分布函数理论,推导出散射光谱的加和性原理。散射光谱加和性是指对于材质质点之间无相互作用的平面漫反射体系,在光源与入射面材质不存在干涉、衍射、荧光、光谱上转换和光谱下转换等相互转换作用,且无光化学现象及非线性效应发生的前提下,且符合能量守恒定律的同时,由单光源或多光源照射的材料的散射光谱,等于该材料中每种材质的散射光谱的线性叠加。实验上,以几种材料的散射光谱为例,通过改变探测条件、照明条件和材质比例,进行了散射光谱加和性的实验验证,并且针对实验结果进行了误差分析。单光源条件下的最大实验误差为2.64%,多光源条件下则为2.35%,加和计算偏差均在实验误差允许范围内。由此证明了材料的散射光谱具有加和性,不受组成的材质差异性、材质的面积比例组合多样性、以及实验条件多变性影响。散射光谱加和性的首次提出,不仅为基于散射光谱的复杂结构体的特征提取及识别研究提供了确切的理论依据和有效的分析方法,而且对相关的实验分析和应用研究有着重要的借鉴和参考意义。     

电子与复杂分子散射的可加性规则研究

独立原予模型IAM(Independent Atomic Model)和可加性规则AR(Additivity Rule)是一个很好的适用于电子与分子中高能正碰撞的有效方法.但是现用的AR对于电子与分子散射的截面计算明显高估了实际值.本文通过从分子的外部特征出发,考虑到屏蔽效应与分子本身的特征和入射电子能量的关系,在GAR和EGAR模型的基础上提出新的EGAR模型,在新的EGAR模型中分子的特点得以体现,可使可加性规则更合理地运用于中高能区的电子-分子散射.     

The “Cameo Principle” and the Origin of Scale-Free Graphs in Social Networks

We formulate a simple edge generation rule based on an inverse like mass action principle for random graphs over a structured vertex set. We show that under very weak assumptions on this structure one obtains a scale free distribution for the degree. We furthermore introduce and study a “my friends are your friends” local search principle which makes the clustering coefficient large.     

Optical rotation of solid solutions of sodium chlorate and sodium bromate

The optical rotary dispersion (ORD) data for a mixed crystal of sodium chlorate and sodium bromate have been analysed. It is found that the ORD exhibited by these solid solutions cannot be explained using Vegard's law of additivity. Based on the model proposed by Wasastjerna, a special form of additivity of polarisability is assumed in which the asymmetric distribution of the anions around the cation is considered. A formula has been proposed for the additivity of optical rotation in solid solutions and this is found to fit the data for optical rotation in mixed crystals of NaClO₃-NaBrO₃ of different compositions.     

Two experiments on the spectral boundary conditions for nonlinear additivity of simultaneous masking.

The present paper describes the results from two experiments which explored the spectral boundaries for the nonlinear additivity of simultaneous masking. The first experiment measured the threshold for detection of a 2-kHz tone in the presence of two 800-Hz-wide bands of noise that had varying degrees of spectral overlap with each other and the 2-kHz signal. Results revealed an abrupt transition from linear to nonlinear additivity of masking as the spectral separation between the two maskers varied from some overlap to none. The second experiment examined alternative explanations for the data. Explanations based on restricted-listening or distortion-product-detection hypotheses were not supported by the results of this experiment. These data indicate that nonlinear additivity of simultaneous masking holds for maskers that do not overlap within the critical band centered on the signal frequency. This interpretation is also consistent with a large body of data on the monaural and binaural summation (additivity) of loudness.     

Landauer's principle and the conservation of information

Erasure of information requires the dissipation of a minimal amount of energy as being formulated in Landauer's principle. This profound concept in information processing has recently been derived by use of basic dynamical principles of statistical mechanics. We present an alternative derivation of Landauer's principle based on dynamical principles and certain properties of the Shannon–Gibbs–Boltzmann entropy, in particular, (sub-)additivity.     

一种霍尔效应测量磁场的设计方法

针对大学物理实验中＂霍尔效应法测量磁场＂项目只能测长直螺线管轴线上一维稳恒磁场分布的不足,提出一种设计方法,来测量任一未知稳恒磁场的二维分布,进而可扩展到测量三维分布。可使学生深刻全面理解霍尔效应测磁场的原理及磁场的性质,并可作为设计性实验项目在大学物理实验课中开出,培养学生的创新意识。     

Surface tension of a molecular fluid

We derive a general expression for surface tension in a dense molecular fluid with an arbitrary many body interaction. This formula reduces to that of Gray and Gubbins under the assumption of pairwise additivity. We then show how this general expression is transformed into a sum rule expression and also into an expression involving the direct correlation function. These last two expressions are analogous to the simple fluid surface tension formulas of Jhon, Desai and Dahler and Yvon-Triezenberg-Zwanzig respectively. We also discuss the case of a fluid in d dimensions.     

Microcanonical ensemble extensive thermodynamics of Tsallis statistics

The microscopic foundation of the generalized equilibrium statistical mechanics based on the Tsallis entropy is given by using the Gibbs idea of statistical ensembles of the classical and quantum mechanics. The equilibrium distribution functions are derived by the thermodynamic method based upon the use of the fundamental equation of thermodynamics and the statistical definition of the functions of the state of the system. It is shown that if the entropic index ξ=1/(q−1) in the microcanonical ensemble is an extensive variable of the state of the system, then in the thermodynamic limit the principle of additivity and the zero law of thermodynamics are satisfied. In particular, the Tsallis entropy of the system is extensive and the temperature is intensive. Thus, the Tsallis statistics completely satisfies all the postulates of the equilibrium thermodynamics. Moreover, evaluation of the thermodynamic identities in the microcanonical ensemble is provided by the Euler theorem. The principle of additivity and the Euler theorem are explicitly proved by using the illustration of the classical microcanonical ideal gas in the thermodynamic limit.     

Statistical thermodynamics from the point of view of statistical theory of estimation

An essentially statistical theory of thermodynamics is developed on the basis of additivity and conservation laws of fundamental entities of thermodynamics. The theory developed by Dutta (1953–59) stresses first the importance of the statistical theory of estimation in the statistical foundation of thermodynamics. The method of finding the distribution law is based on the principle similar to that of Bayes' rule in probability theory and the method of maximum-likelihood estimation of mathematical statistics. The model used is macroscopic in nature and the laws of microscopic distributions (M-B, B-E and F-D statistics) have been obtained by additional axiom regarding the constituents of the system. The object of the paper is to present an outline of the theory with some of its extensions to quantum macro-system and non-equilibrium thermodynamics.     

Total cross sections for electrons scattering from simple molecules containing the larger atom sulfur at 30-5000eV

A complex optical model potential modified by the concept of bonded atom, which takes into consideration the overlapping effect of electron clouds, is employed to calculate the total cross sections for electrons scattering from simple molecules （SO2, H2S, OCS, CS2 and SO3） containing the larger atom, sulfur, at 30-5000eV by using the additivity rule model at Hartree-Fock level. The quantitative molecular total cross section results are compared with those obtained in experiments and other calculations wherever available, and good agreement is obtained. It is shown that the additivity rule model together with the complex optical model potential modified by the concept of bonded atom can give the results closer to the experiments than the one unmodified by it. So, the introduction of bonded-atom concept in complex optical model potential betters the accuracy of the total cross section calculations of electrons from the molecules containing the larger atom, sulfur.     

Effect of Spatial Frequency on Equal-Luminance Point for the Mechanism of Shape from Shading

We examined 1) whether the perception of shape from shading is based on luminance or brightness by testing the additivity law, and 2) whether the spatial frequency contents in the stimulus affect on the spectral sensitivity. We measured the relative radiance at which shading disappeared in a simple shading figure. Results showed that 1) the additivity law holds for shading disappearance settings and that 2) the sensitivity for green to white decreased as higher spatial frequencies in the figure decreases. These results suggest that the perception of shape from shading is based on a luminance type additive mechanism and that the spectral sensitivity of the mechanism varies depending on spatial frequency.Presented at the International Commission of Optics Topical Meeting, Kyoto, 1994.     

Ionization energies and Koopmans' theorem

Trends in the hyperfine splitting constants of alkylated 1,4-semiquinones can be explained by a consideration of inductive and steric influences of the substituent groups, in conjunction with effects of the solvating medium. Using this model, the splittings for t-butyl semiquinones are rationalized and the additivity principle is given a theoretical foundation.     

Determining the statistical weight of multicluster wave functions for light nuclei in a parametrized phase analysis

The experimental angular distributions of light alpha-cluster nuclei are described. Based on fitting, we find that the experimental angular distribution splits into two diffraction modes: the first has a short oscillation period on the nucleus as a whole, and the second has long oscillation periods on the alpha-cluster substructures. Fitting also reveals that the cross sections rising above the Rutherford level for light nuclei is explained by the additivity (modulation) of the alpha-particle mode of elastic scattering (the scattering of alpha particles on alpha-particle clusters).     

中高能正电子被CO，HCl，NH3及SiH4散射的总截面

利用可加性规则，使用Hartree-Fock波函数，采用由束缚原子概念修正过的复光学势(由静电势、极化势及吸收势三部分组成)，在30—3000eV内对正电子被CO，HCl，NH₃和SiH₄散射的总截面进行了计算，且将计算结果与实验结果及其他理论计算结果进行了比较.结果表明，利用被束缚原子概念修正过的复光学势及可加性规则进行计算，所得结果与实验结果的符合程度要比利用未被束缚原子概念修正的复光学势及可加性规则进行计算得到的结果好很多.因此，在复光学势中采用束缚原子概念可提高正电子被分子散射的总截面的计算准确度. 关键词： 正电子散射 可加性规则 束缚原子 总截面     

Additivity principle in high-dimensional deterministic systems

The additivity principle (AP), conjectured by Bodineau and Derrida [Phys. Rev. Lett. 92, 180601 (2004)], is discussed for the case of heat conduction in three-dimensional disordered harmonic lattices to consider the effects of deterministic dynamics, higher dimensionality, and different transport regimes, i.e., ballistic, diffusive, and anomalous transport. The cumulant generating function (CGF) for heat transfer is accurately calculated and compared with the one given by the AP. In the diffusive regime, we find a clear agreement with the conjecture even if the system is high dimensional. Surprisingly, even in the anomalous regime the CGF is also well fitted by the AP. Lower-dimensional systems are also studied and the importance of three dimensionality for the validity is stressed.