Perturbation theory for fluids of rod-like molecules interacting via the Kihara potential

For systems of molecules interacting via the Kihara core potential a first-order perturbation theory is proposed. As a reference system soft convex bodies are employed with interactions given by the entire repulsive part of the original pair potential (i.e. for surface-to-surface distances smaller than that of the potential minimum). Their equilibrium behaviour is interpreted on the basis of the representative hard convex bodies-parallel convex bodies to the assumed cores with temperature-dependent thickness. The shape of the distribution function was approximated by the Verlet-Weis form. Theoretical expressions were used for the determination of the thermodynamic functions of the Kihara-molecule systems at several reduced temperatures and compared with experimental data for nitrogen.     

The excluded volume of hard sphero-zonotopes

Excluded volume effects can account for most ordering transitions in simple liquids and liquid crystals. Starting with the work of Onsager, this has been demonstrated in the case of liquid crystals for a number of simple convex bodies, e.g. sphero-cylinders, for which the orientation-dependent pair-excluded volume could be written down analytically. However, in recent years, experiments and simulations have been reported on ordering transitions in suspensions of more complex convex colloids. For these systems, theoretical understanding is hampered by the fact that no analytical expressions for the pair-excluded volume were available. Here we show that it is possible to obtain explicit expressions for the pair-excluded volume of a much larger class of convex bodies: the so-called sphero-zonotopes. These bodies are obtained by ‘padding’ a special class of convex polytopes with a blanket of uniform thickness. The resultant family of particles encompasses a wide range of shapes that have been considered as models for fluid and liquid crystalline behaviour e.g. spheres, cubes, sphero-cylinders, sphero-platelets. We discuss two explicit examples: sphero-cuboids, the 3D core generalization of the sphero-cylinder and the sphero-platelet, and hexagonal prisms that are models for the recently synthesized colloidal gibbsite platelets. Employing the fact that a cylinder is a zonoid, i.e. the limit of a sequence of right regular prisms, we are able to compute the excluded volume of the ‘true’ sphero-cylinder, a uniformly padded cylinder, of which the oblate-spherocylinder is a known example. Our approach en passant provides a relatively elementary rederivation of Onsager's classical result on cylinders.     

Analytical Model of Doppler Spectra of Light Backscattered from Rotating Convex Bodies of Revolution in the Global Cartesian Coordinate System

We present an analytical model of Doppler spectra in backscattering from arbitrary rough convex bodies of revolution rotating around their axes in the global Cartesian coordinate system. This analytical model is applied to analyse Doppler spectra in backseatter from two cones and two cylinders, as well as two ellipsoids of revolution. We numerically analyse the influences of attitude and geometry size of objects on Doppler spectra. The analytical model can give contribution of the surface roughness, attitude and geometry size of convex bodies of revolution to Doppler spectra and may contribute to laser Doppler velocimetry as well as ladar applications.     

航天器表面环境散射返回流TPMC模拟

介绍试验粒子Monte Carlo(test particle Monte Carlo,TPMC)方法,并采用该方法对4种航天器表面出气分子形成的环境散射返回流进行数值模拟.其中,圆球出气表面的计算结果与已有的DSMC(direct simulation Monte Carlo)结果一致,验证了方法的正确性.此外,对不同出气和来流条件下圆形平板、凸半球和凹半球3种航天器简化表面出气分子形成的环境散射返回流进行计算,结果表明:出气表面外形是影响返回通量比的一个重要因素;圆形平板和凹半球出气表面的返回通量比远大于凸半球表面的;凹半球表面的出气分子会直接和出气表面碰撞形成直接流污染,且其量级远大于返回流污染.因此,在航天器设计中尽可能使用凸形表面作为敏感的出气表面可以有效降低出气分子污染.     

A unified treatment of the equation of state of hard linear bodies

An unified treatment of the equation of state of convex (spherocylinders) and non-convex (dumbells) hard bodies is presented. Comparison of our results with simulation shows very good agreement for diatomics and excellent for triatomics.     

Remarks on Radial Centres of Convex Bodies

The paper concerns a family of selectors for convex bodies in Rⁿ, radial centre maps, defined in the article of M. Moszyńska, Looking for selectors of star bodies, Geom. Dedicata 81 (2000), 131–147. A radial centre of a convex body A is the maximizer of a suitable generalized dual volume of A. We give physical interpretations of the notion of radial centre and study its geometric properties. We prove that these selectors are continuous with respect to the Hausdorff metric and solve the problem of direct additivity for radial centre of order α, which corresponds to the dual volume of order α. Mathematics Subject Classifications (2005) 52A20, 52A40, 51P05, 85A25, 86A20.     

Laser backscattering analytical model of Doppler power spectra about rotating convex quadric bodies of revolution

We propose an analytical model of Doppler power spectra in backscatter from arbitrary rough convex quadric bodies of revolution (whose lateral surface is a quadric) rotating around axes. In the global Cartesian coordinate system, the analytical model deduced is suitable for general convex quadric body of revolution. Based on this analytical model, the Doppler power spectra of cones, cylinders, paraboloids of revolution, and sphere–cones combination are proposed. We analyze numerically the influence of geometric parameters, aspect angle, wavelength and reflectance of rough surface of the objects on the broadened spectra because of the Doppler effect. This analytical solution may contribute to laser Doppler velocimetry, and remote sensing of ballistic missile that spin.     

The center of mass in general relativity

In Dixon's theory of the dynamics of extended bodies in metric theories of gravity, a definition of a center-of-mass line is proposed. We prove the existence and uniqueness of a zero-linear-momentum vector field. Using this vector field we show the existence of a center-of-mass line which is a smooth timelike curve contained in a convex hull of the world-tube of the body.     

Two examples of non-radiative systems—An application of homogeneous functions to Synge's approximation method

A method of finding approximations for the gravitational field of two non-radiative systems is given. The first system consists of a shrinking body with convex boundary, having certain symmetries. The second system consists of two shrinking bodies which, in the first approximation, approach each other along thex ₁-axis with a certain constant relative velocity. The two bodies are assumed to have rotational symmetry around thex ₁-axis.Presented at the International Conference on Gravitation and Relativity, Copenhagen, July 1971.Supported by N.R.C. Grant No. A-5205.     

Dense regular packings of irregular nonconvex particles

We present a new numerical scheme to study systems of nonconvex, irregular, and punctured particles in an efficient manner. We employ this method to analyze regular packings of odd-shaped bodies, both from a nanoparticle and from a computational geometry perspective. Besides determining close-packed structures for 17 irregular shapes, we confirm several conjectures for the packings of a large set of 142 convex polyhedra and extend upon these. We also prove that we have obtained the densest packing for both rhombicuboctahedra and rhombic enneacontrahedra and we have improved upon the packing of enneagons and truncated tetrahedra.     

Entanglement of formation for isotropic states

We give an explicit expression for the entanglement of formation for isotropic density matrices in arbitrary dimensions in terms of the convex hull of a simple function. For two qutrit isotropic states we determine the convex hull and we have strong evidence for its exact form for arbitrary dimension. Unlike for two qubits, the entanglement of formation for two qutrits or more is found to be a nonanalytic function of the maximally entangled fraction in the regime where the density matrix is entangled.     

Modified Parsons-Lee theory for fluids of linear fused hard sphere chains

The Parsons-Lee theory has been modified to study the liquid-crystalline phase behaviour of the linear fused hard sphere chain fluids. The modification of the Parsons-Lee theory is based on the application of the so-called effective molecular volume instead of the real molecular volume. This alteration does not mean any change for the Parsons-Lee treatment of the hard convex bodies but does for the non-convex ones. The results of the modified Parsons-Lee theory show very good agreement with simulations not only for the location of the isotropic-nematic phase transition but for the equation of state.     

波源和接收者在介质体内的客观运动理论

建立介质体概念并指出介质体的内部独立性和外部相关性。建立双列车模型,对波在介质体内的多普勒效应进行量化分析。建立波源和接收者在介质体内的客观运动理论。把客观运动理论应用于天文学。指出天体介质体的边缘凸透镜特性。明确时间和物理介质空间的客观性。指出相对论的错误。明确波和粒子的区别。     

Morphological thermodynamics for hard bodies from a controlled expansion

ABSTRACT

The morphometric approach is a powerful ansatz for decomposing the chemical potential for a complex solute into purely geometrical terms. This method has proven accuracy in hard spheres, presenting an alternative to comparatively expensive (classical) density functional theory approaches. Despite this, fundamental questions remain over why it is accurate and how one might include higher-order terms to improve accuracy. We derive the morphometric approach as the exact resummation of terms in the virial series, providing further justification of the approach. The resulting theory is less accurate than previous morphometric theories, but provides fundamental insights into the inclusion of higher-order terms and to extensions to mixtures of convex bodies of arbitrary shape.     

多边形单元平均值插值的误差估计及应用

对多边形单元上平均值插值的误差进行分析,利用平均值插值形函数的性质和二元函数的Taylor展开式,证明平均值插值的误差估计不等式.给出平均值插值应用于凸域温度分布插值近似的算例,数值算例表明平均值插值能够表现出区域温度分布的特征.