Optimum Shapes of Elastic Bodies: Equistrong Wings of Aircrafts and Equistrong Underground Tunnels

Since the times of Plato (424?-347 BC) and Aristotle (384-322 BC), the form has been considered as a fundamental notion of not only the physical universe, but also the spiritual world. The forms and perfect shapes are like jewels in the rock—their search and discovery make up the highest delight to human beings. This is what constituted the motive and driving force of science and scientists beginning from Pythagoras (ca. 570-ca. 500 BC), Archimedes (ca. 287-ca. 212 BC), Euclid (ca. 330-ca. 260 BC) and all that came after. In the introduction to the present article, a brief account of Plato’s theory of forms and Aristotle’s addition to this theory are given; the theory of optimum shapes of elastic bodies can be considered as a footnote to the Plato’s theory. In the framework of the theory of elasticity, the optimal shape of a body is the shape that meets the principle of equal strength or equistrength advanced by this author in 1963. According to this principle, the safety criterion like ultimate or failure stress is simultaneously satisfied in the utmost part of the body—this body or structure is called equistrong in this case. The equistrong structure has a minimum weight for a given material and safety factor, or a maximum safety factor for a given material and weight. As distinct from traditional problems, there are no existence theorems for equistrong shapes—a success in their search depends on skills of a researcher. In the present paper, a summary of common equistrong shapes and structural elements is brought out, namely: equistrong cable of bathysphere, equistrong tower or skyscraper, equistrong beam by Galileo Galilei, equistrong rotating disk, equistrong heavy chain, equistrong pressure vessels, equistrong arcs, plates and shells, equistrong underground tunnels, equistrong perforated plates, and others. A variety of the swept wings of aircrafts is found out to be equistrong; the front and rear edges of such wings are rectilinear in the plan view, and their chord in the flight direction depends on the task of an aircraft; the equistrong design exists for any task, from transport aviation to hypersonic jet fighters. Some new equistrong shapes of elastic solids with any number of infinite branches being pulled out of a body are also discovered for plane strain and plane stress.     

一种设计环形汇聚光栅反射镜的新方法

提出了一种利用数学变换来快速设计环形汇聚光栅反射镜的方法.通过分析具体的物理场景,抽象出已有条形汇聚光栅的"线"汇聚特性与所要设计的"点"汇聚特性在数学上对应的变换关系,然后用该数学变换对条形汇聚光栅进行外形上的变换,外形变换后的条形光栅即为可以实现"点"汇聚的环形光栅.用有限元算法对设计的环形汇聚光栅进行仿真,仿真证明采用该方法设计的环形光栅可以很好地实现高反、高汇聚.采用这一方法,设计了直径为29.788μm的环形光栅反射镜,当垂直入射的径向偏振光从设计的环形光栅表面反射回来后将发生汇聚,汇聚焦点位于环形光栅表面10μm处.经计算,反射镜的数值孔径为0.8302,反射率为0.9163,在焦点所在的汇聚面上,汇聚光栅电场分布的半高宽为1.5548μm.     

Lagrangian mechanics and the geometry of configuration spacetime

Holonomic rheonomic systems having a finite number of degrees of freedom are considered in classical nonrelativistic mechanics. It is shown that the configuration spacetime manifold $\text{M}$ of such a system can be furnished with a linear symmetric connection (called the “dynamical connection”) in such a way that the worldline of the system is a geodesic on $\text{M}$. The connection is based upon a degenerate metric structure (called a “generalized Galilei structure”) which in turn is uniquely determined by the system and the forces acting on it. The connection is compatible with the generalized Galilei structure in the sense that the covariant derivatives of the latter vanish. Systems which can be described in terms of a Lagrangian give rise to a particularly interesting class of dynamical connections, called “Lagrange connections,” whose geometry is studied in some detail. Within the class of generalized Galilei connections they are characterized by a geometrical condition imposed on the affine curvature tensor. Noether symmetries of the dynamical system turn out to be equivalent to “isometries” of the generalized Galilei structure together with collineations of the Lagrange connection. They form a Lie group. Spacelike generators of Noether symmetries are linked to the existence of “conservors” (i.e., covectors with vanishing symmetrized covariant derivatives). Timelike generators of Noether symmetries give rise to (second rank) Killing tensors.     

Self-organization of particles in the superionic phase of lanthanum trifluoride

When a laser beam (λ = 396.3 nm) propagates through a nonuniformly heated superionic LaF₃ crystal in the direction of lattice constant c, alternating bright and dark fringes arise on the screen. The fringes run from the warmer face to the colder one. The number and width of the fringes are found to depend on the temperature gradient in the crystal: the smaller (greater) the temperature difference between the faces, the smaller (greater) the number of moving fringes. It is the author’s opinion that this effect is due to the wave transfer of applied heat and reflects the self-organization and collective displacements of the ions of the “quasi-liquid” sublattice in a nonuniform temperature field. A qualitative model of heat wave transfer in the LaF₃ superionic phase is suggested.     

Modelling the spot shape influence on high-speed transmission lap welding of thermoplastics films

Modelling high-speed laser lap welding of thermoplastic films has been accomplished and the influence of laser beam spot shape, dimensions, and position relative to sample displacement was analysed.Engineering parameters predicted by the model were applied to lap weld of high- and low-density polyethylene transparent samples with thickness between 10 and 100 μm, and experimentally validated. Experimental set-up allowed reaching welding constant linear velocities up to 10 m/s.Theoretical and experimental data show coincidence. Weld strength increases for larger beam spot diameters, and elliptical beam spots increase weld efficiency, allowing higher processing speeds or decreasing required laser power. An angular deviation of elliptical beam spot with regard to the sample's movement direction causes an increase of weld strength and a decrease of welding speed.     

超高斯渐变反射率激光反射镜

本文介绍了超高斯渐变反射率激光反射镜设计的基本原理。采用中心带孔的固定挡法制备渐变厚度薄膜的工艺方法，用ｅ型电子束枪在光学真空镀膜机中蒸发镀制出了膜斑直径为：３～６ｍｍ，级次为：２５～７的超高斯渐变反射镜     

Interrogating the Legend of Einstein's “Biggest Blunder”

It is well known that, following the emergence of the first evidence for an expanding universe, Albert Einstein banished the cosmological constant term from his cosmology. Indeed, he is reputed to have labelled the term, originally introduced to the field equations of general relativity in 1917 in order to predict a static universe, his “biggest blunder.” However, serious doubts about this reported statement have been raised in recent years. We interrogate the legend of Einstein’s “biggest blunder” statement in the context of our recent studies of Einstein’s cosmology in his later years. We find that the remark is highly compatible with Einstein’s cosmic models of the 1930s, with his later writings on cosmology, and with independent reports by at least three physicists. We conclude that there is little doubt that Einstein came to view the introduction of the cosmological constant term as a serious error and that he very likely labelled the term his “biggest blunder” on at least one occasion. This finding may be of some relevance for those theoreticians today who seek to describe the recently discovered acceleration in cosmic expansion without the use of a cosmological constant term.     

Development of a tuneable channel cut crystal

We have developed the first tuneable channel cut crystal for ultra small angle neutron scattering and neutron optical experiments. The Darwin range of a perfect crystal can be reduced down to a fraction of its natural width. This “Darwin reduction” was realised without any change of the beam geometry which yields an intensity gain relative to conventional asymmetric Bragg diffraction. With such tuneable channel cut crystal peaks nearly δ-peaks can experimentally be realised.     

宽光谱Czerny-Turner光谱仪中的彗差与分辨率

小型光谱仪较多地采用Czerny-Turner(切尼—特纳)光路结构,其设计应遵循Shafer消彗差原理消除中心波长处的初级彗差并尽量平直整个谱面以提高分辨率。但常规设计并未考虑非中心波长处彗差和分辨率的变化情况。在对两种典型切尼—特纳光路结构进行初级彗差分析的基础上,指出交叉型光路结构宽光谱范围内的分辨率呈“V”形,而M型光路结构分辨率在全光谱范围内变化较小,近似呈“一”形,即后者宽光谱范围内的分辨率一致性远好于前者。针对于此,该文设计了光谱范围为400～600 nm的2种光路,并对其进行了理论计算和对比实验,实验结果表明,两者边缘波长处分辨率分别比中心波长处分辨率低3.7倍和1.2倍,与理论计算结果基本一致。     

The effects of size,shape, and surface composition on the diffusive behaviors of nanoparticles at/across water–oil interfaces via molecular dynamics simulations

We have employed molecular dynamics simulations to systematically investigate the effects of nanoparticles’ structural and chemical properties on their diffusive behaviors at/across the water–benzene interface. Four different nanoparticles were studied: modified hydrocarbon nanoparticles with a mean diameter of 1.2 nm (1.2HCPs), modified hydrocarbon nanoparticles with a mean diameter of 0.6 nm (0.6HCPs), single-walled carbon nanotubes (SWCNTs), and buckyballs. We found that the diffusion coefficients of 0.6 and 1.2HCP were larger than the corresponding values predicted using the Stokes–Einstein (SE) equation and attributed this deviation to the small particle size and the anisotropy of the interface system. In addition, the observed directional diffusive behaviors for various particles were well-correlated with the derivative of the potential of mean force (PMF), which might indicate an effective driving force for the particles along the direction perpendicular to the interface. We also found that nanoparticles with isotropic shape and uniform surface, e.g., buckyballs, tend to have smaller diffusion coefficients than those of nanoparticles with comparable dimensions but anisotropic shapes and non-uniform surface composition, e.g., SWCNT and 0.6HCP. One possible hypothesis for this behavior is that the “perfect” isotropic shape and uniform surface of buckyballs result in a better-defined “solvation shell” (i.e., a shell of solution molecules), which leads to a larger “effective radius” of the particle, and thus, a reduced diffusion coefficient.     

径向馈入和轴向馈入对感应加速腔性能的影响

 感应加速腔有径向馈入和轴向馈入两种常用的脉冲功率馈入方式。在理论上分析了不同功率馈入方式对感应加速腔输出电压平顶的影响,并对分析结果进行实验论证。实验采用1B2C结构,用相同的脉冲功率源馈入径向腔和轴向腔,测量此两种加速腔的电压波形。测得轴向腔±1％电压平顶时间为61 ns,径向腔±1％电压平顶时间为62 ns,两种腔都可满足±1%电压平顶大于60 ns的要求。此外对不同功率馈入方式导致的横向阻抗的变化进行了数值模拟,分别计算了采用这两种馈入方式的加速腔模型的横向阻抗,发现轴向加速腔的横向阻抗较小。     

Single-material coupling-tolerant semi-planar microresonator using Littrow diffraction

Resonators carved in a single material such as disc, rings, spheres, do not require genuine mirrors since they exploit shape resonances, but they then suffer from poor coupling to standard free-space collimated beams. Exploiting the idea of Littrow resonators combining total internal reflection and grating diffraction, we propose trapezoidal prism-type geometries that include a strong grating on one face, and total internal reflection on the other face. Resonant modes are localized within a length of the same order as the prism thickness, but are well coupled to free-space beams. The resonator core can be seen as a broad waveguide with multimode coupling of “Littrow modes”, a configuration recently pointed out for its capability to produce a “collective” slow-light regime. A more “planar” version, with a saw-tooth input-coupling grating for vertically collimated beam is also proposed.     

Zum Einsatz metallischer Leitfähigkeit während der Kondensation von Metallschichten

Ag-, Cd-, Tl-, Pb- and Bi-films are condensed at constant deposition rates onto crystalline quartz. Film conductance is measured as a function of the mass condensed. During the growth of the film metallic conductivity appears at a “critical” thickness. This critical thickness is constant at low temperatures and begins to rise exponentially at a certain temperature which depends on the condensation energy of the metal. For metals with low thermal conductivity a large critical thickness is found at low temperatures. If the substrate is pre-sensitized with silver the critical thickness of lead films is reduced considerably while amorphous bismuth films show just the opposite behaviour.     

基于焦斑空间频谱控制的连续相位板设计

 改进了传统的盖斯贝格 撒克斯通（G-S）算法,其中包含：改善了初始相位的选取;远场振幅采用弱调制,迭代中进行解相、滤波,以保证设计的相位板连续;对目标焦斑的频谱控制,使焦斑能量在频谱上重新分配。结果表明：相对传统设计的连续相位板（CPP）,改进后的G-S算法可以控制CPP的加工单元大小,降低CPP的相位梯度,更好地控制焦斑轮廓,降低特定频带的调制。进一步分析表明,新方法设计的CPP与光谱色散匀滑技术耦合的效果更佳。     

Photopyroelectric calorimetry of liquids; recent development and applications

This paper is a synthesis of the main photopyroelectric (PPE) calorimetric techniques proposed in the last years for accurate measurements of dynamic thermal parameters of liquids. The area of interest is restricted to liquids because, due to the perfect sample-sensor thermal contact, accurate quantitative results can be obtained and consequently, intimate processes occurring in liquids (as molecular associations, structural changes in nanofluids, adulteration and spoilage of liquid foodstuffs, etc.) can be studied. The paper describes the possibilities offered by the two main used PPE detection configurations, “back” and “front”in investigating two dynamic thermal parameters: thermal diffusivity and effusivity. In the paper we analyzed only the information contained in the phase of the PPE signal, due to the fact that the phase, as a source of information, leads to more accurate results than the amplitude. A study of the accuracy of the investigations when using the chopping frequency, or sample’s thickness as scanning parameters is also made. Some basic applications concerning high-resolution measurements of thermal diffusivity and effusivity of some “special”liquid samples (magnetic nanofluids, adulterated vegetable oils) are described. A new possibility of using the thickness scan of the phase of the PPE signal of a liquid, in order to obtain the thermal parameters of a solid is analyzed.     

Meron and elliptic solutions in conformally flat space-time

The idea recently advanced by the author that particles arise as distortions of a riemannian background is pursued further. Such distortions represent conformally flat solutions of Einstein's “cosmological” equations extremely large “cosmological” constant. It is shown in particular that merons can be generated by perfect fluid or neutral superfluid distributions of energy and momentum. Perfect fluids can also generate elliptic plane waves of the type discussed by Petiau.     

Growth Rates of Edge-on Lamellar Crystals Confined in Polymer Thin Films

The growth rates of edge-on lamellar polymer crystals in variable thickness films were investigated in terms of dynamic Monte Carlo (MC) simulations. The growth rates linearly decreased with decreasing film thickness for the thinner films and were nearly constant for the thicker films. The mean stem lengths (crystal thickness) were also constant in different thickness films. The crystal widths parallel to the film thickness increased more slowly with increasing film thickness in the thinner films than that in the thicker films, indicating they were restrained by the film thickness. We propose that the growth rate of edge-on lamellar crystals in thin films is dominanted by the crystal width in the thinner films and by the crystal thickness in the thicker films; the variation of the film thickness can change the three-dimensional shape of the crystal growth front, also affecting the growth rate of the edge-on lamellar crystal.     

多基色混合白光LED显色性优化研究

为优化多基色混合白光LED的显色性,得到色彩生动的白光LED照明效果,以评价饱和红色的特殊显色指数R₉为研究对象,通过多基色光源混合白光LED的光谱功率分布的高斯数学模型,选取峰值波长λ_m、半波宽Δλ和幅值A为基色光源光谱功率分布的主要参量,并以“蓝光芯片+YAG黄色荧光粉”和“红、绿和蓝基色LED”为分析模型分别进行二基色和三基色混合白光LED显色性研究,讨论两种基色混合情况下三个参量对混色白光LED的显色性R₉贡献。结果表明：为使多基色混合白光LED的显色性更好,首先确定光源S1的峰值波长λ_m1、半波宽Δλ₁及幅值A₁;然后设定其他基色光源幅值A_i以求此条件下峰值波长λ_mi和半波长Δλ_i取值范围;最后在求得的峰值波长λ_mi和半波长Δλ_i取值范围,反求基色光源的最佳幅值A_iopt,从而使多基色混合白光LED的显色性达到最佳效果。该方法对分析基色混合白光LED的显色性具有理论参考价值。     

The equations of motion of initially stressed Timoshenko tubular beams conveying fluid

In this paper the equations of motion of an initially stressed Timoshenko tubular beam subjected to a tensile follower load and conveying fluid are derived by using the appropriate statement of Hamilton's principle. This latter is obtained first for “open” systems, the instantaneous total mass of which does not necessarily remain constant in the course of deformation—“open” denoting that there is momentum transport in and out of the system. The equations of motion are derived separately for a cantilevered system and for one with both extremities of the tube clamped. Yet another derivation for the cantilevered tube is presented with the system considered to be quasi-closed, where all flow-induced effects are incorporated through the virtual work, as if they were “external” forces. All three sets of equations are found to be identical. These equations are then compared with those obtained, more simply, by the Newtonian force-balance approach. Some differences between them are found to exist, the principal of which are associated with the follower or other tensile forces; these are discussed at some length, and the equations of motion obtained here are compared to those obtained by other researchers for Timoshenko beams subjected to follower or tensile forces.     

Salt fingers in double-diffusive systems

“Salt fingering”, the phenomenon of the double-diffusive convection has been studied experimentally. We prepared a system with vertical density variation, which contains salt and sugar solutions, separated one from the other. The “salt fingers” appear at the interface between these layers of salt and sugar solutions. The “salt fingers” have been observed by means of shadowgraph technique.With the aid of a computer and the video-capture technique, it was possible for the first time to conduct a detailed investigation of the phenomenon. The geometric characteristics of the “salt fingers” such as form, length and width have been investigated.The way in which these quantities depend on the salinity and sugar concentrations, as well as the thickness of the salt and sugar layers has been verified experimentally. We also verified the predicted form of dependence of the average “salt fingers” width on its vertical length.