Position of starting spot in TLC: Influence on average plate height

Summary The influence of the distance between the solvent entry and the starting zone positions, Z₀, on the average plate height was studied. This factor was found to be of major importance and could be optimized. The Guiochon and Siouffi model greatly underestimates the plate height for low values of Z₀.     

Quantum theory of rotation angles: The problem of angle sum and angle difference

We reconsider the problem of the sum and difference of two angle variables in quantum mechanics. The spectra of the sum and difference operators have widths of , but angles differing by are indistinguishable. This means that the angle sum and difference probability distributions must be cast into a range. We obtain probability distributions for the angle sum and difference and relate this problem to the representation of nonbijective canonical transformations. Received: 6 December 1997 / Revised: 15 April 1998 / Accepted: 7 May 1998     

一种位相板衍射图样的图像处理新方法

本文介绍了在半导体激光光纤和位相板相结合的准直情况下，利用ＣＣＤ探测器测量大尺寸形位误差的原理，并针对位相板衍射图像的特点，提出了一种处理此类衍射图样的图像处理新方法——投影法。同在时间上采用的多次平均的方法相比较，投影法相当于采用了空间上的平均，消除了ＣＣＤ表面保护玻璃形成的干涉条纹的影响，对空气扰动也起到了很好的抑制作用。并且使二维图像处理变为一维计算，大大提高了计算速度     

Effect of aerosil dispersions on the nematic-to-isotropic interface

The effect of silica aerosils on the kinetics of the first-order nematic-isotropic (NI) phase transition is phenomenologically described in the framework of the time-dependent Landau-Ginzburg equation. A steady-state solution to the equation is presented such that the NI interface may propagate with a solitary-like wave profile under constant quenching. The results provide a plausible basis for the interpretation of the dynamical effects of quenched disorder in the liquid-crystal systems, caused by randomly interconnected porous media, such as aerosils. In the low silica aerosil ρ_s ( ≤0.1 g/cm^3) regime, the calculated values of the interface velocity v(T,ρ_s), the interface thickness κ(T,ρ_s), and the critical radius of a spherical nucleus of new nematic phase in a bulk isotropic environment, composed of polar molecules, such as 4-n-octyl- 4^′- cyanobiphenyl and 4-n-heptyl- 4^′- cyanobiphenyl shows that the effect of silica aerosils on the kinetics is reflected in a shifting of the set of temperature-dependent curves to lower temperature values.-1     

On the origin of Kaluza’s idea of unification and its relation to earlier work by Thirring

We argue that the starting point of Kaluzas idea of unifying electrodynamics and gravity was the analogy between gravitation and electromagnetism which was pointed out by Einstein and Thirring. It seems that Kaluzas attention was turned to this point by the three papers on the Lense–Thirring effect and the analogy between gravitation and electromagnetism which were published a short time before Kaluzas paper was submitted. We provide here also an English translation of the third of these papers (Phys. Zeits. 19: 204, 1918).     

Maps Between Deformed and Ordinary Gauge Fields

In this paper, we introduce a map between the q-deformed gauge fields defined on the GL_q(N) -covariant quantum hyperplane and the ordinary gauge fields. Perturbative analysis of the q-deformed QED at the classical level is presented and gauge fixing à la BRST is discussed. Another star product defined on the hybrid (q,h) -plane is explicitly constructed.     

<Emphasis Type="Italic">p</Emphasis>-Nuclearity in a New Perspective

In this Letter we try to settle some confused points concerning the use of the notion of p-nuclearity in the mathematical and physical literature, pointing out that the nuclearity index in the physicists’ sense vanishes for any p> 1. Our discussion of these issues suggests a new perspective, in terms of ε-entropy and operator spaces, which might permit connections to be drawn between phase space criteria and quantum energy inequalities.Mathematics Subject Classification (2000): 81T05, 47B10, 47L25.     

Higher spin gauge theories in any dimension

Some general properties of higher spin gauge theories are summarized, with the emphasize on the nonlinear theories in any dimension. To cite this article: M.A. Vasiliev, C. R. Physique 5 (2004).

Résumé

Des propriétés générales des théories de jauge de grands spins sont présentées, en insistant particulièrement sur les théories non-linéaires en dimensions diverses. Pour citer cet article : M.A. Vasiliev, C. R. Physique 5 (2004).     

Origination of In‐Phase Oscillations of Thin Plates with Aeroelastic Interaction

Synchronization of oscillations of thin elastic plates that are walls of a gasfilled channel is considered. The gas motion is described by a system of Navier–Stokes equations, which is solved using the secondorder MacCormack method with time splitting. The motion of the channel walls is described by a system of geometrically nonlinear dynamic equations of the theory of this plates, which is solved by the finitedifference method. Kinematic and dynamic contact conditions are imposed at the interface between the media. A numerical experiment is performed to determine typical dynamic regimes and study the transition of the aeroelastic system to inphase oscillations.     

Feigenbaum Scenario Exhibited by Thin Plate Dynamics

The dimensionless partial differential equations governing thedynamics of a thin flexible isotropic plate with an external load arederived and investigated. The period doubling bifurcations, as well asthe chaotic dynamics, are detected and analyzed. The algorithms leadingto the reduction of the original equations to those of a difference setof ordinary differential and algebraic equations are proposed, comparedto other known methods, and then applied to the problem.Among others, it is shown that, in spite of the system complexity, theFeigenbaum scenario exhibited by one-dimensional maps also governs theroute to chaos in the continuous system under consideration.