An Investigation of the Effect of the Canonical Transformation on the Lagrangian

The transformation of the Euler-Lagrange derivative under the point transformation is explicitly stated, and from this view point, the canonical transformation is reinvestigated. In our arguments, the canonical transformations are discussed strictly separately from the canonical equations. A proof is given that the Lagrangian can be restored after any infinitesimal canonical transformation. Some identities are obtained giving relations between canonically transformed and untransformed Lagrangians. Using the identities, the relation between the Noether charge and the generator of the canonical transformation is investigated. The chiral gauge, Galilei and scale transformations are considered as applications to field theory.     

Thermal change of Alq3, tris(8-hydroxyquinolinato) aluminum(III) studied by TG and XRD-DSC

The thermal change of the tris(8-hydroxyquinolinato)aluminum (Alq₃) is currently investigated by XRD-DSC and TG. The phase transition of Alq₃ from α-phase to γ-phase takes place at 643–669 K. A very sharp peak with the peak temperature at approx. 709 K is ascribed to the melting of the Alq₃. The decomposition of the Alq₃ was observed accompanied with the melting and evaporation at >703K. The effect of the atmospheres on the mass loss procedure was studied by TG. It was found that thermal process of Alq₃ was strongly influenced by the partial pressure of water vapor in the atmosphere instead of oxygen.     

Raman and infrared spectra of the all-trans, 7-cis, 9-cis, 13-cis and 15-cis isomers of β-carotene: Key bands distinguishing stretched or terminal-bent configurations form central-bent configurations

Raman and infrared spectra in the region of 1800-150 cm⁻¹ were recorded for a set of cis-trans isomers of d̃-carotene, i.e. the all-trans, 7-cis, 9-cis, 13-cis and 15-cis isomers. Spectral comparison revealed Raman and infrared key bands which (1) distinguish stretched or terminal-bent configurations (all-trans, 7-cis and 9-cis) from central-bent configurations (13-cis and 15-cis), and (2) distinguish unmethylated 7-cis and 15-cis configuratios. Keybands (1) include Raman bands at 1160 and 1140 cm⁻¹ and infrared bands at 825 and 775 cm⁻¹ (the intensity varies with the position of the cis-bend) Key bands (2) include Raman bands at 1274 and 962 cm⁻¹ and an infrared band at 741 cm⁻¹ (characteristic of the 7-cis configuration), and also a Raman band at 1247 cm⁻¹ and an infrared band at 775 cm⁻¹ (characteristic of the 15-cis configuration). The normal modes for the key bands were determined by a set of normal coordinate calculations for the isomeric configurations of a simplified model of d̃-carotene. The key bands were mainly related to the C H in-plane bendings, coupled with the CC or C C stretching, or to the C H out-of-plane wagging vibrations, some of which coupled with the CC torsion.     

Terahertz radiation generation by beating of two spatial-Gaussian lasers

Terahertz radiation generation is proposed based on beating of two spatial-Gaussian lasers in a periodic density plasma, where a transverse component of current is realized that resonantly excites the radiation with efficiency ∼10⁻³. Importance of laser-beam-width, amplitude and periodicity of density structure is discussed for the efficient THz generation.     

Hybrid mesh generation with embedded surfaces using a multiple marching direction approach

This paper proposes a method for the creation of hybrid meshes with embedded surfaces for viscous flow simulations as an extension of the multiple marching direction approach (AIAA J. 2007; 45 (1):162–167). The multiple marching direction approach enables to place semi‐structured elements around singular points, where valid semi‐structured elements cannot be placed using conventional hybrid mesh generation methods. This feature is discussed first with a couple of examples. Elements sometimes need to be clustered inside a computational domain to obtain more accurate results. For example, solution features, such as shocks, vortex cores and wake regions, can be extracted during the process of adaptive mesh generation. These features can be represented as surface meshes embedded in a computational domain. Semi‐structured elements can be placed around the embedded surface meshes using the multiple marching direction approach with a pretreatment method. Tetrahedral elements can be placed easily instead. A couple of results are presented to demonstrate the capability of the mesh generation method. Copyright © 2008 John Wiley & Sons, Ltd.