Simulation of the nonlinear vibration of a string using the Cellular Automata based on the reflection rule

In this study, the nonlinear dynamic responses of a string are simulated using the Cellular Automata method based on the reflection rule. In the case of nonlinear systems, the velocity of wave propagation is not constant and depends on the amplitude. A new treatment of the dynamic time step is proposed for the Cellular Automata method considering the effect of the propagation velocity. As numerical examples, first, the dynamic responses of a string with linear characteristic are simulated using the Cellular Automata method. A typical resonance curve can be obtained. Second, the dynamic responses of a string with nonlinear characteristic are simulated using the proposed method. Some characteristic types of vibration can be obtained. It is concluded that the linear and nonlinear dynamic responses of a string may be obtained by simulation using the Cellular Automata method.     

Estimation of growth rate in unidirectionally solidified multicrystalline silicon by the growth-induced striation method

Multicrystalline silicon was grown by unidirectional solidification method using the accelerated crucible rotation technique. The application of the accelerated crucible rotation technique in unidirectional solidification method induced growth striations across the axial direction of the grown crystal. This striation pattern was observed from carbon concentration distribution, obtained by using Fourier transform infrared spectroscopy. The generated striation pattern was found to be weak and discontinuous. Some striations were absent, probably due to back melting, caused during each crucible rotation. From the growth striations and applied time period in crucible rotation, the growth rate was estimated by using Fourier transformation analysis.     

Bump formation on a glass surface with a transparent coating using femtosecond laser processing

The morphology of a glass surface having a transparent coating processed with focused femtosecond laser pulses is investigated. The transparent coating is formed of poly-methyl methacrylate (PMMA). When the glass was coated with a PMMA film with a thickness of 2.8 μm, bumps were formed over a wide range of axial focus positions. The same laser pulse energy produced cavities when processing bare glass with no coating. The bumps were formed as a result of suppressing material emission from the glass surface by a shielding effect of plasma generated by ablation of the PMMA film and by physical blocking of the PMMA film. A thinner film with a thickness of 0.7 μm produced a reduced shielding effect, forming an exploded bump with a small pit at its center and debris around the periphery. PACS 44.10.+i; 61.80.Ba; 79.20.Ds     

Recursive Fermion System in Cuntz Algebra. I

Embeddings of the CAR (canonical anticommutation relations) algebra of fermions into the Cuntz algebra ?₂ (or ?_{2 d} more generally) are presented by using recursive constructions. As a typical example, an embedding of CAR onto the U(1)-invariant subalgebra of ?₂ is constructed explicitly. Generalizing this construction to the case of ?_{2 p} , an embedding of CAR onto the U(1)-invariant subalgebra of ?_{2 p} is obtained. Restricting a permutation representation of the Cuntz algebra, we obtain the Fock representation of CAR. We apply the results to embed the algebra of parafermions of order p into ?_{2 p} according to Green's ansatz. Received: 3 September 2001 / Accepted: 19 January 2002     

Synthesis of 3-hydroxyindolin-2-one alkaloids, (±)-donaxaridine and (±)-convolutamydines A and E, through enolization-Claisen rearrangement of 2-allyloxyindolin-3-ones

Claisen rearrangement triggered by enolization of 2-allyloxyindolin-3-ones with DBU was performed in order to prepare 3-allyl-3-hydroxyindolin-2-ones. Total synthesis of 3-hydroxyindolin-2-one alkaloids, (±)-donaxaridine, as well as (±)-convolutamydines A and E, was achieved by transformation of the allyl moiety of 3-allyl-3-hydroxyindolin-2-ones.     

Efficient synthesis of CCR5 antagonist, 2,3-dihydro-1-benzothiepine derivatives by improved intramolecular Claisen type reaction using dialkylcarbonate

The efficient synthesis of 2,3-dihydro-1-benzothiepine derivatives 4 has been developed. The intramolecular Claisen type reaction of the new products, 4-(o-formylphenylthio)butyrate 9, with alcoholate in dialkylcarbonate as a solvent afforded 4 in good yields. According to this new procedure, we have accomplished the practical preparation of CCR5 antagonist 1 as a candidate for oral HIV-1 therapy.     

Determination of237Np in environmental samples using inductively coupled plasma mass spectrometry

Ammonium uranates (AU) obtained by the addition of aqueous NH₄ OH to a solution of UO₂ (NO₃)₂ or the equilibrium reaction of UO₃ · 2H₂ O with the vapour over concentrated NH₄ OH have been studied by X-ray diffraction (XRD) analysis, diffuse reflectance Fourier transform infrared spectrometry (DR-FTIR) and chemical analysis. Ammonia can be present as either NH₃ or NH ₄ ⁺ . For precipitates obtained at a pH of 3.7, ammonia in the form of NH₃ is predominant. For ammonium uranate obtained by reaction over concentrated NH₄OH, most of the ammonia is bonded as NH ₄ ⁺ . The reaction mechanism and structures of the products are also discussed.