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.     

Light Diffraction of Aligned Polymer Fibers Periodically Dispersed by Phase Separation of Liquid Crystal and Polymer

We have confirmed light diffraction of aligned polymer fibers obtained by a phase separation of an anisotropic-phase solution of liquid crystal and polymer. He—Ne laser light passing through the polymer fibers was scattered in the axis vertical to the fibers, and had two peaks of light intensity symmetrical to the center of the transmitting laser spot. The two peaks were found to be caused by light diffraction due to the periodic polymer-fiber dispersion because the peaks corresponded to values calculated by intervals between the fibers. The periodical fiber networks are considered to be formed by anisotropic spinodal decomposition. This effect can be used to measure the dispersion order of the polymer fibers. © 2004 The Optical Society of Japan     

On singularities arising from the contraction op the minimal section of a ruled surface

We will discuss the Gorenstein property of the singularity which is blown down from the minimal section of a ruled surface in terms of the extension class. In the case that the base field has positive characteristic, we find a new example (3.4) of Gorenstein singularity in connection with Theorem B.     

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     

Effects of oblique-incidence evaporation on magnetic properties of Fe20Ni80/Fe70Co30 bilayer film

Evaporative deposition at oblique incidence is shown to enhance the magnetic anisotropy of an Fe₂₀Ni₈₀ magnetic film and induce magnetic anisotropy in an overlying, strongly isotropic Fe₇₀Co₃₀ film. This deposition method for the formation of an underlayer of several lattice parameters in thickness and semi-hard overlayer of a few thousands Angstroms in thickness achieves a significant change in the magnetization process and strong suppression of the coercive forces of Fe₇₀Co₃₀ in the hard magnetization direction. Soft magnetization of the Fe₇₀Co₃₀ overlayer is not achieved when one of the layers is deposited at oblique incidence. It is anticipated that shape magnetic anisotropy is responsible in part for the magnetic anisotropy induced in both in Fe₂₀Ni₈₀ under- and Fe₇₀Co₃₀ overlayer by oblique incidence evaporation.     

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     

Equality cases in matrix norm inequalities of golden-thompson type

The equality cases in several matrix norm (trace) inequalities are characterized. Norm inequalities of Golden-Thompson type and of its complement type are treated as well as a logarithmic trace inequality and norm inequalities for matrix exponentials.     

Synthesis and chiroptical properties of optically active poly(ethynylcarbazole) derivatives: Substituent effect on the helix formation

Novel chiral acetylene monomers containing carbazole, 2‐ethynyl‐9‐[(S)‐2‐methylbutoxycarbonyl]carbazole ( 1 ), 3‐ethynyl‐9‐[(S)‐2‐methylbutoxycarbonyl]carbazole ( 2 ), 2‐ethynyl‐9‐[(S)‐2‐methylbutyl]carbazole ( 3 ), and 2‐ethynyl‐9‐[(S)‐4‐methylhexyl]carbazole ( 4 ) were synthesized and polymerized with [(nbd)RhCl]₂? Et₃N. The corresponding polyacetylenes with number‐average molecular weights ranging from 68,700 to 310,000 were obtained in good yields. Poly( 1 ) exhibited a large specific rotation and an intense Cotton effect in toluene, indicating that it formed a helix with predominantly one‐handed screw sense, while the other three polymers showed no evidence for taking a helical structure. Poly( 1 ) largely decreased the CD intensity upon heating from ?10 to 60 °C. Poly( 1 ) showed a Cotton effect in film state in a manner similar to solution state. No chiral amplification was observed in the copolymerization of 1 with achiral 2‐ethynyl‐9‐tert‐butoxycarbonylcarbazole ( 5 ). © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4450–4458, 2007