Chiral symmetry analysis and rigid rotational invariance for the lattice dynamics of single-wall carbon nanotubes

We provide a detailed expression of the vibrational potential for the lattice dynamics of single-wall carbon nanotubes (SWCNT's) satisfying the requirements of the exact rigid translational as well as rotational symmetries, which is a nontrivial generalization of the valence force model for the planar graphene sheet. With the model, the low-frequency behavior of the dispersion of the acoustic modes as well as the flexure mode can be precisely calculated. Based upon a comprehensive chiral symmetry analysis, the calculated mode frequencies (including all the Raman- and infrared-active modes), velocities of acoustic modes, and the polarization vectors are systematically fitted in terms of the chiral angle and radius, where the restrictions of various symmetry operations of SWCNT's are fulfilled.

Derivation Of A Nonlinear Reynolds Stress Model Using Renormalization Group Analysis And Two-Scale Expansion Technique

Adopting Yoshizawa's two-scale expansion technique, the fluctuating field is expanded around the isotropic field. The renormalization group method is applied for calculating the covariance of the fluctuating field at the lower order expansion. A nonlinear Reynolds stress model is derived and the turbulent constants inside are evaluated analytically. Compared with the two-scale direct interaction approximation analysis for turbulent shear flows proposed by Yoshizawa, the calculation is much more simple. The analytical model presented here is close to the Speziale model, which is widely applied in the numerical simulations for the complex turbulent flows.

Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Pade approximation

The propagation losses in single-line defect waveguides in a two-dimensional (2D) square-lattice photonic crystal (PC) consisted of infinite dielectric rods and a triangular-lattice photonic crystal slab with air holes are studied by finite-difference time-domain (FDTD) technique and a Pade approximation. The decaying constant beta of the fundamental guided mode is calculated from the mode frequency, the quality factor (Q-factor) and the group velocity v(g) as beta = omega/(2Qv(g)). In the 2D square-lattice photonic crystal waveguide (PCW), the decaying rate ranged from 10(3) to 10(-4) cm(-1) can be reliably obtained from 8 x 10(3)-item FDTD output with the FDTD computing time of 0.386 ps. And at most 1 ps is required for the mode with the Q-factor of 4 x 10(11) and the decaying rate of 10(-7) cm(-1). In the triangular-lattice photonic crystal slab, a 10(4)-item FDTD output is required to obtain a reliable spectrum with the Q-factor of 2.5 x 10(8) and the decaying rate of 0.05 cm(-1). (c) 2004 Elsevier B.V. All rights reserved.

the estimation of thyroxine in human plasma by an electrophoretic technique

A new method for the determination of thyroxine in blood is described. It relies upon the quantitative dependence of the distribution of thyroxine between albumin and thyroxine-binding protein when exogenous 131I-labelled thyroxine is added to serum in vitro. Preliminary results suggest an accuracy in the estimate of the hormone of about 5–10%. Results in a group of patients whose plasma P.B.I, levels were also determined are given and shown to be similar.

Improved thermal fractionation technique for chain structure analysis of ethylene/alpha-olefin copolymers

In this report, we describe an improved thermal fractionation technique used to characterize the polydispersity of crystalline ethylene sequence length (CESL) of ethylene/alpha -olefin copolymers. After stepwise isothermal crystallization, the crystalline ethylene sequences are sorted into groups by their lengths. The CESLs are estimated using melting points of known hydrocarbons. The content of each group is determined using the calibrated peak area. The statistical terms: the arithmetic mean (L) over bar (n), the weighted mean (L) over bar (w) and the broadness index I = (L) over bar (w)/(L) over bar (n) are used to describe the distribution of CESL. Results show that improved thermal fractionation technique can quantitatively characterize the polydispersity of CESL with a high degree of accuracy.