Takeaki Enoto

A New Numerical Method for Asymmetrical Abel Inversion

A new asymmetrical Abel inversion is presented for application in asymmetrical data which is obtained from plasma diagnostics (for instance, interferometry or spectroscopy) on the toroidal plasma system, and in which asymmetry exists normal to the direction of observation. In this new numerical method a weight function, which was obtained by separating the integrated quantity into odd and even parts, was used for determination of the asymmetrical local value. To demonstrate the usefulness of this new method, we set up a hypothetical data set, which resulted in a valid local value.

Columnar Assemblies of Aliphatic Poly(acetylene ester)s Prepared with a [Rh(norbornadiene)Cl]2 Catalyst.1H and13C NMR, X-Ray Diffraction and AFM Studies

Alkyl propiolates: HC≡CCOOn-C m H 2m+1 (m = 2∼4), acetylene esters were polymerized with a [Rh(norbornadiene)Cl] 2 catalyst in methanol as the polymerization solvent to produce poly(n-alkyl propiolate)s, PAPAs, called polyacetylene esters, in relatively high yields. The resulting PAPAs were characterized in detail using 1 H and 13 C NMR spectroscopy, X-ray diffraction, and atomic force microscope methods. The data showed that the resulting polymers selectively have cis-transoid form. The cis-transoid isomer is not amorphous but holds a pseudohexagonal structure called a columnar assembly the diameter of which agrees with those estimated by the semiempirical calculation method (AM1). The crystalline ratios of the columnar assemblies were also estimated to be ca. 60∼70%. In the case of poly(ethyl propiolate), PEPA, the crystalline size was found to approximately agree with that estimated from the AFM images of the cast film of PEPA.

Nonlinear Least Square Regression by Adaptive Domain Method With Multiple Genetic Algorithms

In conventional least square (LS) regressions for nonlinear problems, it is not easy to obtain analytical derivatives with respect to target parameters that comprise a set of normal equations. Even if the derivatives can be obtained analytically or numerically, one must take care to choose the correct initial values for the iterative procedure of solving an equation, because some undesired, locally optimized solutions may also satisfy the normal equation. In the application of genetic algorithms (GAs) for nonlinear LS, it is not necessary to use normal equations, and a GA is also capable of avoiding localized optima. However, convergence of population and reliability of solutions depends on the initial domain of parameters, similarly to the choice of initial values in the above mentioned method using the normal equation. To overcome this disadvantage of applying GAs for nonlinear LS, we propose to use an adaptive domain method (ADM) in which the parameter domain can change dynamically by using several real-coded GAs with short lifetimes. Through an example problem, we demonstrate improvements in terms of both the convergence and the reliability by ADM. A further merit in the proposed method is that it does not require any specialized knowledge about GAs or their tuning. Therefore, the nonlinear LS by ADM with GAs are accessible to general scientists for various applications in many fields

Radiation-induced Cis to Trans isomerization of poly(n-butylpropiolate) prepared with a [Rh(norbornadiene)Cl]2 complex as a stereospecific catalyst

Abstract Normal alkylpropiolate, i.e., n -butylpropiolate: HCCCOO n C 4 H 9 was polymerized with [Rh(norbornadiene)Cl] 2 catalyst in methanol solvent to produce poly( n -butylpropiolate), (PBPA) polymer called polyacetylene esters in relatively high yields. The obtained polymer was characterized in detail using 1 HNMR, gel permeation chromatography (GPC), diffuse reflective UV methods. Consequently, the data showed that the resulting polymers selectively have cis-transoid form. We also found that γ -ray irradiation of the cis isomer resulted in isomerization to the trans isomer even at room temperature in air to generate the extended trans sequences which can stabilize mobile unpaired electrons as π -radicals called solitons.

Scattered-field time domain boundary element method and its application to transient electromagnetic field simulation in particle accelerator physics

Authors have been working in particle accelerator wake field analysis by using the Time Domain Boundary Element Method (TDBEM). A stable TDBEM scheme was presented and good agreements with conventional wake field analysis of the FDTD method were obtained. On the other hand, the TDBEM scheme still contains difficulty of initial value setting on interior region problems for infinitely long accelerator beam pipe. To avoid this initial value setting, we adopted a numerical model of beam pipes with finite length and wall thickness on open scattering problems. But the use of such finite beam pipe models causes another problem of unwanted scattering fields at the beam pipe edge, and leads to the involvement of interior resonant solutions. This paper presents a modified TDBEM scheme, Scattered-field Time Domain Boundary Element Method (S-TDBEM) to treat the infinitely long beam pipe on interior region problems. It is shown that the S-TDBEM is able to avoid the excitation of the edge scattering fields and the involvement of numerical instabilities caused by interior resonance, which occur in the conventional TDBEM.

Computer Method for New Elliptical Abel Inversion Applied to Holographic Plasma Diagnostics

A new and simple elliptical Abel inversion for calculating spatial distributions of electron density from elliptical shaped plasma is presented. In this numerical method inversion matrix elements were calculated analytically and examined using a test function. This method was applied to an end-on holographic interferogram of a θ-pinch plasma for the first time.

Power iterative multiple reciprocity boundary element method for solving three-dimensional Helmholtz eigenvalue problems

Abstract The multiple reciprocity boundary element method (MRBEM) has been employed to solve the three-dimensional Helmholtz equation, ▿ 2 gf + k 2 gf = 0. In the present technique, the Helmholtz equation is arranged as ▿ 2 gf + k 0 2 gf + gf / γ = 0 where k 0 is an estimate of k and λ is equal to ( k 2 − k 0 2 ) −1 . As the term gf/λ is treated as a source, the power iteration technique with Wielandts spectral shift is used to find the value of λ. The boundary integral equation is formulated with the fundamental solution to ▿ 2 gf + k 0 2 gf + δ i = 0. The domain integral related to the above source is transformed into a series of boundary integrals, with the aid of the higher order fundamental solutions based on the spherical Bessel functions. The eigenvalue k 2 can also be described using only boundary integrals. Test calculations demonstrate that the present technique is efficient for finding k 2 and easier to handle than the conventional determinant search scheme.

Matrix-type higher order fundamental solutions to three-dimensional two-group neutron diffusion equations

Abstract The zero-order and the higher-order fundamental solutions for the 3-D two-group neutron diffusion equations have been derived in such a way that these solutions satisfy the first and the second group equations simultaneously. Each degree of the solutions has a 2 × 2 matrix form based on two types of function, r p exp (−i Br ) and r p exp(− kr ). Singularities of type (1/ r ) are only found at the diagonal components of the zero-order solutions; however, no singularities are found at any components of the higher-order solutions. These solutions can be used for applying the multiple reciprocity boundary element method to 3-D two-group neutron diffusion problems.

Explicit time domain boundary element scheme for dispersion-free wake field calculation of long accelerator structures

This paper introduces a new explicit scheme with a moving window option for wake field calculation of long accelerator structures. This scheme is based on a time domain boundary element method (TDBEM) which uses a retarded Kirchhoff boundary integral equation for interior region problems. As a corollary of this boundary integral equation, our approach allows a conformal modeling of a structure and time domain wake field simulation without numerical grid dispersion errors in all spatial directions. The implementation of a moving window technique in the framework of TDBEM is presented and it is shown that this moving window technique allows to significantly reduce memory requirement of the TDBEM scheme in the short range wake field calculation. Several numerical examples are demonstrated for the TESLA 9-cell cavity and tapered collimators. The results of the new TDBEM scheme are compared with those of finite difference codes.

An improvement in the simultaneity of images on an ultrahigh-speed x-ray framing camera with a gated microchannel plate detector

Ultra high-speed X-ray framing cameras have improved considerably in recent years. Frames with temporal resolution of less than 100 ps are achievable, due to application of the non-linear amplification properties a microchannel plate (MCP). However, in the case of frame resolution under 100 ps, the propagation delay of the shuttering pulse on the MCP poses a significant problem to the maintenance of simultaneity of gated images. In the present research, a method to augment the simultaneity of images is presented. In previous designs, the photocathode was coated onto the MCP input surface. The improved design presented here separates the photocathode from the MCP detector. The transit time of the photoelectrons is varied at each point on the gated electrode is with respect to the MCP detector. Results show that the simultaneity of images is improved with this new design.