Shusuke Nisiyama

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

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.

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.

Internal field error reduction in boundary element analysis for Helmholtz equation

A systematic analysis has been made to clarify the cause of very large errors in the boundary element solutions at internal points near the boundary. Following the results of the analysis, two new ideas have been developed to reduce the errors when solving the Helmholtz equation. The first idea, which is an extended application of the equipotential condition to Helmholtz type problem, is easily applied to any existing program. The second idea which gives us more accurate solutions is based on the analytic integration of boundary integrals by expanding the fundamental solutions into a sum of elementary functions. Test calculations demonstrate that the two present techniques are efficient to reduce the errors near the boundary.

Infrared phase-shifting interferometry using the nitroanisole as a two-dimensional detector

We propose the application of nitroanisole as a two-dimensional detector for infrared (IR) phase-shifting interferometry. The nitroanisole that is utilized in our experiment is liquid at room temperature and it has significant thermal lens effect, i.e. the refractive index for visible light is dependent on temperature. In addition, we verified by infrared absorption spectroscopy that the nitroanisole has an absorption band around 10.6μm in the IR region. Therefore, the interference fringe pattern that is generated on the nitroanisole by the IR beams may be treated as a phase grating for visible light. A Fresnel diffraction pattern made by visible laser light that is transmitted through the phase grating, i.e. the nitroanisole, can be observed as a superposition of the intensities corresponding to the profile of the phase grating and its harmonic components. Additionally, in response to a shift of the interference fringe on the nitroanisole, the Fresnel diffraction pattern on the observation plane also shifts by an equal amount. Utilizing this characteristic of nitroanisole, we attempted to estimate the IR phase map by applying the phase-shifting method to the diffraction patterns. We conducted an experiment aimed to measure the angle of a wedge of ZnSe, which is an IR transmitting material, and we confirmed the feasibility of obtaining phase measurements in the IR region by this procedure.

A use of BEM and NN System to Estimate Density Distribution of Plasma

In this paper it is discussed an inverse analysis for the sake of a non-destructive estimation system for a measurement of an inhomogeneous distribution of plasma by scattering field. The inverse analysis is based on two techniques; one is a multi-layered NN to solve inverse problem, and the other is a boundary element method to solve a direct problem to generate learning data for the NN. In the case of an analysis using simple technique, the learning procedure in NN did not have a good convergence. Hence, we propose two techniques to improve the convergence. One is a normalization technique for input data with considering of the distribution of amplitude of the input data. The other is a dividing section technique. It is clarified that combining of these techniques provide us a rapid convergence and lead the availability of the estimation system.

FD-TD analysis of scattered fields excited by a high energy pulsed beam of charged particles using point charge responses

In this paper, we show a finite-difference time-domain (FD-TD) analysis of scattered fields excited by a pulsed beam using point charge responses and convolution. The advantages of this approach are easy handling of arbitrary beam trajectories and waveforms; efficient absorption for excited fields on open boundaries; and small amount of incident field calculation. In addition, we describe the relation between the temporal resolution and the allowable aliasing error since the point charge field as an incident field has very high frequency spectrum.

A Novel Boundary Element Method for Nonuniform Neutron Diffusion Problems

An advanced boundary element formulation has been proposed to solve the neutron diffusion equation (NDE) for a ‘nonuniform’ system. The continuous spatial distribution of a nuclear constant is assumed to be described using a polynomial function. Part of the constant term in the polynomial is left on the left-hand-side of the NDE, while the remainding is added to the fission source term on the right-hand-side to create a fictitious source. When the neutron flux is also expanded using a polynomial, the boundary integral equation corresponding to the NDE contains a domain integral related to the polynomial source. This domain integral is transformed into an infinite series of boundary integrals, by repeated application of the particular solution for a Poisson-type equation with the polynomial source. In two-dimensional, one-group test calculations for rectangular domains, the orthogonality of Legendre polynomials was used to determine the polynomial expansion coefficients. The results show good agreement wit...