Hansen, Kaplan, Zamir and Zwick (STOC 2019) introduced a systematic way to use “bias” for predicting an assignment to a Boolean variable in the process of PPSZ and showed that their biased PPSZ algorithm achieves a relatively large success probability improvement of PPSZ for Unique 3SAT. We propose an additional way to use “bias” and show by numerical analysis that the improvement gets increased further.

The Jacobi-Davidson method and the Riccati method for eigenvalue problems are studied. In the methods, one has to solve a nonlinear equation called the correction equation per iteration, and the difference between the methods comes from how to solve the equation. In the Jacobi-Davidson/Riccati method the correction equation is solved with/without linearization. In the literature, avoiding the linearization is known as an improvement to get a better solution of the equation and bring the faster convergence. In fact, the Riccati method showed superior convergence behavior for some problems. Nevertheless the advantage of the Riccati method is still unclear, because the correction equation is solved not exactly but with low accuracy. In this paper, we analyzed the approximate solution of the correction equation and clarified the point that the Riccati method is specialized for computing particular solutions of eigenvalue problems. The result suggests that the two methods should be selectively used depending on target solutions. Our analysis was verified by numerical experiments.

We propose an algorithm for the scattering analyses of gratings with various local defects based on the difference-field boundary-element method (DFBEM). In the algorithm, the defect in the grating is partitioned, and the DFBEM is sequentially applied for each defect section. We validate the proposed algorithm by demonstrating its flexibility for various defect topologies for a locally deformed grating.

We propose an accurate modeling of the wavelength conversion process by dynamic tuning of a dielectric cavity. Since the process involves the long-distance propagation of light, the finite-difference time-domain (FDTD) method is not suitable for modeling of the wavelength conversion process owing to the numerical dispersion error of the FDTD method. The proposed modeling is based on the constrained interpolation profile (CIP) method, which was developed in the field of computational fluid dynamics for the purpose of reducing considerably the numerical dispersion error, and is formulated for a one-dimensional problem using an interpolation function of a higher order than that used in the original CIP method. Numerical experiments reveal that the proposed method can achieve accurate prediction of the wavelength conversion process even with a coarse grid model and is superior to both the original CIP method and the FDTD method.

Constriction resistance is calculated by numerical analysis using Laplace's equations for electric potential of steady state in many cases of contact spot dispersion-status. The results show that contact resistance does not increase beyond 1.5 times even if the total real contact area is about 15% of the apparent contact area. When real contact area is at least about 60% of the apparent contact area, the contact resistance is approximately the same as the constriction resistance acquired from the apparent contact area. When the real contact area is about 50% of the apparent contact area, the contact resistance is approximately constant without regard to the contact shape and contact-point dispersion layout. Therefore, it is proved that contact resistance can be practically calculated using apparent contact area instead of real contact area when there are many contact points caused by metal to metal contact.

This study examines treatment of a boundary between media to simulate an acoustic field using the CIP method. The handling of spatial derivatives of fields is extremely important for CIP acoustic field analysis. We demonstrate a method of handling this boundary and report results of CIP acoustic field analysis using the present treatment.

Eddy-current type proximity sensor is a non-contact type sensing device to detect the approach of a conductor by increase of coil resistance due to eddy-current loss. This paper proposes to add the cap-shaped magnetic flux shield at the top of the ferrite core for the actual sensor. In conventional proximity sensors, main magnetic flux path passes through the air between the target conductor and ferrite core. Proposed sensor, in contrast, has closed magnetic circuit geometry. It means that main magnetic flux path is almost completed by the core and the shield. Therefore, it is predicted that flux does not reach the target conductor and it causes debasement of sensing property. However, it is shown that the calculated results by FEM and measured results of sensing property of the proposed sensor is enhanced compared with the actual sensor. This paper quantitatively accounts the electromagnetisms of the proposed sensor from sensing property, flux distributions and eddy-current loss in each part of the sensor body. Moreover, material characteristics for the proposed shield, such as relative permeability and conductivity, are found.

This paper deals with the scattering of a TM plane wave from a perfectly conductive sinusoidal surface with finite extent. For comparison, however, we briefly discuss the diffraction by the sinusoidal surface with infinite extent, where we use the concept of the total diffraction cross section per unit surface introduced previously. To solve a case where the sinusoidal corrugation width is much wider than wave length, we propose an undersampling approximation as a new numerical technique. For a small rough case, the total scattering cross section is calculated against the angle of incidence for several different corrugation widths. Then we find remarkable results, which are roughly summarized as follows. When the angle of incidence is apparently different from critical angles and diffraction beams are all scattered into non-grazing directions, the total scattering cross section increases proportional to the corrugation width and hence the total scattering cross section per unit surface (the ratio of the total scattering cross section to the corrugation width) becomes almost constant, which is nearly equal to the total diffraction cross section per unit surface in case of the sinusoidal surface with infinite extent. When the angle of incidence is critical and one of the diffraction beams is scattered into a grazing direction, the total scattering cross section per unit surface strongly depends on the corrugation width and approximately approaches to the total diffraction cross section per unit surface as the corrugation width gets wide.

An eddy-current type proximity sensor is a non-contact type sensing device to detect the approach of a conductor by increase of equivalent AC resistance of excitation coil due to eddy current loss in the conductor. In this paper, electromagnetic characteristics of the actual proximity sensor are calculated by FEM and the validity of numerical analysis results are studied. Furthermore, two models that has modified magnetic circuit geometry based on the actual sensor are designed and calculated as numerical experiments. Calculated results are shown as enhanced sensing index or electromagnetic characteristics of the modified sensor. In conclusions, knowledge about the magnetic circuit geometry of the sensor is applied for the enhancement of sensing property.

The theory of the method of moments (MoM), which has been widely used as a numerical technique for analyzing the characteristics of antennas and scatterers, is described. First, the steps of MoM to solve integral equations for conducting wires and planes are presented. It is pointed out that MoM combined with Galerkin's method yields highly accurate results. The importance of ensuring the continuity condition of current on conducting bodies is emphasized and numerical examples for a conducting structure involving junctions of wire segments and planar segments are presented. Finally, MoM for dielectric scatterers including recent developments is described.

Using a full-vector finite element method (FEM) with curvilinear hybrid edge/nodal elements, a single-mode nature of index-guiding photonic crystal fibers, also called holey fibers (HFs), is accurately analyzed as a function of wavelength. The cladding effective index, which is very important design parameter for realizing a single-mode HF and is defined as the effective index of the infinite photonic crystal cladding if the core is absent, is also determined using the FEM. In traditional fiber theory, a normalized frequency, V, is often used to determine the number of guided modes in step-index fibers. In order to adapt the concept of V-parameter to HFs, the effective core radius, aeff, is determined using the actual numerical aperture given by the FEM. Furthermore, the group velocity dispersion of single-mode HFs is calculated as a function of their geometrical parameters, and the modal birefringence of HFs is numerically investigated.

The micro positioning systems using magnetic suspension technique, which is one of precision actuating method, have been suggested. Utilizing the various potentials such as the exclusion of a mechanical friction, they are being applied broadly to multi degrees of freedom (d.o.f) system requesting high accuracy or hybrid system requesting to be controlled position and force simultaneously. This paper presents the entire development procedure of a novel six d.o.f micro positioning system using mag-netic levitation, with a repulsive force mechanism covering the all d.o.f. First, the interactions between magnetic elements are modeled and the system design flow by an optimal location of the elements is given. A kinematic relationship between the measuring instruments and the levitated object is derived, and dynamic characteristics are identified by the narrow gap principles. And the main issues for control are discussed.

In this paper we discuss the limiting behavior of the search direction of the steepest descent method in minimizing the Rayleigh quotient. This minimization problem is equivalent to finding the smallest eigenvalue of a matrix. It is shown that the search direction asymptotically alternates between two directions represented by linear combinations of two eigenvectors of the matrix. This is similar to the phenomenon in minimizing the quadratic form. We also show that these eigenvectors correspond to the largest and second-smallest eigenvalues, unlike in the case of the quadratic form.

A type of Lienard's equation +µf(x)+x=0, where f(x) is not an even function of x, is studied by Le Corbeiller as a model of various biological oscillations, such as breathing, and called two-stroke oscillators. A distinctive feature of this type of oscillators is that the parameter µ has the upper limit µ0 for the oscillator to have some stable limit cycle. This paper gives a numerical method for calculating this upper limit µ0.

A simple algorithm is proposed for representing nonseparable functions by equivalent separable functions. In this algorithm, functions are first represented by computational graphs, which are directed graphs representing the computational process of the functions. Then, the vertices of the computational graphs are searched in preorder or postorder, and the transformation to separable forms is performed at the places where it is necessary. By this repetition of the transformation, nonseparable functions are represented by separable functions automatically. The proposed algorithm will be useful in various fields of science and engineering because funcutions of one variable are easy to deal with.

The dielectric rod waveguides with corrugation consisting of nonintegral-ratio period waves are investigated numerically. The leakage characteristics of HE11-type wave in the waveguide is analyzed by applying Yasuura's method. The complex propagation constants and the far field patterns are presented. The radiation pattern of a fabricated waveguide with corrugation agrees well with the calculated value. The dependence of radiation characteristics on the corrugation form is discussed. It is shown that the leakage directions and the intensity of leaky waves are controlled independently one another. The radiation pattern can be synthesized by choosing the geometric parameters of the corrugation properly.

For estimating the radiated emission from a metallic enclosure, the authors have developed a numerical computational method which applied inverse analysis. A metallic enclosure containing a loop antenna was set up to be a model source for the numerical analysis. Magnetic fields around the enclosure were measured by measurement systems fabricated in the authors' laboratory. Using the measured magnetic fields, current distributions on the enclosure surface were determined by means of an inverse analysis utilizing the least squares method. From this surface current distribution, the electromagnetic field distributions were estimated by forward analysis on a cylindrical surface 3.0m in radius. The amount of the error in the estimated fields distribution was also discussed.

This paper describes a pipelining universal system of discrete time cellular neural networks (DTCNNs). The new relaxation-based algorithm which is called a Pipelining Gauss Seidel (PGS) method is used to solve the CNN state equations in pipelining. In the systolic system of N processor elements {PEi}, each PEi performs the convolusional computation (CC) of all cells and the preceding PEi-1 performs the CC of all cells taking precedence over it by the precedence interval number p. The expected maximum number of PE's for the speeding up is given by n/p where n means the number of cells. For its application, the encoding and decoding process of moving images is simulated.

An estimation method of region is presented, in which a solution path of the so-called Newton type homotopy equation in guaranteed to exist, it is applied to a certain class of uniquely solvable nonlinear equations. The region can be estimated a posteriori, and its upper bound also can be estimated a priori.

A type of infinite dimensional homotopy method is considered for numerically calculating a solution curve of a nonlinear functional equation being a Fredholm operator with index 1 and an A-proper operator. In this method, a property of so-called A-proper homotopy plays an important role.