arXiv subjects

Takeshi Ohtsuka

Publications and source records attributed to Takeshi Ohtsuka.

5 recordsLinked to original sources

arXiv2026

Diffusive method for multiple class data classification

A simple algorithm for multiple class data classification is proposed, which is based on the infinit speed of propagation and the strong maximum principle for the heat equation. In this method, solutions of the heat equation whose initial data are the characteristic function of the training dataset are considered. The classification is established by the sign of the difference of two solutions in a very short time interval. A numerical algorithm for discrete training data in high-dimensional feature space is proposed. As an application of the proposed method, numerical results on the classification of handwritten digits database are presented in this paper.

math.NA↗

arXiv2025

A minimizing movements approach for crystalline eikonal-curvature flows of spirals

We propose an algorithm for evolving spiral curves on a planar domain by normal velocities depending on the so-called crystalline curvatures. The algorithm uses a minimizing movement approach and relies on a special level set method for embedding the spirals. We present numerical simulations and comparisons demonstrating the efficacy of the proposed numerical algorithm.

math.NA↗

arXiv2019

Numerical analysis comparing ODE approach and level set method for evolving spirals by crystalline eikonal-curvature flow

In this paper, the evolution of a polygonal spiral curve by the crystalline curvature flow with a pinned center is considered with two view points, discrete model consist of an ODE system of facet lengths and a level set method. We investigate the difference of these models numerically by calculating the area of the region enclosed by these spiral curves. The area difference is calculated by the normalized L1 norm of the difference of step-like functions which are branches of arg(x) whose discontinuities are only on the spirals. We find the differences of the numerical results considered in this paper are very small even though the evolution laws of these models around the center and the farthest facet are slightly different.

math.NA↗

arXiv2018

Existence of asymptotic speed of solutions to birth and spread type nonlinear partial differential equations

In this paper, we prove the existence of asymptotic speed of solutions to fully nonlinear, possibly degenerate parabolic partial differential equations in a general setting. We then give some explicit examples of equations in this setting and study further properties of the asymptotic speed for each equation. Some numerical results concerning the asymptotic speed are presented.

math.AP↗

arXiv2017

Growth rate of crystal surfaces with several dislocation centers

We study analytically and numerical the growth rate of a crystal surface growing by several screw dislocations. To describe several spiral steps we use the revised level set method for spirals by the authors (Journal of Scientific Computing 62, 831-874, 2015). We carefully compare our simulation results on the growth rates with predictions in a classical paper by Burton et al. (Philos Trans R Soc Lond Ser A Math Phys Sci 243,299-358, 1951). Then, we propose improved estimates on the growth rate with several different configurations, which are in agreement with our numerical simulations. The influence of distribution of screw dislocations in a group on a line to the growth rate, and the growth rate by a group including different rotational orientations of spirals are also studied in this paper.

cond-mat.mtrl-sci↗