JSIAM Letters Vol. 8(2016)

A numerical model of a nonlinear and degenerate diffusion equation on connected graphs, arising in a diversity of industrial applications, is presented. This paper shows that concurrently using a staggered finite volume spatial discretization with an analytical solution-based flux evaluation method and an operator-splitting technique computes stable and physically-consistent numerical solutions to the equation. A demonstrative application example of the numerical model to moisture dynamics in a hypothetical non-woven fibrous strip network under an evaporative environment is presented in order to show its versatility. Mathematical issues to be addressed in a future for better comprehending the model are finally discussed.

In the field of industrial shape design, the plane curves which have radii of curvature proportional to the power of linear functions of their arc-length parameters are called the log-aesthetic curves (LAC) and have been investigated. However, the well-used curves, for example, the parabolic arcs and the typical curves of Mineur et al. are not contained in the family of LACs. In this letter we generalize LAC by the Hamiltonian formalism. This extended family of curves contains some well-known plane curves in classical differential geometry.

In this contribution, we propose a new framework to derive energy-preserving numerical schemes based on the variational principle for Hamiltonian mechanics. We focus on Noether's theorem, which shows that the symmetry with respect to time translation gives the energy conservation law. By reproducing the calculation of the proof of Noether's theorem after discretization using the summation by parts and the discrete gradient, we obtain the scheme and the corresponding discrete energy at the same time. The significant property of efficiency is that the appropriate choice of the discrete gradient makes our schemes explicit if the Hamiltonian is separable.

This study provides a theoretical framework to understand how campaign advertising works in a referendum. Our model analyzes a referendum with a straight choice between two alternatives, Yes or No. In this model, after the parties decide their policies, they promise benefits to voters during the campaign, which ultimately results in a fiscal cost and, thus, a burden to the voters themselves. We construct a two-party two-stage game in which parties choose a policy in the first stage and the benefits in the second stage. We show that one party shifts to a more extreme (polarized) position in an equilibrium.