Some deep learning-based methods have recently been suggested for solving partial differential equations. In these methods, a loss function for training a deep neural network is formulated to satisfy differential operators, boundary conditions, and initial conditions of the intended partial differential equation. After the training, the approximate solution of the partial differential equation can be obtained as a continuous function for the independent variables, specifically a neural network with learned parameters. In this paper, we describe how to solve partial differential equations using deep learning in detail and apply the deep learning-based method to an electrostatic field simulation to solve the Laplace equation. As a result, approximated solutions obtained by the deep learning-based method show generally good agreement with the analytical solutions.

This study proposes a numerical method to treat water freezing and ice melting simultaneously in order to apply the previously proposed numerical method for water-ice phase change on an orthogonal structured grids to a wider range of temperature conditions assuming realistic phenomena. In the proposed method, fluid flow, heat conduction in solids, and solid-liquid phase change are all calculated on orthogonal structured grids. In the calculation of the solid-liquid phase change, the approximate location of the interface in each calculation cell is taken into account, and the Stefan condition is calculated under the assumption that the interface temperature is always equal to the freezing temperature. After a basic check of the reproducibility of natural convection including density inversion region, the proposed method is applied to a problem in which freezing and melting occur simultaneously. From the calculation results, it was confirmed that the natural convection of water including the density inversion region has a significant effect on the freezing of water and melting of ice, and that the temperature of the water-ice interface agrees well with the freezing temperature of water.

The honeycomb core with hexagonal cross section has now the maximum bending stiffness per weight which has made the honeycomb a trillion yen industry. But the cubic core with rectangle cross section here proposed has higher flexural rigidity per weight than the honeycomb core theoretically. This is confirmed also by FEM simulation. In the case of honeycomb core, bonding area between core material and upper or lower face plate is so small that it's hard to apply to the structures which receive vibration load and shear load over a long period of time. On the other hand, in the case of cubic core, it has so much larger bonding area between core material and upper or lower face plate that it eliminates the above drawbacks of the honeycomb. Cubic core molding process only consists of making a hole from one sheet and bending even for the structure with a curved part of which molding cost is much cheaper than honeycomb which is molded by extension type or corrugated type both of which process has a gluing process.

It is thought that the dust piled up is formed and grown by randomly entangling fibers based on actual observations. It is considered thought that elucidating the algorithm of the dust shape and process will lead to the detection of the dust accumulation status and the amount of accumulation. In this paper, basic dust accumulation model is proposed and its simulation is conducted. From the relationship between the fractal dimension of the accumulated dust and the space occupation rate, it is experimentally confirmed that the dust accumulation shape is fractal, and the effectiveness of the rudimentary dust accumulation model is confirmed.