This paper presents a formal approach for generating train timetables in a mesoscopic level that is more concrete than the macroscopic level, where each station is simply expressed in a black-box, and more abstract than the microscopic level, where the infrastructure in each station-area is expressed in detail. The accuracy of generated timetable and the computational effort for the generation is a trade-off. In this paper, we design a formal mesoscopic modeling language by analyzing real railways, for example Tazawako-line as the first step of this work. Then, we define the constraint formulae for generating train timetables with the help of SMT (Satisfiability Module Theories)-Solver, and explain our tool RW-Solver that is an implementation of the constraint formulae. Finally, we demonstrate how RW-Solver with the help of SMT-Solver can be used for generating timetables in a case study of Tazawako-line.

A suggestion for creating an excitable/oscillatory field with solid-state material is proposed. In essence, the idea is to make a spatial array of "mesoscopic particles" with the characteristics of a first-order phase transition. A theoretical computation shows that an auto-wave, or excitable wave, is generated in such an excitable field. A simple example of using this system as a diode in information flow is given.