Changes of Temperature and Moisture Distribution over Time by Thermo-Hydro-Chemical (T-H-C)-Coupled Analysis in Buffer Material Focusing on Montmorillonite Content

Bentonite is used as a buffer material in engineered barriers for the geological disposal of high-level radioactive waste. The buffer material will be made of bentonite, a natural clay, mixed with silica sand. The buffer material is affected by decay heat from high-level radioactive waste, infiltration of groundwater, and swelling of the buffer material. The analysis of these factors requires coupled analysis of heat transfer, moisture transfer, and groundwater chemistry. The purpose of this study is to develop a model to evaluate bentonite types and silica sand content in a unified manner for thermo-hydro-chemical (T-H-C)-coupled analysis in buffer materials. We focused on the content of the clay mineral montmorillonite, which is the main component of bentonite, and developed a model to derive the moisture diffusion coefficient of liquid water and water vapor based on Philip and de Vries, and Kozeny-Carman. The evolutions of the temperature and moisture distribution in the buffer material were analyzed, and the validity of each distribution was confirmed by comparison with the measured data obtained from an in situ experiment at 350 m in depth at the Horonobe Underground Research Center, Hokkaido, Japan

Ronkin/Zeta Correspondence

The Ronkin function was defined by Ronkin in the consideration of the zeros of almost periodic function. Recently, this function has been used in various research fields in mathematics, physics and so on. Especially in mathematics, it has a closed connections with tropical geometry, amoebas, Newton polytopes and dimer models. On the other hand, we have been investigated a new class of zeta functions for various kinds of walks including quantum walks by a series of our previous work on Zeta Correspondence. The quantum walk is a quantum counterpart of the random walk. In this paper, we present a new relation between the Ronkin function and our zeta function for random walks and quantum walks. Firstly we consider this relation in the case of one-dimensional random walks. Afterwards we deal with higher-dimensional random walks. For comparison with the case of the quantum walk, we also treat the case of one-dimensional quantum walks. Our results bridge between the Ronkin function and the zeta function via quantum walks for the first time.Comment: 19 pages. arXiv admin note: substantial text overlap with arXiv:2202.05966; text overlap with arXiv:2109.07664, arXiv:2104.1028

Sound and Relatively Complete Belief Hoare Logic for Statistical Hypothesis Testing Programs

We propose a new approach to formally describing the requirement for statistical inference and checking whether a program uses the statistical method appropriately. Specifically, we define belief Hoare logic (BHL) for formalizing and reasoning about the statistical beliefs acquired via hypothesis testing. This program logic is sound and relatively complete with respect to a Kripke model for hypothesis tests. We demonstrate by examples that BHL is useful for reasoning about practical issues in hypothesis testing. In our framework, we clarify the importance of prior beliefs in acquiring statistical beliefs through hypothesis testing, and discuss the whole picture of the justification of statistical inference inside and outside the program logic