Limit theorem of the max-plus walk (Mathematical structures of integrable systems, its deepening and expansion)

Mathematical structures of integrable systems, its deepening and expansion. September 9-11, 2019. edited by Takao Suzuki. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.The max-plus algebra is a semiring on Rmax = R⋁{-∞} with addition ⊕ and multiplication ⊗ defined by ⊕ = max and ⊗ = +, respectively. It is known that eigenvalues of max-plus matrices are equivalent to the maximal average weight of the corresponding directed graph. In [9], authors introduced the max-plus walk which is a walk model on one dimensional lattice on Z over max-plus algebra, and discussed its properties such as the conserved quantities and the steady state. In this paper, we will discuss the limit measure of the max-plus walk

Thermal Shock Resistances and the Irradiation Effects ot Graphites and C/C-Composites for Fusion Reactor Devices

Graphites and/or C/C-composites as plasma-facing first wall components for fusion reactor devices are subjected occasionally to plasma disruption. Therefore the thermal shock resistances and fracture toughnesses of these materials must be evaluated to assure appropriate performances. In this study, the thermal shock resistance and fracture toughness of several kinds of graphites and C/C-composites for candidate first wall component tiles are evaluated. The mechanical and fracture mechanics properties for these specimens are also measured. Then, two graphites and three C/C-composites are irradiated with 1.1-1.9×10^n/cm^2 (Energy>29fJ) at 650-1000℃ in a fission reactor (Japan Material Testing Reactor, JMTR) and the degradations in the thermal shock resistances and fracture toughnesses and the changes of mechanical and fracture mechanics properties due to the neutron irradiation are quantitatively studied

Neutron Irradiation Effects on Thermal Shock Resistances and Fracture Mechanical Properties of Fuel Compacts for the HTTR

To simulate the nuclear fuel for the High Temperature Engineering Test Reactor (HTTR), a fuel compact model using SiC-kernel coated particles instead of UO_2-kernel coated particles was prepared under the same conditions as those for the real fuel compact. The mechanical and fracture mechanics properties were studied at room temperature. The thermal shock resistance and fracture toughness for thermal stresses of the fuel compact model were experimentally assessed by means of arc discharge heating applied at a central area of the disk specimens. These model specimens were then neutron irradiated in the Japan Material Testing Reactor (JMTR) for fluences up to 1.7×10^n/cm^2 (E>29fJ) at 900℃±50℃. The effects of irradiation on a series of fracture mechanical properties were evaluated and compared with the cases of graphite IG-110 used as the core materials in the HTTR