System thermal-hydraulic modelling of the phénix dissymmetric test benchmark

Phénix is a French pool-type sodium-cooled prototype reactor; before the definitive shutdown, occurred in 2009, a final set of experimental tests are carried out in order to increase the knowledge on the operation and the safety aspect of the pool-type liquid metal-cooled reactors. One of the experiments was the Dissymmetric End-of-Life Test which was selected for the validation benchmark activity in the frame of SESAME project. The computer code validation plays a key role in the safety assessment of the innovative nuclear reactors and the Phénix dissymmetric test provides useful experimental data to verify the computer codes capability in the asymmetric thermal-hydraulic behaviour into a pool-type liquid metal-cooled reactor. This paper shows the comparison of the outcomes obtained with six different System Thermal-Hydraulic (STH) codes: RELAP5-3D©, SPECTRA, ATHLET, SAS4A/SASSYS-1, ASTEC-Na and CATHARE. The nodalization scheme of the reactor was individually achieved by the participants; during the development of the thermal-hydraulic model, the pool nodalization methodology had a special attention in order to investigate the capability of the STH codes to reproduce the dissymmetric effects which occur in each loop and into pools, caused by the azimuthal asymmetry of the boundary conditions. The modelling methodology of the participants is discussed and the main results are compared in this paper to obtain useful guide lines for the future modelling of innovative liquid metal pool-type reactors

Superdiffusion of energy in Hamiltonian systems perturbed by a conservative noise

We review some recent results on the anomalous diffusion of energy in systems of 1D coupled oscillators and we revisit the role of momentum conservation.Comment: Proceedings of the conference PSPDE 2012 https://sites.google.com/site/meetingpspde

Fluctuations of the heat flux of a one-dimensional hard particle gas

Momentum-conserving one-dimensional models are known to exhibit anomalous Fourier's law, with a thermal conductivity varying as a power law of the system size. Here we measure, by numerical simulations, several cumulants of the heat flux of a one-dimensional hard particle gas. We find that the cumulants, like the conductivity, vary as power laws of the system size. Our results also indicate that cumulants higher than the second follow different power laws when one compares the ring geometry at equilibrium and the linear case in contact with two heat baths (at equal or unequal temperatures). keywords: current fluctuations, anomalous Fourier law, hard particle gasComment: 5 figure

A Two-populations Ising model on diluted Random Graphs

We consider the Ising model for two interacting groups of spins embedded in an Erd\"{o}s-R\'{e}nyi random graph. The critical properties of the system are investigated by means of extensive Monte Carlo simulations. Our results evidence the existence of a phase transition at a value of the inter-groups interaction coupling $J_{12}^C$ which depends algebraically on the dilution of the graph and on the relative width of the two populations, as explained by means of scaling arguments. We also measure the critical exponents, which are consistent with those of the Curie-Weiss model, hence suggesting a wide robustness of the universality class.Comment: 11 pages, 4 figure

Criticality in diluted ferromagnet

We perform a detailed study of the critical behavior of the mean field diluted Ising ferromagnet by analytical and numerical tools. We obtain self-averaging for the magnetization and write down an expansion for the free energy close to the critical line. The scaling of the magnetization is also rigorously obtained and compared with extensive Monte Carlo simulations. We explain the transition from an ergodic region to a non trivial phase by commutativity breaking of the infinite volume limit and a suitable vanishing field. We find full agreement among theory, simulations and previous results.Comment: 23 pages, 3 figure

Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition

For the symmetric simple exclusion process on an infinite line, we calculate exactly the fluctuations of the integrated current $Q_t$ during time $t$ through the origin when, in the initial condition, the sites are occupied with density $\rho_a$ on the negative axis and with density $\rho_b$ on the positive axis. All the cumulants of $Q_t$ grow like $\sqrt{t}$. In the range where $Q_t \sim \sqrt{t}$, the decay $\exp [-Q_t^3/t]$ of the distribution of $Q_t$ is non-Gaussian. Our results are obtained using the Bethe ansatz and several identities recently derived by Tracy and Widom for exclusion processes on the infinite line.Comment: 2 figure