Random attractor for second-order stochastic delay lattice sine-Gordon equation

In this paper, we prove the existence of random $\mathcal{D}$ D -attractor for the second-order stochastic delay sine-Gordon equation on infinite lattice with certain dissipative conditions, and then establish the upper bound of Kolmogorov ε-entropy for the random $\mathcal{D}$ D -attractor.

A Note on the Spectral Gap of the Fredrickson–Andersen One Spin Facilitated Model

This note discusses the spectral gap of the Fredrickson–Andersen one spin facilitated model in two different settings. The model describes an interacting particle system on a graph, where each site is either occupied or empty; and a site may change its occupation when at least one of its neighbors is empty. We will first consider the model on the infinite lattice $${\mathbb {Z}}^{d}$$ Z d , with density close to 1. The second result is on finite graphs, with density that grows with the size of the graph in a way that guarantees O(1) empty sites. In both models lower and upper bounds on the spectral gap were known, but in general did not match. The purpose of this paper is to present new upper bounds that have the same asymptotics as the known lower bounds.

ADVANCED HOMOGENIZATION METHODS FOR PRESSURIZED WATER REACTORS

Macroscopic cross section generation is key part of core calculation. Commonly, the data are prepared independently without a knowledge of fuel loading pattern. The fuel assemblies are simulated in infinite lattice (with mirror boundary conditions). Rehomogenization method is based on combination of actual neutron flux in fuel assembly with macroscopic data from infinite lattice. Rehomogenization method was implemented into the macrocode Andrea and tested on a reference cases. Cases consist of fuel cases, cases with strong absorber, cases with absorption rods, or cases with reflector assemblies. Testing method is based on a comparisons of homogenized and rehomogenized macroscopic cross sections and later on a comparisons of relative power of each fuel assembly. Above that there is comparison of eigenvalue.