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A Sequel To β€œA Space Topologized By Functions From Omega To Omega”, Tetsuya Ishiu, Akira Iwasa Dec 2010

A Sequel To β€œA Space Topologized By Functions From Omega To Omega”, Tetsuya Ishiu, Akira Iwasa

Faculty Publications

We consider a topological space βŸ¨π‘‹, 𝜏 (β„±)⟩, where 𝑋 = {𝑝 βˆ—} βˆͺ [πœ” Γ…~ πœ”] and β„± βŠ† πœ”πœ”. Each point in πœ” Γ…~ πœ” is isolated and a neighborhood of π‘βˆ— has the form {π‘βˆ—}βˆͺ{βŸ¨π‘–, π‘—βŸ© : 𝑖 β‰₯ 𝑛, 𝑗 β‰₯ 𝑓(𝑖)} for some 𝑛 ∈ πœ” and 𝑓 ∈ β„±. We show that there are subsets β„± and 𝒒 of πœ”πœ” such that β„± is not bounded, 𝒒 is bounded, yet βŸ¨π‘‹, 𝜏 (β„±)⟩ and βŸ¨π‘‹, 𝜏 (𝒒)⟩ are homeomorphic. This answers a question of the second author posed in A space topologized by functions …


On The Accuracy Of Explicit Finite-Volume Schemes For Fluctuating Hydrodynamics, Aleksandar Donev, Eric Vanden-Eijnden, Alejandro Garcia, John B. Bell Jan 2010

On The Accuracy Of Explicit Finite-Volume Schemes For Fluctuating Hydrodynamics, Aleksandar Donev, Eric Vanden-Eijnden, Alejandro Garcia, John B. Bell

Faculty Publications

This paper describes the development and analysis of finite-volume methods for the Landau–Lifshitz Navier–Stokes (LLNS) equations and related stochastic partial differential equations in fluid dynamics. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by the addition of white noise fluxes whose magnitudes are set by a fluctuation-dissipation relation. Originally derived for equilibrium fluctuations, the LLNS equations have also been shown to be accurate for nonequilibrium systems. Previous studies of numerical methods for the LLNS equations focused primarily on measuring variances and correlations computed at equilibrium and for selected nonequilibrium flows. In this paper, we introduce a more systematic approach …