In this paper, on 4-spheres equipped with Riemannian metrics we study some integral conformal invariants, the sign and size of which under Ricci flow characterize standard 4-sphere. We obtain a gap theorem, for Yamabe positive scalar curvature $L^2$ norm Weyl tensor metric suitably small, establish monotonic decay $L^p$ certain $p>2$ reduced along normalized flow, converging exponentially to

Numerical investigation of laminar, transitional and chaotic flows in convergingdiverging channels are performed by direct numerical simulations in the Reynolds number range 10 < Re < 850. The temporal flow evolution and the onset of turbulence are investigated by combining classical fluid dynamics representations with dynamical system flow characterizations. Modern dynamical system techniques ...

Convergence of multigrid and defect-correction iterations is comprehensively studied within different incompressible and compressible inviscid regimes on high-density grids. Good smoothing properties of the defectcorrection relaxation have been shown using both a modified Fourier analysis and a more general idealizedcoarse-grid analysis. Single-grid defect correction alone has some slowly conve...