Time-distance mapping is a method to obtain a spatial configuration of points, so that the Euclidean distances between points consist with the given time distances. The approaches are divided broadly into two categories. One deals with the time-distances between all pairs of points. Multidimensional scaling (MDS) is generally applied to the solution. Another deals with the limited number of tim...

In a famous calculation of the “large-distance and longtime properties of a randomly stirred fluid,” Forster, Nelson, and Stephen (FNS) analyzed the consequences of various forcing scenarios for the Navier–Stokes equation and, to some extent, Burgers equation. They considered both a conservative forcing (Model A) and a nonconservative one (Model B), and predicted nontrivial properties for the l...

In this paper, we study a phenomenological model for pattern formation in electroconvection, and the effect of noise on pattern. As such consider an anistropic Swift–Hohenberg equation adding additive noise. We prove existence global solution that two dimensional torus. addition, inserting scaling parameter, large domain near its change stability. observe numerically that, under appropriate sca...

In this paper, we analyze a tamed 3D Navier-Stokes equation in uniform C-domains (not necessarily bounded), which obeys the scaling invariance principle, and prove the existence and uniqueness of strong solutions to this tamed equation. In particular, if there exists a bounded solution to the classical 3D Navier-Stokes equation, then this solution satisfies our tamed equation. Moreover, the exi...