A. Szprynger | Searcharxiv

arXiv2003

Noise sensitivity of sub- and supercritically bifurcating patterns with group velocities close to the convective-absolute instability

The influence of small additive noise on structure formation near a forwards and near an inverted bifurcation as described by a cubic and quintic Ginzburg Landau amplitude equation, respectively, is studied numerically for group velocities in the vicinity of the convective-absolute instability where the deterministic front dynamics would empty the system.

physics.flu-dyn↗

arXiv1997

Noise sustained pattern growth: Bulk versus boundary effects

The effect of thermally generated bulk stochastic forces on the statistical growth dynamics of forwards bifurcating propagating macroscopic patterns is compared with the influence of fluctuations at the boundary of a semiinfinite system, $0<x$. To that end the linear complex Ginzburg-Landau amplitude equation with additive stochastic forcing is solved by a spatial Laplace transformation in the presence of arbitrary boundary conditions for the fluctuations of the pattern amplitude at $x=0$. A situation where the latter are advected with an imposed through-flow from an outside upstream part towards the inlet boundary at $x=0$ is investigated in more detail. The spatiotemporal growth behavior in the convectively unstable regime is compared with recent work by Swift, Babcock, and Hohenberg [Physica A 204, 625 (1994)] where a special boundary condition is imposed.

patt-sol↗