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 where a special boundary condition is imposed.
Spatiotemporal properties of convective fluctuations and of their correlations are investigated theoretically in the vicinity of the threshold for onset of convection in the presence of a lateral through-flow using the full linearized equations of fluctuating hydrodynamics. The effect of external forcing by inlet boundary conditions on the downstream evolution of convective fields is separated from the effect of internal bulk thermal forcing with the use of spatial Laplace transformations. They show how the spatial variation of fluctuations and of their correlations are governed by the six spatial characteristic exponents of the field equations.
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.
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