11 research outputs found
Renormalization Group Theory And Variational Calculations For Propagating Fronts
We study the propagation of uniformly translating fronts into a linearly
unstable state, both analytically and numerically. We introduce a perturbative
renormalization group (RG) approach to compute the change in the propagation
speed when the fronts are perturbed by structural modification of their
governing equations. This approach is successful when the fronts are
structurally stable, and allows us to select uniquely the (numerical)
experimentally observable propagation speed. For convenience and completeness,
the structural stability argument is also briefly described. We point out that
the solvability condition widely used in studying dynamics of nonequilibrium
systems is equivalent to the assumption of physical renormalizability. We also
implement a variational principle, due to Hadeler and Rothe, which provides a
very good upper bound and, in some cases, even exact results on the propagation
speeds, and which identifies the transition from ` linear'- to `
nonlinear-marginal-stability' as parameters in the governing equation are
varied.Comment: 34 pages, plain tex with uiucmac.tex. Also available by anonymous ftp
to gijoe.mrl.uiuc.edu (128.174.119.153), file /pub/front_RG.tex (or .ps.Z