We study the propagation of a "pulled" front with multiplicative noise that is created by a local perturbation of an unstable state. Unlike a front propagating into a metastable state, where a... Show moreWe study the propagation of a "pulled" front with multiplicative noise that is created by a local perturbation of an unstable state. Unlike a front propagating into a metastable state, where a separation of time scales for sufficiently large t creates a diffusive wandering of the front position about its mean, we predict that for so-called pulled fronts, the fluctuations are subdiffusive with root mean square wandering Delta(t) approximately t(1/4), not t(1/2). The subdiffusive behavior is confirmed by numerical simulations: For t600, these yield an effective exponent slightly larger than 1/4. Show less
Storm, C.; Spruijt, W.; Ebert, U.; Saarloos, W. van 2000
We investigate the asymptotic relaxation of so-called pulled fronts propagating into an unstable state, and generalize the universal algebraic velocity relaxation of uniformly translating fronts to... Show moreWe investigate the asymptotic relaxation of so-called pulled fronts propagating into an unstable state, and generalize the universal algebraic velocity relaxation of uniformly translating fronts to fronts that generate periodic or even chaotic states. A surprising feature is that such fronts also exhibit a universal algebraic phase relaxation. For fronts that generate a periodic state, like those in the Swift-Hohenberg equation or in a Rayleigh-Benard experiment, this implies an algebraically slow relaxation of the pattern wavelength just behind the front, which should be experimentally testable. Show less
