3 research outputs found
Transient convective instabilities in directional solidification
We study the convective instability of the melt during the initial transient
in a directional solidification experiment in a vertical configuration. We
obtain analytically the dispersion relation, and perform an additional
asymptotic expansion for large Rayleigh number that permits a simpler
analytical analysis and a better numerical behavior. We find a transient
instability, i.e. a regime in which the system destabilizes during the
transient whereas the final unperturbed steady state is stable. This could be
relevant to growth mode predictions in solidification.Comment: 28 pages, 5 figures. The following article has been accepted for
publication in Physics of Fluids. After it is published, it will be found at
http://pof.aip.or
Insight toward the first-passage time in a bistable potential with highly colored noise
The exponential coefficient in the first-passage-time problem for a bistable potential with highly colored noise is predicted to be (8/27 by all existing theories. On the other hand, we show herein that all existing numerical evidence seems to indicate that the coefficient is actually larger by about (4/3, i.e., that the numerical factor in the exponent is approximately (32/81. Existing data cover values of ¿V0/D up to ~20, where V0 is the barrier height, ¿ the correlation time of the noise, and D the noise intensity. We provide an explanation for the modified coefficinet, the explanation also being based on existing numerical simulations. Whether the value (8/27 predicted by all large-¿ theories is achieved for even larger values of ¿V0/D is unknown but appears questionable (except perhaps for enormously large, experimentally inaccessible values of this factor) in view of currently available results
Escape over a potential barrier driven by colored noise: Large but finite correlation times
The recent theory of Tsironis and Grigolini for the mean first-passage time from one metastable state to another of a bistable potential for long correlation times of the noise is extended to large but finite correlation times