Difference between revisions of "SIAM Student Chapter Seminar"

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(Fall 2020)
(Fall 2020)
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|Jan 31
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|TBA
 
|Yu Feng (Math)
 
|Yu Feng (Math)
 
|''[[#TBA, Yu Feng (Math)|Phase separation in the advective Cahn--Hilliard equation]]''
 
|''[[#TBA, Yu Feng (Math)|Phase separation in the advective Cahn--Hilliard equation]]''

Revision as of 23:18, 17 September 2020



Fall 2020

date speaker title
TBA Yu Feng (Math) Phase separation in the advective Cahn--Hilliard equation

Abstracts

TBA, Yu Feng (Math)

Phase separation in the advective Cahn--Hilliard equation

The Cahn--Hilliard equation is a classic model of phase separation in binary mixtures that exhibits spontaneous coarsening of the phases. We study the Cahn--Hilliard equation with an imposed advection term in order to model the stirring and eventual mixing of the phases. The main result is that if the imposed advection is sufficiently mixing then no phase separation occurs, and the solution instead converges exponentially to a homogeneous mixed state. The mixing effectiveness of the imposed drift is quantified in terms of the dissipation time of the associated advection-hyperdiffusion equation, and we produce examples of velocity fields with a small dissipation time. We also study the relationship between this quantity and the dissipation time of the standard advection-diffusion equation.



Past Semesters