15,109 research outputs found
A vicinal surface model for epitaxial growth with logarithmic free energy
We study a continuum model for solid films that arises from the modeling of
one-dimensional step flows on a vicinal surface in the
attachment-detachment-limited regime. The resulting nonlinear partial
differential equation, , gives the evolution
for the surface slope as a function of the local height in a monotone
step train. Subject to periodic boundary conditions and positive initial
conditions, we prove the existence, uniqueness and positivity of global strong
solutions to this PDE using two Lyapunov energy functions. The long time
behavior of converging to a constant that only depends on the initial data
is also investigated both analytically and numerically.Comment: 18 pages, 7 figure
Optimal control-based inverse determination of electrode distribution for electroosmotic micromixer
This paper presents an optimal control-based inverse method used to determine
the distribution of the electrodes for the electroosmotic micromixers with
external driven flow from the inlet. Based on the optimal control method, one
Dirichlet boundary control problem is constructed to inversely find the optimal
distribution of the electrodes on the sidewalls of electroosmotic micromixers
and achieve the acceptable mixing performance. After solving the boundary
control problem, the step-shaped distribution of the external electric
potential imposed on the sidewalls can be obtained and the distribution of
electrodes can be inversely determined according to the obtained external
electric potential. Numerical results are also provided to demonstrate the
effectivity of the proposed method
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