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Droplet phase in a nonlocal isoperimetric problem under confinement Alama, Stanley
Description
We address small volume fraction asymptotic properties of a nonlocal isoperimetric functional with a confinement term, derived as the sharp interface limit of a variational model for self-assembly of diblock copolymers under confinement by nanoparticle inclusion. We introduce a small parameter $\eta$ to represent the size of the domains of the minority phase, and study the resulting droplet regime as $\eta\to 0$. A key role is played by a parameter $M$ which gives the total volume of the droplets at order $\eta^3$ and its relation to existence and non-existence of minimizers to a nonlocal isoperimetric functional on $\mathbb{R}^3$. For large values of $M$, the minority phase splits into several droplets at an intermediate scale $\eta^{1/3}$, while for small $M$ minimizers form a single droplet converging to the maximum of the confinement density.
Item Metadata
Title |
Droplet phase in a nonlocal isoperimetric problem under confinement
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-05-02T13:30
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Description |
We address small volume fraction asymptotic properties of a nonlocal isoperimetric functional with a confinement term, derived as the sharp interface limit of a variational model for self-assembly of diblock copolymers under confinement by nanoparticle inclusion. We introduce a small parameter $\eta$ to represent the size of the domains of the minority phase, and study the resulting droplet regime as $\eta\to 0$. A key role is played by a parameter $M$ which gives the total volume of the droplets at order $\eta^3$ and its relation to existence and non-existence of minimizers to a nonlocal isoperimetric functional on $\mathbb{R}^3$. For large values of $M$, the minority phase splits into several droplets at an intermediate scale $\eta^{1/3}$, while for small $M$ minimizers form a single droplet converging to the maximum of the confinement density.
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Extent |
46 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: McMaster University
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Series | |
Date Available |
2017-10-30
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0357390
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International