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3-dimensional topology and polycontinuous pattern Shimokawa, Koya
Description
Block copolymers produce spherical, cylindrical, lamellar and bicontinuous patterns as microphase-separated structures. Typical examples of bicontinuous patterns are Gyroid, D-surface and P-surface. A mathematical model of such a structure is a triply periodic non-compact surface embedded in the 3-dimensional space which divides it into two possibly disconnected submanifolds. We will consider the case where submanifolds are open neighborhood of networks. Here a network means an infinite graph embedded in the 3-dimensional space. In this case the bicontinuous pattern is uniquely determined by networks up to isotopy. We say such a bicontinuous pattern is associated to a network. On the other hand, for example triblock-arm star-shaped molecules yields a tricontinuous pattern. One mathematical model of such a tricontinuous (resp. poly-continuous) pattern is a triply periodic non-compact multibranched surface (or more generally polyhedron) dividing it into 3 (resp. several) possibly disconnected non-compact submanifolds. We assume that each submanifold is the open neighborhood of three (resp. several) networks. We call such a multibranched surface a tricontinuous pattern(resp. poly-continuous pattern). The relation between poly-continuous patterns and networks is not obvious in this case. Two different poly-continuous patterns are associated to one network and vice versa. In this talk we will give a condition for poly-continuous patterns to give the same network. We will also show that two poly-continuous patterns can be related by a finite sequence of moves and discuss further applications.
Item Metadata
| Title |
3-dimensional topology and polycontinuous pattern
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2019-03-26T20:08
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| Description |
Block copolymers produce spherical, cylindrical, lamellar and bicontinuous patterns as microphase-separated structures. Typical examples of bicontinuous patterns are Gyroid, D-surface and P-surface. A mathematical model of such a structure is a triply periodic non-compact surface embedded in the 3-dimensional space which divides it into two possibly disconnected submanifolds. We will consider the case where submanifolds are open neighborhood of networks. Here a network means an infinite graph embedded in the 3-dimensional space. In this case the bicontinuous pattern is uniquely determined by networks up to isotopy. We say such a bicontinuous pattern is associated to a network. On the other hand, for example triblock-arm star-shaped molecules yields a tricontinuous pattern. One mathematical model of such a tricontinuous (resp. poly-continuous) pattern is a triply periodic non-compact multibranched surface (or more generally polyhedron)
dividing it into 3 (resp. several) possibly disconnected non-compact submanifolds. We assume that each submanifold is the open neighborhood of three (resp. several) networks. We call such a multibranched
surface a tricontinuous pattern(resp. poly-continuous pattern). The relation between poly-continuous patterns and networks is not obvious in this case. Two different poly-continuous patterns are associated to
one network and vice versa. In this talk we will give a condition for poly-continuous patterns to give the same network. We will also show that two poly-continuous patterns can be related by a finite sequence
of moves and discuss further applications.
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| Extent |
23.0 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: Saitama University
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| Series | |
| Date Available |
2019-09-23
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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 |
10.14288/1.0380943
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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 Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International