We show that in an arbitrary o-minimal structure the following are equivalent: (i) conjugates of a definable subgroup of a definably connected, definably compact definable group cover the group if the o-minimal Euler characteristic of the quotient is non zero; (ii) every infinite, definably connecte
The Euler Characteristic of Phantom Elastomeric Polymer Networks
โ Scribed by Vassilios Galiatsatos; Gert Heinrich
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 401 KB
- Volume
- 20
- Category
- Article
- ISSN
- 1022-1344
No coin nor oath required. For personal study only.
โฆ Synopsis
Abstract
It is shown that through a relationship between the Euler characteristic and the cycle rank of polymer networks one has access to a quantitative description of functionality heterogeneity in these fascinating structures. This relationship is applied and extended to study heterogeneous network structures resulting from the random removal of chains from a perfect 2D tetrafunctional network. It is shown that the distribution of crosslink functionality is correlated strongly with the mechanical properties of the networks as those are manifested in the cycle rank. magnified image
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