Construction of two dimensional convex shapes from their excluded volumes

Duration: 39 mins 28 secs

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Description:	Taylor, J Monday 14th January 2019 - 15:15 to 16:00


Created:	2019-01-15 13:51
Collection:	The mathematical design of new materials
Publisher:	Isaac Newton Institute
Copyright:	Taylor, J
Language:	eng (English)


Abstract:	In a dilute system of spatially homogeneous system of hard, non-spherical, particles, Onsager tells us that all phase behaviour can (in principle) be derived by explained by understanding how much volume is excluded to one particle by the presence of another, given their relative orientations. In this talk, we will consider the case of two dimensional convex bodies, and describe forward and inverse problems related to evaluating their so-called excluded volume function, which depends entirely on the particle shape. In particular, we propose and analyse an algorithm which can reconstruct a convex body from an excluded volume function, although such solutions can be shown generally to be non-unique. While only providing results in the simpler two-dimensional setting, these results pave the way for design of particle shape based on desired phase behaviour properties.

Abstract:

In a dilute system of spatially homogeneous system of hard, non-spherical, particles, Onsager tells us that all phase behaviour can (in principle) be derived by explained by understanding how much volume is excluded to one particle by the presence of another, given their relative orientations. In this talk, we will consider the case of two dimensional convex bodies, and describe forward and inverse problems related to evaluating their so-called excluded volume function, which depends entirely on the particle shape. In particular, we propose and analyse an algorithm which can reconstruct a convex body from an excluded volume function, although such solutions can be shown generally to be non-unique. While only providing results in the simpler two-dimensional setting, these results pave the way for design of particle shape based on desired phase behaviour properties.

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