Graph Ginzburg–Landau: discrete dynamics, continuum limits, and applications. An overview

Yves van Gennip

Graph Ginzburg–Landau: discrete dynamics, continuum limits, and applications. An overview

Mathematical Physics

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Abstract

In [BF12, BF16] the graph Ginzburg–Landau functional was introduced. Here u is a real-valued function on the node set V of a simple1, undirected graph (with ui its value at node i), ωij ≥ 0 are edge weights which are assumed to be positive on all edges in the graph and zero between non-neighbouring nodes i and j, ε is a positive parameter, and W is a double well potential with wells of equal depth. A typical choice is the quartic polynomial W(x) = x2(x − 1)2 which has wells of depth 0 at x = 0 and x = 1, but we will encounter some situations where other choices are useful or even necessary.

Original language	English
Title of host publication	Proceedings of 44th Sapporo Symposium on Partial Differential Equations
Editors	S.I. Ei, Y. Giga, N. Hamamuki, S. Jimbo, H. Kubo, H. Kuroda, T. Ozawa, T. Sakajo, K. Tsutaya
Pages	89-102
Publication status	Published - 2019

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title = "Graph Ginzburg–Landau: discrete dynamics, continuum limits, and applications. An overview",

abstract = "In [BF12, BF16] the graph Ginzburg–Landau functional was introduced. Here u is a real-valued function on the node set V of a simple1, undirected graph (with ui its value at node i), ωij ≥ 0 are edge weights which are assumed to be positive on all edges in the graph and zero between non-neighbouring nodes i and j, ε is a positive parameter, and W is a double well potential with wells of equal depth. A typical choice is the quartic polynomial W(x) = x2(x − 1)2 which has wells of depth 0 at x = 0 and x = 1, but we will encounter some situations where other choices are useful or even necessary. ",

author = "{van Gennip}, Yves",

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booktitle = "Proceedings of 44th Sapporo Symposium on Partial Differential Equations",

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Graph Ginzburg–Landau: discrete dynamics, continuum limits, and applications. An overview. / van Gennip, Yves.
Proceedings of 44th Sapporo Symposium on Partial Differential Equations. ed. / S.I. Ei; Y. Giga; N. Hamamuki; S. Jimbo; H. Kubo; H. Kuroda; T. Ozawa; T. Sakajo; K. Tsutaya. 2019. p. 89-102.

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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BT - Proceedings of 44th Sapporo Symposium on Partial Differential Equations

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A2 - Giga, Y.

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Graph Ginzburg–Landau: discrete dynamics, continuum limits, and applications. An overview

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