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arXiv · 2609.29030

Frustrated junctions in interfacial networks

Håkan Hallberg·Vasily V. Bulatov·Bryan W. Reed·Mukul Kumar
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Abstract

Networks of interfaces in materials and living systems evolve through motion and rearrangement of interfaces and junctions. Local equilibrium at a junction requires interfacial force balance. We show that in three dimensions the classical Herring condition for triple lines is necessary but insufficient: four triple lines meeting at a quadruple node may each satisfy Herring equilibrium, while the four conditions remain mutually incompatible. Such a frustrated node has no admissible local equilibrium geometry. In the semi-isotropic limit, the six interfacial energies must form the edge lengths of a non-degenerate tetrahedron, with constructibility determined by the Cayley-Menger determinant. This hidden compatibility constraint arises from three-dimensional geometry and applies broadly to foams, polycrystals, tissues and other interfacial networks.

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Håkan Hallberg, Vasily V. Bulatov, Bryan W. Reed, Mukul Kumar. 2026-09-24. Frustrated junctions in interfacial networks. https://arxiv.org/abs/2609.29030

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