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On a variational model for the continuous mechanics exhibiting hexagonal to square Phase Transitions

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arxiv 2312.02497 v1 pith:6O2MYVQW submitted 2023-12-05 math.AP math.CAmath.NT

Senping Luo , Juncheng Wei This is my paper · ORCID
classification math.APmath.CAmath.NT
keywords phaseresultciteconti2004alatticesmechanicsmodeltheory
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Inspired by Conti and Zanzotto \cite{Conti2004A}, we reformulate a simple variational model for reconstructive phase transitions in crystals arising in continuum mechanics in the framework of Landau's theory of phase transition(with slight modification). We provide and prove that this class of modular invariant functions admit exactly hexagonal-square lattices minimizers without passing through rhombic lattices, being the first rigorous result in this regard. Our result gives an affirmative answer to an open problem by in \cite{Conti2004A}. In addition, our result has independent interest from number theory.

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  1. Signs of high order derivatives for the theta and Epstein zeta functions and application

    math.AP 2025-01 conditional novelty 6.0 of 10

    The authors show that ∂²/∂x∂y of the theta and Epstein zeta functions is strictly positive, and ∂³/∂x∂y² is strictly negative, in the relevant fundamental domain.

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