A string theory and graph Laplacian model recovers the Jiron-Castellon virtual volumes for nematic liquid crystals and predicts anisotropic thermal expansion and refractive indices to better than 0.06% accuracy with no fitted parameters.
A Proof of Delta Conjecture
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abstract
By finding orthogonal representation for a family of simple connected called $\delta$-graphs it is possible to show that $\delta$-graphs satisfy delta conjecture. An extension of the argument to graphs of the form $\overline{P_{\Delta(G)+2}\sqcup G}$ where $P_{\Delta(G)+2}$ is a path and $G$ is a simple connected graph it is possible to find an orthogonal representation of $\overline{P_{\Delta(G)+2}\sqcup G}$ in $\mathbb{R}^{\Delta(G)+1}$. As a consequence we prove delta conjecture.
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physics.gen-ph 1years
2025 1verdicts
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First-Principles Prediction of Material Properties from Topological Invariants
A string theory and graph Laplacian model recovers the Jiron-Castellon virtual volumes for nematic liquid crystals and predicts anisotropic thermal expansion and refractive indices to better than 0.06% accuracy with no fitted parameters.