明治大学MIMS 第51回現象数理学コロキアム開催

応用数理学会会員の皆様へ.
明治大学先端数理科学インスティテュート（ＭＩＭＳ）では、現象数理学の最先端で活躍されている方々によるコロキアムを開催しています。多くの皆様のご参加をお待ちしております。

[講演者] Dwaipayan Chakrabarti 氏　(バーミンガム大学，英国 / WPI-SKCM2，広島大学 客員准教授)
[題目] Tetrahedral Liquids: From a Tale of Two Liquids to a Tale of Topology
[講演概要] Water is a classic example of tetrahedral liquids, where the nature of the molecular interactions favour local, short-ranged tetrahedral order [1]. Water
exhibits a host of anomalous thermodynamic properties, many of which are also displayed by tetrahedral liquids [1]. The existence of a phase transition between
a low-density liquid (LDL) and a high-density liquid (HDL) for water was originally hypothesised more than three decades ago to account for its thermodynamically
anomalies [2] and has now been well-established more generally for tetrahedral liquids by a significant body of computational studies [3-6]. However, the
experimental verification of this liquid-liquid phase transition (LLPT) has proved elusive, in particular, for water [7]. An enduring puzzle is how a pure substance
can have two distinct liquid phases. In this presentation, I will describe how we developed a colloidal model of water, exploiting hierarchical self-assembly [8,9],
to throw light on this puzzle. Our work reveals a topological distinction between the two liquids for water [10], and more generally for tetrahedral liquids [11],
showing that the LDL is unentangled and the HDL – containing an ensemble of topologically complex motifs, including links and knots – is entangled. I will also
illustrate how entanglement can emerge as a general mechanism for densification, with a hierarchy of topological transitions in a model tetrahedral liquid [11], which is
known to densify via two successive LLPTs [12]. Our results thus unravel a topological perspective of the tale of two liquids, which should have far-reaching implications
for understanding LLPTs in tetrahedra

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