{"id":104074,"date":"2024-07-29T13:57:24","date_gmt":"2024-07-29T13:57:24","guid":{"rendered":"https:\/\/news.talkwithrattan.com\/index.php\/2024\/07\/29\/this-intricate-maze-connects-the-dots-on-quasicrystal-surfaces\/"},"modified":"2024-07-29T13:57:24","modified_gmt":"2024-07-29T13:57:24","slug":"this-intricate-maze-connects-the-dots-on-quasicrystal-surfaces","status":"publish","type":"post","link":"https:\/\/news.talkwithrattan.com\/index.php\/2024\/07\/29\/this-intricate-maze-connects-the-dots-on-quasicrystal-surfaces\/","title":{"rendered":"This intricate maze connects the dots on quasicrystal surfaces"},"content":{"rendered":"
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This maze of jagged curls looks like something out of the world\u2019s hardest puzzle book. How fast do you think you can solve it?<\/p>\n\n\n\n

Stuck? Don\u2019t worry. It\u2019s actually more of a connect the dots puzzle.<\/p>\n\n\n\n

The labyrinthine black path is the shortest nonintersecting route to connect every point on a kaleidoscopic, \u201cquasicrystalline\u201d surface<\/a>, researchers report July 10 in Physical Review X<\/em>.<\/p>\n\n\n\n

Shobhna Singh, a theoretical physicist at Cardiff University in Wales and her colleagues examined a type of pattern known as an Ammann-Beenker tiling, which fills a two-dimensional space using square- and rhombus-shaped tiles. Like some kaleidoscope images, Amman-Beenker tilings are organized but the pattern doesn\u2019t repeat itself regularly. The atoms in certain types of quasicrystals \u2014 ordered but nonrepeating chemical structures<\/a> \u2014 adopt a similar geometry (SN: 10\/5\/11<\/em>).<\/p>\n\n\n\n

In an Ammann-Beenker tiling (one shown), squares and rhombuses fill a 2-D space with an organized pattern that doesn\u2019t perfectly repeat itself.<\/span>Claudio Rocchini\/Wikimedia (CC BY 3.0<\/a>)<\/span><\/figcaption><\/figure>\n\n\n\n

The researchers found a path that touches on every vertex in an Amman-Beenker tiling, without crossing itself, before ending back where it started. Called Hamiltonian cycles, these pathways form a closed loop that you can trace without picking up your finger.<\/p>\n\n\n\n

Solving a Hamiltonian cycle for even one type of tiling is no small feat. But this particular cycle \u2014 and possibly others \u2014 could help address scientific challenges. For example, it could make certain quasicrystals more efficient catalysts, substances that reduce the energy required for a chemical reaction. In theory, if molecules involved in the reaction arranged themselves along the Hamiltonian path of such a quasicrystal, they could attach to the surface with maximum efficiency.<\/p>\n\n\n\n

Moving forward, the team will search for Hamiltonian cycles on other types of tilings, Singh says. They\u2019re also looking for new ways to apply their Hamiltonian cycle to existing challenges. \u201cThe most interesting application could be one which we have not thought about.\u201d<\/p>\n\n\n\n\t\t\t<\/div> \n\t\t\t\n