In mathematics, a lattice is an abstract structure that can be visualized as a set equipped with two binary operations, often called meet and join, that satisfy certain axioms of associativity, commutativity, absorption, and idempotency. Lattices are used to study order theory and have applications in various fields such as algebra, geometry, and computer science, particularly in data organization and cryptography.
Clathrate hydrates are crystalline water-based solids physically resembling ice, in which small non-polar molecules or polar molecules with large hydrophobic moieties are trapped inside 'cages' of hydrogen-bonded water molecules. These structures are significant in natural gas storage, carbon dioxide sequestration, and as a potential energy resource, but also pose challenges in pipeline blockages and climate change implications due to methane release.