Emergence of Maximal Symmetry

Emergence, Singularities, and Symmetry Breaking

Maximal symmetry groups of hyperbolic 3-manifolds

Every finite group acts as the full isometry group of some compact hyperbolic 3-manifold. In this paper we study those finite groups which act maximally, that is when the ratio |Isom(M)|/vol(M) is maximal among all such manifolds. In two dimensions maximal symmetry groups are called Hurwitz groups, and arise as quotients of the (2,3,7)–triangle group. Here we study quotients of the minimal co-v...

Emergence of symmetry in homooligomeric biological assemblies.

Naturally occurring homooligomeric protein complexes exhibit striking internal symmetry. The evolutionary origins of this symmetry have been the subject of considerable speculation; proposals for the advantages associated with symmetry include greater folding efficiency, reduced aggregation, amenability to allosteric regulation, and greater adaptability. An alternative possibility stems from th...

Symmetry of Fullerene C_60

Dynamics of Symmetry Breaking in Frw Cosmologies: Emergence of Scaling

The dynamics of a symmetry breaking phase transition is studied in a radiation and matter dominated spatially flat FRW cosmology in the large N limit of a scalar field theory. The quantum density matrix is evolved from an initial state of quasiparticles in thermal equilibrium at a temperature higher than the critical. The cosmological expansion decreases the temperature and triggers the phase t...