Application of the theory of algebraic systems for creating a hierarchy ofsolid structures formed under equilibrium and nonequilibrium conditions

A unified hierarchy is proposed for molecular and solid structures formed u nder equilibrium (ideal crystals) or nonequilibrium conditions (real crysta ls, fractally ordered crystalline, quasicrystalline, and amorphous solids, as well as composite solid materials that are aperiodic on an atomic-molecu lar level but are periodic on a macroscopic level). The construction of thi s hierarchy is based on applying the theory of algebraic systems (groups, r ings, and fields) to the multiplication of an initial structure in space de pending on an inflation coefficient (numbers) expressed in the general form Q = (n + m root l)/k. Examples are presented of molecular and polymer stru ctures described by groups or rings, fractally ordered solids whose structu res are described by fields, and solids with damped or self oscillations in their composition, whose structures are described by fields or periodic ri ngs of fields with complex spatial multiplication factors. (C) 1999 America n Institute of Physics. [S1063-7834(99)01105-3].