Dynamical Scaling, Fractal Morphology and Small-angle Scattering

Abstract

When a system with continuous symmetry is quenched instantly to a broken symmetry state, new phases of topological defects appear in an otherwise homogeneous medium of continuous symmetry. The phenomenon of new phase formation is a representative example of first order transition. The phenomenon is of immense interest as an example of a highly nonlinear process far from equilibrium. The second phase grows with time and in late stages all domain sizes are much larger than all microscopic lengths. In the large time limit, the new phase forming systems exhibit self‐similar growth pattern with dilation symmetry, with time dependent scale, and scaling phenomenon. Extensive investigations on dynamical scaling phenomenon have been carried out so far for Euclidean systems. The question arises about the validity of the scaling laws for dynamical systems in non‐Euclidean fractal geometry. Some of the questions, arising purely because of the geometrical constraints in the physical systems and others on experimental ...