Pattern formation and Instability Phenomena
Researcher: Prof. Nasr Ghoniem
In materials, critical phenomena such as phase transitions, plastic deformation and fracture are intimately related to self-organization. Understanding the origin of spatio-temporal order in systems far from thermal equilibrium and the selection mechanisms of spatial structures and their symmetries is a major theme of present day research on the structure of continuous matter. Furthermore, the development of methods for producing spatially-ordered and self-assembled microstructure in solids by nonequilibrium methods opens the door to many technological applications. Future development of new technologies is expected to benefit from several aspects of modern materials science: experimental, empirical and fundamental. One of the most natural aspects of nonlinearity is the occurrence of instabilities and the development of spatio-temporal patterns. Their description and understanding still raises important and basic questions. Universal behaviors of complex systems close to instabilities have been determined, leading to a wide interdisciplinary field, which is now referred to as nonlinear science, or the science of complexity. Here, the initial concepts of dissipative structures or synergetics are deeply rooted. Some of the patterns studied in Professor Ghoniem’s Lab are shown below.