2 publications
-
Published Subscription Review Article
Symmetry Breaking in Mathematical Models: Bifurcation, Chaos, and Pattern FormationBy Ben Okri
Abstract: Symmetry breaking serves as a central organizing principle in the understanding of nonlinear systems across physics, biology, chemistry, and engineering. When a system transitions from a symmetric state to an asymmetric configuration, it often signals the onset of new structures, dynamic behaviors, or even chaotic regimes. This review explores symmetry breaking from the theoretical and mathematical perspectives of bifurcation theory, chaos theory, and pattern formation. We discuss how small parameter …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 2, 2025 · pp. 25–30 Read article →
-
Published Subscription Review Article
Mechanisms of Crystal Growth: From Spiral Steps to Surface AdhesionBy Ben Okri
Abstract: Crystal growth is a complex interplay between thermodynamic stability and kinetic processes, influenced heavily by the conditions under which crystallization occurs—particularly the degree of supersaturation. This abstract outline three principal regimes of solution-grown crystal growth: defect-driven, two-dimensional, and adhesive growth. At low supersaturation, growth is facilitated at surface defects, such as screw dislocations, where energy barriers to attachment are minimized. This results in the formation of spiraling steps that propagate …
Published in International Journal of Crystalline Materials · Vol. 2, Issue 1, 2025 · pp. 46–31 Read article →