Self-organization in nonlinear dynamical systems and its relation to the materials science

Abstract

This review paper presents briefly the main concepts of nonlinear dynamics and their exemplary manifestations in selected systems, including those important from the point of view of materials science. It is an extended version of the conference presentation. The conditions of instabilities leading to spontaneous formation of dissipative structures are given. Principles of nonlinear dynamics are illustrated with several examples from the homogeneous and heterogeneous and physical and chemical systems: pattern formation in the convective motion of fluids subject to various kinds of driving forces, periodic precipitation phenomena, oscillations, and pattern formation in the Belousov–Zhabotinski (BZ) reaction and the catalytic oxidation of thiocyanate ions with hydrogen peroxide, as well as bistability and tristability in the electrochemical reduction of azide complexes of nickel(II). The application of nonlinear dynamics in materials science is first exemplified by its role in polymerization reactions. Such processes can either exhibit internal couplings leading to oscillations or can be coupled with the chemical oscillatory process through, e.g., the covalent bonding of its catalyst to the polymer network. Other selected examples of the application of nonlinear dynamics in materials science, referring to electrochemical processes, were briefly reviewed. Nonlinear dynamics appears to be useful for designing new materials, including those at the nanoscale.