Competing Interactions and Pattern Formation in Nanoworld

1. Introduction
1.1 How the story begun
1.2 First theoretical approaches for competing interactions
1.3 Beautiful patterns govern the world
2. Self-competition or how to choose the best from the worse
2.1 Frustration: the world is not perfect
2.2 Self-competition of the short-range interactions
2.3 Self-competition of the long-range interactions
2.4 Ordering entropy
2.5 Problems/Solutions
3. Famous competition between a short- and a long-range interaction
3.1 Localized particles
3.2 Delocalized particles
3.3 Problems/Solutions
4. Competition between a long-range dipolar interaction and an anisotropy
4.1 Ultrathin magnetic films
4.2 Ultrthin magnetic particles
5. Competition between two interactions of the same range
5.1 Two short-range interactions
5.2 Two long-range interactions
5.3 Problems/Solutions
6. Dynamics of self-organized systems close to equilibrium
6.1 Polarization reversal
6.2 Wave phenomena
6.3 Diffusion-limited aggregation
6.4 Dynamics of nanoparticles
References