Holistic Solution Methods for Complex Multi-particle Systems Holistic Solution Methods for Complex Multi-particle Systems

The emergence of self-organized behavior is characteristic of multi-particle systems in which individual motion is governed by the application of simple rules of interaction. The resulting dynamic order cannot be understood in terms of individual particles, but can be elucidated by formulating the system in terms of an abstract notion of dimensional coupling. We define this notion and consider two such systems in which the coupling rules are drawn from classical Newtonian mechanics. First we develop a deterministic flocking model based on the principles of consensus and frustration and demonstrate that both rules are required to elicit complex, flock-like behavior from the system. We then employ a quasi-stationary checkerboard lattice to develop a discretized damped Heisenberg model and demonstrate the spontaneous onset of magnetic domains. Finally, we discuss the importance of antagonistic interaction rules in the onset of complex, coherent dynamics away from equilibrium.