Opinion dynamics on an adaptive random network.

We revisit the classical model for voter dynamics in a two-party system with two basic modifications. In contrast to the original voter model studied in regular lattices, we implement the opinion formation process in a random network of agents in which interactions are no longer restricted by geographical distance. In addition, we incorporate the rapidly changing nature of the interpersonal relations in the model. At each time step, agents can update their relationships. This update is determined by their own opinion, and by their preference to make connections with individuals sharing the same opinion, or rather with opponents. In this way, the network is built in an adaptive manner, in the sense that its structure is correlated and evolves with the dynamics of the agents. The simplicity of the model allows us to examine several issues analytically. We establish criteria to determine whether consensus or polarization will be the outcome of the dynamics and on what time scales these states will be reached. In finite systems consensus is typical, while in infinite systems a disordered metastable state can emerge and persist for infinitely long time before consensus is reached.

Coexistence of inertial competitors in chaotic flows.

We investigate the dynamics of inertial particles immersed in open chaotic flows. We consider the generic problem of competition between different species, e.g., phytoplankton populations in oceans. The strong influence from inertial effects is shown to result in the persistence of different species even in cases when the passively advected species cannot coexist. Multispecies coexistence in the ocean can be explained by the fact that the unstable manifold is different for each advected competitor of different size.

Selective sensitivity of open chaotic flows on inertial tracer advection: catching particles with a stick.

We investigate the effects of finite size and inertia of a small spherical particle immersed in an open unsteady flow which, for ideal tracers, generates transiently chaotic trajectories. The inertia effects may strongly modify the chaotic motion to the point that attractors may appear in the configuration space. These studies are performed in a model of the two-dimensional flow past a cylindrical obstacle. The relevance to modeling efforts of biological pathogen transport in large-scale flows is discussed. Since the tracer dynamics is sensitive to the particle inertia and size, simple geometric setups in such flows could be used as a particle mixture segregator separating and trapping particles.