Optimal Self-Organization

We present computational and analytical results indicating that systems of driven entities with repulsive interactions tend to reach an optimal state associated with minimal interaction and minimal dissipation. Using concepts from non-equilibrium thermodynamics and game theoretical ideas, we generalize this finding to an even wider class of self-organizing systems which have the ability to reach a state of maximal overall ``success''. This principle is expected to be relevant for driven systems in physics like sheared granular media, but it is also applicable to biological, social, and economic systems, for which only a limited number of quantitative principles are available yet.Comment: This is the detailled revised version of a preprint on ``Self-Organised Optimality'' (cond-mat/9903319). For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.html and http://angel.elte.hu/~vicsek

Mechanosensitive Self-Replication Driven by Self-Organization

Self-replicating molecules are likely to have played an important role in the origin of life, and a small number of fully synthetic self-replicators have already been described. Yet it remains an open question which factors most effectively bias the replication toward the far-from-equilibrium distributions characterizing even simple organisms. We report here two self-replicating peptide-derived macrocycles that emerge from a small dynamic combinatorial library and compete for a common feedstock. Replication is driven by nanostructure formation, resulting from the assembly of the peptides into fibers held together by β sheets. Which of the two replicators becomes dominant is influenced by whether the sample is shaken or stirred. These results establish that mechanical forces can act as a selection pressure in the competition between replicators and can determine the outcome of a covalent synthesis.

Self Organization and Self Avoiding Limit Cycles

A simple periodically driven system displaying rich behavior is introduced and studied. The system self-organizes into a mosaic of static ordered regions with three possible patterns, which are threaded by one-dimensional paths on which a small number of mobile particles travel. These trajectories are self-avoiding and non-intersecting, and their relationship to self-avoiding random walks is explored. Near $\rho=0.5$ the distribution of path lengths becomes power-law like up to some cutoff length, suggesting a possible critical state

Self-organization of collaboration networks

We study collaboration networks in terms of evolving, self-organizing bipartite graph models. We propose a model of a growing network, which combines preferential edge attachment with the bipartite structure, generic for collaboration networks. The model depends exclusively on basic properties of the network, such as the total number of collaborators and acts of collaboration, the mean size of collaborations, etc. The simplest model defined within this framework already allows us to describe many of the main topological characteristics (degree distribution, clustering coefficient, etc.) of one-mode projections of several real collaboration networks, without parameter fitting. We explain the observed dependence of the local clustering on degree and the degree--degree correlations in terms of the ``aging'' of collaborators and their physical impossibility to participate in an unlimited number of collaborations.Comment: 10 pages, 8 figure

Self-organization in systems of self-propelled particles

We investigate a discrete model consisting of self-propelled particles that obey simple interaction rules. We show that this model can self-organize and exhibit coherent localized solutions in one- and in two-dimensions.In one-dimension, the self-organized solution is a localized flock of finite extent in which the density abruptly drops to zero at the edges.In two-dimensions, we focus on the vortex solution in which the particles rotate around a common center and show that this solution can be obtained from random initial conditions, even in the absence of a confining boundary. Furthermore, we develop a continuum version of our discrete model and demonstrate that the agreement between the discrete and the continuum model is excellent.Comment: 4 pages, 5 figure