Stochastic self-assembly of incommensurate clusters.

Nucleation and molecular aggregation are important processes in numerous physical and biological systems. In many applications, these processes often take place in confined spaces, involving a finite number of particles. Analogous to treatments of stochastic chemical reactions, we examine the classic problem of homogeneous nucleation and self-assembly by deriving and analyzing a fully discrete stochastic master equation. We enumerate the highest probability steady states, and derive exact analytical formulae for quenched and equilibrium mean cluster size distributions. Upon comparison with results obtained from the associated mass-action Becker-Döring equations, we find striking differences between the two corresponding equilibrium mean cluster concentrations. These differences depend primarily on the divisibility of the total available mass by the maximum allowed cluster size, and the remainder. When such mass "incommensurability" arises, a single remainder particle can "emulsify" the system by significantly broadening the equilibrium mean cluster size distribution. This discreteness-induced broadening effect is periodic in the total mass of the system but arises even when the system size is asymptotically large, provided the ratio of the total mass to the maximum cluster size is finite. Ironically, classic mass-action equations are fairly accurate in the coarsening regime, before equilibrium is reached, despite the presence of large stochastic fluctuations found via kinetic Monte-Carlo simulations. Our findings define a new scaling regime in which results from classic mass-action theories are qualitatively inaccurate, even in the limit of large total system size.

Cooperation and punishment in an adversarial game: how defectors pave the way to a peaceful society.

The evolution of human cooperation has been the subject of much research, especially within the framework of evolutionary public goods games, where several mechanisms have been proposed to account for persistent cooperation. Yet, in addressing this issue, little attention has been given to games of a more adversarial nature, in which defecting players, rather than simply free riding, actively seek to harm others. Here, we develop an adversarial evolutionary game using the specific example of criminal activity, recasting the familiar public goods strategies of punishers, cooperators, and defectors in this light. We then introduce a strategy-the informant-with no clear analog in public goods games and show that individuals employing this strategy are a key to the emergence of systems where cooperation dominates. We also find that a defection-dominated regime may be transitioned to one that is cooperation-dominated by converting an optimal number of players into informants. We discuss these findings, the role of informants, and possible intervention strategies in extreme adversarial societies, such as those marred by wars and insurgencies.

Self-propelled particles with soft-core interactions: patterns, stability, and collapse.

Understanding collective properties of driven particle systems is significant for naturally occurring aggregates and because the knowledge gained can be used as building blocks for the design of artificial ones. We model self-propelling biological or artificial individuals interacting through pairwise attractive and repulsive forces. For the first time, we are able to predict stability and morphology of organization starting from the shape of the two-body interaction. We present a coherent theory, based on fundamental statistical mechanics, for all possible phases of collective motion.

Fluctuation-facilitated charge migration along DNA.

We propose a model Hamiltonian for charge transfer along the DNA double helix with temperature-driven fluctuations in the base pair positions acting as the rate limiting factor for charge transfer between neighboring base pairs. We compare the predictions of the model with the recent work of Barton and Zewail on the unusual two-stage charge transfer of DNA.