Invariant barriers to reactive front propagation in fluid flows

We present theory and experiments on the dynamics of reaction fronts in two-dimensional, vortex-dominated flows, for both time-independent and periodically driven cases. We find that the front propagation process is controlled by one-sided barriers that are either fixed in the laboratory frame (time-independent flows) or oscillate periodically (periodically driven flows). We call these barriers burning invariant manifolds (BIMs), since their role in front propagation is analogous to that of invariant manifolds in the transport and mixing of passive impurities under advection. Theoretically, the BIMs emerge from a dynamical systems approach when the advection-reaction-diffusion dynamics is recast as an ODE for front element dynamics. Experimentally, we measure the location of BIMs for several laboratory flows and confirm their role as barriers to front propagation.

Barriers to front propagation in ordered and disordered vortex flows

We present experiments on reactive front propagation in a two-dimensional (2D) vortex chain flow (both time-independent and time-periodic) and a 2D spatially disordered (time-independent) vortex-dominated flow. The flows are generated using magnetohydrodynamic forcing techniques, and the fronts are produced using the excitable, ferroin-catalyzed Belousov-Zhabotinsky chemical reaction. In both of these flows, front propagation is dominated by the presence of burning invariant manifolds (BIMs) that act as barriers, similar to invariant manifolds that dominate the transport of passive impurities. Convergence of the fronts onto these BIMs is shown experimentally for all of the flows studied. The BIMs are also shown to collapse onto the invariant manifolds for passive transport in the limit of large flow velocities. For the disordered flow, the measured BIMs are compared to those predicted using a measured velocity field and a three-dimensional set of ordinary differential equations that describe the dynamics of front propagation in advection-reaction-diffusion systems.

Nation building in Bosnia and Herzegovina: Cooperation, coordination and collaboration

Cross-sectoral interorganizational relationships in post-conflict situations occur regularly. Whether formal task forces, advisory groups or other ad hoc arrangements, these relations take place in chaotic and dangerous situations with urgent and turbulent political, economic and social environments. Furthermore, they typically involve a large number of players from many different nations, operating across sectors, and between multiple layers of bureaucracy and diplomacy. The organizational complexity staggers many participants and observers, as do the tasks they are charged with completing. Reform efforts in Bosnia and Herzegovina starting in 1995 may serve as the archetype model of conflict, transition and development for the 21st century. It wins this honor due not to its particular programmatic successes and failures, rather to the interorganizational complexity of the International Community. From the massive response to the crisis, to the modern nation-building policies it spawned, and the development assistance practices and institutional arrangements it created, the Bosnian development experience has much to offer by way of lessons learned. This manuscript frames the unique Bosnian development situation, and provides lessons learned from the experience of nation building given local realities. Pettigrew (1992) called this "contextualizing." While network and/or organizational structure, strategy and process explain many interorganizational relationship issues, the development variables identified in this manuscript prove equally important, yet elusive and difficult to measure despite their very real and overt presence.