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.

British Monetary Sovereignty: A Cultural Analysis

In this thesis, I will document and analyze historical aspects of the British debate over adopting a common currency with the European Community primarily during the last half of the twentieth century until the present. More specifically, while on the surface such a decision would seem to turn on economic or political considerations, I will show that this historic British decision not to surrender their pound sterling in exchange for the euro was rooted in the nation's cultural identity. During this decades long British debate over the euro, two opposing, but strongly held, positions developed; one side believed that Britain had a compelling interest in bonding with the rest of Europe economically as well as politically, the other side believed that Britain's independent heritage was deeply rooted in many of its traditions including maintaining control of its own monetary matters, which included keeping its pound sterling. As part of this thesis, I have conducted interviews with business leaders, economists, and social scientists as well as researched public records in order to assess many of the arguments favoring and opposing Britain's adoption of the euro. Many Britons strongly believed that it was time to join other Europeans, who were willing to sacrifice their sovereign currency to a bold common currency experiment, while other Britons viewed the pound sterling as too integral a part of British heritage to abandon. Ultimately, British leaders and citizens had to determine whether such a currency tradeoff would be worth it to them as a nation. It was a gamble that twelve other nations (at the time of the euro's 2002 launch) were ready to take, optimistically calculating that easier credit and reduced exchange transaction costs would lead to greater economic prosperity. Many asserted that only with ! ! such a united European monetary coalition would Europe's nations be able to compete trade-wise with powerful economic nations like the United States and China. My conclusion is that Britain's refusal to join the euro was a decision that had less to do with economic opportunity or political motivations and much more to do with how the British people viewed themselves culturally and their identity as an independent nation.