Gentle Dragging of Reaction Waves

Abstract

Using a recently realized ''addressable catalyst surface'' [Science 294, 134 (2001)] we study the interaction of chemical reaction waves with prescribed spatiotemporal fields. In particular, we study how a traveling chemical pulse is ''dragged'' by a localized, moving temperature heterogeneity as a function of its intensity and speed. The acceleration and eventual ''detachment'' of the wave from the heterogeneity is also explored through simulation and stability analysis. DOI: 10.1103/PhysRevLett.90.018302 PACS numbers: 82.40.Bj, 05.45.-a, 82.40.Np, 82.45.Jn As the elements of spontaneous pattern formation are progressively understood through theory, experimentation, and scientific computation [1], ways to purposefully interact with the coherent structures (pulses and fronts) that constitute the building blocks of spatiotemporal patterns are becoming the focus of extensive research [2,3]. In particular, the stabilization and control of various patterns [3-9] through local, nonlocal, or global feedback, and pattern formation in media with designed heterogeneities [10 -12] are the source of novel insights for spatiotemporal dynamics.To explore such phenomena, we have recently constructed an ''addressable catalyst'': A focused laser beam, manipulated through computer-controlled mirrors and capable of ''writing'' spatiotemporal temperature heterogeneity patterns on a metal single crystal catalyst. The loop between this actuation and sensing (both resolved in space and time) through nonintrusive microscopies is then closed through the computer or the experimentalist herself/himself in real time. Our model system is the low-pressure catalytic oxidation of CO on Pt(110), a reaction exhibiting well-documented spatiotemporal patterns [13][14][15][16], and whose macroscopic modeling has reached an advanced level [17][18][19][20].In this Letter we study the interaction of reactive pulses with a single, spatially coherent but temporally mobile heterogeneity. In particular, we use a temperature heterogeneity, localized in space and steadily moving in time, to ''drag'' spontaneously isothermally forming reactive pulses and fronts with speeds differing from their natural speed. We examine the shapes acquired by these dragged waves and their limits of stability (that is, the range of dragging speeds for which they can exist). Through computer-aided analysis we examine the nature of the detachment instability, marking the loss of the ability of the heterogeneity to drag a pulse in 1D or 2D. Two possible paths to instability (depending on the linearized spectrum crossing) are detected. We explore the postdetachment transient dynamics and the interactions of a pulse with successive elements of a 1D periodic, constant speed array of identical heterogeneities. The theme of pulse dragging is currently also being explored in a variety of physically relevant Hamiltonian systems, or weakly perturbed dissipative variations thereof (targeted transfer of pulses in optical media or the motion/displacement of harmonic traps or optical l...

Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems

“…Two feedback loops were used to guide unstable wave segments in the BZ reaction along pre-given trajectories [23]. An open loop control was successfully deployed in dragging traveling chemical pulses of adsorbed CO during heterogeneous catalysis on platinum single crystal surfaces [24]. In these experiments, the pulse velocity was controlled by a laser beam creating a movable localized temperature heterogeneity on an addressable catalyst surface, resulting in a V-shaped pattern [25].…”

Real Time Imaging of Surface Catalytic Reactions

“…Since we used all wavelengths of the multiline laser for maximizing local heating power, EMSI always showed some scattered light, which helped to guide the laser spot as can be seen in the following Fig. 6, reproduced from [42]. There CO fronts move around the surface under controlled conditions, and a slight rise in temperature "erases" them.…”

“…This enabled us in real time to control, form, accelerate, modify, guide and destroy pulses and fronts, the basic building blocks of patterns [42]. To achieve this a laser had to be focused onto the surface and moved to any position on it in real time.…”

Temperature wave‐trains of periodically forced networks of catalytic reactors

“…[2][3][4] A major objective is, in this context, to tailor the spatiotemporal pattern of catalytic reactors so as to optimize the temporal evolution of output variables as, for example, the conversion and the selectivity to a desired product. 5 A common approach followed to achieve this objective is to force reactor operating conditions.…”