Moving and stationary patterns in chemically reacting systems

Chemically reacting systems are known to exhibit a variety of behavior such as multiple steady states, traveling waves, and stationary patterns. It is of interest to identify the operating conditions (parameter values) leading to these different types of behavior. This work investigates traveling waves in nonisothermal mulit-reaction systems and stationary concentration patterns in isothermal systems.;Distributed systems may exhibit transient solutions (traveling waves) in which a narrow moving front separates two segments, each at a different stable steady state; consequently, a system at one stable steady state may be transformed into another due to local triggering. A systematic technique is developed for efficiently predicting the number and types of stable waves when several chemical reactions occur simultaneously on a catalytic wire. The parameter space is divided into regions with different number and types of waves. Some operating conditions may lead to a traveling wave connecting the lowest and the highest steady state, while in other regions, a wave connecting the extreme steady state temperatures is infeasible. Systems having up to four stable steady states are studied. The method can predict wave behavior for an arbitrary large number of steady states, although the interrelation among the number, types and relative velocities of the waves may be complex.;A uniform catalytic wire may exhibit stable nonuniform concentration patterns whereby some parts of the wire are at higher concentrations than the other parts. A systematic procedure is developed to divide the parameter space into regions with different bifurcation diagrams for the nonuniform concentration patterns. In some regions, a stable isolated branch of inhomogeneous solutions may exist in addition to a branch of stable homogeneous steady states. In some others, a hysteresis may occur between the inhomogeneous and the homogeneous steady state branches. Branches of nonuniform solutions, each with a different arrangement of the zones of high and low concentrations may interact to yield seemingly "irregular" (mixed mode) patterns.