On the localized wave patterns supported by convection-reaction-diffusion equation

A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary waves within this family for wide range of parameter values

Self-organized stable pacemakers near the onset of birhythmicity

General amplitude equations for reaction-diffusion systems near to the soft onset of birhythmicity described by a supercritical pitchfork-Hopf bifurcation are derived. Using these equations and applying singular perturbation theory, we show that stable autonomous pacemakers represent a generic kind of spatiotemporal patterns in such systems. This is verified by numerical simulations, which also show the existence of breathing and swinging pacemaker solutions. The drift of self-organized pacemakers in media with spatial parameter gradients is analytically and numerically investigated.Comment: 4 pages, 4 figure

Dynamics and control of loop reactors: a review

In the loop reactor (LR) the system is composed of several reactor units that are organized in a loop and the feeding takes place at one of several ports with switching of the feed port in a periodic way. In its simplest operation a pulse is formed and rotates around it, producing high temperatures which enable combustion of dilute streams. A limiting model with infinite number of units was derived. Rotating pulses, that are steady in a coordinate moving with the switch velocity, emerge in both asymptotic and discrete models when the ratio of switching to front propagation velocities is around unity. But this behavior exists over a narrow domain of this ratio. Simulations were conducted with generic first order Arrhenius kinetics. Experimental observations of simple frozen rotating pulses are reviewed. Outside the narrow frozen rotating patterns domain the system may exhibit multi- or quasi-periodic operation separated by domains of inactive reaction. The bifurcation set incorporates many ’finger’-like domains of complex frequency-locked solutions that allow to significantly extend the operation domain with higher feed temperature or concentration. Control is necessary to attain stable simple rotating frozen patterns within the narrow domains of active operation. Various control approaches that were suggested, or experimentally applied for this purpose, are reviewed. Actual implementation of combustion in LR will involve several reactants of different ignition temperatures and varying concentration. Design and control should be aimed at producing locked fronts and avoid extinction of the slower reaction

Towards nonlinear selection of reaction-diffusion patterns in presence of advection: A spatial dynamics approach

This paper has been withdrawn by the author(s), due to acceptance of the paper for publication in Physical Chemistry Chemical Physics.Comment: This paper has been withdraw