András Volford

Designed patterns: Flexible control of precipitation through electric currents

Understanding and controlling precipitation patterns formed in reaction-diffusion processes is of fundamental importance with high potential for technical applications. Here we present a theory showing that precipitation resulting from reactions among charged agents can be controlled by an appropriately designed, time-dependent electric current. Examples of current dynamics yielding periodic bands of prescribed wavelength, as well as more complicated structures are given. The pattern control is demonstrated experimentally using the reaction-diffusion process 2AgNO3 + K2Cr2O7-->under Ag2Cr2O7 + 2KNO3.

Rotating chemical waves: theory and experiments

After a brief introduction in the first theoretic part of this work the geometrical wave theory and its application for rotating waves are discussed. Here the waves are rotating around a circular obstacle which is surrounded by two homogeneous wave conducting regions with different wave velocities. The interface of the inner slow and the outer fast region is also a circle but the two circles (the obstacle and interface) are not concentric. The various asymmetric cases are classified and described theoretically. In the second experimental part chemical waves rotating in a so-called moderately asymmetric reactor are studied. A piecewise homogeneous wave conducting medium is created applying a novel reactor design. All the three theoretical cases of the moderately asymmetric arrangement are realized experimentally and qualitative and quantitative comparison of these results with the theoretical predictions show a good agreement.

Coarsening of precipitation patterns in a moving reaction-diffusion front

Precipitation patterns emerging in a two-dimensional moving front are investigated on the example of NaOH diffusing into a gel containing AlCl3 . The time evolution of the precipitate Al(OH)_{3} can be observed since the precipitate redissolves in the excess outer electrolyte NaOH and thus it exists only in a narrow optically accessible region of the reaction front. The patterns display self-similar coarsening with a characteristic length xi increasing with time as xi(t) approximately sqrt[t] . A theory based on the Cahn-Hilliard phase-separation dynamics, including redissolution, is shown to yield agreement with the experiments.

Waves of excitation on nonuniform membrane rings, caustics, and reverse involutes

Chemical wave experiments on concentric nonuniform membrane rings are presented together with their theoretical description. A new technique is applied to create a slow inner and a fast outer zone in an annular membrane. An abrupt qualitative change of the wave profile was observed while decreasing the wave velocity in the inner zone. This phenomenon and all the experimental wave profiles can be adequately described by assuming that waves are involutes of a relevant caustic. A possible connection with recent models of atrial flutter is also set forth. (c) 1997 American Institute of Physics.

Refraction of chemical waves propagating in modified membranes

Different possibilities to perform refraction experiments with chemical waves propagating in membranes modified with a fixed catalyst of the oscillatory Belousov–Zhabotinsky (BZ) reaction were investigated. Two methods to modify the velocity of chemical waves were developed. According to the first, barium sulfate was precipitated in certain regions of the modified membrane to decrease the wave velocity. The second method, which is more reproducible, applies barrier membranes, such as plastic foils or Nuclepore porous membranes, placed between the catalyst membrane and the reservoir of the other BZ reagents. Wave velocity maps calculated from the experiments show that the waves are slower in membrane regions which are separated from the reservoir by a barrier. When water evaporation from the membrane was allowed an inverse velocity map can be observed after some hours. A qualitative explanation of these observations is also presented. Finally, experiments made in an oxygen-free atmosphere prove that the wave refraction phenomena reported here are not caused by oxygen from the air.

Stochastic cellular automata modeling of excitable systems

A stochastic cellular automaton is developed for modeling waves in excitable media. A scale of key features of excitation waves can be reproduced in the presented framework such as the shape, the propagation velocity, the curvature effect and spontaneous appearance of target patterns. Some well-understood phenomena such as waves originating from a point source, double spiral waves and waves around some obstacles of various geometries are simulated. We point out that unlike the deterministic approaches, the present model captures the curvature effect and the presence of target patterns without permanent excitation. Spontaneous appearance of patterns, which have been observed in a new experimental system and a chemical lens effect, which has been reported recently can also be easily reproduced. In all cases, the presented model results in a fast computer simulation.

Detailed study of limit cycles and global bifurcations in a circadian rhythm model

A two variable model describing the circadian fluctuation of two proteins (PER and TIM) in cells is considered. The original model was set up by Leloup and Goldbeter [1998], the present form was developed by Tyson et al. [1999]. Periodic solutions with 24-h period were investigated in those papers. Here the possible phase portraits and bifurcations are studied in detail. The saddle-node and Hopf bifurcation curves are determined in the plane of two parameters by using the parametric representation method [Simon et al., 1999]. It is shown that there are four cases according to their mutual position (as the remaining parameters of the system are varied). Using these curves the number and type of the stationary points are determined in all four cases. The global bifurcation diagram, which is a system of bifurcation curves that divide the given parameter plane into regions according to topological equivalence of global phase portraits, is also determined. Finally, the so-called constant period curves are computed numerically. These curves consist of those parameter pairs on the parameter plane for which the system has a limit cycle with a given period. It turns out that in a wide range of parameters the system has limit cycles with period close to 24-h.