Sensing the distance to a source of periodic oscillations in a nonlinear chemical medium with the output information coded in frequency of excitation pulses

A spatially distributed excitable chemical medium can collect and process information coded in the propagating pulses of excitation. We consider the problem of distance sensing with the use of a nonlinear chemical medium. We demonstrate that a sensor that can feel the distance separating it from a source of periodic excitations can be constructed by a proper geometrical arrangement of excitable and nonexcitable regions. The sensor returns information about the distance in the frequency of outgoing pulses. The sensor functionality is tested by simulations based on the Rovinsky-Zhabotinsky model. The results are confirmed in experiments performed for a ruthenium-catalyzed Belousov-Zhabotinsky reaction.

Figure 1

The geometry of a chemical distance sensor. The gray areas are excitable; the white areas are nonexcitable. The source of excitations, $S$, is marked by a black dot.

Figure 2

Two typical snapshots from simulations. The gray areas are excitable; the black areas are nonexcitable. The source of excitations is marked as a light area close to the $OY$ axis around 250. The light color shows the profile of a high concentration of $x$ for times $\tau =4$ (a) and $\tau =12$ (b). The $x$- and $y$-axis scales are grid points.

Figure 3

(a) and (b) show the concentration of $x$ in channels 1, 2, 3, and 4 as functions of time for the system presented in Fig. 2. (a) and (b) correspond to the distances between the source and detector gap equal to 5.77 and 25.97, respectively. The concentrations are shifted vertically by a value equal to the number of channels.

Figure 4

The firing number in channels 1 (dots), 2 (triangles), 3 (squares), and 4 (crosses) as a function of distance; the barrier width ${\Delta }_G=2.885$, excitation at the level 0.02.

Figure 5

The firing number in channels 1 (dots), 2 (triangles), 3 (squares), and 4 (crosses) as a function of distance; the barrier width ${\Delta }_G=3.2$, excitation at the level 0.015.

Figure 6

The chemical distance sensor with a modified geometry. Like in Fig. 1 the gray areas are excitable and the white areas are nonexcitable. The source of excitations, $S$, is marked by a black dot. ${\Delta }_G=2.9$.

Figure 7

The firing number in channels 1 (dots), 2 (triangles), 3 (squares), and 4 (crosses) as a function of distance for the detector with a modified geometry $({\Delta }_G=2.9)$.

Figure 8

(a) and (b) are snapshots from the experimental realization of the distance sensor. The upper figure shows the source ($1\text{−}\mathrm{mm}$-thick silver wire) placed $2\mathrm{mm}$ away from the sensor; in the lower one the source was $12\mathrm{mm}$ away. The firing numbers are given next to the corresponding channels. (c) The distances between centers of signal channels and the distance source.