Date Published: December 20, 2016
Publisher: Public Library of Science
Author(s): Andrew Adamatzky, Irene Sendiña-Nadal.
Flueric devices are fluidic devices without moving parts. Fluidic devices use fluid as a medium for information transfer and computation. A Belousov-Zhabotinsky (BZ) medium is a thin-layer spatially extended excitable chemical medium which exhibits travelling excitation wave-fronts. The excitation wave-fronts transfer information. Flueric devices compute via jets interaction. BZ devices compute via excitation wave-fronts interaction. In numerical model of BZ medium we show that functions of key flueric devices are implemented in the excitable chemical system: signal generator, and, xor, not and nor Boolean gates, delay elements, diodes and sensors. Flueric devices have been widely used in industry since late 1960s and are still employed in automotive and aircraft technologies. Implementation of analog of the flueric devices in the excitable chemical systems opens doors to further applications of excitation wave-based unconventional computing in soft robotics, embedded organic electronics and living technologies.
Three designs of interaction-based computing—by using fluid streams, signals propagating along conductors and excitation wave fronts—have been conceived and evolved independently for over half-a-century.
We use two-variable Oregonator equations  adapted to a light-sensitive Belousov-Zhabotinsky (BZ) reaction with applied illumination . The Oregonator equations in chemistry bear the same importance as Hodgkin-Huxley and FitzHugh-Nagumo equations in neurophysiology, Brusselator in thermodynamics, Meinhardt-Gierer in biology, Lotka-Volterra in ecology, and Fisher equation in genetics. The Oregonator equations are used to model a wide range of phenomena in BZ, e.g. analysis of rotating waves , chaos in flow BZ , stochastic resonance in BZ , effect of macro mixing . The Oregonator equations is the simplest continuous model of the BZ medium yet showing very good agreement with laboratory experiments. Let us provide few examples. A stable three-dimensional organising centre that periodically emits trigger excitation waves found experimentally is reproduced in the Oregonator model . Studies of the BZ system with a global negative feedback demonstrate that the Oregonator model shows the same bifurcation scenario of bulk oscillations and wave patterns emerging when the global feedback exceed a critical value as the bifurcation scenario observed in laboratory experiments . There is a good match between lab experiments on modifying excitation wave patterns in BZ using external DC field and the Oregonator model of the same phenomena . The Oregonator model used in  to evaluate the dispersion relation for periodic wave train solutions in BZ shows agrees with experimental results. Patterns produced by the Oregonator model of a three-dimensional scrolls waves are indistinguishable from patterns produced in the laboratory experiments . Excitation spiral breakup demonstrated in the Oregonator model is verified in experiments . The Oregonator model can be finely tuned, e.g. adjusted for temperature dependence , scaled , modified for oxygen sensitivity . Author with colleagues personally used the Oregonator model as a fast-prototyping tool and virtual testbed in designing BZ medium based computing devices which were implemented experimentally [38–42, 52].
The excitable medium’s analog of the fluidic jet stream generators is a device shown in Fig 2. It is comprised of an excitable ring [69, 70] with outlets. When the medium inside the ring is perturbed by an asymmetric excitation, e.g. a domain of 1 by 20 nodes is forced into excitable state, u = 0.1, v = 0 and a parallel domain of 1 by 20 nodes into refractory state u = 0, v = 0.1, an excitation wave-front forms and runs along the ring. If we attach outlets of excitable channels to the ring, the excitation will spread into the outlets. A frequency of the signal generation at the outlets is determined by speed of the wave front and the diameter of the ring. Speed of the wave front is determined by width of a channel (see Sect. 11). Therefore, one can achieve any frequency (in a ring with perimeter exceeding the excitation wave-length) by changing geometrical parameters of the ring.
The and gate is the most known, a par with a bistable amplifier, devices in the fluidics (Fig 3a). Two nozzles are placed at right angles to each other. When there are jet flows in both nozzle they collide and merge into a single jet entering the central outlet. If the jet flow is present only in one of the input nozzles it goes into the vent. To implement this and gate in excitable medium we cross three excitable, ϕ = 0.07, channels as shown in Fig 3b, and slightly illuminate the junction to make it sub-excitable, ϕ = 0.0768. When input x is excited the excitation wave propagates towards the junction and across into the output channel c (Fig 3c). The wave-front does not expand into the channels a and b because the junction is sub-excitable, so the wave-fragment conserves its shape. Similarly, if the input y is excited the excitation propagates into channel b (Fig 3d). When both inputs x and y are excited the wave-fragments collide with each other at the junction. They merge into a single wave-fragment which propagates into the output channel a (Fig 3e). The central output channel represents a conjunction of signals: a = xy. Lateral output channels represent a conjuction of one signal with negation of another signals: b=x¯y and c=xy¯. By merging channels b and c into a single channel we obtain exclusive disjunction x ⊕ y thus producing a one bit half-adder. As we have already shown in , the gate can be further cascaded into a multiple bit full adder.
Logical negation can not be implemented in passive devices, because a source of constant True is required. The signal generator (Fig 2) is used to make the not gate as demonstrated in Fig 4a. When no input signal is present the wave-front from the generator s exits via output a (Fig 4b). If excitation is generated in input x the wave-fragment x collides with the wave-fragment s. The fragments merge into a single wave-front (Fig 4c). This newly formed wave-front collides into the channel’s wall and annihilates. Thus a=x¯.
A monostable beam deflection device is comprised of a power supply, controls/inputs and vents (Fig 5a and 5b). When no inputs are present the power jet from the power source exits through the output (Fig 5a). When one or both input jets are present, the jet from the power source is deflected into the vent and discharged (Fig 5b) . The power jet exits the output only if none of the input jets are present. This is nor operation. The excitable medium implementation consists of four intersecting channels (Fig 5c). The channels are excitable (ϕ = 0.07) and the junctions, encircled in (Fig 5c) are sub-excitable (ϕ = 0.077). The power source is s and inputs are x and y. We extend the scheme (Fig 5a and 5b) with two outputs. The output a in (Fig 5c) has the same purpose as the output in (Fig 5a and 5b). The output b produces results of additional operation. The power source can be represented by a generator described in Sect. 3; we do not show it here. When the power source is off the excitation wave-front generated at one of the inputs x or y proceeds to the output b (Fig 5d). When both inputs are present their wave-fragments merge and also proceed to output b (Fig 5e). Suppressed excitability of the medium at the junction prevents the wave-fragment from spreading to the horizontal channel. When the power source is on and no inputs are present the signal from the power source exits through the output a (Fig 5f). If travelling excitation is present in one (Fig 5g) or both (Fig 5h) inputs x and y the excitation wave-fragment originated at the inputs collide with the wave-fragment originated at the power source and annihilate. The output a represents x+y¯ and the output b represents s¯(x+y).
The monostable beam deflection device (Fig 5a and 5b) can be transformed into nor-or gate (Fig 6a) by adding an output outlet instead of a vent . When no control jets are present the jet from the power source exits via the outlet O1. If one or both signal jets are present, the jet from the power source is deflected in the outlet O2. This device is implemented in excitable medium as follows (Fig 6b). Assume the power source is always on. When neither of the signals is present the excitation wave-front from s travels into output a (Fig 6c). If excitation wave front is generated in one of the inputs it collides with the excitation wave-front originated in the power source s (Fig 6c). The collided wave-fronts merge and divert into the output b. If excitation is generated in both inputs, the wave-fronts from x and y merge into a single wave-front before colliding with the wave-fronts s. The resultant wave-front collides with s, and is diverted into the output b. Thus, a=x+y¯ and b = x + y.
A fluidic diode is a two-terminal device which restricts, or even cancels, flow in one direction (backward direction). Tesla diode  (Fig 7a) and scroll diode [1, 76] (Fig 8a) are most known fluidic diodes (as well as vortex diode which is not discussed here).
A delay in fluidic systems is implemented as volumetric tank (Fig 10a) with input and output pipes. A step change in the input pressure on the input appears as a similar change in the output pressure on the output after a delay. The delay is caused by turbulence. The amount of the delay is determined by the volume of the tank .
Interrupted jet sensor, see e.g. , is a device comprised a single nozzle positioned in spaced registry with an inlet. The nozzle is supplied with pressurised fluid, the fluid is ejected form the nozzle as a free jet towards the inlet. If there is an object between the nozzle and the inlet, the jet steam becomes disturbed and a phase shift in pressure occurs, which is reflected by the inlet [83, 84]. Applications of the interrupted jet sensors are limited to counting and fabric positing devices, because it is impractical to place large objects between the jet and the inlet. The implementation of an analog of the interrupted jet sensor such as sensor in an excitable medium would be a trivial task.
A jet flow attached itself to a nearby surface (Fig 14a) and remains attached even when the surface curves away from the initial direction of the power jet (Fig 14b). This is the Coanda effect . The wall attachment of the jet happens due to a difference in space from the jet to an object’s surface. The effect is used to implement bistable amplifiers (they are called amplifiers because stronger power jets are deflected by weaker control jets) and flip-flop elements in fluidic devices. The exemplar bi-stable device has a power jet source, two output channels and two control channels (Fig 14c). The power jet entering the junction, or a branching site, with no controls present would become attached to a wall of one the channels, chosen arbitrarily. The jet attracts air in the space between itself and one wall, and makes a vacuum in the space between itself and another wall . By activating a control jet one can divert the power source jet to another channel, where the jet got attached and continues to be attached after the control signal is switched off. This allows us to implement flip-flop devices in fluidic circuits which are key components of fluidic computers, e.g. register shift devices [87, 88].
A modulation is a change of the medium’s excitability on the fly to prevent the excitation wave-fragment from collapsing or exploding. The modulation is implemented as follows. When the wave-fragment just forms, we calculate activity level γ, as a number of nodes with u > 0.1. On further steps of simulation we calculate activity level α and compare it with the standard activity level γ. If α > γ we decrease excitability of the medium by increasing ϕ as ϕ → ϕ + 0.001; if If α < γ we decrease ϕ by 0.001. The similar method of modulation was used in the experimental laboratory routing of excitation wave-fragments in BZ medium . Example of the modulated wave-fragment is shown in Fig 15a, slight oscillation in the wave-fragment size is visible. When a non-modulated shape preserving compact wave-front collides to or brushes by the non-excitable domain the wave-fragment collapses (Fig 14g, 14h and 14i). The modulated wave-fragment annihilates only in a head-on collision with a non-excitable domain (Fig 15b). In scenarios of a partial contact with the non-excitable domain the wave-fragment recovers and reflects pf the domain (Fig 15c–15f). The deficiency of the global modulation is that when two or more wave-fragments present they might implicitly compete for the ‘quote of activity’ allocated: large fragments would become larger and small fragments would collapse, as illustrated in Fig 15g. The jet streams in flueric (fluidic without moving parts) devices and excitation wave-fronts in excitable media have different physical nature. Despite this we demonstrated that it is possible to emulate most common flueric devices in the excitable media, the Belousov-Zhabotinsky (BZ) system: power sources (emulated by excitable rings with outlets), delay elements, diodes, not, and and nor gates, and proximity sensors. Two basic principles of fluidic devices have been emulated with the excitation wave-fragments: laminar flow and jet interaction. We have been unable to implement bistable devices because the excitation wave-fragments do not attach the walls as the jet streams do. There may be other ways, not inspired by Coanda effect, to make the bistable devices in the sub-excitable media. Further studies can focus on analogous implementations of wall-attachment based devices, laminar turbulent effect, vortex effect and vortex diodes, and moving part devices where excitation wave-fragments can manipulate objects. The application domain for excitable media computing and sensing devices is presently very limited, comparing to the applications of fluidic devices (which have already over half-a-century track record of industrial implementations) however the field of unconventional computing and novel materials is rapidly changing and more potential applications and laboratory prototypes emerge. Source: http://doi.org/10.1371/journal.pone.0168267