PHYSICS OF PLASMAS 21, 093503 (2014)
Glow discharge based device for solving mazes Alexander E. Dubinov,1,2,a) Artem N. Maksimov,1 Maxim S. Mironenko,1,2 Nikolay A. Pylayev,1 and Victor D. Selemir1,2
1 Russian Federal Nuclear Center All-Russian Scientific and Research Institute of Experimental Physics (RFNC-VNIIEF), Sarov, Nizhni Novgorod region 607188, Russia 2 Sarov Institute of Physics and Technology (SarFTI) of National Research Nuclear University “MEPhI,” Sarov, Nizhni Novgorod region 607188, Russia
(Received 1 April 2014; accepted 19 August 2014; published online 5 September 2014) A glow discharge based device for solving mazes has been designed and tested. The device consists of a gas discharge chamber and maze-transformer of radial-azimuth type. It allows changing of the maze pattern in a short period of time (within several minutes). The device has been tested with low pressure air. Once switched on, a glow discharge has been shown to find the shortest way through the maze from the very first attempt, even if there is a section with potential barrier for electrons on the way. It has been found that ionization waves (striations) can be excited in the maze along the length of the plasma channel. The dependancy of discharge voltage on the length of the optimal path through the maze has been measured. A reduction in discharge voltage with one or two potential barriers present has been found and explained. The dependency of the magnitude of discharge ignition voltage on the length of the optimal path through the maze has been measured. The reduction of the ignition voltage with the presence of one or two potential barriers has C 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4894677] been observed and explained. V
I. INTRODUCTION
Recently there has been a number of attempts to find and study nonliving, physical systems, able to solve mazes (i.e., find optimum path between the two set points in a maze) independently, without human assistance. This was the purpose, for example, of studies of mechanisms of solving mazes using chemical waves in the Belousov–Zhabotinsky reactions,1,2 using fluids flows3 or chemotactic drops transport4 in microcapillaries and also by means of supersaturated solutions crystallization.5 Such systems are essentially capable of performing analogue topological calculations and will be of particular interest as devices for complex navigation in robotics. Reference 6 describes gas discharge cells in the shape of chips, where mazes were solved using plasma of a glow discharge. Chips had rectangular microchannels, either in the shape of a given maze with the dimensions of 16.2 26.0 mm2 or in the shape of the London street network. The microchannels were made by means of laser lithography and had transversal section of 250 100 lm2. Tungsten electrodes of 25 lm diameter were installed on the maze input and output. Gas was depressurized in the chip’s channels and later helium was pumped in up to the pressure of 11486 Torr. The glow discharge was ignited in the chip with rectangular maze at 46 kV voltage supply to the electrodes, and in the chip with the London street network at 2030 kV voltage supply to the electrodes. Luminescence of the discharge showed the shortest path in the maze. Less than 500 ms was being spent on finding the solution from the very first attempt. In case of voltage increase between the electrodes, longer paths could be found in the maze. a)
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The use of helium, as well as a very high voltage for a glow discharge, and also the need in a new chip for each maze design make this research both expensive and very time consuming (production time of each chip is 2–3 days depending on the maze complexity). The purpose of this work was development, manufacture and testing of a glow discharge based device capable of solving mazes, while working with low pressure air at less than 2 kV voltage, and allowing quick change of maze design. II. DESCRIPTION OF GAS-DISCHARGE DEVICE WITH MAZE-TRANSFORMER
The developed device consists of gas-discharge chamber with maze-transformer inside. It is possible to change the pattern of channels within several minutes. The gas-discharge chamber was made of polyamide in the form of a cylindrical pan of 450 mm diameter and 50 mm height. Replaceable copper cathode in the form of rectangular plate of 15 8 mm2 size was fitted on its side surface in a cathode holder. Stainless steel rod anode of 10 mm diameter was located at the center of the chamber. At the top the chamber was sealed with transparent quartz window of 60 mm thickness. Digital photo camera FE-280 «OLYMPUS» on the basis of the CCD matrix 1/2.300 with 8.5 106 pixels was fitted above the window. The chamber had several side pipes for pump connection, power supply to the electrodes and measurement circuits. Previously this chamber was used in the experiments7 on glow discharge with radial current and circular striations. The maze-transformer of radial-azimuth type was designed and manufactured. It consisted of a Plexiglas disk of 287 mm diameter and 50 mm height. Five ring channels of 25 mm width and 40 mm depth were cut into the disk. Wall
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thickness between the channels was 5 mm. The indexing of the walls was as follows: 1—external wall, 2, 3, 4—intermediate walls, 5—internal wall. There was one window of 40 mm width in the wall 1, four windows of 40 mm width in each wall 2 and 3, four windows of 30 mm width in the wall 4, and one window of 20 mm width in the wall 5. The windows of the neighboring walls were shifted relative to each other on azimuth to avoid having them in front of each other. Polyamide curved doors were made for each window, able to completely seal the path from one channel to another. 25 polyamide flat barriers were also made to form dead ends in the maze. The doors and barriers were placed and secured in the maze using predesigned grooves in the channel walls. As a result, one could create different radial-azimuth patterns of the maze using these doors and barriers, with the total number of possible permutations: 237 > 1.371011. Hole for the anode was made in the center of the disk. Change of maze configuration can be completed within 3 min. It is important to note that all gaps: between the maze walls, doors, barriers and transparent window should be hermetically sealed, for example, by elastic material. Otherwise, the discharge would find the shortest path through open gaps. Design of the device for solving mazes, based on a gasdischarge chamber with installed maze-transformer is shown in Fig. 1. Electrodes of the gas-discharge chamber were usually connected to a DC power source via dividing resistors R1 ¼ 36 kX and R2 ¼ 750 X.
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applied to the electrodes. Trajectory of the discharge channel was recorded by the photo camera in video regime at 7 fps. Fig. 2 shows one of the examples of the maze solution found by plasma. In this example, the possible path through the maze was relatively simple and unique. It passed from the cathode to anode, using direction of electron flow in the discharge, coming from the external channel into the neighboring internal one (Fig. 2(a)). The path length was 82 cm. It turned out that the glow discharge ignited immediately along the optimal path (Fig. 2(b)). Fig. 3 shows an example of the solution of a more complicated maze with 105 cm length. Its complexity is in the fact that the found path contains one section, in which electrons have to move away from the anode and overcome a potential barrier (Fig. 3(a)). Nevertheless, one can see that plasma solves the maze containing that potential barrier (Fig. 3(b)). More than ten different maze patterns were tested, and it was found that the glow discharge plasma was always able to find the optimal path from the first attempt. Video recording of the moment of discharge ignition and discharge stationary existence has observed that a significant luminescence is not in the wrong ways (up to the limit of the light sensitivity of the digital cameras ISO 1600, which corresponds to the luminous exposure 1/1600 lxs). This proves that the discharge finds the right way on the first attempt. It is important to note that ignition voltage of the glow discharge rises, when the length of the found path also increases.
III. DEVICE TEST RESULTS
Testing of the device was performed using low pressure air (0.110 Torr) in the discharge chamber in order to operate the device in the regime of DC glow discharge. The experiments were carried out in a darkened room without unwanted light sources. The work was carried out using the following framework. Subject maze pattern was installed in the mazetransformer using doors and barriers. The chamber was then sealed and pumped out to the required pressure before the voltage, necessary for DC glow discharge ignition was
FIG. 1. Design of the device for maze solutions: 1—cathode holder (without replaceable cathode), 2—gas-discharge chamber (without see-through window), 3—flat barrier, 4—maze-transformer, 5—door, 6—anode, 7—pump connector.
FIG. 2. Solution of a simple maze by the glow discharge: (a) scheme of the maze, arrows show the only possible path; (b) glow discharge plasma luminescence along the found path (at air pressure 5 Torr, voltage 1.7 kV).
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However, explanation of the electrons passage through the curved dielectric channels alone is not enough to understand mazes. It is also necessary to explain why electrons choose the correct turn, which leads to the anode, on each fork; and why they do not choose the turn leading to a dead end. Near the forks both directions are equal from the point of view of the electric field distribution, and the dead end could be far. How do electrons “feel” it? We do not have the full understanding of this yet. Reference 17 is interesting in this respect. Passage of ionization waves in the discharge under atmospheric pressure through a channel, divided into two similar channels, is simulated here. Reference 17 shows that discharge passes symmetrically through both channels. We carried out such experiments with glow discharge at low pressure. If both channels are similar, we get symmetrical images of ionization waves in the channels similar to results of Ref. 17. However, if we close one channel and make a barrier half way, there would be neither a discharge channel nor ionization waves. If the specified mechanism of the discharge in the closed channel was at work, we would expect to see at least some short-time glow until the halfway mark. Selection of the correct way by electrons near the forks is the key element needed to explain how mazes are solved, and it is even more important than motion along the curved channel with charged walls. FIG. 3. Solution of the maze with potential barrier by the glow discharge: (a) scheme of the maze, arrows show the only path, light arrow shows the section with potential barrier; (b) glow discharge plasma luminescence along the found path (at air pressure 5 Torr, voltage 1.9 kV).
Images in Figs. 2(b) and 3(b) show that ionization waves—striations8 could be excited in the discharges, similar to the discharges in straight tubes. One could say that the ionization waves also solve the maze, passing through it, following along the plasma channel, like Theseus moving along the Ariadne’s golden thread. To explain the dynamics of the maze solution by plasma of the glow discharge, one can draw an analogy with the way mazes are solved by animals. It is known that higher animals, such as mice, dogs, and others are able to find the shortest path in the maze very quickly.9,10 It turns out that even singlecellular organisms can solve the mazes.11–13 The most important requirement for finding the maze solution by living creatures is existence of a motive. Such motives could be getting out of the maze, a treat or an animal of the opposite sex at the exit, etc. The discharge in plasma, as a rule, is created by means of gas ionization by electron impact, and the number of the electrons determines further behavior of the discharge. The electrons always have strong electrostatic motive—to reach the anode—and they move towards it. Explanation of low pressure glow discharge ignition in curved dielectric channels with walls negatively charged due to electron impact is well known (see, for example, Ref. 14, pp. 171172). Reference 15 is a wonderful illustration of this explanation for atmospheric pressure discharge. Let us also point to a recently published experimental Ref. 16, in which electrons repeatedly pass through the circular vacuum channel with negatively charged walls.
IV. MEASUREMENT OF GLOW DISCHARGE IGNITION VOLTAGE IN THE MAZE
As discussed above, the voltage required for glow discharge ignition in a maze depends on the length of the optimal path. With the same gas pressure in the discharge chamber, the ignition voltage was expected to rise with the length of the path, analogous to the upward slope in the right branch of the well known Paschen curve. It was also expected that the presence of addition potential barriers along the optimal path would further increase the required voltage. In order to measure this dependency a few tens of various maze configurations were used. Over 30 of these had a simple optimal path and had no potential barriers. Five configurations had one potential barrier between the cathode and anode, analogous to the one shown on Fig. 3. Five configurations had two potential barriers. Experiments to investigate the ignition voltage were conducted using the framework similar to Ref. 18. The right hand side of the curve of dependency of discharge voltage U on the length of the path through the maze L has been measured at p ¼ 0.1 Torr pressure. Only the right hand side of the curve has been measured, analogous to the right-hand side of high pressure Paschen’s curve, as it was not possible to conduct the measurements for small pd values in our conditions due to a relatively high length of the shortest path through the maze. The results of the measurements are presented in Fig. 4. Each experimental point on the graph and it’s error is the result of the data from five discharges. It is observed that if simple optimal path mazes are used all results are fitted on the curve “0,” which shows that the dependency of the
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FIG. 4. The measured dependency of the magnitude of discharge ignition voltage on the length of the optimal path through the maze at 0.1 Torr: the curve “0” for paths without barriers, the curve “1” for paths with one barrier, and the curve “2” for paths with two barriers.
discharge voltage on the length of the path is indeed upward sloping. Yet, unexpectedly, it was found that if one potential barrier is present the results fit on the curve “1,” which is upward sloping but lies significantly lower than the curve “0.” Curve “2,” which represents the results of using two potential barriers lies even lower. This suggests that the presence of sections of the path where electrons have to move from anode to cathode, does not hinder the ignition of the charge, but, on the contrary, appears to help it. We can give the following explanation to this phenomenon. Let us imagine a curved gas discharge tube with three sections—the cathode section, the middle section, and the anode section (Fig. 5). This tube is a simplified 1D-model of the path with a barrier in a maze. If the distance between the cathode and anode is d and the length of the middle section is s then the overall length of the tube is L ¼ d þ 2s.
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During the initial phase of the discharge the electron avalanches are directed from cathode to anode in all three sections of the tube, in accordance with the applied electric field. Therefore the dependency, defining the Paschen curve should be defined by the product of pd, not pL. Nevertheless, once the plasma column is formed and the stationary electric field is gone, the conductivity electrons would drift along the path of length L and in the middle section they would be drifting from anode towards cathode (top part of Fig. 5), i.e., against the direction of avalanche. These electrons will complete the electric circuit. If the length of the middle section is increased as shown on the lower part of Fig. 5, the ignition voltage should not change. It is therefore possible to shift for example the curve “1” on Fig. 4 to the right by a distance equal to double the length of the section with barrier 2s in accordance with d ¼ L 2s (s is approximately equal to the length of the light arrow on Fig. 3(a), s 50 mm). As a result it would coincide with curve “0.” Therefore, in order to fit the results with the Paschen dependency the argument pL should be substituted for pd ¼ pðL 2sÞ when potential barriers are present. V. SUMMARY
The device, based on glow discharge, intended to solve mazes was designed, built, and tested. The device consists of the gas discharge chamber and maze-transformer of radialazimuth type, which allows change of the maze pattern within several minutes. The device was tested with low pressure air as a plasmaforming gas. It was shown that the glow discharge can find the shortest path in the maze from the first attempt after its ignition, even in cases, when a section with the potential barrier for the electrons was in its way. The dependency of the magnitude of discharge ignition voltage on the length of the optimal path through the maze has been measured. The reduction of the ignition voltage with the presence of one or two potential barriers, where the direction of electron flow is inverted from “cathode!anode” at the avalanche stage to “anode!cathode” at the glow stage, has been observed and explained. Under certain conditions ionization waves (striation) were observed along the whole length of the plasma channel. The developed device could become a prototype for a system working with analogue topological calculations in robotics. T O. Steinbock, A. oth, and K. Showalter, Science 267(5199), 868871 (1995). 2 O. Steinbock, P. Kettunen, and K. Showalter, J. Phys. Chem. 100(49), 1897018975 (1996). 3 M. J. Fuerstman, P. Deschatelets, R. Kane, A. Schwartz, P. J. A. Kenis, J. M. Deutch, and G. M. Whitesides, Langmuir 19(11), 47144722 (2003). 4 I. Lagzi, S. Soh, P. J. Wesson, K. P. Browne, and B. A. Grzybowsky, J. Am. Chem. Soc. 132(4), 11981199 (2010). 5 A. Adamatzky, Phys. Lett. A 374(2), 264271 (2009). 6 D. R. Reyes, M. M. Ghanem, G. M. Whitesides, and A. Manz, Lab Chip 2(2), 113116 (2002). 7 A. N. Belonogov, A. E. Dubinov, A. N. Maksimov, and V. D. Selemir, IEEE Trans. Plasma Sci. 41(1), 3642 (2013). 8 V. I. Kolobov, J. Phys. D. Appl. Phys. 39(24), R487–R506 (2006). 9 W. S. Hunter, J. Animal Behav. 1, 278304 (1911). 1
FIG. 5. The 1D-model of a path with a potential barrier in a maze which explains stages of glow discharge with reduction of the ignition voltage; short arrows show the direction of electron motion at the avalanche stage, and long arrows show the direction of electron drift at the glow stage.
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