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The Electron in the Maze

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Part of the book series: Emergence, Complexity and Computation ((ECC,volume 32))

Abstract

A physical method to solve a maze using an electric circuit is presented. The temperature increase due to Joule heating is observed with a thermal camera and the correct path is instantaneously enlightened. Various mazes are simulated with Kirchhoff’s circuit laws. Finally, the physical mechanisms explaining how the electric current chooses the correct path are discussed.

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Notes

  1. 1.

    The title of this chapter is a tribute to the American sci-fi writer Robert Silverberg and his novel “The Man in the Maze”.

  2. 2.

    In the following discussion, we do not consider the thermal equilibration of the system, which requires more time than electric equilibration.

References

  1. M.J. Fuerstman, P. Deschatelets, R. Kane, A. Schwartz, P.J. Kenis, J.M. Deutch, G.M. Whitesides, Solving mazes using microfluidic networks. Langmuir 19(11), 4714–4722 (2003)

    Article  Google Scholar 

  2. Y.V. Pershin, M. Di Ventra, Solving mazes with memristors: A massively parallel approach. Phys. Rev. E 84, 046703 (2011)

    Google Scholar 

  3. L.O. Stratton, W.P. Coleman, Maze learning and orientation in the fire ant (solenopsis saevissima). J. Compa. Physiol. Psychol. 83(1), 7 (1973)

    Article  Google Scholar 

  4. S. Zhang, A. Mizutani, M.V. Srinivasan, Maze navigation by honeybees: Learning path regularity. Learn. Mem. 7(6), 363–374 (2000)

    Article  Google Scholar 

  5. T. Nakagaki, H. Yamada, Á. Tóth, Intelligence: Maze-solving by an amoeboid organism. Nature 407(6803), 470–470 (2000)

    Article  Google Scholar 

  6. J. Qin, A.R. Wheeler, Maze exploration and learning in c. elegans. Lab on a Chip 7(2), 186–192 (2007)

    Article  Google Scholar 

  7. A. Adamatzky, Towards plant wires. Biosystems 122, 1–6 (2014)

    Article  Google Scholar 

  8. D.R. Reyes, M.M. Ghanem, G.M. Whitesides, A. Manz, Glow discharge in microfluidic chips for visible analog computing. Lab on a Chip 2(2), 113–116 (2002)

    Article  Google Scholar 

  9. S. Ayrinhac, Electric current solves mazes. Phys. Educ. 49(4), 443 (2014)

    Article  Google Scholar 

  10. J. Adam, New correlations between electrical current and temperature rise in PCB traces, in Twentieth Annual IEEE Semiconductor Thermal Measurement and Management Symposium, 2004 (IEEE, 2004), pp. 292–299

    Google Scholar 

  11. M. Vollmer, K.-P. Möllmann, F. Pinno, D. Karstädt, There is more to see than eyes can detect. The Phys. Teach. 39(6), 371–376 (2001)

    Article  Google Scholar 

  12. K.-P. Möllmann, M. Vollmer, Infrared thermal imaging as a tool in university physics education. Eur. J. Phys. 28(3), S37 (2007)

    Article  Google Scholar 

  13. C. Xie, E. Hazzard, Infrared imaging for inquiry-based learning. The Phys. Teach. 49, 368 (2011)

    Article  Google Scholar 

  14. J. Haglund, F. Jeppsson, E. Melander, A.-M. Pendrill, C. Xie, K.J. Schönborn, Infrared cameras in science education. Infrared Phys. Technol. 75, 150–152 (2016)

    Article  Google Scholar 

  15. E. Netzell, F. Jeppsson, H. Jesper, K. Schönborn, Visualising energy transformations in electric circuits with infrared cameras. Sch. Sci. Rev. 98(364), 19–22 (2017)

    Google Scholar 

  16. M. Vollmer, K.-P. Möllmann, Infrared Thermal Imaging: Fundamentals Research and Applications (Wiley, 2011)

    Google Scholar 

  17. C. Xie, Visualizing chemistry with infrared imaging. J. Chem. Educ. 88(7), 881–885 (2011)

    Article  Google Scholar 

  18. N.A. Gross, M. Hersek, A. Bansil, Visualizing infrared phenomena with a webcam. Am. J. Phys. 73, 986–990 (2005)

    Article  Google Scholar 

  19. U. Besson, Paradoxes of thermal radiation. Eur. J. Phys. 30(5), 995 (2009)

    Article  Google Scholar 

  20. R.W. Chabay, B.A. Sherwood, Matter and Interactions, vol. 2 (Wiley, New York, 2011)

    Google Scholar 

  21. J. Stasiek, M. Jewartowski, T.A. Kowalewski, The use of liquid crystal thermography in selected technical and medical applications—Recent development. J. Cryst. Process Technol. 4(1), 46–59 (2014)

    Article  Google Scholar 

  22. G. Liebmann, Solution of partial differential equations with a resistance network analogue. Br. J. Appl. Phys. 1(4), 92 (1950)

    Article  Google Scholar 

  23. L. Tarassenko, A. Blake, Analogue computation of collision-free paths. In Proceedings. 1991 IEEE International Conference on Robotics and Automation, 1991 (IEEE, 1991), pp. 540–545

    Google Scholar 

  24. S. Rainson, G. Tranströmer, L. Viennot, Students’ understanding of superposition of electric fields. Am. J. Phys. 62(11), 1026–1032 (1994)

    Article  Google Scholar 

  25. W.G.V. Rosser, Magnitudes of surface charge distributions associated with electric current flow. Am. J. Phys. 38(2), 265–266 (1970)

    Article  Google Scholar 

  26. A.M. Heald. Electric fields and charges in elementary circuits. Am. J. Phys. 52(6), 522–526 (1984)

    Article  Google Scholar 

  27. J.D. Jackson, Surface charges on circuit wires and resistors play three roles. Am. J. Phys. 64(7), 855–870 (1996)

    Article  Google Scholar 

  28. N.W. Preyer, Transient behavior of simple RC circuits. Am. J. Phys. 70, 1187–1193 (2002)

    Article  Google Scholar 

  29. R. Müller, A semiquantitative treatment of surface charges in DC circuits. Am. J. Phys. 80(9), 782–788 (2012)

    Article  Google Scholar 

  30. A.K.T. Assis, J.A. Hernandes, The Electric Force of a Current: Weber and the Surface Charges of Resistive Conductors Carrying Steady Currents (Apeiron, 2007). This book is freely available at the following address: http://www.ifi.unicamp.br/~assis/

  31. K.W. Oh, K. Lee, B. Ahn, E.P. Furlani, Design of pressure-driven microfluidic networks using electric circuit analogy. Lab on a Chip 12(3), 515–545 (2012)

    Article  Google Scholar 

  32. A. Adamatzky, Physical maze solvers. All twelve prototypes implement 1961 Lee algorithm. arXiv:1601.04672 (2016)

    Google Scholar 

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Acknowledgements

The thermal camera was provided by the “unité de Formation et de Recherche de Physique” at Sorbonne Université, Faculté des Sciences et Ingénierie. The author is indebted to M. Fioc for his valuable comments on the manuscript.

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Correspondence to Simon Ayrinhac .

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Ayrinhac, S. (2018). The Electron in the Maze. In: Adamatzky, A. (eds) Shortest Path Solvers. From Software to Wetware. Emergence, Complexity and Computation, vol 32. Springer, Cham. https://doi.org/10.1007/978-3-319-77510-4_16

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  • DOI: https://doi.org/10.1007/978-3-319-77510-4_16

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  • Print ISBN: 978-3-319-77509-8

  • Online ISBN: 978-3-319-77510-4

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