Diffusive oscillators capture the pulsating states of deformable particles.

Coarse Graining; Coarse-grained; Collective dynamics; Deformable particles; Dynamical arrests; Effective energy; Energy landscape; Internal state; Rotational invariances; Spiral waves; Statistical and Nonlinear Physics; Statistics and Probability; Condensed Matter Physics; Physics - Statistical Mechanics; Physics - Soft Condensed Matter

Abstract :

[en] We study a model of diffusive oscillators whose internal states are subject to a periodic drive. These models are inspired by the dynamics of deformable particles with pulsating sizes, where repulsion leads to arrest the internal pulsation at high density. We reveal that, despite the absence of any repulsion between the diffusive oscillators, our model still captures the emergence of dynamical arrest. We demonstrate that arrest here stems from the discrete nature of internal states, which enforces an effective energy landscape analogous to that of deformable particles. Moreover, we show that the competition between arrest and synchronization promotes spiral waves reminiscent of the pulsating states of deformable particles. Using analytical coarse graining, we derive and compare the collective dynamics of diffusive oscillators with that of deformable particles. This comparison leads to rationalizing the emergence of spirals in terms of a rotational invariance at the coarse-grained level, and to elucidating the role of hydrodynamic fluctuations.

Disciplines :

Physics

Author, co-author :

MANACORDA, Alessandro ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Physics and Materials Science > Team Etienne FODOR ; Institute of Complex Systems, CNR , Uos Sapienza, Piazzale A. Moro 5, 00185 Rome, Italy

FODOR, Etienne ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)

External co-authors :

yes

Language :

English

Title :

Diffusive oscillators capture the pulsating states of deformable particles.

Publication date :

May 2025

Journal title :

Physical Review. E

ISSN :

2470-0045

eISSN :

2470-0053

Publisher :

American Physical Society, United States

Volume :

111

Issue :

Pages :

L053401

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://link.aps.org/article/10.1103/PhysRevE.111.L053401

Funders :

H2020 Marie Skłodowska-Curie Actions
Fonds National de la Recherche Luxembourg
Minnesota Ovarian Cancer Alliance

Funding text :

Acknowledgments. We acknowledge fruitful discussions with L. K. Davis, M. Esposito, J. Meihbom, and Y. Zhang. This project has received funding from the European Union's Horizon Europe research and innovation programme under the Marie Sk\u0142odowska-Curie Grant Agreement No. 101056825 (NewGenActive), and from the Luxembourg National Research Fund (FNR), Grant reference No. 14389168. A.M. acknowledges financial support from the project MOCA funded by MUR PRIN2022 Grant No. 2022HNW5YL.

Commentary :

7+11 pages, 4+4 figures

Available on ORBilu :

since 16 December 2025

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Bibliography

T. Vicsek and A. Zafeiris, Collective motion, Phys. Rep. 517, 71 (2012) 0370-1573 10.1016/j.physrep.2012.03.004.
M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Hydrodynamics of soft active matter, Rev. Mod. Phys. 85, 1143 (2013) 0034-6861 10.1103/RevModPhys.85.1143.
C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Rev. Mod. Phys. 88, 045006 (2016) 0034-6861 10.1103/RevModPhys.88.045006.
É. Fodor and M. C. Marchetti, The statistical physics of active matter: From self-catalytic colloids to living cells, Physica A 504, 106 (2018) 0378-4371 10.1016/j.physa.2017.12.137.
M. E. Cates and J. Tailleur, Motility-induced phase separation, Annu. Rev. Condens. Matter Phys. 6, 219 (2015) 1947-5454 10.1146/annurev-conmatphys-031214-014710.
H. Chaté, Dry aligning dilute active matter, Annu. Rev. Condens. Matter Phys. 11, 189 (2020) 1947-5454 10.1146/annurev-conmatphys-031119-050752.
M. L. Manning, Essay: Collections of deformable particles present exciting challenges for soft matter and biological physics, Phys. Rev. Lett. 130, 130002 (2023) 0031-9007 10.1103/PhysRevLett.130.130002.
S. Zehnder, M. Suaris, M. Bellaire, and T. Angelini, Cell volume fluctuations in MDCK monolayers, Biophys. J. 108, 247 (2015) 0006-3495 10.1016/j.bpj.2014.11.1856.
J. Solon, A. Kaya-Çopur, J. Colombelli, and D. Brunner, Pulsed forces timed by a Ratchet-like mechanism drive directed tissue movement during dorsal closure, Cell 137, 1331 (2009) 0092-8674 10.1016/j.cell.2009.03.050.
A. C. Martin, M. Kaschube, and E. F. Wieschaus, Pulsed contractions of an actin-myosin network drive apical constriction, Nature (London) 457, 495 (2009) 0028-0836 10.1038/nature07522.
G. B. Blanchard, S. Murugesu, R. J. Adams, A. Martinez-Arias, and N. Gorfinkiel, Cytoskeletal dynamics and supracellular organisation of cell shape fluctuations during dorsal closure, Development 137, 2743 (2010) 1477-9129 10.1242/dev.045872.
K. Kruse and D. Riveline, Chapter three-spontaneous mechanical oscillations: Implications for developing organisms, in Forces and Tension in Development, edited by M. Labouesse, Current Topics in Developmental Biology Vol. 95 (Academic Press, New York, 2011), pp. 67-91.
X. Serra-Picamal, V. Conte, R. Vincent, E. Anon, D. T. Tambe, E. Bazellieres, J. P. Butler, J. J. Fredberg, and X. Trepat, Mechanical waves during tissue expansion, Nat. Phys. 8, 628 (2012) 1745-2473 10.1038/nphys2355.
C.-P. Heisenberg and Y. Bellaïche, Forces in tissue morphogenesis and patterning, Cell 153, 948 (2013) 0092-8674 10.1016/j.cell.2013.05.008.
J. Xu, S. N. Menon, R. Singh, N. B. Garnier, S. Sinha, and A. Pumir, The role of cellular coupling in the spontaneous generation of electrical activity in uterine tissue, PLoS ONE 10, e0118443 (2015) 10.1371/journal.pone.0118443.
K. M. Myers and D. Elad, Biomechanics of the human uterus, Wiley Interdiscip. Rev. Syst. Biol. Med. 9, e1388 (2017) 1939-5094 10.1002/wsbm.1388.
A. Karma, Physics of cardiac arrhythmogenesis, Annu. Rev. Condens. Matter Phys. 4, 313 (2013) 1947-5454 10.1146/annurev-conmatphys-020911-125112.
S. Alonso, M. Bär, and B. Echebarria, Nonlinear physics of electrical wave propagation in the heart: A review, Rep. Prog. Phys. 79, 096601 (2016) 0034-4885 10.1088/0034-4885/79/9/096601.
T. Nagai and H. Honda, A dynamic cell model for the formation of epithelial tissues, Philos. Mag. B 81, 699 (2001) 1364-2812 10.1080/13642810108205772.
D. Bi, J. H. Lopez, J. M. Schwarz, and M. L. Manning, A density-independent rigidity transition in biological tissues, Nat. Phys. 11, 1074 (2015) 1745-2473 10.1038/nphys3471.
D. Bi, X. Yang, M. C. Marchetti, and M. L. Manning, Motility-driven glass and jamming transitions in biological tissues, Phys. Rev. X 6, 021011 (2016) 2160-3308 10.1103/PhysRevX.6.021011.
E. Tjhung and T. Kawasaki, Excitation of vibrational soft modes in disordered systems using active oscillation, Soft Matter 13, 111 (2017) 1744-683X 10.1039/C6SM00788K.
E. Tjhung and L. Berthier, Discontinuous fluidization transition in time-correlated assemblies of actively deforming particles, Phys. Rev. E 96, 050601 (R) (2017) 2470-0045 10.1103/PhysRevE.96.050601.
C. Brito, E. Lerner, and M. Wyart, Theory for swap acceleration near the glass and jamming transitions for continuously polydisperse particles, Phys. Rev. X 8, 031050 (2018) 2160-3308 10.1103/PhysRevX.8.031050.
N. Oyama, T. Kawasaki, H. Mizuno, and A. Ikeda, Glassy dynamics of a model of bacterial cytoplasm with metabolic activities, Phys. Rev. Res. 1, 032038 (R) (2019) 2643-1564 10.1103/PhysRevResearch.1.032038.
Y. Togashi, Modeling of nanomachine/micromachine crowds: Interplay between the internal state and surroundings, J. Phys. Chem. B 123, 1481 (2019) 1520-6106 10.1021/acs.jpcb.8b10633.
Y. Zhang and E. Fodor, Pulsating active matter, Phys. Rev. Lett. 131, 238302 (2023) 0031-9007 10.1103/PhysRevLett.131.238302.
D. R. Parisi, L. E. Wiebke, J. N. Mandl, and J. Textor, Flow rate resonance of actively deforming particles, Sci. Rep. 13, 9455 (2023) 2045-2322 10.1038/s41598-023-36182-5.
W. hua Liu, W. J. Zhu, and B. Q. Ai, Collective motion of pulsating active particles in confined structures, New J. Phys. 26, 023017 (2024) 1367-2630 10.1088/1367-2630/ad23a5.
H. Ikeda and Y. Kuroda, Continuous symmetry breaking of low-dimensional systems driven by inhomogeneous oscillatory driving forces, Phys. Rev. E 110, 024140 (2024) 2470-0045 10.1103/PhysRevE.110.024140.
Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).
J. A. Acebrón, L. L. Bonilla, C. J. Pérez Vicente, F. Ritort, and R. Spigler, The Kuramoto model: A simple paradigm for synchronization phenomena, Rev. Mod. Phys. 77, 137 (2005) 0034-6861 10.1103/RevModPhys.77.137.
W. D. Piñeros and E. Fodor, Biased ensembles of pulsating active matter, Phys. Rev. Lett. 134, 038301 (2025) 0031-9007 10.1103/PhysRevLett.134.038301.
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevE.111.L053401 for details of the analytical calculations and numerical simulations, as well as two videos, which also includes Refs. [65-67].
I. S. Aranson and L. Kramer, The world of the complex Ginzburg-Landau equation, Rev. Mod. Phys. 74, 99 (2002) 0034-6861 10.1103/RevModPhys.74.99.
In Mathematical Biology I: An Introduction edited by J. D. Murray (Springer, New York, 2002).
J. D. Murray, Mathematical Biology II: Spatial models and biomedical applications (Springer, New York, 2003).
G. Ódor, Universality classes in nonequilibrium lattice systems, Rev. Mod. Phys. 76, 663 (2004) 0034-6861 10.1103/RevModPhys.76.663.
A. G. Thompson, J. Tailleur, M. E. Cates, and R. A. Blythe, Lattice models of nonequilibrium bacterial dynamics, J. Stat. Mech. (2011) P02029 1742-5468 10.1088/1742-5468/2011/02/P02029.
C. Maes and S. Shlosman, Rotating states in driven clock-and XY-models, J. Stat. Phys. 144, 1238 (2011) 0022-4715 10.1007/s10955-011-0325-5.
A. P. Solon and J. Tailleur, Revisiting the flocking transition using active spins, Phys. Rev. Lett. 111, 078101 (2013) 0031-9007 10.1103/PhysRevLett.111.078101.
A. P. Solon and J. Tailleur, Flocking with discrete symmetry: The two-dimensional active Ising model, Phys. Rev. E 92, 042119 (2015) 1539-3755 10.1103/PhysRevE.92.042119.
A. Manacorda and A. Puglisi, Lattice model to derive the fluctuating hydrodynamics of active particles with inertia, Phys. Rev. Lett. 119, 208003 (2017) 0031-9007 10.1103/PhysRevLett.119.208003.
A. Manacorda, Lattice Models for Fluctuating Hydrodynamics in Granular and Active Matter (Springer, Berlin, 2018).
M. Kourbane-Houssene, C. Erignoux, T. Bodineau, and J. Tailleur, Exact hydrodynamic description of active lattice gases, Phys. Rev. Lett. 120, 268003 (2018) 0031-9007 10.1103/PhysRevLett.120.268003.
A. Solon, H. Chaté, J. Toner, and J. Tailleur, Susceptibility of polar flocks to spatial anisotropy, Phys. Rev. Lett. 128, 208004 (2022) 0031-9007 10.1103/PhysRevLett.128.208004.
F. Y. Wu, The Potts model, Rev. Mod. Phys. 54, 235 (1982) 0034-6861 10.1103/RevModPhys.54.235.
T. Herpich, J. Thingna, and M. Esposito, Collective power: Minimal model for thermodynamics of nonequilibrium phase transitions, Phys. Rev. X 8, 031056 (2018) 2160-3308 10.1103/PhysRevX.8.031056.
T. Herpich and M. Esposito, Universality in driven Potts models, Phys. Rev. E 99, 022135 (2019) 2470-0045 10.1103/PhysRevE.99.022135.
E. Panteley, A. Loria, and A. E. Ati, On the stability and robustness of Stuart-Landau oscillators, IFAC-PapersOnLine 48, 645 (2015) 2405-8963 10.1016/j.ifacol.2015.09.260.
T. Reichenbach, M. Mobilia, and E. Frey, Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games, Nature (London) 448, 1046 (2007) 0028-0836 10.1038/nature06095.
T. Reichenbach, M. Mobilia, and E. Frey, Self-organization of mobile populations in cyclic competition, J. Theor. Biol. 254, 368 (2008) 0022-5193 10.1016/j.jtbi.2008.05.014.
S. Shankar, A. Souslov, M. J. Bowick, M. C. Marchetti, and V. Vitelli, Topological active matter, Nat. Rev. Phys. 4, 380 (2022) 2522-5820 10.1038/s42254-022-00445-3.
B. Mahault, E. Tang, and R. Golestanian, A topological fluctuation theorem, Nat. Commun. 13, 3036 (2022) 2041-1723 10.1038/s41467-022-30644-6.
Y. Avni, M. Fruchart, D. Martin, D. Seara, and V. Vitelli, Nonreciprocal Ising model, Phys. Rev. Lett. 134, 117103 (2025) 10.1103/PhysRevLett.134.117103.
Y. Avni, M. Fruchart, D. Martin, D. Seara, and V. Vitelli, Dynamical phase transitions in the nonreciprocal Ising model, Phys. Rev. E 111, 034124 (2025) 10.1103/PhysRevE.111.034124.
H. Noguchi, F. van Wijland, and J.-B. Fournier, Cycling and spiral-wave modes in an active cyclic Potts model, J. Chem. Phys. 161, 025101 (2024) 0021-9606 10.1063/5.0221050.
H. Noguchi and J.-B. Fournier, Spatiotemporal patterns in the active cyclic Potts model, New J. Phys. 26, 093043 (2024) 1367-2630 10.1088/1367-2630/ad7dac.
T. Banerjee, T. Desaleux, J. Ranft, and É. Fodor, Hydrodynamics of pulsating active liquids, arXiv:2407.19955.
T. Agranov, R. L. Jack, M. E. Cates, and É. Fodor, Thermodynamically consistent flocking: From discontinuous to continuous transitions, New J. Phys. 26, 063006 (2024) 1367-2630 10.1088/1367-2630/ad4dd6.
J. Meibohm and M. Esposito, Small-amplitude synchronization in driven Potts models, Phys. Rev. E 110, 044114 (2024) 2470-0045 10.1103/PhysRevE.110.044114.
J. Meibohm and M. Esposito, Minimum-dissipation principle for synchronized stochastic oscillators far from equilibrium, Phys. Rev. E 110, L042102 (2024) 2470-0045 10.1103/PhysRevE.110.L042102.
F. Avanzini, T. Aslyamov, E. Fodor, and M. Esposito, Nonequilibrium thermodynamics of non-ideal reaction-diffusion systems: Implications for active self-organization, J. Chem. Phys. 161, 174108 (2024) 0021-9606 10.1063/5.0231520.
A. Manacorda, Species interconversion of deformable particles yields transient phase separation data set, 2025, doi: 10.17605/OSF.IO/DEV23.
O. Tange, GNU parallel-The command-line power tool, USENIX Mag. 36, 42 (2011) 10.5281/zenodo.16303.
C. W. Gardiner, Stochastic Methods: A Handbook for the Natural and Social Sciences (Springer, Berlin, 2009), Vol. 4.
W. Liu and U. C. Täuber, Nucleation of spatiotemporal structures from defect turbulence in the two-dimensional complex Ginzburg-Landau equation, Phys. Rev. E 100, 052210 (2019) 2470-0045 10.1103/PhysRevE.100.052210.