Papers
Topics
Authors
Recent
Search
2000 character limit reached

Diffusion of an Active Particle Bound to a Generalized Elastic Model: Fractional Langevin Equation

Published 24 Jan 2024 in cond-mat.soft, cond-mat.stat-mech, math-ph, and math.MP | (2401.13457v1)

Abstract: We investigate the influence of a self-propelling, out-of-equilibrium active particle on generalized elastic systems, including flexible and semiflexible polymers, fluid membranes, and fluctuating interfaces, while accounting for long-ranged hydrodynamic effects. We derive the fractional Langevin equation governing the dynamics of the active particle, as well as that of any other passive particle (or probe) bound to the elastic system. This equation demonstrates analytically how the active particle dynamics is influenced by the interplay of both the non-equilibrium force and of the viscoelastic environment. Our study explores the diffusional behavior emerging for both the active particle and a distant probe.The active particle undergoes three different surprising and counterintuitive regimes identified by the distinct dynamical time-scales: a pseudo-ballistic initial phase, a drastic decrease of the mobility and an asymptotic subdiffusive regime.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (130)
  1. Active particles in complex and crowded environments. Reviews of Modern Physics, 88(4):045006, 2016.
  2. Hydrodynamics of soft active matter. Reviews of modern physics, 85(3):1143, 2013.
  3. Physics of microswimmers—single particle motion and collective behavior: a review. Reports on progress in physics, 78(5):056601, 2015.
  4. Active brownian particles: From individual to collective stochastic dynamics. The European Physical Journal Special Topics, 202:1–162, 2012.
  5. Sriram Ramaswamy. The mechanics and statistics of active matter. Annu. Rev. Condens. Matter Phys., 1(1):323–345, 2010.
  6. Craig W Reynolds. Flocks, herds and schools: A distributed behavioral model. In Proceedings of the 14th annual conference on Computer graphics and interactive techniques, pages 25–34, 1987.
  7. Reza Olfati-Saber. Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE Transactions on automatic control, 51(3):401–420, 2006.
  8. Collective motion of self-propelled particles: Kinetic phase transition in one dimension. Physical Review Letters, 82(1):209, 1999.
  9. Statistical mechanics for natural flocks of birds. Proceedings of the National Academy of Sciences, 109(13):4786–4791, 2012.
  10. Scale-free correlations in starling flocks. Proceedings of the National Academy of Sciences, 107(26):11865–11870, 2010.
  11. Information transfer and behavioural inertia in starling flocks. Nature physics, 10(9):691–696, 2014.
  12. Uninformed individuals promote democratic consensus in animal groups. science, 334(6062):1578–1580, 2011.
  13. Collective animal behavior from bayesian estimation and probability matching. Nature Precedings, pages 1–1, 2011.
  14. Self-organization and collective behavior in vertebrates. Advances in the Study of Behavior, 32(1):10–1016, 2003.
  15. Howard C Berg. E. coli in Motion. Springer, 2004.
  16. Dance of the microswimmers. Physics Today, 65(9):30–35, 2012.
  17. E. coli superdiffusion and chemotaxis—search strategy, precision, and motility. Biophysical journal, 97(4):946–957, 2009.
  18. Particle diffusion in a quasi-two-dimensional bacterial bath. Physical review letters, 84(13):3017, 2000.
  19. Dynamics of enhanced tracer diffusion in suspensions of swimming eukaryotic microorganisms. Physical Review Letters, 103(19):198103, 2009.
  20. Experimental evidence of strong anomalous diffusion in living cells. Physical Review E, 81(2):020903, 2010.
  21. Memoryless self-reinforcing directionality in endosomal active transport within living cells. Nature Materials, 14(6):589–593, 2015.
  22. Particle tracking in living cells: a review of the mean square displacement method and beyond. Rheologica Acta, 52:425–443, 2013.
  23. Random bursts determine dynamics of active filaments. Proceedings of the National Academy of Sciences, 112(34):10703–10707, 2015.
  24. Sedimentation and effective temperature of active colloidal suspensions. Physical Review Letters, 105(8):088304, 2010.
  25. Self-motile colloidal particles: from directed propulsion to random walk. Physical review letters, 99(4):048102, 2007.
  26. Microscopic artificial swimmers. Nature, 437(7060):862–865, 2005.
  27. Controlled swimming in confined fluids of magnetically actuated colloidal rotors. Physical review letters, 101(21):218304, 2008.
  28. Controlled propulsion of artificial magnetic nanostructured propellers. Nano letters, 9(6):2243–2245, 2009.
  29. Emergence of macroscopic directed motion in populations of motile colloids. Nature, 503(7474):95–98, 2013.
  30. Roberto Di Leonardo. Controlled collective motions. Nature materials, 15(10):1057–1058, 2016.
  31. Reconfiguring active particles by electrostatic imbalance. Nature materials, 15(10):1095–1099, 2016.
  32. Flagellar dynamics of chains of active janus particles fueled by an ac electric field. New Journal of Physics, 20(1):015002, 2018.
  33. Memory-less response and violation of the fluctuation-dissipation theorem in colloids suspended in an active bath. Scientific reports, 7(1):17588, 2017.
  34. How far from equilibrium is active matter? Physical review letters, 117(3):038103, 2016.
  35. Generalized energy equipartition in harmonic oscillators driven by active baths. Physical review letters, 113(23):238303, 2014.
  36. Motility-induced phase separation. Annu. Rev. Condens. Matter Phys., 6(1):219–244, 2015.
  37. Superdiffusion dominates intracellular particle motion in the supercrowded cytoplasm of pathogenic acanthamoeba castellanii. Scientific reports, 5(1):11690, 2015.
  38. Dynamics of formation of symmetrical patterns by chemotactic bacteria. Nature, 376(6535):49–53, 1995.
  39. Physical mechanisms for chemotactic pattern formation by bacteria. Biophysical journal, 74(4):1677–1693, 1998.
  40. Phase diagram of active brownian spheres: Crystallization and the metastability of motility-induced phase separation. Physical review letters, 126(18):188002, 2021.
  41. Active turbulence. Annual Review of Condensed Matter Physics, 13:143–170, 2022.
  42. Steady-state chemotaxis in escherichia coli. Physical review letters, 100(23):238101, 2008.
  43. J Tailleur and ME Cates. Statistical mechanics of interacting run-and-tumble bacteria. Physical review letters, 100(21):218103, 2008.
  44. Modeling the dynamics of a tracer particle in an elastic active gel. Physical Review E, 92(1):012716, 2015.
  45. Non-gaussian statistics for the motion of self-propelled janus particles: Experiment versus theory. Physical Review E, 88(3):032304, 2013.
  46. Active ornstein–uhlenbeck model for self-propelled particles with inertia. Journal of Physics: Condensed Matter, 34(3):035101, 2021.
  47. Dynamics of active particles with space-dependent swim velocity. Soft Matter, 18(7):1412–1422, 2022.
  48. Dynamics of active particles with translational and rotational inertia. Journal of Physics: Condensed Matter, 35(30):305101, 2023.
  49. Active particles driven by competing spatially dependent self-propulsion and external force. SciPost Physics, 13(3):065, 2022.
  50. Chain reconfiguration in active noise. Journal of Physics A: Mathematical and Theoretical, 49(19):195601, 2016.
  51. Actin gels. Current Opinion in Solid State and Materials Science, 2(3):350–357, 1997.
  52. Conformational properties of active semiflexible polymers. Polymers, 8(8):304, 2016.
  53. How does a flexible chain of active particles swell? The Journal of chemical physics, 142(12), 2015.
  54. Behavior of active filaments near solid-boundary under linear shear flow. Soft Matter, 15(19):4008–4018, 2019.
  55. Facilitation of polymer looping and giant polymer diffusivity in crowded solutions of active particles. New Journal of Physics, 17(11):113008, 2015.
  56. Enhanced diffusion, swelling, and slow reconfiguration of a single chain in non-gaussian active bath. The Journal of chemical physics, 150(9), 2019.
  57. Active particles with soft and curved walls: Equation of state, ratchets, and instabilities. Physical review letters, 117(9):098001, 2016.
  58. Activity-induced collapse and reexpansion of rigid polymers. Physical Review E, 90(6):062312, 2014.
  59. Nonthermal atp-dependent fluctuations contribute to the in vivo motion of chromosomal loci. Proceedings of the National Academy of Sciences, 109(19):7338–7343, 2012.
  60. Loss of lamin a function increases chromatin dynamics in the nuclear interior. Nature communications, 6(1):8044, 2015.
  61. Transient anomalous diffusion of telomeres in the nucleus of mammalian cells. Physical review letters, 103(1):018102, 2009.
  62. Actin-network architecture regulates microtubule dynamics. Current Biology, 28(16):2647–2656, 2018.
  63. Spontaneous motion in hierarchically assembled active matter. Nature, 491(7424):431–434, 2012.
  64. Chemically cross-linked microtubule assembly shows enhanced dynamic motions on kinesins. RSC Advances, 4(62):32953–32959, 2014.
  65. Anomalous dynamics of the endoplasmic reticulum network. Physical Review E, 98(1):012406, 2018.
  66. Structure and dynamics of er: minimal networks and biophysical constraints. Biophysical Journal, 107(3):763–772, 2014.
  67. Nonequilibrium mechanics of active cytoskeletal networks. Science, 315(5810):370–373, 2007.
  68. Dynamics in steady state in vitro acto-myosin networks. Journal of Physics: Condensed Matter, 29(16):163002, 2017.
  69. Scale dependence of the mechanics of active gels with increasing motor concentration. Soft matter, 13(40):7352–7359, 2017.
  70. Actomyosin dynamics drive local membrane component organization in an in vitro active composite layer. Proceedings of the National Academy of Sciences, 113(12):E1645–E1654, 2016.
  71. Viscoelastic properties and dynamics of porcine gastric mucin. Biomacromolecules, 6(3):1329–1333, 2005.
  72. A rheological study of the association and dynamics of muc5ac gels. Biomacromolecules, 18(11):3654–3664, 2017.
  73. Mussel-inspired contact-active antibacterial hydrogel with high cell affinity, toughness, and recoverability. Advanced Functional Materials, 29(1):1805964, 2019.
  74. Non-gaussian, non-ergodic, and non-fickian diffusion of tracers in mucin hydrogels. Soft Matter, 15(12):2526–2551, 2019.
  75. Enhanced diffusion in active intracellular transport. Physical Review Letters, 85(26):5655, 2000.
  76. In vivo anomalous diffusion and weak ergodicity breaking of lipid granules. Physical review letters, 106(4):048103, 2011.
  77. Non-gaussian athermal fluctuations in active gels. Soft Matter, 7(7):3234–3239, 2011.
  78. Tunable dynamics of microtubule-based active isotropic gels. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 372(2029):20140142, 2014.
  79. Tuning the permeability of dense membranes by shaping nanoscale potentials. Physical review letters, 122(10):108001, 2019.
  80. Real-time single-molecule imaging of the infection pathway of an adeno-associated virus. Science, 294(5548):1929–1932, 2001.
  81. Sliding movement of single actin filaments on one-headed myosin filaments. Nature, 326(6115):805–808, 1987.
  82. Subdiffusion and anomalous local viscoelasticity in actin networks. Physical review letters, 77(21):4470, 1996.
  83. Anomalous diffusion probes microstructure dynamics of entangled f-actin networks. Physical review letters, 92(17):178101, 2004.
  84. Actin, a central player in cell shape and movement. science, 326(5957):1208–1212, 2009.
  85. Neuronal messenger ribonucleoprotein transport follows an aging lévy walk. Nature communications, 9(1):1–8, 2018.
  86. Bio-microrheology: a frontier in microrheology. Biophysical journal, 91(11):4296–4305, 2006.
  87. Claire Wilhelm. Out-of-equilibrium microrheology inside living cells. Physical review letters, 101(2):028101, 2008.
  88. Active transport on disordered microtubule networks: The generalized random velocity model. Physical Review E, 78(5):051912, 2008.
  89. Rapid telomere motions in live human cells analyzed by highly time-resolved microscopy. Epigenetics & chromatin, 1(1):1–19, 2008.
  90. Non-equilibrium forces drive the anomalous diffusion of telomeres in the nucleus of mammalian cells. New Journal of Physics, 19(11):113048, 2017.
  91. Effects of transcription-dependent physical perturbations on the chromosome dynamics in living cells. Frontiers in Cell and Developmental Biology, 10:822026, 2022.
  92. Formulation of chromatin mobility as a function of nuclear size during c. elegans embryogenesis using polymer physics theories. Physical Review Letters, 128(17):178101, 2022.
  93. Formation of membrane networks in vitro by kinesin-driven microtubule movement. The Journal of cell biology, 107(6):2233–2241, 1988.
  94. Antina Ghosh and NS Gov. Dynamics of active semiflexible polymers. Biophysical journal, 107(5):1065–1073, 2014.
  95. Self-propelled worm-like filaments: spontaneous spiral formation, structure, and dynamics. Soft matter, 11(36):7181–7190, 2015.
  96. Dynamics of self-propelled filaments pushing a load. Soft Matter, 12(41):8495–8505, 2016.
  97. Abhrajit Laskar and R Adhikari. Filament actuation by an active colloid at low reynolds number. New Journal of Physics, 19(3):033021, 2017.
  98. Flow-induced helical coiling of semiflexible polymers in structured microchannels. Physical review letters, 109(17):178101, 2012.
  99. Unusual swelling of a polymer in a bacterial bath. The Journal of chemical physics, 141(4), 2014.
  100. Configuration dynamics of a flexible polymer chain in a bath of chiral active particles. The Journal of chemical physics, 151(17), 2019.
  101. Motion transition of active filaments: Rotation without hydrodynamic interactions. Soft Matter, 10(7):1012–1017, 2014.
  102. Coarse-grained simulations of an active filament propelled by a self-generated solute gradient. Physical Review E, 93(3):032508, 2016.
  103. Crowding-activity coupling effect on conformational change of a semi-flexible polymer. Polymers, 11(6):1021, 2019.
  104. Dynamically generated patterns in dense suspensions of active filaments. Physical Review E, 97(2):022606, 2018.
  105. Globulelike conformation and enhanced diffusion of active polymers. Physical review letters, 121(21):217802, 2018.
  106. Collective dynamics of self-propelled semiflexible filaments. Soft matter, 14(22):4483–4494, 2018.
  107. How a local active force modifies the structural properties of polymers. Soft Matter, 16(10):2594–2604, 2020.
  108. Anomalous diffusion of active brownian particles cross-linked to a networked polymer: Langevin dynamics simulation and theory. Soft Matter, 16(40):9188–9201, 2020.
  109. Nonequilibrium diffusion of active particles bound to a semi-flexible polymer network: simulations and fractional langevin equation. arXiv preprint arXiv:2303.05851, 2023.
  110. Generalized elastic model yields a fractional langevin equation description. Physical review letters, 104(16):160602, 2010.
  111. Correlations in a generalized elastic model: Fractional langevin equation approach. Physical Review E, 82(6):061104, 2010.
  112. Bruno H Zimm. Dynamics of polymer molecules in dilute solution: viscoelasticity, flow birefringence and dielectric loss. The journal of chemical physics, 24(2):269–278, 1956.
  113. Fractional integrals and derivatives (theory and applications), 1993.
  114. Fractional kinetic equations: solutions and applications. Chaos: an interdisciplinary journal of nonlinear science, 7(4):753–764, 1997.
  115. Unusual response to a localized perturbation in a generalized elastic model. Physical Review E, 84(2):021101, 2011.
  116. Generalized elastic model: fractional langevin description, fluctuation relation and linear response. Mathematical Modelling of Natural Phenomena, 8(2):127–143, 2013.
  117. Alessandro Taloni et al. Kubo fluctuation relations in the generalized elastic model. Advances in Mathematical Physics, 2016, 2016.
  118. Langevin dynamics driven by a telegraphic active noise. Frontiers in Physics, 7:143, 2019.
  119. Stefan G Samko. Fractional integrals and derivatives. Theory and applications, 1993.
  120. Igor Podlubny. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier, 1998.
  121. Handbook of mathematical functions with formulas, graphs, and mathematical tables, 1988.
  122. Table of integrals, series, and products. Academic press, 2014.
  123. Fractional brownian motions, fractional noises and applications. SIAM review, 10(4):422–437, 1968.
  124. Godfrey Harold Hardy. Divergent series, volume 334. American Mathematical Soc., 2000.
  125. Generalized elastic model: Thermal vs. non-thermal initial conditions—universal scaling, roughening, ageing and ergodicity. Europhysics Letters, 97(3):30001, 2012.
  126. Dynamics of active rouse chains. Soft matter, 13(5):963–968, 2017.
  127. Dino Osmanović. Properties of rouse polymers with actively driven regions. The Journal of chemical physics, 149(16), 2018.
  128. Active diffusion of model chromosomal loci driven by athermal noise. Soft Matter, 13(1):81–87, 2017.
  129. Debabrata Panja. Anomalous polymer dynamics is non-markovian: memory effects and the generalized langevin equation formulation. Journal of Statistical Mechanics: Theory and Experiment, 2010(06):P06011, 2010.
  130. Debabrata Panja. Generalized langevin equation formulation for anomalous polymer dynamics. Journal of Statistical Mechanics: Theory and Experiment, 2010(02):L02001, 2010.
Citations (2)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Authors (1)

  1. Alessandro Taloni 

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 2 tweets with 8 likes about this paper.

Sign Up for Free