pith. sign in

arxiv: 2511.13270 · v1 · submitted 2025-11-17 · ❄️ cond-mat.stat-mech · cond-mat.soft

Crossover dynamics and non-Gaussian fluctuations in inertial active chains

Manish Patel , Subhajit Paul , Debasish Chaudhuri This is my paper

Pith reviewed 2026-05-17 21:28 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.soft
keywords inertial active particlesactive matterchain dynamicsmean squared displacementnon-Gaussian fluctuationsGreen's functioncrossover regimeskurtosis
0
0 comments X

The pith

Inertial active particle chains display multiple dynamical crossovers and evolving non-Gaussian velocity statistics.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines one-dimensional chains of inertial active particles linked by harmonic springs. It derives exact expressions for the mean-squared displacement and the mean-squared change in velocity using a Green's function method. These expressions uncover a sequence of crossovers among ballistic, diffusive, and subdiffusive regimes whose locations depend on the persistence time of the active force, the interaction strength, and the inertial mass. Excess kurtosis is used to track non-Gaussian features that produce heavy-tailed, bounded, or bimodal velocity distributions at different times. The resulting scaling collapses of the probability distributions confirm that the same functional forms hold across wide ranges of parameters.

Core claim

A Green's function approach yields closed-form results for the mean-squared displacement and mean-squared change in velocity of an inertial active chain. The formulas exhibit multiple crossovers between ballistic, diffusive, and subdiffusive regimes together with explicit scaling prefactors and crossover times. Non-Gaussian character is quantified by the excess kurtosis, which evolves in time and signals distributions that can be heavy-tailed, of finite support, or bimodal. Time-dependent probability distributions collapse onto master curves within each regime.

What carries the argument

Green's function solution of the coupled underdamped Langevin equations for the chain with constant active force persistence and nearest-neighbor harmonic springs

If this is right

  • Explicit formulas give the locations of all crossover times in terms of the microscopic timescales of persistence, friction, inertia, and spring stiffness.
  • Excess kurtosis serves as a direct experimental observable that evolves from positive values indicating heavy tails to negative values indicating bimodality.
  • Probability distributions of position and velocity exhibit data collapse when properly rescaled inside each dynamical regime.
  • The same Green's function technique can be applied to other linear active systems to obtain exact statistics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The predicted crossovers should be visible in experiments with chains of colloidal particles or micro-robots driven by persistent forces.
  • Non-Gaussian signatures may persist even when the mean-squared displacement appears diffusive, offering a finer probe of activity.
  • Extensions to two or three dimensions or to disordered interaction strengths would test the robustness of the scaling picture.

Load-bearing premise

The analysis relies on linear harmonic interactions and constant active force persistence that permit exact solution via Green's functions without nonlinear effects.

What would settle it

Measuring the mean-squared displacement of a physical chain of inertial active particles and finding the sequence of power-law regimes with the predicted crossover times and scaling coefficients would support the derivation.

Figures

Figures reproduced from arXiv: 2511.13270 by Debasish Chaudhuri, Manish Patel, Subhajit Paul.

Figure 1
Figure 1. Figure 1: FIG. 1. Time evolution of MSCV ( [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. ( [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Velocity autocorrelation and spatial velocity correlations. ( [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Excess kurtosis for velocity and displacement, [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. ( [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. ( [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The late time probability distribution of change in velocity [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. ( [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Steady-state velocity distribution, [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: (b) shows the MSCV for various tagged particles l, with continuous lines representing the numerical integration of Eq. (I2). All tagged particles exhibit MSCV behavior similar to that of bulk particles, displaying a crossover from ballistic motion to late-time saturation. In contrast, under pinned boundary conditions, the MSD of boundary particles deviates from that of the bulk, as they are effectively co… view at source ↗
read the original abstract

We study the dynamics of inertial active particles in a one-dimensional chain with harmonic nearest-neighbor interactions, highlighting the interplay of persistence, interaction, and inertial timescales. Using a Green's function approach, we derive the mean-squared displacement (MSD) and mean-squared change in velocity (MSCV), revealing multiple crossovers between ballistic, diffusive, and subdiffusive regimes and providing analytic expressions for scaling coefficients and crossover times. Non-Gaussian deviations in active Brownian particles are captured through excess kurtosis, reflecting heavy-tailed, finite-support, or bimodal distributions that evolve systematically over time. Time-dependent probability distributions exhibit distinct data collapses within different temporal regimes, confirming the robustness of the scaling behavior. Overall, this framework connects multiparticle interactions to microscopic dynamics, revealing experimentally accessible signatures of inertia in active matter.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript studies inertial active particles in a one-dimensional harmonic chain, using a Green's function approach to derive analytic expressions for the mean-squared displacement (MSD) and mean-squared change in velocity (MSCV). It identifies multiple crossovers among ballistic, diffusive, and subdiffusive regimes, supplies scaling coefficients and crossover times, and examines non-Gaussian features via excess kurtosis together with time-dependent probability distributions that exhibit data collapses in distinct temporal windows.

Significance. If the derivations are complete, the work supplies closed-form results for second moments and explicit crossover times in an interacting inertial active system, which are useful for connecting microscopic persistence and inertia to observable dynamics. The emphasis on non-Gaussian signatures and data collapses adds value for experimental active-matter studies.

major comments (1)
  1. [non-Gaussian fluctuations / kurtosis analysis] Discussion of excess kurtosis and non-Gaussian deviations: the position is a linear functional of the active-force history, so the fourth cumulant that enters the excess kurtosis requires the four-time correlation function of the active force (e.g., telegraph or Ornstein-Uhlenbeck process) propagated through the Green's function. The manuscript re-uses the second-order noise spectrum without deriving or stating these higher-order correlators; this leaves the reported kurtosis expressions and associated data collapses without explicit justification.
minor comments (1)
  1. [Abstract] The abstract states that analytic expressions and data collapses are obtained; it would help to list the explicit scaling variables used for each collapse.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comment on the non-Gaussian analysis. We address the point below and will revise the manuscript to provide the requested explicit justification.

read point-by-point responses

  1. Referee: [non-Gaussian fluctuations / kurtosis analysis] Discussion of excess kurtosis and non-Gaussian deviations: the position is a linear functional of the active-force history, so the fourth cumulant that enters the excess kurtosis requires the four-time correlation function of the active force (e.g., telegraph or Ornstein-Uhlenbeck process) propagated through the Green's function. The manuscript re-uses the second-order noise spectrum without deriving or stating these higher-order correlators; this leaves the reported kurtosis expressions and associated data collapses without explicit justification.

    Authors: We agree that a rigorous derivation of the excess kurtosis must incorporate the four-time correlation functions of the active force. In the revised manuscript we will add an explicit derivation of these higher-order correlators for both the telegraph and Ornstein-Uhlenbeck active forces, show how they are propagated through the Green's function to obtain the fourth cumulant of the particle position, and thereby justify the reported kurtosis expressions together with the observed data collapses in the distinct temporal windows. This addition will be placed in the main text or a dedicated appendix without changing the physical conclusions. revision: yes

Circularity Check

0 steps flagged

Green's function derivations of MSD/MSCV and kurtosis are self-contained first-principles results

full rationale

The paper derives MSD and MSCV via Green's functions applied to the linear underdamped Langevin equations with harmonic springs and additive active forces. No quoted steps reduce any reported crossover time, scaling coefficient, or kurtosis expression to a fitted input or self-citation by construction. The reader's assessment confirms the expressions do not collapse to quantities defined by the same parameters they predict. Kurtosis is presented as capturing non-Gaussian features from the active force statistics, without evidence that fourth moments are obtained merely by reusing the second-order spectrum. The derivation chain remains independent of the target observables and does not invoke load-bearing self-citations or ansatzes smuggled from prior work by the same authors.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central results rest on standard linear Langevin dynamics for active particles plus harmonic interactions; no new entities are introduced.

axioms (2)
  • domain assumption The active force has constant magnitude and exponentially decaying direction correlations (standard active Brownian particle model).
    Invoked to close the equations of motion for the chain.
  • domain assumption Interactions are strictly nearest-neighbor harmonic springs in one dimension.
    Allows Green's function solution via linear algebra.

pith-pipeline@v0.9.0 · 5435 in / 1277 out tokens · 24556 ms · 2026-05-17T21:28:17.401701+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

61 extracted references · 61 canonical work pages · 2 internal anchors

  1. [1]

    Averaging over all particles yields ⟨∆v2⟩(t) = γ2v2 0τa π Z ∞ −∞ Bv(ω) 2[1−cos(ωt)] 1 +ω 2τ 2a dω,(11) whereB v(ω) encodes the frequency-dependent response of the chain

    Mean-squared change in velocity We characterize the velocity dynamics through the mean-squared change in velocity (MSCV), defined as Cv l,m(t) =⟨[v l(t)−v l(0)][vm(t)−v m(0)]⟩, which, forl=m, gives the MSCV of thel-th particle. Averaging over all particles yields ⟨∆v2⟩(t) = γ2v2 0τa π Z ∞ −∞ Bv(ω) 2[1−cos(ωt)] 1 +ω 2τ 2a dω,(11) whereB v(ω) encodes the fr...

    work page

  2. [2]

    Mean-squared displacement We analyze the mean-squared displacement (MSD) of particles in the chain, which serves as a key measure for characterizing the influence of interactions within the system. The interplay between particle interactions, activity, and inertia can lead to anomalous transport behaviors – such as subdiffusion and superdiffusion – in add...

    work page

  3. [3]

    tcoF2kBonyy83nDKk91sAWSeX9s=

    Spatio-temporal correlations The integral for finitetin Eq. (9) does not admit a closed-form expression, so we evaluate it numerically. Fig. 3(a) shows normalized velocity autocorrelation as a function of time for different parameters, compared with numerical simulations (symbols), showing good agreement. For the underdamped case (I), inertiaτm and the re...

    work page

  4. [4]

    Insets (i) – (iv) show the probability distributions of velocity changes, and insets (v) – (vi) those of displacements

    Solid lines correspond toτ abp = 0.05,τ k = 20, while dashed lines correspond toτ abp = 50, τk = 1. Insets (i) – (iv) show the probability distributions of velocity changes, and insets (v) – (vi) those of displacements. Insets (i), (iv), (v), and (vi) correspond to the blue-curve parameters:τ abp = 0.05,τ k = 20,τ m = 0.01, while (ii) and (iii) correspond...

    work page 2020

  5. [5]

    + z∗ 1 (z∗ 1 −z 1)(z∗ 1 −z 2)(z∗ 1 −z ∗ 2) = τ 2 k γ2 " 1 2τ 3/2 k ω3/2 p (ωτm −i)(4−ωτ k(ωτm −i)) + −1 2τ 3/2 k ω3/2 p (ωτm +i)(4−ωτ k(ωτm +i)) # .(D9) As it turns out, the above quantity is real and can be expressed in a more compact form as Bx(ω) = 1 γ2 Re " √τk ω3/2 p (ωτm −i)(4−ωτ k(ωτm −i)) # .(D10) To calculateB v(ω), we follow the same steps to wr...

    work page

  6. [6]

    1 1 −30 −20 −10 0 10 20 30 (a) ( b)

    work page

  7. [7]

    1 τm = 1 τm = 10 τm = 100 P (∆ v) ∆ v τk = 100 τk = 10 τk = 1 τk = 0

    1 1 −30 −20 −10 0 10 20 30 (a) ( b)τm = 0. 1 τm = 1 τm = 10 τm = 100 P (∆ v) ∆ v τk = 100 τk = 10 τk = 1 τk = 0. 1 P (∆ v) ∆ v FIG. 7. The late time probability distribution of change in velocityP(∆v) as a function of inertia (a) and interaction time scale (b). The parameter values were taken asτ k = 100 in (a) andτ m = 0.1 along withτ abp =τ a = 10, andv...

    work page

  8. [8]

    1 1 −10 0 10 (a) ( b)

    work page

  9. [9]

    1 τm = 1 τm = 10 τm = 100 P (v) v τk = 100 τk = 10 τk = 1 τk = 0

    1 1 −10 0 10 (a) ( b)τm = 0. 1 τm = 1 τm = 10 τm = 100 P (v) v τk = 100 τk = 10 τk = 1 τk = 0. 1 P (v) v FIG. 9. Steady-state velocity distribution,P(v), as a function of inertia (a) and interaction timescale (b). Parameters are τk = 100 in (a) andτ m = 0.1 in (b);τ abp =τ a = 10,v abp = √ 2v 0 = 10 in both panels. interactions. For small inertia or weak ...

    work page

  10. [10]

    Active Particles in Complex and Crowded Environments

    C. Bechinger, R. Di Leonardo, H. L¨ owen, C. Reichhardt, G. Volpe, and G. Volpe, Active Particles in Complex and Crowded Environments, Rev. Mod. Phys.88, 045006 (2016), 1602.00081. 17

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  11. [11]

    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)

    work page 2013

  12. [12]

    Romanczuk, M

    P. Romanczuk, M. B¨ ar, W. Ebeling, B. Lindner, and L. Schimansky-Geier, Active brownian particles: From individual to collective stochastic dynamics: From individual to collective stochastic dynamics, European Physical Journal: Special Topics202, 1–162 (2012)

    work page 2012

  13. [13]

    Ramaswamy, Active fluids, Nat

    S. Ramaswamy, Active fluids, Nat. Rev. Phys.1, 640 (2019)

    work page 2019

  14. [14]

    Reimann, Brownian motors: Noisy transport far from equilibrium, Physics Report361, 57 (2002), arXiv:0010237 [cond-mat]

    P. Reimann, Brownian motors: Noisy transport far from equilibrium, Physics Report361, 57 (2002), arXiv:0010237 [cond-mat]

    work page 2002

  15. [15]

    H. C. Berg and D. A. Brown, Chemotaxis in e coli analysed by 3d tracking, Nature239, 500–504 (1972)

    work page 1972

  16. [16]

    M. J. Schnitzer, Theory of continuum random walks and application to chemotaxis, Physical Review E48, 2553–2568 (1993)

    work page 1993

  17. [17]

    J. R. Howse, R. A. L. Jones, A. J. Ryan, T. Gough, R. Vafabakhsh, and R. Golestanian, Self-motile colloidal particles: From directed propulsion to random walk, Physical Review Letters99, 048102 (2007)

    work page 2007

  18. [18]

    M. E. Cates and J. Tailleur, When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation, Europhys. Lett. , 200101206.1805

    work page internal anchor Pith review Pith/arXiv arXiv

  19. [19]

    Szamel, Self-propelled particle in an external potential: Existence of an effective temperature, Phys

    G. Szamel, Self-propelled particle in an external potential: Existence of an effective temperature, Phys. Rev. E90, 012111 (2014)

    work page 2014

  20. [20]

    Fodor, C

    E. Fodor, C. Nardini, M. E. Cates, J. Tailleur, P. Visco, and F. van Wijland, How far from equilibrium is active matter?, Phys. Rev. Lett.117, 038103 (2016)

    work page 2016

  21. [21]

    Vicsek, A

    T. Vicsek, A. Czir´ ok, E. Ben-Jacob, I. Cohen, and O. Shochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett.75, 1226 (1995)

    work page 1995

  22. [22]

    Tailleur and M

    J. Tailleur and M. E. Cates, Statistical mechanics of interacting run-and-tumble bacteria, Phys. Rev. Lett.100, 218103 (2008)

    work page 2008

  23. [23]

    Fily and M

    Y. Fily and M. Marchetti, Athermal phase separation of self-propelled particles with no alignment, Physical Review Letters 108, 235702 (2012)

    work page 2012

  24. [24]

    M. E. Cates and J. Tailleur, Motility-induced phase separation, Annual Review of Condensed Matter Physics6, 219 (2015)

    work page 2015

  25. [25]

    Kurzthaler, C

    C. Kurzthaler, C. Devailly, J. Arlt, T. Franosch, W. C. K. Poon, V. A. Martinez, and A. T. Brown, Probing the spatiotem- poral dynamics of catalytic janus particles with single-particle tracking and differential dynamic microscopy, Phys. Rev. Lett.121, 078001 (2018)

    work page 2018

  26. [26]

    Scholz, S

    C. Scholz, S. Jahanshahi, A. Ldov, and H. L¨ owen, Inertial delay of self-propelled particles, Nature Communications9, 5156 (2018)

    work page 2018

  27. [27]

    Leoni, M

    M. Leoni, M. Paoluzzi, S. Eldeen, A. Estrada, L. Nguyen, M. Alexandrescu, K. Sherb, and W. W. Ahmed, Surfing and crawling macroscopic active particles under strong confinement: Inertial dynamics, Phys. Rev. Res.2, 043299 (2020)

    work page 2020

  28. [28]

    Dauchot and V

    O. Dauchot and V. D´ emery, Dynamics of a self-propelled particle in a harmonic trap, Phys. Rev. Lett.122, 068002 (2019)

    work page 2019

  29. [29]

    Tapia-Ignacio, L

    C. Tapia-Ignacio, L. L. Gutierrez-Martinez, and M. Sandoval, Trapped active toy robots: theory and experiment, Journal of Statistical Mechanics: Theory and Experiment2021, 053404 (2021)

    work page 2021

  30. [30]

    H. L. Devereux, C. R. Twomey, M. S. Turner, and S. Thutupalli, Whirligig beetles as corralled active brownian particles, Journal of The Royal Society Interface18, 20210114 (2021)

    work page 2021

  31. [31]

    Mukundarajan, T

    H. Mukundarajan, T. C. Bardon, D. H. Kim, and M. Prakash, Surface tension dominates insect flight on fluid interfaces, J. Exp. Biol.219, 752 (2016)

    work page 2016

  32. [32]

    Rabault, R

    J. Rabault, R. A. Fauli, and A. Carlson, Curving to Fly: Synthetic Adaptation Unveils Optimal Flight Performance of Whirling Fruits, Phys. Rev. Lett.122, 24501 (2019)

    work page 2019

  33. [33]

    Mandal, B

    S. Mandal, B. Liebchen, and H. L¨ owen, Motility-induced temperature difference in coexisting phases, Physical Review Letters123, 228001 (2019)

    work page 2019

  34. [34]

    L¨ owen, Inertial effects of self-propelled particles: From active brownian to active langevin motion, The Journal of Chemical Physics152, 040901 (2020)

    H. L¨ owen, Inertial effects of self-propelled particles: From active brownian to active langevin motion, The Journal of Chemical Physics152, 040901 (2020)

    work page 2020

  35. [35]

    Patel and D

    M. Patel and D. Chaudhuri, Exact moments and re-entrant transitions in the inertial dynamics of active brownian particles, New Journal of Physics25, 123048 (2023)

    work page 2023

  36. [36]

    Fazelzadeh, E

    M. Fazelzadeh, E. Irani, Z. Mokhtari, and S. Jabbari-Farouji, Effects of inertia on conformation and dynamics of tangentially driven active filaments, Phys. Rev. E108, 024606 (2023)

    work page 2023

  37. [37]

    Patel and D

    M. Patel and D. Chaudhuri, Exact moments for trapped active particles: inertial impact on steady-state properties and re-entrance, New Journal of Physics26, 073048 (2024)

    work page 2024

  38. [38]

    Dutta, A

    D. Dutta, A. Kundu, S. Sabhapandit, and U. Basu, Harmonically trapped inertial run-and-tumble particle in one dimension, Phys. Rev. E110, 044107 (2024)

    work page 2024

  39. [39]

    Karan, A

    C. Karan, A. Chaudhuri, and D. Chaudhuri, Inertia and activity: spiral transitions in semi-flexible, self-avoiding polymers, Soft Matter20, 6221 (2024)

    work page 2024

  40. [40]

    S. S. Khali, F. Peruani, and D. Chaudhuri, When an active bath behaves as an equilibrium one, Phys. Rev. E109, 024120 (2024)

    work page 2024

  41. [41]

    Dutta, A

    D. Dutta, A. Kundu, and U. Basu, Inertial dynamics of run-and-tumble particle, Chaos: An Interdisciplinary Journal of Nonlinear Science35, 033109 (2025)

    work page 2025

  42. [42]

    Caprini and U

    L. Caprini and U. Marini Bettolo Marconi, Spatial velocity correlations in inertial systems of active brownian particles, Soft Matter17, 4109 (2021)

    work page 2021

  43. [43]

    Shankar and M

    S. Shankar and M. C. Marchetti, Hidden entropy production and work fluctuations in an ideal active gas, Phys. Rev. E 98, 020604 (2018). 18

    work page 2018

  44. [44]

    Chatterjee, N

    R. Chatterjee, N. Rana, R. A. Simha, P. Perlekar, and S. Ramaswamy, Inertia drives a flocking phase transition in viscous active fluids, Phys. Rev. X11, 031063 (2021)

    work page 2021

  45. [45]

    Caprini, R

    L. Caprini, R. K. Gupta, and H. L¨ owen, Role of rotational inertia for collective phenomena in active matter, Phys. Chem. Chem. Phys.24, 24910 (2022)

    work page 2022

  46. [46]

    collisions

    T. E. Harris, Diffusion with “collisions” between particles, Journal of Applied Probability2, 323 (1965)

    work page 1965

  47. [47]

    Kollmann, Single-file diffusion of atomic and colloidal systems: Asymptotic laws, Phys

    M. Kollmann, Single-file diffusion of atomic and colloidal systems: Asymptotic laws, Phys. Rev. Lett.90, 180602 (2003)

    work page 2003

  48. [48]

    C. Lutz, M. Kollmann, and C. Bechinger, Single-file diffusion of colloids in one-dimensional channels, Phys. Rev. Lett.93, 026001 (2004)

    work page 2004

  49. [49]

    A. B. Slowman, M. R. Evans, and R. A. Blythe, Exact solution of two interacting run-and-tumble random walkers with finite tumble duration, J. Phys. A: Math. Theor.50, 375601 (2017)

    work page 2017

  50. [50]

    A. Das, A. Dhar, and A. Kundu, Gap statistics of two interacting run and tumble particles in one dimension, J. Phys. A: Math. Theor.53, 345003 (2020)

    work page 2020

  51. [51]

    P. L. Doussal, S. N. Majumdar, and G. Schehr, Noncrossing run-and-tumble particles on a line, Phys. Rev. E100, 012113 (2019)

    work page 2019

  52. [52]

    A. B. Slowman, M. R. Evans, and R. A. Blythe, Jamming and attraction of interacting run-and-tumble random walkers, Phys. Rev. Lett.116, 218101 (2016)

    work page 2016

  53. [53]

    Kourbane-Houssene, C

    M. Kourbane-Houssene, C. Erignoux, T. Bodineau, and J. Tailleur, Exact hydrodynamic description of active lattice gases, Phys. Rev. Lett.120, 268003 (2018)

    work page 2018

  54. [54]

    Dolai, A

    P. Dolai, A. Das, A. Kundu, C. Dasgupta, A. Dhar, and K. V. Kumar, Universal scaling in active single-file dynamics, Soft Matter16, 7077 (2020)

    work page 2020

  55. [55]

    Banerjee, R

    T. Banerjee, R. L. Jack, and M. E. Cates, Tracer dynamics in one dimensional gases of active or passive particles, J. Stat. Mech.: Theor. Expt. , 013209 (2022)

    work page 2022

  56. [56]

    Agranov, S

    T. Agranov, S. Ro, Y. Kafri, and V. Lecomte, Macroscopic fluctuation theory and current fluctuations in active lattice gases, SciPost Phys.14, 045 (2023)

    work page 2023

  57. [57]

    S. Paul, A. Dhar, and D. Chaudhuri, Dynamical crossovers and correlations in a harmonic chain of active particles, Soft Matter20, 8638 (2024)

    work page 2024

  58. [58]

    Singh and A

    P. Singh and A. Kundu, Crossover behaviours exhibited by fluctuations and correlations in a chain of active particles, J. Phys. A: Math. Theor.54, 305001 (2021)

    work page 2021

  59. [59]

    U. M. B. Marconi, H. L¨ owen, and L. Caprini, Active fluctuations in the harmonic chain: phonons, entropons and velocity correlations, Molecular Physics122, e2407009 (2024)

    work page 2024

  60. [60]

    Khatri, D

    D. Khatri, D. Ngo, and C. Daraio, Highly nonlinear solitary waves in chains of cylindrical particles, Granular Matter14, 63–69 (2012)

    work page 2012

  61. [61]

    Lin and C

    W.-H. Lin and C. Daraio, Wave propagation in one-dimensional microscopic granular chains, Physical Review E94, 052907 (2016)

    work page 2016