Harnessing density to control the duration of intermittent L\'evy walks in bacterial turbulence

Letter

Harnessing density to control the duration of intermittent Lévy walks in bacterial turbulence

Dhananjay Gautam, Hemlata Meena, Saravanan Matheshwaran, and Sivasurender Chandran

Phys. Rev. E 110, L012601 – Published 2 July 2024

Abstract

Dense bacterial suspensions display collective motion exhibiting coherent flow structures reminiscent of turbulent flows. However, in contrast to inertial turbulence, the microscopic dynamics underlying bacterial turbulence is only beginning to be understood. Here, we report experiments revealing correlations between microscopic dynamics and the emergence of collective motion in bacterial suspensions. Our results demonstrate the existence of three microscopic dynamical regimes: initial ballistic dynamics followed by an intermittent Lévy walk before the intriguing decay to random Gaussian fluctuations. Our experiments capture that the fluid correlation time earmarks the transition from Lévy to Gaussian fluctuations demonstrating the microscopic reason underlying the observation. By harnessing the flow activity via bacterial concentration, we reveal systematic control over the flow correlation timescales, which, in turn, allows controlling the duration of the Lévy walk.

Received 19 September 2023
Revised 8 March 2024
Accepted 29 May 2024

DOI:https://doi.org/10.1103/PhysRevE.110.L012601

Physics Subject Headings (PhySH)

Collective behavior Flocking Levy flights Swarming Turbulence

Active Brownian particles Bacteria Living matter & active matter

Physics of Living SystemsPolymers & Soft MatterStatistical Physics & ThermodynamicsInterdisciplinary PhysicsCondensed Matter, Materials & Applied PhysicsFluid Dynamics

Authors & Affiliations

Dhananjay Gautam ¹, Hemlata Meena ¹, Saravanan Matheshwaran ², and Sivasurender Chandran ^1,*

¹Soft and Biological Matter Laboratory, Department of Physics, Indian Institute of Technology, Kanpur-208016, India
²Department of Biological Sciences and Bioengineering, Indian Institute of Technology, Kanpur-208016, India

^*Contact author: schandran@iitk.ac.in

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Vol. 110, Iss. 1 — July 2024

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Figure 1
Microscopic dynamics underlying bacterial turbulence: (a) Mean velocities of the colloids ( ${\bar{v}}_{c}$ , closed circles) and the fluid ( ${\bar{v}}_{f}$ , open squares) vs bacterial concentration ( $c / c_{0}$ ). Inset: Eulerian two-dimensional velocity fields with overlaid streamlines for two different $c / c_{0}$ , as indicated by the arrows. Velocities are in the units of $µ m / s$ and the scale bar is 80 $µ m$ . At lower concentrations, specific regions display high velocities, indicating the bacteria movement in those locations. At higher concentrations, the velocity map displays larger regions of high activity, revealing the collective motion of bacteria. (b) Double logarithmic representation of ensemble-averaged mean-square displacements (MSDs, $〈 Δ r^{2} 〉$ ) of colloids as a function of time lag ( $Δ t$ ). Dashed lines are guides to the eyes with corresponding slopes. Temporal evolution of the exponents for suspensions with (c) $c \leq c_{c}$ and (d) $c > c_{c}$ , where $c_{c} = 10 c_{0}$ marks the concentration defining the transition from isolated to collective dynamics. The dashed black line in (c) and (d) corresponds to diffusive motion ( $α = 1$ ). The shaded region in (d) highlights the intermediate superdiffusive regime with a plateau at $α = α_{s}$ , where $1 < α_{s} < 2$ . Different symbols in (b)–(d) represent different concentrations of bacteria in the units of $c / c_{0}$ as defined in (b).
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Figure 2
Intermittent dynamics and Lévy walks manifest as bacterial turbulence: (a) Displacement ( $Δ r$ ) fluctuations normalized with a mean displacement ( $\bar{Δ r}$ ) display dips of more than an order of magnitude, revealing the intermittent nature of the dynamics. (b) Double logarithmic representation of the waiting-time ( $τ$ ) distribution of colloids for different bacterial concentrations, as defined in the respective legends in the units of $c / c_{0}$ . The continuous blue line represents the Gaussian fit, and the dashed black line corresponds to $τ^{- 8 / 3}$ . (c) $α_{s} + γ$ vs $c / c_{0}$ . Clearly, $α_{s} + γ \approx 3$ demonstrates the existence of the Lévy walks
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Figure 3
Harnessing density (activity) to control microscopic dynamics: (a) Semilogarithmic representation of time ( $Δ t$ ) dependent orientational correlation function $C_{θ θ}$ of colloidal trajectories, and (inset) velocity-velocity correlation $C_{vv}$ of the underlying fluid. Different symbols represent different bacterial concentrations as defined in the units of $c / c_{0}$ . Continuous lines are best fits to the data. (b) Persistent time of colloids ( $τ_{c}$ , closed circles) and flow correlation time ( $τ_{f}$ , open squares) as a function of $c / c_{0}$ . Inset: Compressed exponent ( $β_{c}, β_{f}$ ) vs $c / c_{0}$ . Dashed black lines are guides to the eyes. (c) Rescaled waiting-time distribution for the concentrations $c > c_{c}$ , where the $y$ axis is rescaled by $τ^{- γ - 1}$ , and the $x$ axis is normalized by correlation time ( $τ_{f}$ ) of underlying flow. The horizontal dashed line represents a zero-slope line. The vertical dashed line corresponds to $τ / τ_{f} = 1$ .
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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics

Harnessing density to control the duration of intermittent Lévy walks in bacterial turbulence

Dhananjay Gautam, Hemlata Meena, Saravanan Matheshwaran, and Sivasurender Chandran

Phys. Rev. E 110, L012601 – Published 2 July 2024

Abstract

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics

Harnessing density to control the duration of intermittent Lévy walks in bacterial turbulence

Dhananjay Gautam, Hemlata Meena, Saravanan Matheshwaran, and Sivasurender Chandran

Phys. Rev. E 110, L012601 – Published 2 July 2024

Abstract

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