Loopy Lévy flights enhance tracer diffusion in active suspensions

  title={Loopy L{\'e}vy flights enhance tracer diffusion in active suspensions},
  author={Kiyoshi Kanazawa and Tomohiko G. Sano and Andrea Cairoli and Adrian Baule},
Brownian motion is widely used as a model of diffusion in equilibrium media throughout the physical, chemical and biological sciences. However, many real-world systems are intrinsically out of equilibrium owing to energy-dissipating active processes underlying their mechanical and dynamical features 1 . The diffusion process followed by a passive tracer in prototypical active media, such as suspensions of active colloids or swimming microorganisms 2 , differs considerably from Brownian motion… 
Rapid-prototyping a Brownian particle in an active bath.
A minimal model for experiment and theory covering the wide time and length scales of usual active matter systems and can be used as a stochastic dynamic simulator for Brownian objects in various active baths without mechanistic understanding.
Transport and diffusion enhancement in non-Gaussian correlated ratchets
Living cells are known to generate non-Gaussian active fluctuations that are significantly larger than thermal fluctuations owing to various metabolic activities. Understanding the effect of active
Colossal Brownian yet non-Gaussian diffusion in a periodic potential: Impact of nonequilibrium noise amplitude statistics.
The influence of nonequilibrium noise amplitude statistics on the colossal Brownian, yet non-Gaussian diffusion is investigated by investigating the tail of amplitude distribution, which impacts both the magnitude of diffusion amplification and the Gaussianity of the position and increments statistics.
Transport and Diffusion Enhancement in Experimentally Realized Non-Gaussian Correlated Ratchets.
It is found that occasional kicks of an active Brownian ratchet comprising a colloidal particle in an optically generated asymmetric periodic potential driven by non-Gaussian noise having finite-amplitude active bursts, each arriving at random and decaying exponentially, are more efficient for transport and diffusion enhancement of the particle.
Distribution and pressure of active Lévy swimmers under confinement
Many active matter systems are known to perform Lévy walks during migration or foraging. Such superdiffusive transport indicates long-range correlated dynamics. These behavior patterns have been
Anomalous Diffusion and Lévy Walks Distinguish Active from Inertial Turbulence.
It is shown that such dense active suspensions manifest superdiffusion, via Lévy walks, which masquerades as a crossover from ballistic to diffusive scaling in measurements of mean-squared displacements, and is tied to the emergence of hitherto undetected oscillatory streaks in the flow.
Active carpets drive non-equilibrium diffusion and enhanced molecular fluxes
The enhanced diffusivity of molecules or passive particles are derived as a function of distance from an active carpet using Schnitzer's telegraph model and generalised Fick’s laws to elucidate certain non-equilibrium properties of active coating materials and life at interfaces.
Enhanced velocity fluctuations in interacting swimmer suspensions
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Extended Poisson-Kac theory: A unifying framework for stochastic processes with finite propagation velocity
Extended Poisson-Kac theory not only ensures by construction a mathematical representation of physical reality that is ontologically valid at all time and length scales, but also provides a toolbox of stochastic processes that can be used to model potentially any kind of finite velocity dynamical phenomena observed experimentally.
Optimization identification of superdiffusion processes in biology: an algorithm for processing observational data and a self-similar solution of the kinetic equation
The approximate self-similar solution for the parameters of step-length PDF and T is shown to provide reasonable accuracy of the space-time evolution of migrant's density.


Enhanced diffusion of tracer particles in dilute bacterial suspensions.
It is demonstrated that the effective diffusion coefficient is a product of the bacterial number density, their swimming speed, a geometric factor characterising the velocity field created by a single bacterium, and a numerical factor, and that these dependencies have to be taken into account to quantitatively predict the enhanced diffusivity.
Swimmer-tracer scattering at low Reynolds number
Understanding the stochastic dynamics of tracer particles in active fluids is important for identifying the physical properties of flow generating objects such as colloids, bacteria or algae. Here,
Lévy fluctuations and mixing in dilute suspensions of algae and bacteria
A systematic theoretical description of anomalous tracer diffusion in active suspensions is developed, based on a simplified tracer-swimmer interaction model that captures the typical distance scaling of a microswimmer's flow field and shows that the experimentally observed non-Gaussian tails are generic and arise owing to a combination of truncated Lévy statistics for the velocity field and algebraically decaying time correlations in the fluid.
Non-Gaussian limit fluctuations in active swimmer suspensions.
It is shown that the non-Gaussian shape of the observed distribution obeys the analytic theory concomitantly with independently determined parameters such as the strength of force generations and the concentration of Chlamydomonas.
Enhancement of biomixing by swimming algal cells in two-dimensional films
This work investigates the mixing produced by swimming unicellular algal cells in quasi-two-dimensional liquid films by simultaneously tracking the motion of the cells and that of microscopic passive tracer particles advected by the fluid.
Induced diffusion of tracers in a bacterial suspension: theory and experiments
Abstract The induced diffusion of tracers in a bacterial suspension is studied theoretically and experimentally at low bacterial concentrations. Considering the swimmer–tracer hydrodynamic
Dynamics of enhanced tracer diffusion in suspensions of swimming eukaryotic microorganisms.
The role of flagellar beating in creating oscillatory flows that exceed brownian motion far from each swimmer is emphasized, with a time-dependent but self-similar probability distribution function of displacements consisting of a gaussian core and robust exponential tails.
Fluid dynamics and noise in bacterial cell–cell and cell–surface scattering
Direct measurements of the bacterial flow field generated by individual swimming Escherichia coli both far from and near to a solid surface are reported, implying that physical interactions between bacteria are determined by steric collisions and near-field lubrication forces.
Distribution of particle displacements due to swimming microorganisms.
  • J. Thiffeault
  • Physics, Medicine
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2015
A simple model where the particles undergo repeated "kicks" due to the swimmers to explain the shape of the distribution as a function of the volume fraction of swimmers, and gives a criterion for convergence to a Gaussian distribution in terms of moments of the drift function.
Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities
A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean squared displacement, yet with a non-Gaussian