scholarly journals Lévy fluctuations and mixing in dilute suspensions of algae and bacteria

2011 ◽  
Vol 8 (62) ◽  
pp. 1314-1331 ◽  
Author(s):  
Irwin M. Zaid ◽  
Jörn Dunkel ◽  
Julia M. Yeomans
Keyword(s):  
Graphics Processing Units ◽  
Interaction Model ◽  
Tracer Diffusion ◽  
Theoretical Description ◽  
Active Suspensions ◽  
Tracer Particles ◽  
Dilute Suspensions ◽  
Nutrient Influx ◽  
Non Gaussian ◽  
Micro Organisms

Swimming micro-organisms rely on effective mixing strategies to achieve efficient nutrient influx. Recent experiments, probing the mixing capability of unicellular biflagellates, revealed that passive tracer particles exhibit anomalous non-Gaussian diffusion when immersed in a dilute suspension of self-motile Chlamydomonas reinhardtii algae. Qualitatively, this observation can be explained by the fact that the algae induce a fluid flow that may occasionally accelerate the colloidal tracers to relatively large velocities. A satisfactory quantitative theory of enhanced mixing in dilute active suspensions, however, is lacking at present. In particular, it is unclear how non-Gaussian signatures in the tracers' position distribution are linked to the self-propulsion mechanism of a micro-organism. Here, we develop a systematic theoretical description of anomalous tracer diffusion in active suspensions, based on a simplified tracer-swimmer interaction model that captures the typical distance scaling of a microswimmer's flow field. We show 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. Our analytical considerations are illustrated through extensive simulations, implemented on graphics processing units to achieve the large sample sizes required for analysing the tails of the tracer distributions.

scholarly journals Composition Effect on Shrinkage of Hollow Binary Alloy Nanospheres

2009 ◽  
Vol 289-292 ◽  
pp. 665-672 ◽  
Author(s):  
Alexander V. Evteev ◽  
Elena V. Levchenko ◽  
Irina V. Belova ◽  
Graeme E. Murch
Keyword(s):  
Steady State ◽  
Binary Alloy ◽  
Kinetic Monte Carlo ◽  
Geometric Mean ◽  
Tracer Diffusion ◽  
Theoretical Description ◽  
Radial Dependence ◽  
Atomic Fraction ◽  
Steady State Condition ◽  
Self Diffusion

In this paper, a hollow random binary alloy nanosphere and initially homogeneous is considered under the approximation that the radial dependence of the vacancy formation free energy can be neglected. On the basis of a theoretical description and kinetic Monte Carlo simulations it is shown that the steady-state condition for the atomic components is not achievable during its shrinkage at any composition when the ratio of the tracer diffusion coefficients is not greater than two orders of magnitude. In the theoretical description, the dependence of the collapse time of the hollow random binary alloy nanosphere on the atomic fraction of the faster diffusing species at can be estimated by using the geometric mean of the ratios of the atomic fluxes at self-diffusion and steady-state. At the ratio of the atomic fluxes approaches the self-diffusion ratio as increases.

Toward a more biologically accurate model of diffusion: adhesion and collisions

SIMULATION ◽  
2017 ◽  
Vol 93 (12) ◽  
pp. 1037-1044
Author(s):  
Ahmed M Fouad ◽  
John A Noel
Keyword(s):  
Large Scale ◽  
Particle Density ◽  
File Systems ◽  
Tracer Diffusion ◽  
Transport Processes ◽  
Average Particle ◽  
Diffusion Behavior ◽  
Single File ◽  
Tracer Particles ◽  
The One

In single-file dynamics, Brownian particles (referred to as tracer or tagged particles) diffuse and collide with each other in one-dimensional domains. If the average particle density is kept fixed during the diffusion, the collisions between the tracer particles result in their famous anomalous sub-diffusion behavior with time to the one half dependence. Many systems in nature are found to obey single-file dynamics, such as ion transport processes, and inter-particle adhesion plays a crucial role, either structurally or functionally, in the diffusion of such systems; however, the exact effect of adhesion on the diffusion has not been studied so far. We have examined the effect of adhesion on the collective diffusion of single-file systems. Here, we extend previous work where we perform large-scale numerical simulations that utilize Monte Carlo techniques and high-performance computing resources to examine the effect of adhesion on the diffusion of the tracer particles in systems that obey single-file dynamics. We show that if all the tracer particles experience the same adhesion coefficient, adhesion only slows down the diffusion by reducing the magnitude of the tracer diffusion coefficient; however, both the anomalous sub-diffusion behavior and time to the one half dependence of the tracer particles remain almost intact, independent of the adhesion.

scholarly journals Loopy Lévy flights enhance tracer diffusion in active suspensions

Nature ◽  
2020 ◽  
Vol 579 (7799) ◽  
pp. 364-367 ◽  
Author(s):  
Kiyoshi Kanazawa ◽  
Tomohiko G. Sano ◽  
Andrea Cairoli ◽  
Adrian Baule
Keyword(s):  
Tracer Diffusion ◽  
Lévy Flights ◽  
Active Suspensions ◽  
Levy Flights

scholarly journals Lagrangian Statistics of Heat Transfer in Homogeneous Turbulence Driven by Boussinesq Convection

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 127
Author(s):  
Jane Pratt ◽  
Angela Busse ◽  
Wolf-Christian Müller
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Turbulent Flows ◽  
Statistical Approach ◽  
Homogeneous Turbulence ◽  
Turbulent Convection ◽  
Clear Trend ◽  
Tracer Particles ◽  
Non Gaussian ◽  
Natural Settings

The movement of heat in a convecting system is typically described by the nondimensional Nusselt number, which involves an average over both space and time. In direct numerical simulations of turbulent flows, there is considerable variation in the contributions to the Nusselt number, both because of local spatial variations due to plumes and because of intermittency in time. We develop a statistical approach to more completely describe the structure of heat transfer, using an exit-distance extracted from Lagrangian tracer particles, which we call the Lagrangian heat structure. In a comparison between simulations of homogeneous turbulence driven by Boussinesq convection, the Lagrangian heat structure reveals significant non-Gaussian character, as well as a clear trend with Prandtl number and Rayleigh number. This has encouraging implications for simulations performed with the goal of understanding turbulent convection in natural settings such as Earth’s atmosphere and oceans, as well as planetary and stellar dynamos.

Migration of Ion Implanted Hydrogen in Amorphous and Polycrystalline Si3N4:H Films: Experiments and Numerical Simulations

2005 ◽  
Vol 237-240 ◽  
pp. 566-571 ◽  
Author(s):  
Harald Schmidt ◽  
Günter Borchardt
Keyword(s):  
Secondary Ion Mass Spectrometry ◽  
Tracer Diffusion ◽  
Dissociation Rate ◽  
Dangling Bonds ◽  
Exponential Factor ◽  
Implantation Damage ◽  
Computer Calculations ◽  
Effective Diffusivities ◽  
Non Gaussian ◽  
Ion Implanted

The tracer diffusion of ion implanted deuterium is studied in amorphous and polycrystalline magnetron-sputtered Si3N4:H films with secondary ion mass spectrometry (SIMS). The experimentally obtained diffusion profiles are numerically simulated by computer calculations based on the concept of trap-limited diffusion where the tracer atoms form immobile complexes with: (a) intrinsic film defects like dangling bonds and (b) extrinsic defects caused by the implantation damage. For amorphous Si3N4:H films a moderately high dissociation rate of intrinsic complexes (dangling bonds) is present and time independent effective diffusivities are observed, which obey an Arrhenius law with an activation energy of DE = 3.4 eV and a pre-exponential factor of D0 = 4 x 10-4 m2/s. For polycrystalline Si3N4 films non-Gaussian depth profiles and strongly time dependent diffusivities are observed, which have their reason in the presence of intrinsic traps with negligible dissociation, presumably located at the grain boundaries.

scholarly journals Anomalous tracer diffusion in hard-sphere suspensions

2021 ◽  
Author(s):  
Stephen Peppin
Keyword(s):  
Hard Sphere ◽  
Structural Heterogeneity ◽  
Tracer Diffusion ◽  
Host Matrix ◽  
Uphill Diffusion ◽  
Cross Diffusion ◽  
Coupled Equations ◽  
Tracer Particles ◽  
Sphere Suspensions ◽  
Matrix Concentration

Coupled equations describing diffusion and cross-diffusion of tracer particles in hard-sphere suspensions are derived and solved numerically. In concentrated systems with strong excluded volume and viscous interactions the tracer motion is subdiffusive. Cross diffusion generates transient perturbations to the host-particle matrix, which affect the motion of the tracer particles leading to nonlinear mean squared displacements. Above a critical host-matrix concentration the tracers experience clustering and uphill diffusion, moving in opposition to their own concentration gradient. A linear stability analysis indicates that cross diffusion can lead to unstable concentration fluctuations in the suspension. The instability is a potential mechanism for the appearance of dynamic and structural heterogeneity in suspensions near the glass transition.

scholarly journals Anomalous, non-Gaussian tracer diffusion in crowded two-dimensional environments

2016 ◽  
Vol 18 (1) ◽  
pp. 013027 ◽  
Author(s):  
Surya K Ghosh ◽  
Andrey G Cherstvy ◽  
Denis S Grebenkov ◽  
Ralf Metzler
Keyword(s):  
Tracer Diffusion ◽  
Two Dimensional ◽  
Non Gaussian

scholarly journals Tracer diffusion in active suspensions

2017 ◽  
Vol 95 (5) ◽  
Author(s):  
Eric W. Burkholder ◽  
John F. Brady
Keyword(s):  
Tracer Diffusion ◽  
Active Suspensions

scholarly journals Convective overshoot and macroscopic diffusion in pure-hydrogen-atmosphere white dwarfs

2019 ◽  
Vol 488 (2) ◽  
pp. 2503-2522 ◽  
Author(s):  
Tim Cunningham ◽  
Pier-Emmanuel Tremblay ◽  
Bernd Freytag ◽  
Hans-Günter Ludwig ◽  
Detlev Koester
Keyword(s):  
Diffusion Coefficients ◽  
White Dwarfs ◽  
Hydrogen Atmosphere ◽  
Theoretical Description ◽  
Time Variability ◽  
Pure Hydrogen ◽  
Temperature Range ◽  
Tracer Particles ◽  
Order Of Magnitude ◽  
Convective Overshoot

Abstract We present a theoretical description of macroscopic diffusion caused by convective overshoot in pure-hydrogen DA white dwarfs using 3D, closed-bottom, radiation hydrodynamics co5bold simulations. We rely on a new grid of deep 3D white dwarf models in the temperature range $11\, 400 \le T_{\mathrm{eff}} \le 18\, 000$ K where tracer particles and a tracer density are used to derive macroscopic diffusion coefficients driven by convective overshoot. These diffusion coefficients are compared to microscopic diffusion coefficients from 1D structures. We find that the mass of the fully mixed region is likely to increase by up to 2.5 orders of magnitude while inferred accretion rates increase by a more moderate order of magnitude. We present evidence that an increase in settling time of up to 2 orders of magnitude is to be expected, which is of significance for time-variability studies of polluted white dwarfs. Our grid also provides the most robust constraint on the onset of convective instabilities in DA white dwarfs to be in the effective temperature range from 18 000 to 18 250 K.

scholarly journals Learning the Macroscopic Flow Model of Short Fiber Suspensions from Fine-Scale Simulated Data

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 30
Author(s):  
Minyoung Yun ◽  
Clara Argerich Martin ◽  
Pierre Giormini ◽  
Francisco Chinesta ◽  
Suresh Advani
Keyword(s):  
Diffusion Mechanism ◽  
Interaction Model ◽  
Simulated Data ◽  
Short Fiber ◽  
Concentrated Suspensions ◽  
Fiber Concentration ◽  
Orientation State ◽  
Dilute Suspensions ◽  
Final Orientation ◽  
Fiber Interaction

Fiber–fiber interaction plays an important role in the evolution of fiber orientation in semi-concentrated suspensions. Flow induced orientation in short-fiber reinforced composites determines the anisotropic properties of manufactured parts and consequently their performances. In the case of dilute suspensions, the orientation evolution can be accurately described by using the Jeffery model; however, as soon as the fiber concentration increases, fiber–fiber interactions cannot be ignored anymore and the final orientation state strongly depends on the modeling of those interactions. First modeling frameworks described these interactions from a diffusion mechanism; however, it was necessary to consider richer descriptions (anisotropic diffusion, etc.) to address experimental observations. Even if different proposals were considered, none of them seem general and accurate enough. In this paper we do not address a new proposal of a fiber interaction model, but a data-driven methodology able to enrich existing models from data, that in our case comes from a direct numerical simulation of well resolved microscopic physics.

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