Hyperballistic Superdiffusion and Explosive Solutions to the Non-Linear Diffusion Equation

Flekkøy, Eirik Grude; Hansen, Alex; Baldelli, Beatrice

doi:10.3389/fphy.2021.640560

Cited by 9 publications

(7 citation statements)

References 42 publications

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“…Anomalous diffusion has also been observed in granular systems, such as in the velocity profile of fluid-driven silo discharge [54], in granular gases near a shear instability [55], and in the height fluctuations in graphene [56]. In such cases, one often expects subdiffusive processes α < 1, whereas there are also cases where superdiffusion with α > 1 occurs, such as in Lévy flights, random acceleration processes, tracers in the turbulent flow, active particles with time-dependent self-propulsion forces, and in diffusion with density-dependent diffusivity [57][58][59][60][61][62]. For a review of theoretical models of anomalous diffusion, see, for example [63].…”

Section: When the Underlying Process Is Anomalousmentioning

confidence: 99%

Dynamics of inertial particles under velocity resetting

Olsen,

Löwen

2024

J. Stat. Mech.

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We investigate stochastic resetting in coupled systems involving two degrees of freedom, where only one variable is reset. The resetting variable, which we think of as hidden, indirectly affects the remaining observable variable via correlations. We derive the Fourier–Laplace transforms of the observable variable’s propagator and provide a recursive relation for all the moments, facilitating a comprehensive examination of the process. We apply this framework to inertial transport processes where we observe the particle position while the velocity is hidden and is being reset at a constant rate. We show that velocity resetting results in a linearly growing spatial mean squared displacement at later times, independently of reset-free dynamics, due to resetting-induced tempering of velocity correlations. General expressions for the effective diffusion and drift coefficients are derived as a function of the resetting rate. A non-trivial dependence on the rate may appear due to multiple timescales and crossovers in the reset-free dynamics. An extension that incorporates refractory periods after each reset is considered, where post-resetting pauses can lead to anomalous diffusive behavior. Our results are of relevance to a wide range of systems, such as inertial transport where the mechanical momentum is lost in collisions with the environment or the behavior of living organisms where stop-and-go locomotion with inertia is ubiquitous. Numerical simulations for underdamped Brownian motion and the random acceleration process confirm our findings.

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Section: When the Underlying Process Is Anomalousmentioning

confidence: 99%

Dynamics of inertial particles under velocity resetting

Olsen,

Löwen

2024

J. Stat. Mech.

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“…To sample the local concentration around particle i , we use a scheme similar to that in Ref. [ 40 ]. Here, a number of interaction partners

is introduced, along an associated volume

of a sphere that contains the

nearest neighbors.…”

Section: Simulation Modelmentioning

confidence: 99%

“…One way in which hyper-ballistic diffusion can appear is when the particle velocity is allowed to grow without bounds [ 40 ]. For normal Langevin systems, such behavior is not possible, since the fluctuation-dissipation theorem ensures a balance between the fluctuations driving the system and the dissipation.…”

Section: Introductionmentioning

confidence: 99%

Hyper-Ballistic Superdiffusion of Competing Microswimmers

Olsen,

Hansen,

Flekkøy

2024

Entropy

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Hyper-ballistic diffusion is shown to arise from a simple model of microswimmers moving through a porous media while competing for resources. By using a mean-field model where swimmers interact through the local concentration, we show that a non-linear Fokker–Planck equation arises. The solution exhibits hyper-ballistic superdiffusive motion, with a diffusion exponent of four. A microscopic simulation strategy is proposed, which shows excellent agreement with theoretical analysis.

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“…A rate equation model can describe such behavior by making the diffusion constant dependent on time or exciton density. [47,48] In materials such as organic semiconductors where there are multiple varieties of excitons, incorporating their interconversion into the rate equation can identify effects such as negative diffusion. [49] Additional phenomena could further exploit diffusion to improve performance.…”

Section: Nanophotonic Enhancement In Relevant Excitonic Materialsmentioning

confidence: 99%

Exciton Diffusion and Annihilation in Nanophotonic Purcell Landscapes

Raziman

Visser

Wang

et al. 2022

Advanced Optical Materials

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Hyperballistic Superdiffusion and Explosive Solutions to the Non-Linear Diffusion Equation

Cited by 9 publications

References 42 publications

Dynamics of inertial particles under velocity resetting

Dynamics of inertial particles under velocity resetting

Hyper-Ballistic Superdiffusion of Competing Microswimmers

Exciton Diffusion and Annihilation in Nanophotonic Purcell Landscapes

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