Nonequilibrium statistical description of anomalous diffusion

Wang, K. G.; Tokuyama, Michio

doi:10.1016/s0378-4371(98)00644-x

Cited by 156 publications

(137 citation statements)

References 22 publications

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“…Simulations based on the simplest model with magnetic and viscous forces showed good agreement with β = 1.82. Theoretical work using generalized Langevin and Fokker-Planck equations has predicted anomalous diffusion with β = 1.66 [25], in good agreement with our results. …”

Section: Braid Theory and Zipf Relation Used In Dynamics Of Magnetic supporting

confidence: 90%

Self-Assembly and Dynamics of Magnetic Holes

Skjeltorp

Akselvoll

Kristiansen

et al. 2004

Forces, Growth and Form in Soft Condensed Matter: At the Interface Between Physics and Biology

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Nonmagnetic particles in magnetized ferrofluids have been denoted magnetic holes and are in many ways ideal model systems to test various forms of particle self assembly and dynamics. Some case studies to be reviewed here include:• Chaining of magnetic holes • Braid theory and Zipf relation used in dynamics of magnetic microparticles • Interactions of magnetic holes in ferrofluid layersThe objectives of these works have been to find simple characterizations of complex behavior of particles with dipolar interactions.

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Section: Braid Theory and Zipf Relation Used In Dynamics Of Magnetic supporting

confidence: 90%

Self-Assembly and Dynamics of Magnetic Holes

Skjeltorp

Akselvoll

Kristiansen

et al. 2004

Forces, Growth and Form in Soft Condensed Matter: At the Interface Between Physics and Biology

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“…(c) Fractional Brownian motion (FBM) [33,36,37,61] (see [34,35,62] for reviews) and, more generally, diffusion associated with a generalized Langevin equation (GLE) [33,35,61,63,64]. This class is characterized by a complex environment (e.g., a polymer network) of which the probe particle is just one part, interacting with the rest in a complicated way.…”

Section: Appendix B: Degeneracy Problems In Diffusionmentioning

confidence: 99%

Probing the quantum nature of spacetime by diffusion

2013

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Many approaches to quantum gravity have resorted to diffusion processes to characterize the spectral properties of the resulting quantum spacetimes. We critically discuss these quantum-improved diffusion equations and point out that a crucial property, namely positivity of their solutions, is not preserved automatically. We then construct a novel set of diffusion equations with positive semidefinite probability densities, applicable to asymptotically safe gravity, Hořava-Lifshitz gravity and loop quantum gravity. These recover all previous results on the spectral dimension and shed further light on the structure of the quantum spacetimes by assessing the underlying stochastic processes. Pointing out that manifestly different diffusion processes lead to the same spectral dimension, we propose the probability distribution of the diffusion process as a refined probe of quantum spacetime.

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“…Mostly, a generalization of the equations of normal Brownian diffusion to fractional dynamics [16][17][18][19][20] is used. Particularly important role was played here by a concept of the continuous-time random walk [21][22][23][24][25], i.e.…”

Section: Theoretical Backgroundmentioning

confidence: 99%