Anomalous diffusion spreads its wings

By Joseph Klafter, Igor M. Sokolov. 2005

414 citations recorded by the source corpus.

Subfields: Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3cd1b2f028b08d4d645b6a7789c169d11575a68f

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In Statistical and Nonlinear Physics

Citations in the corpus

Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer (2007, neutral): “Akaike’s Information Criterion18, 19 (AIC) for modeli (i = 1, 2) is AICi = −2 log[Li(θ̂i|datax)] + 2Ki (9) whereθ̂1 = μ̂, θ̂2 = λ̂, andKi is the number of parameters being estimated for model i (K1 = K2 here).”
Fractional vector calculus for fractional advection–dispersion (2006, background): “Sokolov and Klafter [33] give a nice, brief overview of anomalous diffusion in physics.”
TEMPERED FRACTIONAL CALCULUS (2015, background): “Sokolov and Klafter [63] review the modern theory of anomalous diffusion, where the integer order derivatives in the diffusion equation are replaced by their fractional analogues: ∂ t p(x, t) = ∂α x p(x, t).”
A movement ecology paradigm for unifying organismal movement research (2008, methodology): “The prevailing approach in the random paradigm is characterized by simple phenomenological descriptions of movement paths and by null models related to the theories of random walk (2), diffusion (11), and anomalous diffusion (38).”
A BIRD’S EYE VIEW: TRACKING SLOW NANOMETER-SCALE MOVEMENTS OF SINGLE MOLECULAR NANO-ASSEMBLIES (2010, neutral): “as anomalous diffusion and are commonplace in nature (Klafter and Sokolov, 2005).”
A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations (2015, background): “Anomalous diffusion phenomena are ubiquitous in nature [29, 35]; among the several applications of these nonlocal models let us mention image processing [8, 22, 24, 32], finance [11, 13], electromagnetic fluids [34], peridynamics [42] and porous media flow [2, 14].”
Global well-posedness of slightly supercritical active scalar equations (2012, background): “This type of diffusion has many applications in the physical sciences, see for example [19] and the references therein.”