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- W4383105668 abstract "Abstract This paper presents and explores a diffusion model that generalizes Brownian motion (BM). On the one hand, as BM: the model’s mean square displacement grows linearly in time, and the model is Gaussian and selfsimilar (with Hurst exponent <?CDATA $frac{1}{2}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> ). On the other hand, in sharp contrast to BM: the model is not Markov, its increments are not stationary, and its non-overlapping increments are not independent. Moreover, the model exhibits a host of statistical properties that are dramatically different than those of BM: aging and anti-aging, positive and negative momenta, correlated velocities, persistence and anti-persistence, aging Wiener–Khinchin spectra, and more. Conventionally, researchers resort to anomalous-diffusion models—e.g. fractional BM and scaled BM (both with Hurst exponents different than <?CDATA $frac{1}{2}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> )—to attain such properties. This model establishes that such properties are attainable well within the realm of diffusion. As it is seemingly Brownian yet highly non-Brownian, the model is termed Weird BM." @default.
- W4383105668 created "2023-07-05" @default.
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- W4383105668 date "2023-07-19" @default.
- W4383105668 modified "2023-09-26" @default.
- W4383105668 title "Weird Brownian motion" @default.
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- W4383105668 doi "https://doi.org/10.1088/1751-8121/ace406" @default.
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