Superuniversality of acceleration correlations for random walks on fractals

H. Nakanishi; Y. Meir; Y. Gefen; A. Aharony; P. Schofield

doi:10.1088/0305-4470/20/3/007

Superuniversality of acceleration correlations for random walks on fractals

H. Nakanishi, Y. Meir, Y. Gefen, A. Aharony, P. Schofield

Department of Physics

Research output: Contribution to journal › Article › peer-review

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Abstract

The acceleration-acceleration correlation function, K(t)=(a(t).a(0)) (a=d²r/dt², where r is the displacement), of a random walker on a fractal lattice is studied analytically and numerically on percolation clusters and on diffusion-limited aggregates at dimensions d=2,3. After t(>>1) discrete time steps, the authors find K(t)=A(t)/(r ²(t)), with A(t) approximately (-1)^t. At a fixed distance R from the origin they find the superuniversal law K(R) approximately R ^-2 on all fractals and for all d.

Original language	English
Article number	007
Pages (from-to)	L153-L158
Journal	Journal of Physics A: Mathematical and General
Volume	20
Issue number	3
DOIs	https://doi.org/10.1088/0305-4470/20/3/007
State	Published - 1 Dec 1987

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy

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abstract = "The acceleration-acceleration correlation function, K(t)=(a(t).a(0)) (a=d2r/dt2, where r is the displacement), of a random walker on a fractal lattice is studied analytically and numerically on percolation clusters and on diffusion-limited aggregates at dimensions d=2,3. After t(>>1) discrete time steps, the authors find K(t)=A(t)/(r 2(t)), with A(t) approximately (-1)t. At a fixed distance R from the origin they find the superuniversal law K(R) approximately R -2 on all fractals and for all d.",

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AU - Nakanishi, H.

AU - Meir, Y.

AU - Gefen, Y.

AU - Aharony, A.

AU - Schofield, P.

PY - 1987/12/1

Y1 - 1987/12/1

N2 - The acceleration-acceleration correlation function, K(t)=(a(t).a(0)) (a=d2r/dt2, where r is the displacement), of a random walker on a fractal lattice is studied analytically and numerically on percolation clusters and on diffusion-limited aggregates at dimensions d=2,3. After t(>>1) discrete time steps, the authors find K(t)=A(t)/(r 2(t)), with A(t) approximately (-1)t. At a fixed distance R from the origin they find the superuniversal law K(R) approximately R -2 on all fractals and for all d.

AB - The acceleration-acceleration correlation function, K(t)=(a(t).a(0)) (a=d2r/dt2, where r is the displacement), of a random walker on a fractal lattice is studied analytically and numerically on percolation clusters and on diffusion-limited aggregates at dimensions d=2,3. After t(>>1) discrete time steps, the authors find K(t)=A(t)/(r 2(t)), with A(t) approximately (-1)t. At a fixed distance R from the origin they find the superuniversal law K(R) approximately R -2 on all fractals and for all d.

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Superuniversality of acceleration correlations for random walks on fractals

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