Anomalous diffusion in asymmetric random walks with a quasi-geostrophic flow example Export

@article{weeks96, abstract = {We present a model of one-dimensional symmetric and asymmetric random walks. The model is applied to an experiment studying fluid transport in a rapidly rotating annulus. In the model, random walkers alternate between flights (steps of constant velocity) and sticking (pauses between flights). Flight time and sticking time probability distribution functions (PDFs) have power law decays: P(t) \~{} t-[mu] and t-[nu] for flights and sticking, respectively. We calculate the dependence of the variance exponent [gamma] ([sigma]2 \~{} t[gamma]) on the PDF exponents [mu] and [nu]. For a broad distribution of flight times ([mu] < 3), the motion is superdiffusive (1 < [gamma] < 2), and the PDF has a divergent second moment, i.e., it is a L\'{e}vy distribution. For a broad distribution of sticking times ([nu] < 3), either superdiffusion or subdiffusion ([gamma] < 1) can occur, with qualitative differences between symmetric and asymmetric walks. For narrow PDFs ([mu] > 3, [nu] > 3), normal diffusion ([gamma] = 1) is recovered. Predictions of the model are related to experimental observations of transport in a rotating annulus. The Eulerian velocity field is chaotic, yet it is still possible to distinguish between well-defined sticking events (particles trapped in vortices) and flights (particles making long excursions in a jet). The distribution of flight lengths is well described by a power law with a divergent second moment (L\'{e}vy distribution). The observed transport is strongly asymmetric and is well described by the proposed model.}, author = {Weeks, Eric R. and Urbach, J. S. and Swinney, Harry L.}, citeulike-article-id = {2895021}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/0167-2789(96)00082-6}, citeulike-linkout-1 = {http://www.sciencedirect.com/science/article/B6TVK-3VSFD4S-1W/1/02d491964c9ff322bbf59327877788ec}, day = {1}, doi = {10.1016/0167-2789(96)00082-6}, journal = {Physica D: Nonlinear Phenomena}, keywords = {anomalous-diffusion, geostrophic, levy-flights}, month = {October}, number = {1-3}, pages = {291--310}, posted-at = {2008-06-14 21:28:29}, priority = {0}, title = {Anomalous diffusion in asymmetric random walks with a quasi-geostrophic flow example}, url = {http://dx.doi.org/10.1016/0167-2789(96)00082-6}, volume = {97}, year = {1996} }

TY - JOUR ID - weeks96 L3 - citeulike-article-id:2895021 N2 - We present a model of one-dimensional symmetric and asymmetric random walks. The model is applied to an experiment studying fluid transport in a rapidly rotating annulus. In the model, random walkers alternate between flights (steps of constant velocity) and sticking (pauses between flights). Flight time and sticking time probability distribution functions (PDFs) have power law decays: P(t) ~ t-[mu] and t-[nu] for flights and sticking, respectively. We calculate the dependence of the variance exponent [gamma] ([sigma]2 ~ t[gamma]) on the PDF exponents [mu] and [nu]. For a broad distribution of flight times ([mu] < 3), the motion is superdiffusive (1 < [gamma] < 2), and the PDF has a divergent second moment, i.e., it is a Lévy distribution. For a broad distribution of sticking times ([nu] < 3), either superdiffusion or subdiffusion ([gamma] < 1) can occur, with qualitative differences between symmetric and asymmetric walks. For narrow PDFs ([mu] > 3, [nu] > 3), normal diffusion ([gamma] = 1) is recovered. Predictions of the model are related to experimental observations of transport in a rotating annulus. The Eulerian velocity field is chaotic, yet it is still possible to distinguish between well-defined sticking events (particles trapped in vortices) and flights (particles making long excursions in a jet). The distribution of flight lengths is well described by a power law with a divergent second moment (Lévy distribution). The observed transport is strongly asymmetric and is well described by the proposed model. IS - 1-3 JF - Physica D: Nonlinear Phenomena EP - 310 TI - Anomalous diffusion in asymmetric random walks with a quasi-geostrophic flow example VL - 97 SP - 291 KW - anomalous-diffusion KW - geostrophic KW - levy-flights AU - Weeks, Eric AU - Urbach, JS AU - Swinney, Harry PY - 1996/10/01/ UR - http://dx.doi.org/10.1016/0167-2789(96)00082-6 ER -