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• W137048261 abstract "This paper presents an efficient group-theoretic approach for computing the statisticsof non-reversal random walks (NRRW) on lattices. These framed walks evolve on proper crystallographicspace groups. In a previous paper we introduced a convolution method for computingthe statistics of NRRWs in which the convolution product is defined relative to the space-groupoperation. Here we use the corresponding concept of the fast Fourier transform for functions oncrystallographic space groups together with a non-Abelian version of the convolution theorem. Wedevelop the theory behind this technique and present numerical results for two-dimensional andthree-dimensional lattices (square, cubic and diamond). In order to verify our results, the statisticsof the end-to-end distance and the probability of ring closure are calculated and compared withresults obtained in the literature for the random walks for which closed-form expressions exist." @default.
• W137048261 created "2016-06-24" @default.
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• W137048261 date "2010-04-30" @default.
• W137048261 modified "2023-09-23" @default.
• W137048261 title "Position and Orientation Distributions for Non-Reversal Random Walks using Space-Group Fourier Transforms" @default.
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• W137048261 doi "https://doi.org/10.18409/jas.v1i1.6" @default.
• W137048261 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/2965612" @default.
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