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原文連結
論文資訊
- 類型：已發表論文
- 日期：2016-06-14
摘要
We introduce a generalized d-dimensional Fermi-Pasta-Ulam model in the presence of long-range interactions, and perform a first-principle study of its 混沌 for d = 1,2,3 through large-scale numerical simulations. The 非線性 interaction is assumed to decay algebraically as d(ij)(-alpha) (alpha >= 0), {d(ij)} being the distances between N oscillator sites. Starting from random initial conditions we compute the maximal 李雅普諾夫 exponent lambda(max) as a function of N. Our N >> 1 results strongly indicate that lambda(max) remains constant and positive for alpha/d > 1 (implying strong 混沌, mixing, and 遍歷ity), and that it vanishes like N (kappa) for 0 <= alpha/d < 1 (thus approaching weak 混沌 and opening the possibility of breakdown of 遍歷ity). The suitably rescaled exponent kappa exhibits universal 縮放律, n
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