In this study, we regard written texts as time series data and try to investigate dynamic correlations of word occurrences by utilizing an autocorrelation function (ACF). After defining appropriate formula for the ACF...In this study, we regard written texts as time series data and try to investigate dynamic correlations of word occurrences by utilizing an autocorrelation function (ACF). After defining appropriate formula for the ACF that is suitable for expressing the dynamic correlations of words, we use the formula to calculate ACFs for frequent words in 12 books. The ACFs obtained can be classified into two groups: One group of ACFs shows dynamic correlations, with these ACFs well described by a modified Kohlrausch-Williams-Watts (KWW) function;the other group of ACFs shows no correlations, with these ACFs fitted by a simple stepdown function. A word having the former ACF is called a Type-I word and a word with the latter ACF is called a Type-II word. It is also shown that the ACFs of Type-II words can be derived theoretically by assuming that the stochastic process governing word occurrence is a homogeneous Poisson point process. Based on the fitting of the ACFs by KWW and stepdown functions, we propose a measure of word importance which expresses the extent to which a word is important in a particular text. The validity of the measure is confirmed by using the Kleinburg’s burst detection algorithm.展开更多
The stress relaxation of semi-crystalline nylon 1010 cannot be fitted by the Kohlrausch-Williams-Watts formula when the experiments were performed at pre-yielding regime below the glass transition temperature.We study...The stress relaxation of semi-crystalline nylon 1010 cannot be fitted by the Kohlrausch-Williams-Watts formula when the experiments were performed at pre-yielding regime below the glass transition temperature.We study this problem and identify the two-step mechanism of stress relaxation.At short time scale,relaxation is fast,dominated by stress biased thermal fluctuation with a fixed short-range length scale(activation volume).At long time scale,relaxation is slow due to the emergence of a cooperative long-range length scale determined by the stress fluctuation.The cooperative length scale is proportional to the reciprocal of stress and the amplitude of stress fluctuation is the product of stress and activation volume.Based on this two-step mechanism,we propose a new kinetics equation to capture the stress relaxation effectively,where the short time relaxation is described by an Eyring-like local activation and the long-time relaxation is captured by a cooperative excitation process resorting to an extension from the random first order transition theory.Our equation fits the experimental data well and can serve as a model to guide the related experiments of relaxation processes in crystalline solids.展开更多
文摘In this study, we regard written texts as time series data and try to investigate dynamic correlations of word occurrences by utilizing an autocorrelation function (ACF). After defining appropriate formula for the ACF that is suitable for expressing the dynamic correlations of words, we use the formula to calculate ACFs for frequent words in 12 books. The ACFs obtained can be classified into two groups: One group of ACFs shows dynamic correlations, with these ACFs well described by a modified Kohlrausch-Williams-Watts (KWW) function;the other group of ACFs shows no correlations, with these ACFs fitted by a simple stepdown function. A word having the former ACF is called a Type-I word and a word with the latter ACF is called a Type-II word. It is also shown that the ACFs of Type-II words can be derived theoretically by assuming that the stochastic process governing word occurrence is a homogeneous Poisson point process. Based on the fitting of the ACFs by KWW and stepdown functions, we propose a measure of word importance which expresses the extent to which a word is important in a particular text. The validity of the measure is confirmed by using the Kleinburg’s burst detection algorithm.
基金financially supported by the National Natural Science Foundation of China (Nos.21873054,21774131 and 21544007)the National Natural Science Foundation of China (Nos.U1862205 and 51673110)China Petroleum & Chemical Corporation for financial support。
文摘The stress relaxation of semi-crystalline nylon 1010 cannot be fitted by the Kohlrausch-Williams-Watts formula when the experiments were performed at pre-yielding regime below the glass transition temperature.We study this problem and identify the two-step mechanism of stress relaxation.At short time scale,relaxation is fast,dominated by stress biased thermal fluctuation with a fixed short-range length scale(activation volume).At long time scale,relaxation is slow due to the emergence of a cooperative long-range length scale determined by the stress fluctuation.The cooperative length scale is proportional to the reciprocal of stress and the amplitude of stress fluctuation is the product of stress and activation volume.Based on this two-step mechanism,we propose a new kinetics equation to capture the stress relaxation effectively,where the short time relaxation is described by an Eyring-like local activation and the long-time relaxation is captured by a cooperative excitation process resorting to an extension from the random first order transition theory.Our equation fits the experimental data well and can serve as a model to guide the related experiments of relaxation processes in crystalline solids.
