The relation between continued fractions and Berlekamp’s algorithm was studied by some reseachers. The latter is an iterative procedure proposed for decoding BCH codes. However, there remains an unanswered question w...The relation between continued fractions and Berlekamp’s algorithm was studied by some reseachers. The latter is an iterative procedure proposed for decoding BCH codes. However, there remains an unanswered question whether each of the iterative steps in the algorithm can be interpreted in terms of continued fractions. In this paper, we first introduce the so-called refined convergents to the continued fraction expansion of a binary sequence s, and then give a thorough answer to the question in the context of Massey’s linear feedback shift register synthesis algorithm which is equivalent to that of Berlekamp, and at last we prove that there exists a one- to-one correspondence between the n-th refined convergents and the length n segments.展开更多
Mixtures of binary spheres are numerically simulated using a relaxation algorithm to investigate the effects of volume fraction and size ratio, A complete profile of the packing properties of binary spheres is given. ...Mixtures of binary spheres are numerically simulated using a relaxation algorithm to investigate the effects of volume fraction and size ratio, A complete profile of the packing properties of binary spheres is given. The density curve with respect to the volume fraction has a triangular shape with a peak at 70% large spheres. The density of the mixture increases with the size ratio, but the growth becomes slow in the case of a large size disparity, The volume fraction and size ratio effects are reflected in the height and movement, respectively, of specific peaks in the radial distribution functions. The structure of the mixture is further analyzed in terms of contact types, and the mean coordination number is demonstrated to be primarily affected by ＂large-small＂ contacts. A novel method for estimating the average relative excluded volume for binary spheres by weighting the percentages of contact types is proposed and extended to polydisperse packings of certain size distributions. The method can be applied to explain the density trends of polydisperse mixtures in disordered sphere systems,展开更多
Towards the development of a predictive model for computing the minimum fluidization velocity, the volume-contraction phenomenon arising from the mixing of unequal solid species is accounted for in the prediction of t...Towards the development of a predictive model for computing the minimum fluidization velocity, the volume-contraction phenomenon arising from the mixing of unequal solid species is accounted for in the prediction of the bed void fraction of binary-solid mixtures at the incipient fluidization conditions. Com- parison with experimental data obtained from the literature clearly shows that significantly improved predictions are obtained except for cases where the stratification pattern whether arising from the slow defluidization or the difference in the densities of the two species affects the mixing of the constituent species.展开更多
文摘The relation between continued fractions and Berlekamp’s algorithm was studied by some reseachers. The latter is an iterative procedure proposed for decoding BCH codes. However, there remains an unanswered question whether each of the iterative steps in the algorithm can be interpreted in terms of continued fractions. In this paper, we first introduce the so-called refined convergents to the continued fraction expansion of a binary sequence s, and then give a thorough answer to the question in the context of Massey’s linear feedback shift register synthesis algorithm which is equivalent to that of Berlekamp, and at last we prove that there exists a one- to-one correspondence between the n-th refined convergents and the length n segments.
基金supported by the National Natural Science Foundation of China(Grant No.11272010)the National Basic Research Program of China(Grant No.2010CB832701)
文摘Mixtures of binary spheres are numerically simulated using a relaxation algorithm to investigate the effects of volume fraction and size ratio, A complete profile of the packing properties of binary spheres is given. The density curve with respect to the volume fraction has a triangular shape with a peak at 70% large spheres. The density of the mixture increases with the size ratio, but the growth becomes slow in the case of a large size disparity, The volume fraction and size ratio effects are reflected in the height and movement, respectively, of specific peaks in the radial distribution functions. The structure of the mixture is further analyzed in terms of contact types, and the mean coordination number is demonstrated to be primarily affected by ＂large-small＂ contacts. A novel method for estimating the average relative excluded volume for binary spheres by weighting the percentages of contact types is proposed and extended to polydisperse packings of certain size distributions. The method can be applied to explain the density trends of polydisperse mixtures in disordered sphere systems,
基金supported by the SABIC grant (Project ENG-3034),King Saud University,Riyadh
文摘Towards the development of a predictive model for computing the minimum fluidization velocity, the volume-contraction phenomenon arising from the mixing of unequal solid species is accounted for in the prediction of the bed void fraction of binary-solid mixtures at the incipient fluidization conditions. Com- parison with experimental data obtained from the literature clearly shows that significantly improved predictions are obtained except for cases where the stratification pattern whether arising from the slow defluidization or the difference in the densities of the two species affects the mixing of the constituent species.
