Artificial neural networks （ANNs） and genetic programming （GP） have recently been used for the estimation of hydraulic data. In this study, they were used as alternative tools to estimate the characteristics of hy...Artificial neural networks （ANNs） and genetic programming （GP） have recently been used for the estimation of hydraulic data. In this study, they were used as alternative tools to estimate the characteristics of hydraulic jumps, such as the free surface location and energy dissipation. The dimensionless hydraulic parameters, including jump depth, jump length, and energy dissipation, were determined as functions of the Froude number and the height and length of corrugations. The estimations of the ANN and GP models were found to be in good agreement with the measured data. The results of the ANN model were compared with those of the GP model, showing that the proposed ANN models are much more accurate than the GP models.展开更多
In 1992, Brualdi and Jung first introduced the maximum jump number M(n, k), that is, the maximum number of the jumps of all (0, 1)-matrices of order n with k 1's in each row and column, and then gave a table about...In 1992, Brualdi and Jung first introduced the maximum jump number M(n, k), that is, the maximum number of the jumps of all (0, 1)-matrices of order n with k 1's in each row and column, and then gave a table about the values of M(n, k) when 1 ≤ k ≤ n ≤ 10. They also put forward several conjectures, including the conjecture M(2k - 2, k) = 3k - 4 + [k-2/2]. In this paper, we prove that b(A) ≥ 4 for every A ∈ A(2k - 2, k) if k ≥ 11, and find another counter-example to this conjecture .展开更多
This paper provides a proof of robustness of the restricted additive Schwarz preconditioner with harmonic overlap(RASHO)for the second order elliptic problems with jump coefficients.By analyzing the eigenvalue distrib...This paper provides a proof of robustness of the restricted additive Schwarz preconditioner with harmonic overlap(RASHO)for the second order elliptic problems with jump coefficients.By analyzing the eigenvalue distribution of the RASHO preconditioner,we prove that the convergence rate of preconditioned conjugate gradient method with RASHO preconditioner is uniform with respect to the large jump and meshsize.展开更多
The maxinmum jump number M(n, k) over a class of n×n matrices of zerosand ones with constant row and column sum k has been investigated by Brualdi andJung in [1] where they proposed the conjectureM(2k, k + 1) = 3...The maxinmum jump number M(n, k) over a class of n×n matrices of zerosand ones with constant row and column sum k has been investigated by Brualdi andJung in [1] where they proposed the conjectureM(2k, k + 1) = 3l - 1 + [k-1/2]In this note, we give two counter-examples to this conjecture.展开更多
In this paper, the equilibrium entrainment into a shear-free, linearly stratified atmosphere is discussed under the framework of bulk models, namely, the zero-order jump model （ZOM） and the first-order jump model （...In this paper, the equilibrium entrainment into a shear-free, linearly stratified atmosphere is discussed under the framework of bulk models, namely, the zero-order jump model （ZOM） and the first-order jump model （FOM）. The parameterizations for the dimensionless entrainment rate versus the convective Richard- son number in the two models are compared. Based on the assumption that the parameterized entrainment rates in ZOM and FOM should be the same, the inherent relationships among the entrainment parameters in the bulk models are revealed. These relationships are supported by tank experiments and large-eddy sim- ulations. The validity of these inherent relationships indicates that, for a convective boundary layer growing into a linearly stratified free atmosphere, the only dominant factors of the growth rate are the turbulent buoyancy in the mixed layer and the stratification in the free atmosphere. In the point of the similarity view, the former is characterized by turbulent temperature and mixing length scales （mixed layer depth）, and the latter is characterized by the lapse rate of potential temperature in the free atmosphere. Thus, the commonly-used Richardson number scheme for the parameterization of the entrainment rate is just as an equivalent description. The variability of the total entrainment flux ratio in FOM, which is connected with the entrainment zone thickness, can implicitly describe the effect of the stratification in the free atmosphere, but the entrainment zone thickness is not an independent parameter. These results demonstrate the validity of the hypothesis that there exists a similarity limit in which the mixed layer depth is the only lengthscale.展开更多
文摘Artificial neural networks （ANNs） and genetic programming （GP） have recently been used for the estimation of hydraulic data. In this study, they were used as alternative tools to estimate the characteristics of hydraulic jumps, such as the free surface location and energy dissipation. The dimensionless hydraulic parameters, including jump depth, jump length, and energy dissipation, were determined as functions of the Froude number and the height and length of corrugations. The estimations of the ANN and GP models were found to be in good agreement with the measured data. The results of the ANN model were compared with those of the GP model, showing that the proposed ANN models are much more accurate than the GP models.
基金Hainan Natural Science Foundation of Hainan (10002)
文摘In 1992, Brualdi and Jung first introduced the maximum jump number M(n, k), that is, the maximum number of the jumps of all (0, 1)-matrices of order n with k 1's in each row and column, and then gave a table about the values of M(n, k) when 1 ≤ k ≤ n ≤ 10. They also put forward several conjectures, including the conjecture M(2k - 2, k) = 3k - 4 + [k-2/2]. In this paper, we prove that b(A) ≥ 4 for every A ∈ A(2k - 2, k) if k ≥ 11, and find another counter-example to this conjecture .
基金supported by Research Starting Funds for Imported Talents of Ningxia University(BQD2014010)the Natural Science Foundations of China(No.11501313).The second author is supported by the Natural Science Foundations of China(No.11271298 and No.11362021).
文摘This paper provides a proof of robustness of the restricted additive Schwarz preconditioner with harmonic overlap(RASHO)for the second order elliptic problems with jump coefficients.By analyzing the eigenvalue distribution of the RASHO preconditioner,we prove that the convergence rate of preconditioned conjugate gradient method with RASHO preconditioner is uniform with respect to the large jump and meshsize.
基金Supported by the Science Foundation of Hainan(10002)
文摘The maxinmum jump number M(n, k) over a class of n×n matrices of zerosand ones with constant row and column sum k has been investigated by Brualdi andJung in [1] where they proposed the conjectureM(2k, k + 1) = 3l - 1 + [k-1/2]In this note, we give two counter-examples to this conjecture.
基金supported by the National Natural Science Foundation of China underGrant No. 40475009
文摘In this paper, the equilibrium entrainment into a shear-free, linearly stratified atmosphere is discussed under the framework of bulk models, namely, the zero-order jump model （ZOM） and the first-order jump model （FOM）. The parameterizations for the dimensionless entrainment rate versus the convective Richard- son number in the two models are compared. Based on the assumption that the parameterized entrainment rates in ZOM and FOM should be the same, the inherent relationships among the entrainment parameters in the bulk models are revealed. These relationships are supported by tank experiments and large-eddy sim- ulations. The validity of these inherent relationships indicates that, for a convective boundary layer growing into a linearly stratified free atmosphere, the only dominant factors of the growth rate are the turbulent buoyancy in the mixed layer and the stratification in the free atmosphere. In the point of the similarity view, the former is characterized by turbulent temperature and mixing length scales （mixed layer depth）, and the latter is characterized by the lapse rate of potential temperature in the free atmosphere. Thus, the commonly-used Richardson number scheme for the parameterization of the entrainment rate is just as an equivalent description. The variability of the total entrainment flux ratio in FOM, which is connected with the entrainment zone thickness, can implicitly describe the effect of the stratification in the free atmosphere, but the entrainment zone thickness is not an independent parameter. These results demonstrate the validity of the hypothesis that there exists a similarity limit in which the mixed layer depth is the only lengthscale.
