Stochastic approximation problem is to find some root or extremum of a nonlinear function for which only noisy measurements of the function are available. The classical algorithm for stochastic approximation problem i...Stochastic approximation problem is to find some root or extremum of a nonlinear function for which only noisy measurements of the function are available. The classical algorithm for stochastic approximation problem is the Robbins-Monro （RM） algorithm, which uses the noisy evaluation of the negative gradient direction as the iterative direction. In order to accelerate the RM algorithm, this paper gives a flame algorithm using adaptive iterative directions. At each iteration, the new algorithm goes towards either the noisy evaluation of the negative gradient direction or some other directions under some switch criterions. Two feasible choices of the criterions are proposed and two corresponding frame algorithms are formed. Different choices of the directions under the same given switch criterion in the frame can also form different algorithms. We also proposed the simultanous perturbation difference forms for the two frame algorithms. The almost surely convergence of the new algorithms are all established. The numerical experiments show that the new algorithms are promising.展开更多
The transition phase and elastic properties of SrS from NaCl structure （B1） to CsCl structure （B2） are investigated by ab initio plane-wave pseudopotential density functional theory method and by the quasi-harmoni...The transition phase and elastic properties of SrS from NaCl structure （B1） to CsCl structure （B2） are investigated by ab initio plane-wave pseudopotential density functional theory method and by the quasi-harmonic Debye model. The transition pressure varies non-linearly with temperature, and the pressure of the mechanical instability increases linearly with increasing temperature. It is shown that the B1 structure SrS is a most elastically anisotropic minerat any pressure. The Debye temperature, the heat capacity, thermal expansion and Gruneisen parameter over a wide range of pressures and temperatures are also obtained.展开更多
First-principle calculations based on density functional theory were used to study the adsorption of atomic sulfur and carbon on the Mg(0001) surface in a wide range of coverages from 1/4 ML(monolayer) to 1 ML. It is ...First-principle calculations based on density functional theory were used to study the adsorption of atomic sulfur and carbon on the Mg(0001) surface in a wide range of coverages from 1/4 ML(monolayer) to 1 ML. It is found that the adsorption of atomic S and C on the high coordinate hollow site is more energetically favorable than that on other adsorption sites. S atom is favorable to be adsorbed at on-surface site and C atom is favorable to be adsorbed at subsurface site. The results suggest that when the coverage increases, the binding energy for S and C atoms will decrease and the interaction between adsorbed atoms tends to be stronger. It indicates that as coverage increases, S-Mg and C-Mg interaction weakens.展开更多
基金supported by the Chinese NSF grants 10571171 and 40233029.
文摘Stochastic approximation problem is to find some root or extremum of a nonlinear function for which only noisy measurements of the function are available. The classical algorithm for stochastic approximation problem is the Robbins-Monro （RM） algorithm, which uses the noisy evaluation of the negative gradient direction as the iterative direction. In order to accelerate the RM algorithm, this paper gives a flame algorithm using adaptive iterative directions. At each iteration, the new algorithm goes towards either the noisy evaluation of the negative gradient direction or some other directions under some switch criterions. Two feasible choices of the criterions are proposed and two corresponding frame algorithms are formed. Different choices of the directions under the same given switch criterion in the frame can also form different algorithms. We also proposed the simultanous perturbation difference forms for the two frame algorithms. The almost surely convergence of the new algorithms are all established. The numerical experiments show that the new algorithms are promising.
基金National Natural Science Foundation of China under Grant No.10576020
文摘The transition phase and elastic properties of SrS from NaCl structure （B1） to CsCl structure （B2） are investigated by ab initio plane-wave pseudopotential density functional theory method and by the quasi-harmonic Debye model. The transition pressure varies non-linearly with temperature, and the pressure of the mechanical instability increases linearly with increasing temperature. It is shown that the B1 structure SrS is a most elastically anisotropic minerat any pressure. The Debye temperature, the heat capacity, thermal expansion and Gruneisen parameter over a wide range of pressures and temperatures are also obtained.
文摘First-principle calculations based on density functional theory were used to study the adsorption of atomic sulfur and carbon on the Mg(0001) surface in a wide range of coverages from 1/4 ML(monolayer) to 1 ML. It is found that the adsorption of atomic S and C on the high coordinate hollow site is more energetically favorable than that on other adsorption sites. S atom is favorable to be adsorbed at on-surface site and C atom is favorable to be adsorbed at subsurface site. The results suggest that when the coverage increases, the binding energy for S and C atoms will decrease and the interaction between adsorbed atoms tends to be stronger. It indicates that as coverage increases, S-Mg and C-Mg interaction weakens.
