Damage and fracture are the most extensive failure modes of rock materials,which may easily induce disaster and instability of engineering structures.This study developed a nonlocal damage fracture phase field model f...Damage and fracture are the most extensive failure modes of rock materials,which may easily induce disaster and instability of engineering structures.This study developed a nonlocal damage fracture phase field model for rocks considering the heterogeneity of rocks.The modified phase field model introduced the heterogeneity of fracture parameters and modified the governing equations.Meanwhile,the free energy was constructed by the elastic strain energy sphere‐bias decomposition and the plastic strain energy.As for the numerical implementation,the three layers finite elements method structure was used in the frame of the finite element method.The ability of the modified phase field model has been illustrated by reproducing the experiment results of rock samples with pre‐existing cracks under compression.展开更多
We present two schemes for preparing cluster states with atomic qubits in an ion-trap system. In the first scheme an auxiliary atomic level is needed. While in the second scheme an additional classical driven field is...We present two schemes for preparing cluster states with atomic qubits in an ion-trap system. In the first scheme an auxiliary atomic level is needed. While in the second scheme an additional classical driven field is used, and the multi-ion cluster states can be generated by one step. Both the schemes are insensitive to thermal motion of the ions, all the facilities used in them are well within state of the art.展开更多
A new kind of multifractal is constructed by fractional Fourier transform of Cantor sets. The wavelet transform modulus maxima method is applied to calculate the singularity spectrum under an operational definition of...A new kind of multifractal is constructed by fractional Fourier transform of Cantor sets. The wavelet transform modulus maxima method is applied to calculate the singularity spectrum under an operational definition of multifractal. In particular, an analysing procedure to determine the spectrum is suggested for practice. Nonanalyticities of singularity spectra or phase transitions are discovered, which are interpreted as some indications on the range of Boltzmann temperature q, on which the scaling relation of partition function holds.展开更多
基金Key Laboratory of Geological Safety of Coastal Urban Underground Space,Ministry of Natural Resources,Grant/Award Number:BHKF2022Y03。
文摘Damage and fracture are the most extensive failure modes of rock materials,which may easily induce disaster and instability of engineering structures.This study developed a nonlocal damage fracture phase field model for rocks considering the heterogeneity of rocks.The modified phase field model introduced the heterogeneity of fracture parameters and modified the governing equations.Meanwhile,the free energy was constructed by the elastic strain energy sphere‐bias decomposition and the plastic strain energy.As for the numerical implementation,the three layers finite elements method structure was used in the frame of the finite element method.The ability of the modified phase field model has been illustrated by reproducing the experiment results of rock samples with pre‐existing cracks under compression.
基金The project supported by the Scientific Research Fund of the Education Department of Hunan Province under Grant No.06C354the Natural Science Foundation of Hunan Province under Grant No.06JJ5015
文摘We present two schemes for preparing cluster states with atomic qubits in an ion-trap system. In the first scheme an auxiliary atomic level is needed. While in the second scheme an additional classical driven field is used, and the multi-ion cluster states can be generated by one step. Both the schemes are insensitive to thermal motion of the ions, all the facilities used in them are well within state of the art.
文摘A new kind of multifractal is constructed by fractional Fourier transform of Cantor sets. The wavelet transform modulus maxima method is applied to calculate the singularity spectrum under an operational definition of multifractal. In particular, an analysing procedure to determine the spectrum is suggested for practice. Nonanalyticities of singularity spectra or phase transitions are discovered, which are interpreted as some indications on the range of Boltzmann temperature q, on which the scaling relation of partition function holds.
