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
How to regulate the supramolecular structures in the assembly of graphene quantum dots(GQDs)is still a great challenge to be overcome.Herein,the GQDs of 1-3 layers with high quality are synthesized from the new precur...How to regulate the supramolecular structures in the assembly of graphene quantum dots(GQDs)is still a great challenge to be overcome.Herein,the GQDs of 1-3 layers with high quality are synthesized from the new precursor m-trihydroxybenzene in a green method.More importantly,a strategy for designing the supramolecular structures of GQDs is demonstrated,and the novel supramolecular morphologies of GQDs have been constructed for the first time.Moreover,the supramolecular morphologies of GQDs can be well controlled by regulating the preparation conditions,and the formation mechanism of the branch-like supramolecular structure has been explained by the the diffusion-limited aggregation(DLA)model.This work not only develops a new precoursor to synthesize GQDs,but also opens up an effective route toform the polymorphic supermolecules,thus greatly facilitating their potential applications.展开更多
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.
基金the work from the National Natural Science Foundation of China(No.21805166)the 111 Project of Hubei Province(No.D20015)Foundation of Science and Technology Bureau of Yichang City(No.A18-302-a07).
文摘How to regulate the supramolecular structures in the assembly of graphene quantum dots(GQDs)is still a great challenge to be overcome.Herein,the GQDs of 1-3 layers with high quality are synthesized from the new precursor m-trihydroxybenzene in a green method.More importantly,a strategy for designing the supramolecular structures of GQDs is demonstrated,and the novel supramolecular morphologies of GQDs have been constructed for the first time.Moreover,the supramolecular morphologies of GQDs can be well controlled by regulating the preparation conditions,and the formation mechanism of the branch-like supramolecular structure has been explained by the the diffusion-limited aggregation(DLA)model.This work not only develops a new precoursor to synthesize GQDs,but also opens up an effective route toform the polymorphic supermolecules,thus greatly facilitating their potential applications.
