Density of excess modes below the first phonon mode in four-dimensional glasses

Glasses are known to possess low-frequency excess modes beyond the Debye prediction.For decades,it has been assumed that evolution of low-frequency density of excess modes D(ω) with frequency ω follows a power-law scaling:D(ω)~ω~γ.However,it remains debated on the value of γ at low frequencies below the first phonon-like mode in finitesize glasses.Early simulation studies reported γ=4 at low frequencies in two-(2D),three-(3D),and four-dimensional(4D)glasses,whereas recent observations in 2D and 3D glasses suggested γ=3.5 in a lower-frequency regime.It is uncertain whether the low-frequency scaling of D(ω)~ω^(3.5) could be generalized to 4D glasses.Here,we conduct numerical simulation studies of excess modes at frequencies below the first phonon-like mode in 4D model glasses.It is found that the system size dependence of D(ω) below the first phonon-like mode varies with spatial dimensions:D(ω) increases in2D glasses but decreases in 3D and 4D glasses as the system size increases.Furthermore,we demonstrate that the ω^(3.5)scaling,rather than the ω~4 scaling,works in the lowest-frequency regime accessed in 4D glasses,regardless of interaction potentials and system sizes examined.Therefore,our findings in 4D glasses,combined with previous results in 2D and 3D glasses,suggest a common low-frequency scaling of D(ω)~ ω^3.5) below the first phonon-like mode across different spatial dimensions,which would inspire further theoretical studies.

Research on the Low-carbon-high-value Agriculture Technology in the Comprehensive Improvement of Intra-county Environment Pollution——Taking the Development of Cultivation and Breeding Industry in the Ecological Cyclic Agricultural Garden in Shaoshan Irri

The comprehensive improvement strategy of intra-county environment pollution in the city and countryside was searched.By the research method which combined the microscopic view,the macroscopic view with the dynamic perspective,the seriousness of rural water quality,soil and atmospheric pollution in Xiangxiang,Xiangtan and the surrounding areas in Shaoshan irrigated area was revealed.The control measure which was 'four-dimensional pollution in the city and countryside'—— low-carbon-high-value agriculture and the technology innovation was proposed.The low-carbon-high-value technology innovation industrialization demonstration in three parts which included the pre-production,mid-production and post-production deep-processing of cultivation and breeding industry in the ecological cyclic agricultural garden in Shaoshan irrigated area was the driving force.We tried to propel the low-carbon ecological cultivation and breeding industry which included the paddy rice,grass,tree,medicinal herbs and pig,cow,chick,duck,fish.We wanted to relieve the structural unbalance of previous cultivation and breeding industry,'cheap grain hurting the farmers' and the short-leg problem of social-economic-ecological benefit.The results showed that the low-carbon-high-value agricultural system was a poly-generation technology system which promoted the multi-level and grading utilization,saved the energy,reduced the consumption and cleaned the production based on the ecology.