In order to steer the population distribution of a large number of agents interacting over a large-scale complex network towards a set of desired probability distributions for each sub-population,an approximate contro...In order to steer the population distribution of a large number of agents interacting over a large-scale complex network towards a set of desired probability distributions for each sub-population,an approximate control scheme is proposed and developed by the use of Graphon Mean Field theory and Convex Duality Optimal Control.For a general class of multi-agent nonlinear systems interacting over large networks,the original problem for a finite population over a finite network is reformulated as an optimal control problem for an infinite population over an infinite network by letting the number of nodes in the graph and the number of agents within each cluster approach infinity.Subsequently,the associated control problem for the graphon limit system is reformulated as a linear program over the space of Radon measures and is solved using the duality relationship between the space of measures and that of continuous functions.A numerical example of a network with randomly sampled weightings is presented to illustrate the effectiveness of the graphon control probability assignment methodology.展开更多
Moirépatterns from two-dimensional(2D)graphene heterostructures assembled via van der Waals interactions have sparked considerable interests in physics with the purpose to tailor the electronic properties of grap...Moirépatterns from two-dimensional(2D)graphene heterostructures assembled via van der Waals interactions have sparked considerable interests in physics with the purpose to tailor the electronic properties of graphene.Here we report for the first time the observation of moire patterns arising from a bilayer graphone/graphene superlattice produced through direct single-sided hydrogenation of a bilayer graphene on substrate.Compared to pristine graphene,the bilayer superlattice exhibits a rippled surface and two types of moire patterns are observed:triangular and linear moire patterns with the periodicities of 11 nm and 8-9 nm,respectively.These moire patterns are revealed from atomic force microscopy and further confirmed by following fast Fourier transform(FFT)analysis.Density functional theory(DFT)calculations are also performed and the optimized lattice constants of bilayer superlattice heterostructure are in line with our experimental analysis.These findings show that well-defined triangular and linear periodic potentials can be introduced into the graphene system through the single-sided hydrogenation and also open a route towards the tailoring of electronic properties of graphene by various moirépotentials.展开更多
文摘In order to steer the population distribution of a large number of agents interacting over a large-scale complex network towards a set of desired probability distributions for each sub-population,an approximate control scheme is proposed and developed by the use of Graphon Mean Field theory and Convex Duality Optimal Control.For a general class of multi-agent nonlinear systems interacting over large networks,the original problem for a finite population over a finite network is reformulated as an optimal control problem for an infinite population over an infinite network by letting the number of nodes in the graph and the number of agents within each cluster approach infinity.Subsequently,the associated control problem for the graphon limit system is reformulated as a linear program over the space of Radon measures and is solved using the duality relationship between the space of measures and that of continuous functions.A numerical example of a network with randomly sampled weightings is presented to illustrate the effectiveness of the graphon control probability assignment methodology.
基金We acknowledge the financial support from the National Natural Science Foundation of China(No.51905306)the China Postdoctoral Science Fund(No.2018M642650)the Special Support for Post-doc Creative Funding of Shandong Province(No.201902005).We are also grateful for the funding support from the University of Manchester Donator Foundation and Swedish Research Council Formas(No.2019-01538).Dr.Chloe Holyord from National Graphene Institute,University of M anchester is gratefully acknowledged for the help with AFM m easurem ents.Dr.Linqing Zhang and Mr.Malachy Mcgowan are greatly acknowledged for the experimental support in the sample preparation.
文摘Moirépatterns from two-dimensional(2D)graphene heterostructures assembled via van der Waals interactions have sparked considerable interests in physics with the purpose to tailor the electronic properties of graphene.Here we report for the first time the observation of moire patterns arising from a bilayer graphone/graphene superlattice produced through direct single-sided hydrogenation of a bilayer graphene on substrate.Compared to pristine graphene,the bilayer superlattice exhibits a rippled surface and two types of moire patterns are observed:triangular and linear moire patterns with the periodicities of 11 nm and 8-9 nm,respectively.These moire patterns are revealed from atomic force microscopy and further confirmed by following fast Fourier transform(FFT)analysis.Density functional theory(DFT)calculations are also performed and the optimized lattice constants of bilayer superlattice heterostructure are in line with our experimental analysis.These findings show that well-defined triangular and linear periodic potentials can be introduced into the graphene system through the single-sided hydrogenation and also open a route towards the tailoring of electronic properties of graphene by various moirépotentials.
