The gamma-graphyne nanoribbons(γ-GYNRs) incorporating diamond-shaped segment(DSSs) with excellent thermoelectric properties are systematically investigated by combining nonequilibrium Green’s functions with adaptive...The gamma-graphyne nanoribbons(γ-GYNRs) incorporating diamond-shaped segment(DSSs) with excellent thermoelectric properties are systematically investigated by combining nonequilibrium Green’s functions with adaptive genetic algorithm. Our calculations show that the adaptive genetic algorithm is efficient and accurate in the process of identifying structures with excellent thermoelectric performance. In multiple rounds, an average of 476 candidates(only 2.88% of all16512 candidate structures) are calculated to obtain the structures with extremely high thermoelectric conversion efficiency.The room temperature thermoelectric figure of merit(ZT) of the optimal γ-GYNR incorporating DSSs is 1.622, which is about 5.4 times higher than that of pristine γ-GYNR(length 23.693 nm and width 2.660 nm). The significant improvement of thermoelectric performance of the optimal γ-GYNR is mainly attributed to the maximum balance of inhibition of thermal conductance(proactive effect) and reduction of thermal power factor(side effect). Moreover, through exploration of the main variables affecting the genetic algorithm, it is revealed that the efficiency of the genetic algorithm can be improved by optimizing the initial population gene pool, selecting a higher individual retention rate and a lower mutation rate. The results presented in this paper validate the effectiveness of genetic algorithm in accelerating the exploration of γ-GYNRs with high thermoelectric conversion efficiency, and could provide a new development solution for carbon-based thermoelectric materials.展开更多
We propose a dual Markov chain model to accommodate probabilities as well as perturbation,error bounds,or variances,in the Markov chain process.This motivates us to extend the Perron-Frobenius theory to dual number ma...We propose a dual Markov chain model to accommodate probabilities as well as perturbation,error bounds,or variances,in the Markov chain process.This motivates us to extend the Perron-Frobenius theory to dual number matrices with primitive and irreducible nonnegative standard parts.It is shown that such a dual number matrix always has a positive dual number eigenvalue with a positive dual number eigenvector.The standard part of this positive dual number eigenvalue is larger than or equal to the modulus of the standard part of any other eigenvalue of this dual number matrix.An explicit formula to compute the dual part of this positive dual number eigenvalue is presented.The Collatz minimax theorem also holds here.The results are nontrivial as even a positive dual number matrix may have no eigenvalue at all.An algorithm based upon the Collatz minimax theorem is constructed.The convergence of the algorithm is studied.An upper bound on the distance of stationary states between the dual Markov chain and the perturbed Markov chain is given.Numerical results on both synthetic examples and the dual Markov chain including some real world examples are reported.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11974300,11974299,12074150)the Natural Science Foundation of Hunan Province,China(Grant No.2021JJ30645)+3 种基金Scientific Research Fund of Hunan Provincial Education Department(Grant Nos.20K127,20A503,and 20B582)Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT13093)the Hunan Provincial Innovation Foundation for Postgraduate(Grant No.CX20220544)Youth Science and Technology Talent Project of Hunan Province,China(Grant No.2022RC1197)。
文摘The gamma-graphyne nanoribbons(γ-GYNRs) incorporating diamond-shaped segment(DSSs) with excellent thermoelectric properties are systematically investigated by combining nonequilibrium Green’s functions with adaptive genetic algorithm. Our calculations show that the adaptive genetic algorithm is efficient and accurate in the process of identifying structures with excellent thermoelectric performance. In multiple rounds, an average of 476 candidates(only 2.88% of all16512 candidate structures) are calculated to obtain the structures with extremely high thermoelectric conversion efficiency.The room temperature thermoelectric figure of merit(ZT) of the optimal γ-GYNR incorporating DSSs is 1.622, which is about 5.4 times higher than that of pristine γ-GYNR(length 23.693 nm and width 2.660 nm). The significant improvement of thermoelectric performance of the optimal γ-GYNR is mainly attributed to the maximum balance of inhibition of thermal conductance(proactive effect) and reduction of thermal power factor(side effect). Moreover, through exploration of the main variables affecting the genetic algorithm, it is revealed that the efficiency of the genetic algorithm can be improved by optimizing the initial population gene pool, selecting a higher individual retention rate and a lower mutation rate. The results presented in this paper validate the effectiveness of genetic algorithm in accelerating the exploration of γ-GYNRs with high thermoelectric conversion efficiency, and could provide a new development solution for carbon-based thermoelectric materials.
基金supported by the National Natural Science Foundation of China(Grant Nos.12126608,12131004)the R&D project of Pazhou Lab(Huangpu)(Grant No.2023K0603)the Fundamental Research Funds for the Central Universities(Grant No.YWF-22-T-204).
文摘We propose a dual Markov chain model to accommodate probabilities as well as perturbation,error bounds,or variances,in the Markov chain process.This motivates us to extend the Perron-Frobenius theory to dual number matrices with primitive and irreducible nonnegative standard parts.It is shown that such a dual number matrix always has a positive dual number eigenvalue with a positive dual number eigenvector.The standard part of this positive dual number eigenvalue is larger than or equal to the modulus of the standard part of any other eigenvalue of this dual number matrix.An explicit formula to compute the dual part of this positive dual number eigenvalue is presented.The Collatz minimax theorem also holds here.The results are nontrivial as even a positive dual number matrix may have no eigenvalue at all.An algorithm based upon the Collatz minimax theorem is constructed.The convergence of the algorithm is studied.An upper bound on the distance of stationary states between the dual Markov chain and the perturbed Markov chain is given.Numerical results on both synthetic examples and the dual Markov chain including some real world examples are reported.
