The presence of circles in the network maximum flow problem increases the complexity of the preflow algorithm.This study proposes a novel two-stage preflow algorithm to address this issue.First,this study proves that ...The presence of circles in the network maximum flow problem increases the complexity of the preflow algorithm.This study proposes a novel two-stage preflow algorithm to address this issue.First,this study proves that at least one zero-flow arc must be present when the flow of the network reaches its maximum value.This result indicates that the maximum flow of the network will remain constant if a zero-flow arc within a circle is removed;therefore,the maximum flow of each network without circles can be calculated.The first stage involves identifying the zero-flow arc in the circle when the network flow reaches its maximum.The second stage aims to remove the zero-flow arc identified and modified in the first stage,thereby producing a new network without circles.The maximum flow of the original looped network can be obtained by solving the maximum flow of the newly generated acyclic network.Finally,an example is provided to demonstrate the validity and feasibility of this algorithm.This algorithm not only improves computational efficiency but also provides new perspectives and tools for solving similar network optimization problems.展开更多
We investigate the influence of A1 preflow time on surface morphology and quality of AIN and GaN. The AIN and GaN layers are grown on a Si （111） substrate by metal organic chemical vapor deposition. Scanning electro...We investigate the influence of A1 preflow time on surface morphology and quality of AIN and GaN. The AIN and GaN layers are grown on a Si （111） substrate by metal organic chemical vapor deposition. Scanning electron microscopy, atomic force microscopy, x-ray diffraction and optical microscopy are used for analysis. Consequently, we find significant differences in the epitaxial properties of AlN buffer and the GaN layer, which are dependent on the AI preflow time. A1 preflow layers act as nucleation sites in the case of AiN growth. Compact and uniform AIN nucleation sites are observed with optimizing A1 preflow at an early nucleation stage, which will lead to a smooth AIN surface. Trenches and AlN grain clusters appear on the AIN surface while meltoback etching occurs on the GaN surface with excessive A1 preflow. The GaN quality variation keeps a similar trend with the AIN quality, which is influenced by AI preflow. With an optimized duration orAl preflow, crystal quality and surface morphology of AIN and GaN could be improved.展开更多
基金The National Natural Science Foundation of China(No.72001107,72271120)the Fundamental Research Funds for the Central Universities(No.NS2024047,NP2024106)the China Postdoctoral Science Foundation(No.2020T130297,2019M660119).
文摘The presence of circles in the network maximum flow problem increases the complexity of the preflow algorithm.This study proposes a novel two-stage preflow algorithm to address this issue.First,this study proves that at least one zero-flow arc must be present when the flow of the network reaches its maximum value.This result indicates that the maximum flow of the network will remain constant if a zero-flow arc within a circle is removed;therefore,the maximum flow of each network without circles can be calculated.The first stage involves identifying the zero-flow arc in the circle when the network flow reaches its maximum.The second stage aims to remove the zero-flow arc identified and modified in the first stage,thereby producing a new network without circles.The maximum flow of the original looped network can be obtained by solving the maximum flow of the newly generated acyclic network.Finally,an example is provided to demonstrate the validity and feasibility of this algorithm.This algorithm not only improves computational efficiency but also provides new perspectives and tools for solving similar network optimization problems.
基金Supported by the National Key Research and Development Program of China under Grant No 2016YFB0400200
文摘We investigate the influence of A1 preflow time on surface morphology and quality of AIN and GaN. The AIN and GaN layers are grown on a Si （111） substrate by metal organic chemical vapor deposition. Scanning electron microscopy, atomic force microscopy, x-ray diffraction and optical microscopy are used for analysis. Consequently, we find significant differences in the epitaxial properties of AlN buffer and the GaN layer, which are dependent on the AI preflow time. A1 preflow layers act as nucleation sites in the case of AiN growth. Compact and uniform AIN nucleation sites are observed with optimizing A1 preflow at an early nucleation stage, which will lead to a smooth AIN surface. Trenches and AlN grain clusters appear on the AIN surface while meltoback etching occurs on the GaN surface with excessive A1 preflow. The GaN quality variation keeps a similar trend with the AIN quality, which is influenced by AI preflow. With an optimized duration orAl preflow, crystal quality and surface morphology of AIN and GaN could be improved.
