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Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection

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Science China Mathematics 2021年第5期64卷 887-902页

作者： Hong-Lin Liao Xuehua Song Tao Tang Tao Zhou Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211101China Department of Mathematics and International Center for Mathematics Southern University of Science and TechnologyShenzhen 518055China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China NCMIS&LSEC Institute of Computational Mathematics and Scientific Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

In this work,we are concerned with the stability and convergence analysis of the second-order backward difference formula(BDF2)with variable steps for the molecular beam epitaxial model without slope selection.We first show that the variable-step BDF2 scheme is convex and uniquely solvable under a weak time-step constraint.Then we show that it preserves an energy dissipation law if the adjacent time-step ratios satisfy r_(k):=τ_(k)/τ_(k-1)<3.561.Moreover,with a novel discrete orthogonal convolution kernels argument and some new estimates on the corresponding positive definite quadratic forms,the L^(2)norm stability and rigorous error estimates are established,under the same step-ratio constraint that ensures the energy stability,i.e.,0

关键词： molecular beam epitaxial growth variable-step BDF2 scheme discrete orthogonal convolution kernels energy stability convergence analysis

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Towards Quantum Ballistic Field-Effect Transistors:Design and Experimental Results

Towards Quantum Ballistic Field-Effect Transistors:Design an...

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2006 8th International Conference on Solid-State and Integrated Circuit Technology

作者： Y.Jin E.Gremion A.Cavanna U.Gennser B.Etienne C.Ulysse Laboratoire de Photonique et de Nanostructures CNRS/UPR20Route de Nozay91460 MarcoussisFrance

ISBN: (纸本)1424401607

＜正＞During the last two decades,the size of a typical field-effect transistor（FET） in a microcomputer chip has steadily been reduced to reach now around one hundred nanometers.Its operation however remains essentially classical,i.***.in the diffusive regime.Devising a FET operating in the ballistic regime has been the dream of physicists and electrical engineers alike for several decades.A ballistic FET - a perfect FET - has no defects, kinks or obstacles other than a connection at each end to allow current flow through an external circuit. Significant performance improvement is hence expected as a consequence of the ballistic transport but also of

关键词： FETs Reservoirs Conductors Voltage Electron mobility Gallium arsenide molecular beam epitaxial growth Nanostructures Microcomputers Circuits

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