We establish an integration by parts formula on the path space with reference measure P,the law of the(reflecting)diffusion process on manifolds with possible boundary carrying geometric flow,which leads to the standa...We establish an integration by parts formula on the path space with reference measure P,the law of the(reflecting)diffusion process on manifolds with possible boundary carrying geometric flow,which leads to the standard log-Sobolev inequality for the associated Dirichlet form.To this end,we first modify Hsu's multiplicative functionals to define the damp gradient operator,which links to quasi-invariant flows;and then establish the derivative formula for the associated inhomogeneous diffusion semigroup.展开更多
Enhancing the strength of nanotwinned aluminum(Al)is essential for the development of nextgeneration high-end chip technology.To better understand the detwinning behavior of nanotwinned Al under conditions with no res...Enhancing the strength of nanotwinned aluminum(Al)is essential for the development of nextgeneration high-end chip technology.To better understand the detwinning behavior of nanotwinned Al under conditions with no resolved shear stress acting on the twin boundaries,we conducted molecular dynamics simulations of uniaxial tensile deformation in nanotwinned single-crystal Al at room temperature.Detwinning is observed only when the twin boundary spacing is 7.01 A.At larger spacings,twin boundaries remain parallel to the loading direction,with no rotation or bending,indicating negligible migration.Detwinning is triggered by localized stress from dislocation interactions,with detwinning fraction evolving synchronously with dislocation density.In the absence of detwinning,dislocations inclined toward twin boundaries interact frequently with them,leading to a loss of coherency that intensifies with increasing twin boundary spacing.These findings enhance understanding of the plastic deformation mechanisms in nanotwinned metals at very small twin boundary spacings,supplement the conventional understanding of twin boundary stability,and therefore suggest potential pathways for designing Al-based nanostructures with enhanced stability or controllable plastic deformation.展开更多
基金supported by the National Natural Science Foundation of Zhejiang University of Technology(Grant No.2014X2011)the Starting-up Research Fund supplied by Zhejiang University of Technology(Grant No.1009007329)
文摘We establish an integration by parts formula on the path space with reference measure P,the law of the(reflecting)diffusion process on manifolds with possible boundary carrying geometric flow,which leads to the standard log-Sobolev inequality for the associated Dirichlet form.To this end,we first modify Hsu's multiplicative functionals to define the damp gradient operator,which links to quasi-invariant flows;and then establish the derivative formula for the associated inhomogeneous diffusion semigroup.
基金founded by the National Natural Science Foundation of China under grant numbers 52375325,52105410Anhui Provincial Natural Science Foundation under grant number 2308085ME164.
文摘Enhancing the strength of nanotwinned aluminum(Al)is essential for the development of nextgeneration high-end chip technology.To better understand the detwinning behavior of nanotwinned Al under conditions with no resolved shear stress acting on the twin boundaries,we conducted molecular dynamics simulations of uniaxial tensile deformation in nanotwinned single-crystal Al at room temperature.Detwinning is observed only when the twin boundary spacing is 7.01 A.At larger spacings,twin boundaries remain parallel to the loading direction,with no rotation or bending,indicating negligible migration.Detwinning is triggered by localized stress from dislocation interactions,with detwinning fraction evolving synchronously with dislocation density.In the absence of detwinning,dislocations inclined toward twin boundaries interact frequently with them,leading to a loss of coherency that intensifies with increasing twin boundary spacing.These findings enhance understanding of the plastic deformation mechanisms in nanotwinned metals at very small twin boundary spacings,supplement the conventional understanding of twin boundary stability,and therefore suggest potential pathways for designing Al-based nanostructures with enhanced stability or controllable plastic deformation.
