Although possible non-homogeneous strain effects in semiconductors have been investigated for over a half century and the strain-gradient can be over 1% per micrometer in flexible nanostructures, we still lack an unde...Although possible non-homogeneous strain effects in semiconductors have been investigated for over a half century and the strain-gradient can be over 1% per micrometer in flexible nanostructures, we still lack an understanding of their influence on energy bands. Here we conduct a systematic cathodoluminescence spectroscopy study of the strain-gradient induced exciton energy shift in elastically curved CdS nanowires at low temperature, and find that the red-shift of the exciton energy in the curved nanowires is proportional to the strain-gradient, an index of lattice distortion. Density functional calculations show the same trend of band gap reduction in curved nanostructures and reveal the underlying mechanism. The significant linear straingradient effect on the band gap of semiconductors should shed new light on ways to tune optical-electronic properties in nanoelectronics.展开更多
Consider the following Cauchy problem for the first order quasilinear strictly hy- perbolic system ?u ?u + A(u) = 0, ...Consider the following Cauchy problem for the first order quasilinear strictly hy- perbolic system ?u ?u + A(u) = 0, ?t ?x t = 0 : u = f(x). We let M = sup |f (x)| < +∞. x∈R The main result of this paper is that under the assumption that the system is weakly linearly degenerated, there exists a positive constant ε independent of M, such that the above Cauchy problem admits a unique global C1 solution u = u(t,x) for all t ∈ R, provided that +∞ |f (x)|dx ≤ ε, ?∞ +∞ ε |f(x)|dx ≤ . M∞展开更多
The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with "slow" decay initial data. By con...The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with "slow" decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the life-span of classical solutions are given in the case that the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.1-1.3 in [2] are still valid for this kind of initial data.展开更多
For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the globa...For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the global existence of H 2 classical solution to the Cauchy problem with small initial data is obtained.展开更多
According to previous studies,stiffened shells with convex hyperbolic generatrix shape are less sensitive to imperfections.In this study,the effects of generatrix shape on the performances of elastic and plastic buckl...According to previous studies,stiffened shells with convex hyperbolic generatrix shape are less sensitive to imperfections.In this study,the effects of generatrix shape on the performances of elastic and plastic buckling in stiffened shells are investigated.Then,a more general description of generatrix shape is proposed,which can simply be expressed as a convex B-spline curve(controlled by four key points).An optimization framework of stiffened shells with a convex B-spline generatrix is established,with optimization objective being measured in terms of nominal collapse load,which can be expressed as a weighted sum of geometrically imperfect shells.The effectiveness of the proposed framework is demonstrated by a detailed comparison of the optimum designs for the B-spline and hyperbolic generatrix shapes.The decrease of imperfection sensitivity allows for a significant weight saving,which is particularly important in the development of future heavy-lift launch vehicles.展开更多
基金This study was supported by the National Natural Science Foundation of China （NSFC）, the State Key Research Projects for Fundamental Science （Nos. 2007CB936200, 2007CB936202, and 2009CB623703） of Ministry of Science and Technology of China （MOST）, and Natural Science Foundation （NSF） of Jiangsu Province of China.
文摘Although possible non-homogeneous strain effects in semiconductors have been investigated for over a half century and the strain-gradient can be over 1% per micrometer in flexible nanostructures, we still lack an understanding of their influence on energy bands. Here we conduct a systematic cathodoluminescence spectroscopy study of the strain-gradient induced exciton energy shift in elastically curved CdS nanowires at low temperature, and find that the red-shift of the exciton energy in the curved nanowires is proportional to the strain-gradient, an index of lattice distortion. Density functional calculations show the same trend of band gap reduction in curved nanostructures and reveal the underlying mechanism. The significant linear straingradient effect on the band gap of semiconductors should shed new light on ways to tune optical-electronic properties in nanoelectronics.
基金Project supported by the National Natural Science Foundation of China (No.10225102) the 973 Project of the Ministry of Science and Technology of China and the Doctoral Programme Foundation of the Ministry of Education of China.
文摘Consider the following Cauchy problem for the first order quasilinear strictly hy- perbolic system ?u ?u + A(u) = 0, ?t ?x t = 0 : u = f(x). We let M = sup |f (x)| < +∞. x∈R The main result of this paper is that under the assumption that the system is weakly linearly degenerated, there exists a positive constant ε independent of M, such that the above Cauchy problem admits a unique global C1 solution u = u(t,x) for all t ∈ R, provided that +∞ |f (x)|dx ≤ ε, ?∞ +∞ ε |f(x)|dx ≤ . M∞
基金Project supported by the National Natural Science Foundation of China
文摘The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with "slow" decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the life-span of classical solutions are given in the case that the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.1-1.3 in [2] are still valid for this kind of initial data.
基金supported by the Fudan University Creative Student Cultivation Program in Key Disciplinary Areas (No. EHH1411208)
文摘For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the global existence of H 2 classical solution to the Cauchy problem with small initial data is obtained.
基金supported by the National Basic Research Program of China("973"Project)(Grant Nos.2014CB049000,2014CB046596)the National Natural Science Foundation of China(Grant Nos.11402049,11372062)+2 种基金the Project funded by China Postdoctoral Science Foundation(Grant No.2014M551070)the Fundamental Research Funds for Central University of China(Grant No.DUT14RC(3)028)the"111"Program(Grant No.B14013)
文摘According to previous studies,stiffened shells with convex hyperbolic generatrix shape are less sensitive to imperfections.In this study,the effects of generatrix shape on the performances of elastic and plastic buckling in stiffened shells are investigated.Then,a more general description of generatrix shape is proposed,which can simply be expressed as a convex B-spline curve(controlled by four key points).An optimization framework of stiffened shells with a convex B-spline generatrix is established,with optimization objective being measured in terms of nominal collapse load,which can be expressed as a weighted sum of geometrically imperfect shells.The effectiveness of the proposed framework is demonstrated by a detailed comparison of the optimum designs for the B-spline and hyperbolic generatrix shapes.The decrease of imperfection sensitivity allows for a significant weight saving,which is particularly important in the development of future heavy-lift launch vehicles.
