The influence of the distribution of nano-pores on the mechanical properties evaluation of porous low-k films by surface acoustic waves （SAW） is studied. A theoretical SAW propagation model is set up to characterize...The influence of the distribution of nano-pores on the mechanical properties evaluation of porous low-k films by surface acoustic waves （SAW） is studied. A theoretical SAW propagation model is set up to characterize the periodic porous dielectrics by transversely isotropic symmetry. The theoretical deductions of SAW propagating in the low-k film/Si substrate layered structure are given in detail. The dispersive characteristics of SAW in differ- ent propagation directions and the effects of the Young＇s moduli E, E′ and shear modulus G′ of the films on these dispersive curves are found. Computational results show that E′ and G′ cannot be measured along the propagation direction that is perpendicular to the nano-pores＇ direction.展开更多
This paper concentrates on studying the symmetries and a new type of conserved quantities called Mei conserved quantity. The criterions of the Mei symmetry, the Noether symmetry and the Lie symmetry are given. The con...This paper concentrates on studying the symmetries and a new type of conserved quantities called Mei conserved quantity. The criterions of the Mei symmetry, the Noether symmetry and the Lie symmetry are given. The conditions and the forms of the Mei conserved quantities deduced from these three symmetries are obtained. An example is given to illustrate the application of the result.展开更多
Two new types of conserved quantities deduced by Noether-Mei symmetry of nonholonomic mechanicalsystem are studied.The definition and criterion of Noether-Mei symmetry for the system are given.A coordinationfunction i...Two new types of conserved quantities deduced by Noether-Mei symmetry of nonholonomic mechanicalsystem are studied.The definition and criterion of Noether-Mei symmetry for the system are given.A coordinationfunction is introduced,and the conditions under which the Noether-Mei symmetry leads to the two types of conservedquantities and the forms of the two types of conserved quantities are obtained.An illustrative example is given.Thecoordination function can be selected according to the demand for finding the gauge function,and the choice of thecoordination function has multiformity,so more conserved quantities deduced from Noether-Mei symmetry of mechanicalsystem can be obtained.展开更多
Based on the total time derivative along the trajectory of the system, the unified symmetry of nonholonomic mechanical system with non-Chetaev＇s type constraints is studied. The definition and criterion of the unifie...Based on the total time derivative along the trajectory of the system, the unified symmetry of nonholonomic mechanical system with non-Chetaev＇s type constraints is studied. The definition and criterion of the unified symmetry of nonholonomic mechanical systems with non-Ohetaev＇s type constraints are given. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, is obtained. Two examples are given to illustrate the application of the results.展开更多
文摘The influence of the distribution of nano-pores on the mechanical properties evaluation of porous low-k films by surface acoustic waves （SAW） is studied. A theoretical SAW propagation model is set up to characterize the periodic porous dielectrics by transversely isotropic symmetry. The theoretical deductions of SAW propagating in the low-k film/Si substrate layered structure are given in detail. The dispersive characteristics of SAW in differ- ent propagation directions and the effects of the Young＇s moduli E, E′ and shear modulus G′ of the films on these dispersive curves are found. Computational results show that E′ and G′ cannot be measured along the propagation direction that is perpendicular to the nano-pores＇ direction.
基金The project supported by the Graduate Student＇s Innovative Foundation of China University of Petroleum （East China） under Grant No. S2006-31 .
文摘This paper concentrates on studying the symmetries and a new type of conserved quantities called Mei conserved quantity. The criterions of the Mei symmetry, the Noether symmetry and the Lie symmetry are given. The conditions and the forms of the Mei conserved quantities deduced from these three symmetries are obtained. An example is given to illustrate the application of the result.
文摘Two new types of conserved quantities deduced by Noether-Mei symmetry of nonholonomic mechanicalsystem are studied.The definition and criterion of Noether-Mei symmetry for the system are given.A coordinationfunction is introduced,and the conditions under which the Noether-Mei symmetry leads to the two types of conservedquantities and the forms of the two types of conserved quantities are obtained.An illustrative example is given.Thecoordination function can be selected according to the demand for finding the gauge function,and the choice of thecoordination function has multiformity,so more conserved quantities deduced from Noether-Mei symmetry of mechanicalsystem can be obtained.
文摘Based on the total time derivative along the trajectory of the system, the unified symmetry of nonholonomic mechanical system with non-Chetaev＇s type constraints is studied. The definition and criterion of the unified symmetry of nonholonomic mechanical systems with non-Ohetaev＇s type constraints are given. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, is obtained. Two examples are given to illustrate the application of the results.
