Applying invariant eigen-operator method to deriving normal coordinates of general classical Hamiltonian

For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （IEO） method （Fan et al. 2004 Phys. Lett. A 321 75） to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.

Quantitative law of diffusion induced fracture

Through dimension analysis, an almost analytical model for the maximum diffusion induced stress（DIS）and critical temperature（or concentration） difference at which cracks begin to initiate in the diffusion process is developed. It interestingly predicts that the spacing of diffusioninduced cracks is constant, independent of the thickness of specimen and the temperature difference. These conclusions are validated by our thermal shock experiments on alumina plates. Furthermore, the proposed model can interpret observed hierarchical crack patterns for high temperature jump cases, and a three-stage relation between the residual strength and the temperature difference. The prediction for crack spacing can guide the biomimetic thermal-shockfailure proof design, in which the hard platelets smaller than the predicted diffusion induced by constant crack-spacing are embedded in a soft matrix, and, therefore, no fracture will happen. This may guide the design of the thermal protection system and the lithium ion battery. Finally we present the maximum normalized DISes for various geometry and boundary conditions by single-variable curves for the stressindependent diffusion process and two-variable contour plots for the stress-dependent diffusion process, which can provideengineers and materialists a simple and easy way to quickly evaluate the reliability of related materials and devices.

Simulations of fast component and slow component of SMBI on HL-2A tokamak

It is very important to improve the penetration depth and fueling efficiency of supersonic molecular beam injection（SMBI） especially for the next generation fusion devices such as ITER. Two components, a fast component（FC） and a slow component（SC）, have been observed in the HL-2A SMBI experiments for several years, and the FC can penetrate much more deeply than the common SMBIs which draws a great deal of attention for a better fueling method. It is the first time to the FC and SC of SMBI have been simulated and interpreted in theory and simulation in this paper with the trans-neut module of the BOUT＋＋ code. The simulation results of the FC and SC are clear and distinguishable in the same way as the observation in experiment. For the major mechanism of the FC and SC, it is found that although the difference in the injection velocity has some effect on the penetration depth difference between the FC and SC, it is mainly caused by the self-blocking effect of the first ionized SMB. We also discuss the influence of the initial plasma density on the FC and SC,and the variation of the SC penetration depth with its injection velocity.

Dielectric Breakdown Model for an Electrically Semi-Permeable Penny-Shaped Crack in Three-Dimensional Piezoelectric Media

The dielectric breakdown（DB） model for a penny-shaped crack under a semipermeable boundary condition in a three-dimensional piezoelectric medium is studied.An approximate analytical solution is derived by using the boundary integral equation with extended displacement discontinuity,and the corresponding boundary element method with double iterative approaches is developed to analyze the semi-permeable crack.The effect of electric boundary conditions on crack faces is discussed on the basis of DB model.By comparing the DB model with the polarization saturation（PS） model for different piezoelectric materials,some interesting phenomena related to the electric yielding zone and local J-integral are observed.

Ab initio study of vibrational frequencies, force field and normal coordinate analysis of the cis- and trans-isomers of nitrosomethanol

In this paper, the equilibrium geometries of two isomers of the newly found compound ——nitrosomethanol——have been optimized by ab initio SCF MO method with 3-21G basic set by gradient technique. And the second derivatives of potential energy (i. e. the force constant matrix elements) have been calculated analytically. Hence the entire force fields of the two isomers of nitro- somethanol have been obtained theoretically. The theoretical vibrational frequencies and the corres- ponding normal modes were obtained and compared with the experimental values. and the structures of two isomeric forms of nitrosomethanol are established.