Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior

In the light of the visual angle model (VAM), an improved car-following model considering driver's visual angle, anticipated time and stabilizing driving behavior is proposed so as to investigate how the driver's behavior factors affect the stability of the traffic flow. Based on the model, linear stability analysis is performed together with bifurcation analysis, whose corresponding stability condition is highly fit to the results of the linear analysis. Furthermore, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived by nonlinear analysis, and we obtain the relationship of the two equations through the comparison. Finally, parameter calibration and numerical simulation are conducted to verify the validity of the theoretical analysis, whose results are highly consistent with the theoretical analysis.     

Orientation dependent size effects in thermal buckling and post-buckling of nanoplates with cubic anisotropy

In this work, a continuum model is presented for size and orientation dependent thermal buckling and post-buckling of anisotropic nanoplates considering surface and bulk residual stresses. The model with von-Karman nonlinear strains and material cubic anisotropy of single crystals contains two parameters that reflect the orientation effects. Using Ritz method, closed form solutions are given for buckling temperature and post-buckling deflections. Regarding self-instability states of nanoplates and their recovering at higher temperatures, an experiment is discussed based on low pressurized membranes to verify the predictions. For simply supported nanoplates, the size effects are lowest when they are aligned in [100] direction. When the edges get clamped, the orientation dependence is ignorable and the behavior becomes symmetric about [510] axis. The surface residual stress makes drastic increase in buckling temperature of thinner nanoplates for which a minimum thickness is pointed to stay far from material softening at higher temperatures. Deflection of [100]-oriented buckled nanoplates is higher than [110] ones but this reverses at higher temperatures. The results for long nanoplates show that the buckling mode numbers are changed by orientation which is verified by FEM.     

In vivo comprehensive multiphase NMR

Traditionally, due to different hardware requirements, nuclear magnetic resonance (NMR) has developed as two separate fields: one dealing with solids, and one with solutions. Comprehensive multiphase (CMP) NMR combines all electronics and hardware (magic angle spinning [MAS], gradients, high power Radio Frequency (RF) handling, lock, susceptibility matching) into a universal probe that permits a comprehensive study of all phases (i.e., liquid, gel-like, semisolid, and solid), in intact samples. When applied in vivo, it provides unique insight into the wide array of bonds in a living system from the most mobile liquids (blood, fluids) through gels (muscle, tissues) to the most rigid (exoskeleton, shell). In this tutorial, the practical aspects of in vivo CMP NMR are discussed including: handling the organisms, rotor preparation, sample spinning, water suppression, editing experiments, and finishes with a brief look at the potential of other heteronuclei (²H, ¹⁵N, ¹⁹F, ³¹P) for in vivo research. The tutorial is aimed as a general resource for researchers interested in developing and applying MAS-based approaches to living organisms. Although the focus here is CMP NMR, many of the approaches can be adapted (or directly applied) using conventional high-resolution magic angle spinning, and in some cases, even standard solid-state NMR probes.     

C^n中子空间之间极端主角的一些应用

本文给出了Ｃ＾ｎ中子空间之间最大和最小主角在矩阵逼近，投影算子的扰动分析，群逆以及Ｏｒａｘｉｎ逆的扰动估计，条件数理论，Ｂｏｔｔ－Ｄｕｆｆｉｎ系统扰动分析中一些应用。     

Geometric visualization of the Brewster angle from dielectric-magnetic interface

A geometric visualization is presented for the Brewster angle for a plane wave reflecting from an interface. The surface is assumed to be isotropic but it is allowed to display both dielectric and magnetic susceptibility, and hence the Brewster (polarizing) angle can attain any value between 0 and 90^°, and can exist for both parallel and perpendicular polarizations. The geometric construction (a tetrahedron) is spanned by the basic material parameters of the surface. The Brewster angle appears in one of the faces of the tetrahedron.     

The many proofs of an identity on the norm of oblique projections

Given an oblique projector P on a Hilbert space, i.e., an operator satisfying P ²=P, which is neither null nor the identity, it holds that ||P|| = ||I –P||. This useful equality, while not widely-known, has been proven repeatedly in the literature. Many published proofs are reviewed, and simpler ones are presented.     

空气/水界面水分子的取向和运动

对四种不同的实验构型下空气／水界面自由O-H键在3700cm~(-1)的和频振动光谱的分析表明,水分子在空气／水界面的取向运动只可能是在平衡位置附近有限角度之内的受限转动。界面水分子的自由O-H键取向距界面法线约33°,而取向分布或运动的宽度不超过15°。这一图像显著地不同于Wei等人(Phys. Rev. Lett.86,4799(2001))只通过单一的SFG实验构型所得出结论,即：空气／水界面的水分子在超快的振动弛豫时间内在很大的角度范围内运动。     

不同入射角度下强流脉冲电子束能量沉积剖面和束流传输系数模拟计算

 强流脉冲电子束在材料中的能量沉积剖面、能量沉积系数和束流传输系数受其入射角的影响很大，理论计算了0.5~2.0MeV的电子束以不同的入射角在Al材料中的能量沉积剖面和能量沉积系数，并且还计算了0.4~1.4MeV电子束以不同入射角穿透不同厚度C靶的束流传输系数。计算结果表明，随着入射角的增大，靶材表面层单位质量中沉积的能量增大，电子在靶材料中穿透深度减小，能量沉积系数减小，相应的束流传输系数也减小；能量为0.5~2.0MeV的电子束当入射角在60°~70°时在材料表面层单位质量中沉积的能量较大。     

Explicit Formulas for Generalized Action–Angle Variables in a Neighborhood of an Isotropic Torus and Their Application

Different versions of the Darboux–Weinstein theorem guarantee the existence of action–angle-type variables and the harmonic-oscillator variables in a neighborhood of isotropic tori in the phase space. The procedure for constructing these variables is reduced to solving a rather complicated system of partial differential equations. We show that this system can be integrated in quadratures, which permits reducing the problem of constructing these variables to solving a system of quadratic equations. We discuss several applications of this purely geometric fact in problems of classical and quantum mechanics.