Impact non-pénétrant sur le thorax : influence de la courbure sur la propagation des ondesNonpenetrating impact on the thorax: influence of curvature on wave propagation

Theoretical studies of the propagation of impact waves through the thorax are needed to improve the design of bulletproof jackets and blast protections (Fung in ‘Biomechanics Motions, Flow, Stress, and Growth’, Springer-Verlag, 1990; Cooper et al., J. Trauma 40 (1996) S38–S41). The influence of the weak acoustic coupling at the interface between the thoracic wall and the lung were described in (Grimal et al., C. R. Acad. Sci. IIB 329 (2001) 655–662); in this work, we study, within the frame of elastodynamics and with an approximate analytical method, the effects of the curvature of this interface. Results are given in terms of strain energy for the pressure wave, transmitted or converted. Focalisation of energy in the medium representing the lung is important for curvatures measured in humans. To cite this article: Q. Grimal et al., C. R. Mecanique 330 (2002) 569–574.     

搓绳子的弹性力学分析

 用能量法解决了一个类似于搓绳子的问题. 两根相同的弹性直杆, 并在一起沿相同的方向扭转N 圈后, 把两端焊接起来, 看能够回绕几圈. 杆轴线在回绕后变成了螺旋线, 本文利用螺旋线的曲率和挠率求出了回 绕后的变形能, 并利用回绕前后杆的变形能相等求出了两杆回转的圈数. 并用相同的方法求出了三根杆时回转的圈数.     

高能炸药爆速曲率关系的一种计算方法

研究平面爆轰波爆轰化学能和状态方程之间的关系,得到平面爆轰波关系式和CJ条件.基于柱坐标系下的一维流体力学方程组,采用坐标变换方法得到含曲率的爆轰波关系式及广义声速条件.在反应区内采用压力平衡和温度平衡的混合规则,在给定的复杂状态方程和复杂反应率下求解,得到PBX9404和PBX9502炸药的爆速和曲率的关系.已知炸药...     

相位光栅型曲率传感器的波前校正算法

 针对相位光栅曲率传感器能够测量波前曲率在光瞳面上分布的特点,提出了一种采用整个空间分布的曲率信号来实现波前校正的算法。用曲率型变形镜影响函数的曲率信号在光瞳面上的分布来拟合待校正波前的曲率信号,采用最小二乘方法得到变形镜的控制电压,实现波前校正过程。数值模拟了一种41单元曲率型自适应光学系统采用该算法的波前校正过程。结果表明,对4至28阶Zernike像差体现了校正效果,对曲率为0的Zernike像差校正效果略好于曲率不为0的Zernike像差。与传统分区法的校正效果相比,整体法对Zernike像差的校正效果基本相当。整体法无需对光瞳面上的曲率信号进行与电极分布相同的分区,降低了对系统校准的要求。     

双凹厚透镜曲率半径和折射率的测定

观察双凹厚透镜的球面反射成像,利用这一实验现象结合物像公式测定双凹厚透镜前后表面的曲率半径和折射率。利用两次球面反射成像可求出双凹厚透镜的曲率半径,两种方法可比较。对于薄透镜,这种方法可以修正在实际测量中忽略透镜厚度所产生的误差。     

具有两个不同Ricci主曲率的局部共形平坦Riemann流形

得到了具有常m阶Schouten曲率与两个不同Schouten主曲率(或者等价地,两个不同Ricci主曲率)的完备局部共形平坦Riemann流形的分类结果.作为应用,得到了若干Schouten张量的pinching性质.     

Local Aronson-Benilan Estimates for Porous Medium Equations under Ricci Flow

In this work we derive local gradient estimates of the Aronson-Benilan type for positive solutions of porous medium equations under Ricci flow with bounded Ricci curvature. As an application, we derive a Harnack type inequality.     

A novel compensation method for the measurement of radius of curvature

A test method for spherical mirrors with super-long radius of curvature that only one compensator is employed to measure the radii of curvature of both concave and convex mirrors is presented. With this testing system, the surface figure and radius of curvature of spherical mirrors can be measured simultaneously. Using the ABCD matrix method, a precise formula for radius of curvature calculation is deduced. Experimental results show that the relative measurement error of this method is less than 4.2×10⁻⁴.     

Greatest lower bounds on Ricci curvature for toric Fano manifolds

In this short note, based on the work of Wang and Zhu (2004) [8], we determine the greatest lower bounds on Ricci curvature for all toric Fano manifolds.     

Shape gradient and classical gradient of curvatures: driving forces on micro/nano curved surfaces

Recent experiments and molecule dynamics simulations have shown that adhesion droplets on conical surfaces may move spontaneously and directionally. Besides, this spontaneous and directional motion is independent of the hydrophilicity and hydrophobicity of the conical surfaces. Aimed at this important phenomenon, a general theoretical explanation is provided from the viewpoint of the geometrization of micro/nano mechanics on curved surfaces. In the extrinsic mechanics on micro/nano soft curved surfaces, we disclose that the curvatures and their extrinsic gradients form the driving forces on the curved spaces. This paper focuses on the intrinsic mechanics on micro/nano hard curved surfaces and the experiment on the spontaneous and directional motion. Based on the pair potentials of particles, the interactions between an isolated particle and a micro/nano hard curved surface are studied, and the geometric foundation for the interactions between the particle and the hard curved surface is analyzed. The following results are derived: (a) Whatever the exponents in the pair potentials may be, the potential of the particle/hard curved surface is always of the unified curvature form, i.e., the potential is always a unified function of the mean curvature and the Gaussian curvature of the curved surface. (b) On the basis of the curvature-based potential, the geometrization of the micro/nano mechanics on hard curved surfaces may be realized. (c) Similar to the extrinsic mechanics on micro/nano soft curved surfaces, in the intrinsic mechanics on micro/nano hard curved surfaces, the curvatures and their intrinsic gradients form the driving forces on the curved spaces. In other words, either on soft curved surfaces or hard curved surfaces and either in the extrinsic mechanics or the intrinsic mechanics, the curvatures and their gradients are all essential factors for the driving forces on the curved spaces. (d) The direction of the driving force induced by the hard curved surface is independent of the hydrophilicity and hydrophobicity of the curved surface, explaining the experimental phenomenon of the spontaneous and directional motion.