Applications of ‐invariant distributions

In this sequel to the article 17 , a criterion for the regularity of fundamental solutions of differential operators with positive symbol is proved in analogy to Hörmander's criteria, see 9 , 12 . It implies that the temperate fundamental solution of the operator is not regular. Furthermore, a formula for the convolution of two ‐invariant distributions is presented, and, finally, L. Schwartz' question on the surjectivity of linear partial differential operators with constant coefficients on the space is completely answered in the case of ‐invariant differential operators.     

Torsion simple modules over the quantum spatial ageing algebra

Various classes of simple torsion modules are classified over the quantum spatial ageing algebra (this is a Noetherian algebra of Gelfand-Kirillov dimension 4). Explicit constructions of these modules are given and for each module its annihilator is found.     

弹性力学混合状态方程的小波解法

应用小波理论求解弹性力学混合状态方程，讨论了解的收敛性。从文中的数值算例不难看出，该方法不失为混合状态方程一种新的求解途径。     

通用有限元系统实现无限域波动仿真方法

在有限元模型中加入人工边界,可以进行无限域波动仿真。本文将介绍一种改进的Higdon人工边界,并通过适当的变换形式,将其在通用有限元软件上实现。最后通过数值实验验证了这种方法具有良好的稳定性和计算精度,并且实施简单方便,其他人工边界条件可参照本文方法,通过变换形式在通用有限元程序中实现。     

添加剂与铝合金的相互作用研究 Ⅰ.静态反应膜及油润滑下的摩擦学性能

静态下分别于２５℃，９０℃及１８０℃下进行硫化异丁烯（ＳＯ）、亚磷酸二正丁酯（ＤＢＰ）、ＳＯ＋ＤＢＰ的混合物（质量比２０∶１）、二烷基二硫代磷酸锌（ＺＤＤＰ）及十二酸（ＬＡ）５种添加剂均以质量分数为２％的比例添加到液体石蜡（ＬＰ）中与铝合金进行油浸试验．用动－静摩擦系数精密测定仪评价了在铝合金表面上所形成的静态反应膜的摩擦磨损行为，并考察了上述添加剂在ＬＰ中对铝合金－钢摩擦副的润滑作用．结果表明：静态反应膜的摩擦磨损行为与添加剂的化学活性密切相关，其中ＤＢＰ最易与铝合金发生反应，故其反应膜具有最低的摩擦系数和最长的耐磨寿命；ＺＤＤＰ在１８０℃下的静态反应膜具有较低的摩擦系数和较长的耐磨寿命；ＳＯ、ＳＯ与ＤＢＰ的混合物及ＬＡ的静态反应膜则不具有减摩抗磨性能，预示这些添加剂在ＬＰ中不与铝合金发生较强的化学作用．含上述添加剂的ＬＰ润滑下的摩擦磨损试验显示，ＤＢＰ与ＺＤＤＰ具有较好的摩擦学性能．这表明添加剂在铝合金表面静态反应膜的摩擦磨损试验结果与其在常规润滑下的具有较好的相关性．     

落锤试验中炸药样品表面能的多重分形性质

从能量守恒和质量守恒出发结合炸药样品在受冲击压缩时的分形性质，证明在样品周边的表面能具有多重分形的结构。     

低浓度固液两相流的颗粒相动理学模型

用广义Fokker-Planck扩散模型描述液相湍动对颗粒的挟带作用，用修正的BGK模型描述粒间碰撞效应，建立了封闭的颗粒相PDF输运方程．运用Chapman-Enskog迭代法求得方程的二阶近似解，获得颗粒相脉动速度二阶矩和三阶矩闭合关系．模型与颗粒流模型相容，与液相湍流闭合模型是否相容依赖于扩散模型的具体形式，并据此比较了不同的涡一颗粒作用模型．模型与二维明渠流轻质沙和天然沙试验资料符合很好．表明细小粒径颗粒能够充分跟随水流运动；大粒径颗粒的相间平均速度差和壁面滑移速度明显，近壁区内的颗粒沿流向和垂向脉动强度都可能大于水流，并存在一定程度的颗粒碰撞效应．     

Regime diagram of the development of long-wave near-wall disturbances in a hypersonic boundary layer

A regime diagram of the development of slow near-wall disturbances induced by an unsteady self-induced pressure perturbation in a hypersonic boundary layer is constructed for a disturbance wavelength greater than the boundary layer thickness. It is shown that the main factors shaping the perturbed flow are the gas enthalpy near the body surface, the intensity of the viscous-inviscid interaction, and the nature (sub- or supersonic) of the main part of the boundary layer. Nonlinear boundary-value problems are formulated for regimes in which the near-wall boundary layer region plays a decisive role. Numerical and analytical solutions are obtained in the linear approximation. It is shown that intensification of the viscous-inviscid interaction or an increase in the role of the supersonic main region of the boundary layer impart generally supersonic properties to the main part of the boundary layer, i.e. the upstream propagation of the disturbances is damped and the disturbance growth downstream becomes more intense. Damping of the viscous-inviscid interaction and an increase in the role of the subsonic main part of the boundary layer have the opposite effect. Surface cooling increases the effect of the main part of the boundary layer on the formation of pressure disturbances and surface heating leads to an increase in the effect of the near-wall boundary layer region. It is also shown that for the regimes considered disturbances propagate in a direction opposite to that of the free stream from the turbulent flow region located downstream of the local disturbance development region.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 59–71. Original Russian Text Copyright © 2004 by Bogolepov and Neiland.     

Strong explosion near a parallelepipedic structure

The purpose of this paper is to report the blast loading characteristics resulting from the detonation of a stoichiometric propane–oxygen mixture, and to validate the approach which relies on simulating TNT explosions at large scale by small-scale experiments of gaseous explosions. Several dimensionless correlations are obtained from experimental data. These relationships allow determination of the parameters of a blast wave interacting with a structure as a function of the positions of the explosive charge and the structure. Simulations carried out with the Autodyn code show good correlation with experimental results. The Hopkinson law is suggested to predict the blast wave’s parameters at large scale on the basis of small-scale experiments and simulations. This paper was based on work that was presented at the 20th International Colloquium on the Dynamics of Explosions and Reactive Systems, Montreal, Canada, July 31–August 5, 2005.     

Variation in the wave resistance of an amphibian air-cushion vehicle moving over a broken-ice field

The nonstationary rectilinear motion of an amphibian air-cushion vehicle (AACV) on a water surface covered with finely broken ice is considered for various modes of velocity variation. The influence of the water depth, flotation parameters, and mode of motion on the wave resistance of the vehicle is analyzed. Maneuvering methods for increasing or decreasing the wave resistance of AACVs are proposed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 97–102, January–February, 2007.