Necking in non-isothermal high-speed spinning as a problem of sensitivity to external disturbances

Necking in non-isothermal high-speed melt spinning is treated as a problem of sensitivity to external disturbances at both ends of the spin-line. Necessary conditions for existence of necking are formulated in terms of the corresponding increments of velocities, forces, viscosities, etc. It is shown that necking may be present in the high-inertia range for a rather small viscosity variation. Small inertia effects require higher values of the radial viscosity gradients.     

Interval analysis method and convex models for impulsive response of structures with uncertain-but-bounded external loads

Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories of interval mathematics and convex models. The uncertain-but-bounded impulses are assumed to be a convex set, hyper-rectangle or ellipsoid. For the two non-probabilistic methods, less prior information is required about the uncertain nature of impulses than the probabilistic model. Comparisons between the interval analysis method and the convex model, which are developed as an anti-optimization problem of finding the least favorable impulsive response and the most favorable impulsive response, are made through mathematical analyses and numerical calculations. The results of this study indicate that under the condition of the interval vector being determined from an ellipsoid containing the uncertain impulses, the width of the impulsive responses predicted by the interval analysis method is larger than that by the convex model; under the condition of the ellipsoid being determined from an interval vector containing the uncertain impulses, the width of the interval impulsive responses obtained by the interval analysis method is smaller than that by the convex model.The project supported by the National Outstanding Youth Science Foundation of China (10425208), the National Natural Science Foundation of China and Institute of Engineering Physics of China (10376002) The English text was polished by Keren Wang.     

Effect of acoustic disturbances on a free convective flow

A gas-dynamic flow in an axisymmetric convective jet is studied experimentally. It is demonstrated that the jet flow with Grashof numbers Gr = (0.4–2.0) · 10⁶ is self-similar. Acoustic oscillations directed perpendicular to the axis of symmetry transform the profiles of the gas-flow parameters; two temperature maximums located outside the axis can appear. The results obtained indicate that flow instability is generated in high-gradient regions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 27–33, September–October, 2006.     

带展向曲率的超音速混合层中扰动演化的研究

超音速混合层的流动不稳定性较之亚音速或不可压的混合层大大减弱,为了提高混合效率, 通过数值模拟的方法分别研究了展向曲率、展向速度、来流马赫数等因素对混合效率所 起的作用. 计算结果表明：在给定展向速度的情况下,带有展向曲率的三维混合层,曲率越 大三维扰动增长率越大,而且法向的卷起范围也越大. 当展向曲率不为零时,展向速度的增 大也能有效地增强混合能力. 由流场中的高频扰动波产生的涡,在向下游发展过程中会有破 碎、拉伸,低频扰动波没有发现这一现象. 对于有展向曲率和展向速度的混合层,提高来流 马赫数时,流场中最不稳定扰动的增长率仍很大. 因此,这是一种提高混合层混合效率的新 途径.     

Numerical modeling of the disturbances of the separated flow in a rounded compression corner

Numerical modeling of the time-dependent supersonic flow over a compression corner with different roundness radii is performed on the basis of the solution of the two-dimensional Navier-Stokes equations in the regimes corresponding to local boundary layer separation. The development of unstable disturbances generated by local periodic injection/suction in the preseparated boundary layer is calculated. The results are compared with those of similar calculations for a flat plate. It is shown that the natural oscillations of the boundary-layer second mode stabilize in the separation zone and grow intensely downstream of the reattachment point. The acoustic modes excited within a separation bubble are studied using numerical calculations and an asymptotic analysis.     

Industrial application of impulsive high pressures in sheet forming with parameter optimization

Abstract

Impulsive high pressures for sheet forming are widely used in the modem industry. Applied aspects of the impulsive forming problem, including both control external stress and heat influence parameters are stated in the present research. The problem is reproduced in the vector representation in the multidimensional space of optimizing functions. In the case of a limited number of measurements the task leads to well known scalar representations with similar physical characteristics'.     

Three-dimensional Tollmien-Schlichting waves generated by sound in the boundary layer on an elastic surface at transonic free-stream velocities

Within the framework of the triple-deck theory, the effect of surface elasticity on three-dimensional packets of Tollmien-Schlichting waves generated by acoustic disturbances induced near the boundary layer at transonic free-stream velocities is investigated. It is shown that the elasticity of the surface considerably weakens the most unstable oblique waves but does not change the characteristic horseshoe shape of wave packets with two disturbance peaks propagating at an angle to the incoming flow.     

A study on time-limited control of single-pest with stage-structure

Two kinds of time-limited pest control models of single-pest with stage-structure, which can be described by the boundary value problem of ordinary differential equation and impulsive differential equation, are presented according to the ways of artificial control (continuous control and impulsive control). The conditions under which the corresponding model has a solution are given. If the model has a solution, the corresponding aim of pest control can be achieved. The theoretical results show that both the mature and the immature pest should be controlled synchronously, otherwise the aims of pest control can not be achieved in a finite time. Finally, some discussions and numerical simulations show that the impulsive control is more practical than the continuous control.     

Nonlinear boundary value problem of first order impulsive functional differential equations

This paper discusses nonlinear boundary value problem for first order impulsive functional differential equations. We establish several existence results by using the lower and upper solutions and monotone iterative techniques. Two examples are discussed to illustrate the efficiency of the obtained results.     

Convexity and characterization of optimal policies in a dynamic routing problem

An infinite horizon, expected average cost, dynamic routing problem is formulated for a simple failure-prone queueing system, modelled as a continuous time, continuous state controlled stochastic process. We prove that the optimal average cost is independent of the initial state and that the cost-to-go functions of dynamic programming are convex. These results, together with a set of optimality conditions, lead to the conclusion that optimal policies are switching policies, characterized by a set of switching curves (or regions), each curve corresponding to a particular state of the nodes (servers).