Mechanical effects of corrosion: an old problem in a new setting

The alloys used for fuel and structural components in nuclear reactors suffer intense bombardment by damaging irradiation. For example, there are components in which every atom may be knocked off its lattice site and replaced by another several times during its lifetime in the core. It is not surprising, therefore, that much of the effort of nuclear metallurgists has been devoted to studying the rather esoteric subject of irradiation damage in metals and alloys. In the event, with thermal nuclear reactors at least, it has been relatively common metallurgical and chemical phenomena, such as thermal creep, fatigue, and corrosion, that have caused the majority of the difficulties.     

The inverse trochoid problem

If a circle in the plane is to roll along a track so that a given point on the circle traces out another circle, what must the shape of the track be? In this paper we give a full answer to this question. This question arises in the design of internal combustion engines and other machines. It is a sort of inverse problem to the classical problem of the trajectories of points on circles rolling inside other circles; the problem whose solution is hypocycloids and hypotrochoids. We derive a system of nonlinear differential equations for the coordinates of the track regarded as a parametric curve. We express the solution of this differential equation in terms of an elliptic integral. We establish the uniqueness of this solution for a given choice of the relevant parameters, the radius of the circle to be traced out and the location on the rolling circle of the tracing point. We show that if we allow the rolling circle to intersect the track, there is at least one track for any circle. We find all possible tracks, and we derive formulas to determine, for a given radius of the circle to be traced out, how many different tracks produce circles of that radius; there is always a finite number, and the number increases roughly linearly with the radius. We characterize those tracks that are mathematical solutions but are not practical physical solutions; tracks that the rolling circle intersects in such a way that it would get stuck.     

崩塌灾害的定量评价

通过对崩塌机理的分析,以及大量崩塌实例考察,对崩塌进行了定性分析,总结出判断崩塌发生可能性的定量指标.对影响崩塌发生的定量指标进行综合分析,运用回归分析总结出崩塌发生的可能性判别式.通过对实例的分析与规范验证对比,证明了模型的正确性.     

新手与专家问题

在科学实践和生活世界中,针对某一个问题,面对两个专家给出的不一致的或相矛盾的专家意见,外行或新手是否能又如何能获得辩护地相信一个专家意见而不是另一个专家意见,本文给出了这方面的分析。     

The inverse lure problem of optimal control

Given the linear system $\text{x}\text{}$ = Ax - bu, y = c^Tx, it is shown that, for a certain non-quadratic cost functional, the optimal control is given by u_opt(x) = h(c^Tx), where the function h(y) must satisfy the conditions ky²?h(y)y>0 for y≠0, h(0) = 0 and existence of h^-1 everywhere. The linear system considered must satisfy the Popov condition 1/k + (1 +?ωβ) G(?ω)>0 for all ω, G(s) being the y(s)/u(s) transfer function.