Discrete Markov ballistic missile defense system modeling

Expected value is a common and useful baseline used to compare different multi-layered missile defense strategies or fire doctrines (number of interceptors fired at one target). However, expected value by itself does not render enough information to the military or national security researchers regarding the probability distribution of the effectiveness of the entire missile defense system. The objective of this paper is to provide relevant probability distribution functions (pdf) for ballistic missile defense (BMD) planning and cost-effective analyzing. To achieve this goal, discrete time Markov process is utilized to model multi-layered BMD system. Most issues of the multi-layered BMD system are covered in this model, including multi-reentry vehicles, discrimination probabilities and accompanying risk and waste of defensive resources, probability to engage all of the hostile objects, and required inventory levels. The effectiveness of a multi-layered BMD system is expressed in the pdf form of the number of warheads or missiles penetrating the BMD system. This paper also suggests that by changing fire doctrines and comparing the resulting effectiveness against cost the BMD system might be optimized. Since Markov process modeling requires initial state, military intelligence and information will be necessary to generate the initial state.     

手指活动时大脑中磁共振信号的变化

用磁共振成像方法研究了大脑对手指活动的响应,观测到磁共振响应的反常时间过程曲线及很大的相对象元强度变化,特别是在大血管及脑脊液所在的区域。     

A microslip friction model with normal load variation induced by normal motion

A two-dimensional microslip friction model with normal load variation induced by normal motion is presented in this paper. The model is a distributed parameter model, which characterizes the stick-slip-separation of the contact interface and determines the resulting friction force, including its time variance and spatial distribution, between two elastic structures. When the relative motion is simple harmonic motion, the stick-slip-separation transition angles associated with any point in the contact area can be analytically determined within a cycle of motion. In addition, if the relative motion is given, stick-slip-separation transition boundaries inside the contact area and their time variances can be determined. Along with an iterative multi-mode solution approach utilizing harmonic balance method (HBM), the developed model can be employed to determine the forced response of frictionally constrained structures. In the approach, the forced response is constructed in terms of the free mode shapes of the structure; consequently, it can be determined at any excitation frequency and for any type of normal load distribution. Two examples, a one-dimensional beam like damper and a more realistic blade to ground damper, are employed to illustrate the predictive abilities of the developed model. It is shown that while employing a single mode model, transition boundaries for the beam like damper agrees with the results given in the literature, the developed method identifies the phase difference along the slip to stick transition boundary when a multi-mode model is employed. Moreover, while partial slip is illustrated in the two examples, typical softening and hardening effects, due to separation of the contact surface, are also predicted for the blade to ground damper.