Widely repetition-tunable 200 fs pulse source using a Mach-Zehnder-modulator-based flat comb generator and dispersion-flattened dispersion-decreasing fiber

By combining a Mach-Zehnder-modulator-based flat comb generator (MZ-FCG) with a dispersion-flattened dispersion-decreasing fiber, femtosecond pulses have been generated from a cw light. Near-Fourier-transform-limit picosecond pulses generated from the MZ-FCG were compressed into femtosecond order by pulse compression. Our system enables flexible tuning of the repetition rate and pulse width, because those depend on the driving signal of the MZ-FCG. Pulse trains of 200 fs width were continuously and stably generated without mode hopping, with a repetition rate range from 5 to 17 GHz. Our system consists of a modulator and compression fiber; thus, the configuration is simpler and more stable.     

不同爆炸载荷下TA2钛合金圆管膨胀破坏过程

金属柱壳破坏过程与材料、结构及载荷等相关,断裂结果呈现多种形式,采用有限元结合实验对不同爆炸载荷作用下,TA2钛合金圆管的破坏机制开展研究。有限元结果显示:对于理想均质柱壳,由于冲击波传播使壁厚中间形成二次塑性区,圆管壁厚中部的等效塑性应变总是大于内、外壁。在较高爆压下,裂纹在加载阶段从试样壁厚中部起始,沿45°或135°向内外壁剪切扩展;而在较低爆压下,破坏发生在自由膨胀阶段,断裂从内壁起始向外壁剪切扩展,两者破坏过程和机制不同,总体来说,与实验现象符合较好。相关实验中出现的一些外壁拉伸断裂现象,可能与试样的几何、材料缺陷等因素相关,其对金属圆管爆炸破坏的影响值得进一步关注。     

A limiting analysis on regularization of singular SDP and its implication to infeasible interior-point algorithms

We consider primal-dual pairs of semidefinite programs and assume that they are singular, i.e., both primal and dual are either weakly feasible or weakly infeasible. Under such circumstances, strong duality may break down and the primal and dual might have a nonzero duality gap. Nevertheless, there are arbitrary small perturbations to the problem data which would make them strongly feasible thus zeroing the duality gap. In this paper, we conduct an asymptotic analysis of the optimal value as the perturbation for regularization is driven to zero. Specifically, we fix two positive definite matrices, \(I_p\) and \(I_d\), say, (typically the identity matrices), and regularize the primal and dual problems by shifting their associated affine space by \(\eta I_p\) and \(\varepsilon I_d\), respectively, to recover interior feasibility of both problems, where \(\varepsilon \) and \(\eta \) are positive numbers. Then we analyze the behavior of the optimal value of the regularized problem when the perturbation is reduced to zero keeping the ratio between \(\eta \) and \(\varepsilon \) constant. A key feature of our analysis is that no further assumptions such as compactness or constraint qualifications are ever made. It will be shown that the optimal value of the perturbed problem converges to a value between the primal and dual optimal values of the original problems. Furthermore, the limiting optimal value changes “monotonically” from the primal optimal value to the dual optimal value as a function of \(\theta \), if we parametrize \((\varepsilon , \eta )\) as \((\varepsilon , \eta )=t(\cos \theta , \sin \theta )\) and let \(t\rightarrow 0\). Finally, the analysis leads us to the relatively surprising consequence that some representative infeasible interior-point algorithms for SDP generate sequences converging to a number between the primal and dual optimal values, even in the presence of a nonzero duality gap. Though this result is more of theoretical interest at this point, it might be of some value in the development of infeasible interior-point algorithms that can handle singular problems.