Anderson transition in a three dimensional kicked rotor

We investigate Anderson localization in a three dimensional (3d) kicked rotor. By a finite size scaling analysis we have identified a mobility edge for a certain value of the kicking strength $k = k_c$. For $k > k_c$ dynamical localization does not occur, all eigenstates are delocalized and the spectral correlations are well described by Wigner-Dyson statistics. This can be understood by mapping the kicked rotor problem onto a 3d Anderson model (AM) where a band of metallic states exists for sufficiently weak disorder. Around the critical region $k \approx k_c$ we have carried out a detailed study of the level statistics and quantum diffusion. In agreement with the predictions of the one parameter scaling theory (OPT) and with previous numerical simulations of a 3d AM at the transition, the number variance is linear, level repulsion is still observed and quantum diffusion is anomalous with $\propto t^{2/3}$. We note that in the 3d kicked rotor the dynamics is not random but deterministic. In order to estimate the differences between these two situations we have studied a 3d kicked rotor in which the kinetic term of the associated evolution matrix is random. A detailed numerical comparison shows that the differences between the two cases are relatively small. However in the deterministic case only a small set of irrational periods was used. A qualitative analysis of a much larger set suggests that the deviations between the random and the deterministic kicked rotor can be important for certain choices of periods. Contrary to intuition correlations in the deterministic case can either suppress or enhance Anderson localization effects.Comment: 10 pages, 5 figure

A unified primal dual active set algorithm for nonconvex sparse recovery

In this paper, we consider the problem of recovering a sparse signal based on penalized least squares formulations. We develop a novel algorithm of primal-dual active set type for a class of nonconvex sparsity-promoting penalties, including ℓ 0 , bridge, smoothly clipped absolute deviation, capped ℓ 1 and minimax concavity penalty. First, we establish the existence of a global minimizer for the related optimization problems. Then we derive a novel necessary optimality condition for the global minimizer using the associated thresholding operator. The solutions to the optimality system are coordinatewise minimizers, and under minor conditions, they are also local minimizers. Upon introducing the dual variable, the active set can be determined using the primal and dual variables together. Further, this relation lends itself to an iterative algorithm of active set type which at each step involves first updating the primal variable only on the active set and then updating the dual variable explicitly. When combined with a continuation strategy on the regularization parameter, the primal dual active set method is shown to converge globally to the underlying regression target under certain regularity conditions. Extensive numerical experiments with both simulated and real data demonstrate its superior performance in terms of computational efficiency and recovery accuracy compared with the existing sparse recovery methods

Approach for testing the material behavior in roll forming in a small scale

Roll forming of ultra-high strength steels (UHSS) and other high strength alloys is an advanced manufacturing methodology with the ability of cold forming those materials to complex three-dimensional shapes for lightweight structural applications. Due to their high strength, most of these materials have a reduced ductility which excludes conventional sheet forming methods under cold forming conditions. Roll forming is possible due to its low strains and incremental forming characteristic. Recent research investigates the development of high strength nano-structured aluminum sheet and titanium alloys, as well as their behaviour in roll forming with regard to formability, material behaviour and shape defects. The development of new materials is often limited to small scale samples due to the high preparation costs. In contrast, industrial application needs larger scale tests for validation, especially in roll forming where a minimum sheet length is required to feed the sample trough the roll forming machine. This work describes a novel technique for studying roll forming of a short length of experimental material. DP780 steel strips (500mm &ndash; 1300mm length) were welded between two mild steel carrier sheets of similar width and thickness giving an overall strip length of 2m. Roll forming trials were performed and longitudinal edge strain, bow and springback determined on the welded samples and samples formed of full length DP780 strip before and after cut off. The experimental results of this work show that this method gives a reasonable approach for predicting material behavior in roll forming transverse to the rolling direction. In contrast to that significant differences in longitudinal bow were observed between the welded sections and the sections formed of full length DP780 strip; this indicates that the applicability of this method is limited with regard to predicting longitudinal material behavior in roll forming.<br /

Failure analysis of a diesel engine crankshaft

In this paper, the macroscopic observation and chemical composition analysis of the third crankshaft journal have been carried out. Moreover, macroscopic observation, chemical composition analysis and metallographic analysis were carried out, and were compared with the journal with cracks and without cracks. Based on the experimental results and the causes of crankshaft neck cracks, it can be concluded that the crack form of crankshaft goes along with the grain brittle direction