Multi-Scale Jacobi Method for Anderson Localization

A new KAM-style proof of Anderson localization is obtained. A sequence of local rotations is defined, such that off-diagonal matrix elements of the Hamiltonian are driven rapidly to zero. This leads to the first proof via multi-scale analysis of exponential decay of the eigenfunction correlator (this implies strong dynamical localization). The method has been used in recent work on many-body localization [arXiv:1403.7837].Comment: 34 pages, 8 figures, clarifications and corrections for published version; more detail in Section 4.

End-to-end Distance from the Green's Function for a Hierarchical Self-Avoiding Walk in Four Dimensions

In [BEI] we introduced a Levy process on a hierarchical lattice which is four dimensional, in the sense that the Green's function for the process equals 1/x^2. If the process is modified so as to be weakly self-repelling, it was shown that at the critical killing rate (mass-squared) \beta^c, the Green's function behaves like the free one. - Now we analyze the end-to-end distance of the model and show that its expected value grows as a constant times \sqrt{T} log^{1/8}T (1+O((log log T)/log T)), which is the same law as has been conjectured for self-avoiding walks on the simple cubic lattice Z^4. The proof uses inverse Laplace transforms to obtain the end-to-end distance from the Green's function, and requires detailed properties of the Green's function throughout a sector of the complex \beta plane. These estimates are derived in a companion paper [math-ph/0205028].Comment: 29 pages, v2: reference

Effects of leading-edge devices on the low-speed aerodynamic characteristics of a highly-swept arrow-wing

An investigation was conducted in the Texas A&M University 7 by 10 foot Low Speed Wind Tunnel to provide a direct comparison of the effect of several leading edge devices on the aerodynamic performance of a highly swept wing configuration. Analysis of the data indicates that for the configuration with undeflected leading edges, vortex separation first occurs on the outboard wing panel for angles of attack of approximately 2, and wing apex vorticies become apparent for alpha or = 4 deg. However, the occurrence of the leading edge vortex flow may be postponed with leading edge devices. Of the devices considered, the most promising were a simple leading edge deflection of 30 deg and a leading edge slat system. The trailing edge flap effectiveness was found to be essentially the same for the configuration employing either of these more promising leading edge devices. Analysis of the lateral directional data showed that for all of the concepts considered, deflecting leading edge downward in an attempt to postpone leading edge vortex flows, has the favorable effect of reducing the effective dihedral

High-resolution stress mapping of polycrystalline alumina compression using synchrotron X-ray diffraction

The ability to achieve uniform stress in uniaxial compression tests of polycrystalline alumina is of significance for the calibration of piezospectroscopic coefficients as well as strength studies in ceramics. In this study high-energy X-rays were used to capture powder diffraction profiles over a half-section of a polycrystalline alumina parallelepiped sample under an increasing uniaxial compressive load. The data were converted to strain and results were used for stress mapping of the sample. Stress maps from the study quantify the higher stresses at the sample-platen contact interface and reveal the evolution of the stress distribution in these specimens with load. For the geometry of the samples used, at the center section of the specimen the overall magnitudes of the compressive stresses were found to be 20% higher compared with the average expected theoretical stress based on the applied load and cross-sectional area. The observed compressive stresses at the corners of the parallelepiped specimen were 62% higher and shear stresses were observed at the specimen interface to the load mechanism. The effects, seen at the interface, can lead to premature failure at these locations and can affect the accuracy of calibration of spectral peaks with stress as well as compression strength measurements. The results provide important information that can be used to establish guidelines on material and geometry considerations in developing compression tests on high-strength ceramics