Grid structure impact in sparse point representation of derivatives

In the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions.

Determination of stresses around a cylindrical single pile caused by horizontal movements of soils with the finitive element method

This study was carried out with the aim of modeling in 2D, in plain strain, the movement of a soft cohesive soil around a pile, in order to enable the determination of stresses resulting along the pile, per unit length. The problem in study fits into the large deformations problem and can be due to landslide, be close of depth excavations, to be near of zones where big loads are applied in the soil, etc. In this study is used an constitutive Elasto-Plastic model with the failure criterion of Mohr-Coulomb to model the soil behavior. The analysis is developed considering the soil in undrained conditions. To the modeling is used the finite element program PLAXIS, which use the Updated Lagrangian - Finite Element Method (UL-FEM). In this work, special attention is given to the soil-pile interaction, where is presented with some detail the formulation of the interface elements and some studies for a better understand of his behavior. It is developed a 2-D model that simulates the effect of depth allowing the study of his influence in the stress distribution around the pile. The results obtained give an important base about how behaves the movement of the soil around a pile, about how work the finite element program PLAXIS and how is the stress distribution around the pile. The analysis demonstrate that the soil-structure interaction modeled with the UL-FEM and interface elements is more appropriate to small deformations problems.

A Sensorless PMDC Motor Speed Controller with a Logical Overcurrent Protection

A method to control the speed or the torque of a permanent-magnet direct current motor is presented. The rotor speed and the external torque estimation are simultaneously provided by appropriate observers. The sensorless control scheme is based on current measurement and switching states of power devices. The observer’s performances are dependent on the accurate machine parameters knowledge. Sliding mode control approach was adopted for drive control, providing the suitable switching states to the chopper power devices. Despite the predictable chattering, a convenient first order switching function was considered enough to define the sliding surface and to correspond with the desired control specifications and drive performance. The experimental implementation was supported on a single dsPIC and the controller includes a logic overcurrent protection.

Internal structure of the nanogratings generated inside bulk fused sílica by ultrafast laser direct writing

The aim of the present work was to characterize the internal structure of nanogratings generated inside bulk fused silica by ultrafast laser processing and to study the influence of diluted hydrofluoric acid etching on their structure. The nanogratings were inscribed at a depth of 100 mu m within fused silica wafers by a direct writing method, using 1030 nm radiation wavelength and the following processing parameters: E = 5 mu J, tau = 560 fs, f = 10 kHz, and v = 100 mu m/s. The results achieved show that the laser-affected regions are elongated ellipsoids with a typical major diameter of about 30 mu m and a minor diameter of about 6 mu m. The nanogratings within these regions are composed of alternating nanoplanes of damaged and undamaged material, with an average periodicity of 351 +/- 21 nm. The damaged nanoplanes contain nanopores randomly dispersed in a material containing a large density of defects. These nanopores present a roughly bimodal size distribution with average dimensions for each class of pores 65 +/- 20 x 16 +/- 8 x 69 +/- 16 nm(3) and 367 +/- 239 x 16 +/- 8 x 360 +/- 194 nm(3), respectively. The number and size of the nanopores increases drastically when an hydrofluoric acid treatment is performed, leading to the coalescence of these voids into large planar discontinuities parallel to the nanoplanes. The preferential etching of the damaged material by the hydrofluoric acid solution, which is responsible for the pores growth and coalescence, confirms its high defect density. (C) 2014 AIP Publishing LLC.