Elliptic Reconstruction and a Posteriori Error Estimates for Fully Discrete Semilinear Parabolic Optimal Control Problems

This article studies a posteriori error analysis of fully discrete finite element approximations for semilinear parabolic optimal control problems. Based on elliptic reconstruction approach introduced earlier by Makridakis and Nochetto [25], a residual based a posteriori error estimators for the state, co-state and control variables are derived. The space discretization of the state and co-state variables is done by using the piecewise linear and continuous finite elements, whereas the piecewise constant functions are employed for the control variable. The temporal discretization is based on the backward Euler method. We derive a posteriori error estimates for the state, co-state and control variables in the $L^\infty(0,T;L^2(\Omega))$-norm. Finally, a numerical experiment is performed to illustrate the performance of the derived estimators.     

Effect of initial orientation on twinning in commercially pure titanium

Abstract

The effect of initial orientation on twinning micro-mechanisms during tensile deformation of commercially pure titanium has been studied using micro focus X-ray diffraction and electron back scatter diffraction (EBSD) in a scanning electron microscope. Three orientations A, B and C obtained from a rolled and annealed block of commercially pure titanium were deformed in uniaxial tension till failure and the tested specimens were characterised with regard to bulk texture, microstructure and crystal orientation mapping using EBSD. Orientation B along the transverse direction in ND-TD plane exhibits higher strength and lower strain hardening compared to orientations A and C along the rolling direction in TD-RD and ND-RD plane, respectively. This is attributed to different texture of sample B compared to samples A and C leading to dissimilar twinning micro-mechanisms and characteristic variation in nature of twinning. It is observed that limited twin nucleation and prominent lateral growth plays a dominant role in orientation B while multiple twin nucleation with significant non-Schmid behaviour is dominant for the other two orientations. It is proposed from this study that conventional factors associated with twin formation like Schmid factor play a main role in twin nucleation and propagation, however, growth or lateral thickening of the twins is explained by elastic stiffness variation across twins and their parent grains.     

Gamma-induced modifications of polycarbonate polymer

Gamma-induced modifications in polycarbonate polymer have been studied in the dose range of 10¹–10⁶ Gy. Thin films of polycarbonate have been irradiated with different gamma doses from a Co⁶⁰ source. To monitor the modifications caused by gamma radiation, FT-IR, differential scanning calorimetry and X-ray diffraction studies have been performed. The studies have indicated that at the dose of 10⁶ Gy, phenolic group forms through scissioning of ester linkage. Though the effect of radiation is most significant at the highest dose, the process of modifications starts at 10³ Gy. Scissioning of the polymeric chain initiates a different morphological zone within the polymer matrix, and the polymer becomes more crystalline with increasing dose. Owing to chain scissioning, the mobility of the polymer increases, which in turn reduces the glass transition temperature of the polymer.     

Coupling and crosstalk characteristics of hybrid silicon plasmonic waveguides

In this paper, the design and analysis of an ultracompact coupler based on a hybrid silicon plasmonic waveguide (HSPW) is proposed and its coupling and crosstalk characteristics have been theoretically investigated for the development of optical interconnects that can be realized using well-established complementary metal-oxide-semiconductor-compatible fabrication techniques. To determine the minimum horizontal separation distance and efficient coupling length for the designed coupler, the symmetric and antisymmetric supermodes are obtained and their characteristics are studied at a wavelength of 1.55 μm. Efficient light coupling is exhibited by the HSPW coupler with 75 % of power transfer between the two HSPWs with ultrashort coupling length of 2.14 μm when the separation distance is 50 nm. Further, it is shown that the crosstalk is significantly reduced with the insertion of metallic strip between the two HSPWs for realizing highly dense integrated plasmonic circuits.     

Dielectric relaxation of CdSe nanoparticles

Nanoparticles of cadmium selenide (CdSe) have been synthesized by soft chemical route using mercaptoethanol as a capping agent. X-ray diffraction and transmission electron microscope measurements show that the prepared sample belongs to sphalerite structure with the average particle size of 25 nm. The band gap of the material is found to be 2.1 eV. The photoluminescence (PL) emission spectra of the sample are measured at various excitation wavelengths. The PL spectra appear in the visible region, and the emission feature depends on the wavelength of the excitation. Impedance spectroscopy is applied to investigate the dielectric relaxation of the sample in a temperature range from 323 to 473 K and in a frequency range from 42 Hz to 1.1 MHz. The complex impedance plane plot has been analyzed by an equivalent circuit consisting of two serially connected R-CPE units, each containing a resistance (R) and a constant phase element (CPE). The dielectric relaxation of the sample is investigated in the electric modulus formalism. The temperature dependent relaxation times obey the Arrhenius law. The Havriliak–Negami model is used to investigate the dielectric relaxation mechanism in the sample. The frequency dependent conductivity spectra are found to obey the power law.     

Behavior of nonlinear fluid viscous dampers for control of shock vibrations

Fluid viscous dampers have been widely used for suppression of high velocity shocks. While linear fluid viscous dampers have been used for a long time, nonlinear fluid viscous dampers show considerable promise due to their superior energy dissipation characteristics and significant reduction in the damper force compared to a linear fluid viscous damper for the same peak displacement. This paper presents results from experimental study to characterize fluid viscous dampers when subjected to half-cycle sine shock excitation. The mathematical formulation and a numerical study to evaluate the relative performance of structures with fluid viscous dampers subjected to short-duration shock (impulse) loading are also discussed. The influence of damper nonlinearity (α) and the supplemental damping ratio (ξ_sd) on response has been investigated. The supplemental damping ratio of nonlinear fluid viscous dampers when subjected to shock excitation is found by equivalent linearization using the concept of equal energy dissipation. The paper also presents some design charts, which can be used for preliminary decisions on parameters of nonlinear dampers to be used in design.     

Evaluating the information content of a measure of plant output: An application to high-technology manufacturing

Commonly used measures of plant output have been criticized for their inability to provide information required to manage the dynamic operations of high-technology manufacturing plants. In this paper, we propose tests to evaluate the information content of a measure of plant output that is specifically directed at these issues. These tests are based on recent developments in DATA Envelopment Analysis (DEA), namely the Cone Ratio Envelopments. In this new application of DEA models, we shift the focus from Decision Making Units (DMUs) being evaluated to the DMUs that are being used to effect evaluations. The proposed tests are applied to evaluate the information contnet of a complexity adjusted measure of plant output, which we refer to as Total Net Die Equivalent (TNDE). Developed recently in the context of a high-technology manufacturing plant—a wafer fabrication plant of a merchant semiconductor manufacturing company-TNDE reflects the ongoing changes in product and process technologies, process flow characteristics, and volume of production. Evaluating the information content on joint criteria of recency and efficiency, the results of our tests, conducted over a 28-month period in the wafer fabrication plant,show that TNDE as a single aggregate (scalar) measure of plant output outperforms the two outputs from which it is synthesized. Thus, TNDE as a single measure of output can be used to provide an improved basis for planning a plant's future operations. En route to the development and application of the proposed tests, we illustrate how DEA concepts and models provide a rigorous and systematic basis for conducting ex post technology evaluation to guide continuous improvements in a plant's current operations.     

Ballistic transmission through quasi-periodic shape barrier resonant tunneling structures

A theoretical model is proposed to study the ballistic electron transport for a quasi-periodic multibarrier structure where two different barrier shapes are arranged according to the Thue–Morse sequence. Important tunneling features are revealed form such arrangements. It is noted that the tunneling band spectrum could be fragmented by tailoring the shape of the barriers in the structure. Results for the transmission coefficients and the current densities are compared with the corresponding periodic and single shape barrier arrangements. The quasi-periodic structure consisting of the rectangular and triangular barrier shapes is suggested to be more suitable for the electronic and opto-electronic devices due to its high negative differential conducting effect.