A penalty approach for nonlinear optimization with discrete design variables

Introduced here is a simple approach to minimization problems with discrete design variables by modifying the penaly function approach of converting the constrained problems into sequential unconstrained minimization technique (SUMT) problems. It was discovered, during the course of the present work, that a similar idea was suggested by Marcal and Gellatly. However, no further work has been encountered. A brief description of the SUMT is presented. The form of the penalty function for the discrete-valued design variables and strategy used for the implementation of the procedure is discussed next. Finally, several design examples are used to demonstrate the procedure, and results are compared with the ones available in the literature

Lifetime determination of excited states in Cd-106

Two separate experiments using the Differential Decay Curve Method have been performed to extract mean lifetimes of excited states in 106 Cd. The inedium-spin states of interest were populated by the Mo-98(C-12, 4n) Cd-106 reaction performed at the Wright Nuclear Structure Lab., Yale University. From this experiment, two isomeric state mean lifetimes have been deduced. The low-lying states were populated by the Mo-96(C-13, 3n)Cd-106 reaction performed at the Institut fur Kernphysik, Universitat zu Koln. The mean lifetime of the I-pi = 2(1)(+) state was deduced, tentatively, as 16.4(9) ps. This value differs from the previously accepted literature value from Coulomb excitation of 10.43(9) ps

Formation of Ge-Sn nanodots on Si(100) surfaces by molecular beam epitaxy

The surface morphology of Ge0.96Sn0.04/Si(100) heterostructures grown at temperatures from 250 to 450°C by atomic force microscopy (AFM) and scanning tunnel microscopy (STM) ex situ has been studied. The statistical data for the density of Ge0.96Sn0.04 nanodots (ND) depending on their lateral size have been obtained. Maximum density of ND (6 × 1011 cm-2) with the average lateral size of 7 nm can be obtained at 250°C. Relying on the reflection of high energy electron diffraction, AFM, and STM, it is concluded that molecular beam growth of Ge1-xSnx heterostructures with the small concentrations of Sn in the range of substrate temperatures from 250 to 450°C follows the Stranski-Krastanow mechanism. Based on the technique of recording diffractometry of high energy electrons during the process of epitaxy, the wetting layer thickness of Ge0.96Sn0.04 films is found to depend on the temperature of the substrate

Isomeric Decay of \u3csup\u3e208\u3c/sup\u3eRa

Low-energy excited states of 208Ra were investigated using the 182W(30Si, 4n) reaction at the Wright Nuclear Structure Laboratory of Yale University. Fusion evaporation recoils were selected using the gas-filled spectrometer SASSYER. Delayed γ rays, following isomeric decays, were detected at the focal plane of SASSYER with a small array of three clover Ge detectors. Transitions following a proposed J π = 8+ isomer were observed, and the half-life was measured

High-spin States in \u3csup\u3e191, 193\u3c/sup\u3eAu and \u3csup\u3e192\u3c/sup\u3ePt: Evidence for Oblate Deformation and Triaxial Shapes

High-spin states of 191, 193Au and 192Pt have been populated in the 186W(11B, xn) and 186W(11B, p4n) reactions, respectively, at a beam energy of 68 MeV and their γ decay was studied using the YRAST Ball detector array at the Wright Nuclear Structure Laboratory at Yale University. The level scheme of 193Au has been extended up to Iπ = 55/2+. New transitions were observed also in 191Au and 192Pt. Particle-plus-Triaxial-Rotor (PTR) and Total Routhian Surface (TRS) calculations were performed to determine the equilibrium deformations of the Au isotopes. The predictions for oblate deformations in these nuclei are in agreement with the experimental data. Development of nonaxial shapes is discussed within the framework of the PTR model

Isomers and Seniority in the Trans-Pb Nuclei

Low-energy excited states of 210Ra and 208Ra were investigated at the Wright Nuclear Structure Laboratory of Yale University. Fusion evaporation recoils were selected using the gas-filled spectrometer, SASSYER. Delayed γ -rays, following isomeric decays, were detected at the focal plane of SASSYER with a small array of HPGe detectors. Transitions following the proposed J π = 8+ isomers were observed, and the half-lives measured. The experiments are discussed and results compared to expectations from the seniority scheme

Free vibration analysis and design optimization of SMA/Graphite/Epoxy composite shells in thermal environments

Composite shells, which are being widely used in engineering applications, are often under thermal loads. Thermal loads usually bring thermal stresses in the structure which can significantly affect its static and dynamic behaviors. One of the possible solutions for this matter is embedding Shape Memory Alloy (SMA) wires into the structure. In the present study, thermal buckling and free vibration of laminated composite cylindrical shells reinforced by SMA wires are analyzed. Brinson model is implemented to predict the thermo-mechanical behavior of SMA wires. The natural frequencies and buckling temperatures of the structure are obtained by employing Generalized Differential Quadrature (GDQ) method. GDQ is a powerful numerical approach which can solve partial differential equations. A comparative study is carried out to show the accuracy and efficiency of the applied numerical method for both free vibration and buckling analysis of composite shells in thermal environment. A parametric study is also provided to indicate the effects of like SMA volume fraction, dependency of material properties on temperature, lay-up orientation, and pre-strain of SMA wires on the natural frequency and buckling of Shape Memory Alloy Hybrid Composite (SMAHC) cylindrical shells. Results represent the fact that SMAs can play a significant role in thermal vibration of composite shells. The second goal of present work is optimization of SMAHC cylindrical shells in order to maximize the fundamental frequency parameter at a certain temperature. To this end, an eight-layer composite shell with four SMA-reinforced layers is considered for optimization. The primary optimization variables are the values of SMA angles in the four layers. Since the optimization process is complicated and time consuming, Genetic Algorithm (GA) is performed to obtain the orientations of SMA layers to maximize the first natural frequency of structure. The optimization results show that using an optimum stacking sequence for SMAHC shells can increase the fundamental frequency of the structure by a considerable amount