Multistage Markov Chain Modeling of the Genetic Algorithm and Convergence Results

The genetic algorithm (GA) has been widely used to solve combinatorial global optimization problems. Despite the successes that GA encounters in practical applications, there exist few precise results on its behavior. In this article, we formulate a fully rigorous mathematical modeling of GA as a multistage Markov chain and derive convergence results. Variations that include the simulated annealing algorithm and the GA with superindividual are considered.     

GENERALIZATION OF AN INVERTIBLE TRANSFORMATION AND EXAMPLES OF ITS APPLICATIONS

Recently we highlighted the remarkable nature of an explicitly invertible transformation, we reported some generalizations of it and examples of its expediency in several mathematical contexts: algebraic and Diophantine equations, dynamical systems (with continuous and discrete time), nonlinear PDEs, analytical geometry, functional equations. In this paper we report a significant generalization of this approach and we again illustrate via some analogous examples its expediency to identify problems which appear far from trivial but are in fact explicitly solvable.     

Evolution of local atomic structure in a melt-spun Ni25Ti50Cu25 shape memory alloy during crystallization

The local atomic environment of a melt-spun Ni₂₅Ti₅₀Cu₂₅ amorphous alloy and bond evolution during crystallization were studied by extended X-ray absorption fine structure (EXAFS) spectroscopy and differential scanning calorimetry. In the amorphous alloy, the interatomic distances of Ni–Ti and Cu–Ti are distinct from Ti–Ti and can be indicative of the formation of two types of dominant polyhedra or distorted polyhedral clusters centered with Ni and Cu, with the majority of shell atoms being Ti. The overall increase in the coordination numbers of Ni, Ti, and Cu by crystallization and evidence for structural relaxation suggest that the melt-spun ribbon contains a combination of ordered structures and free volume prior to the heat treatment. Copper and nickel are co-located as their absorption spectra are similar. Although crystallization occurs rapidly (within 4?min at 500 °C), the local atomic environment change persists at longer annealing durations (up to 10?min). An increase in the Ti–Ti and Cu–Cu homo-bond fractions at short and intermediate annealing times suggests that these species segregate between Cu-rich and Cu-poor phases. Crystallization continues through a short-range Ti and Cu diffusion-dominated process, as the near-neighbor structures of Ti and Cu change considerably more than for Ni during annealing. This homogenizes the microstructure followed by possible precipitation of a TiCu compound.     

Annealing behaviour of ultrafine-grained aluminium

Ultrafine-grained (UFG) aluminium, processed under fast cooling rate conditions (12?K?s^?1) following hot rolling (water quenched) exhibits enhanced thermal stability due to an increase in concentration of solid solution atoms, relative to the furnace cooled material. The influence of fraction recrystallized on yield stress and uniform elongation is reported to exhibit a slight deviation from the linear behaviour that is anticipated on the basis of the rule-of-mixtures. This result was rationalized on the basis of differences in the spatial distributions of the UFG and coarse grains and/or dislocation recovery mechanisms.     

Thermal stability of ultrathin amorphous carbon films synthesized by plasma-enhanced chemical vapor deposition and filtered cathodic vacuum arc

Abstract

Ultrathin hydrogenated amorphous carbon (a-C:H) films deposited by plasma-enhanced chemical vapor deposition (PECVD) and hydrogen-free amorphous carbon (a-C) films of similar thickness deposited by filtered cathodic vacuum arc (FCVA) were subjected to rapid thermal annealing (RTA). Cross-sectional transmission electron microscopy (TEM) and electron energy loss spectroscopy (EELS) were used to study the structural stability of the films. While RTA increased the thickness of the intermixing layer and decreased the sp³ content of the a-C:H films, it did not affect the thickness or the sp³ content of the a-C films. The superior structural stability of the FCVA a-C films compared with PECVD a-C:H films, demonstrated by the TEM and EELS results of this study, illustrates the high potential of these films as protective overcoats in applications where rapid heating is critical to the device functionality and performance, such as heat-assisted magnetic recording.     

Two-step annealed CdS/CdSe co-sensitizers for quantum dot-sensitized solar cells

CdS/CdSe co-sensitizers on TiO₂ films were annealed using a two-step procedure; high temperature (300 °C) annealing of TiO₂/CdS quantum dots (QDs), followed by low temperature (150 °C) annealing after the deposition of CdSe QDs on the TiO₂/CdS. For comparison, two types of films were prepared; CdS/CdSe-assembled TiO₂ films conventionally annealed at a single temperature (150 or 300 °C) and non-annealed films. The 300 °C-annealed TiO₂/CdS/CdSe showed severe coalescence of CdSe QDs, leading to the blocked pores and hindered ion transport. The QD-sensitized solar cell (QD-SSC) with the 150 °C-annealed TiO₂/CdS/CdSe exhibited better overall energy conversion efficiency than that with the non-annealed TiO₂/CdS/CdSe because the CdSe QDs annealed at a suitable temperature (150 °C) provided better light absorption over long wavelengths without the hindered ion transport. The QD-SSC using the two-step annealed TiO₂/CdS/CdSe increased the cell efficiency further, compared to the QD-SSC with the 150 °C-annealed TiO₂/CdS/CdSe. This is because the 300 °C-annealed, highly crystalline CdS in the two-step annealed TiO₂/CdS/CdSe improved electron transport through CdS, leading to a significantly hindered recombination rate.     

Solvent‐Annealing‐Induced Nanowetting in Templates: Towards Tailored Polymer Nanostructures

We study the solvent‐annealing‐induced nanowetting in templates using porous anodic aluminum oxide membranes. The morphology of polystyrene and poly(methyl methacrylate) nanostructures can be controlled, depending on whether the swollen polymers are in the partial or complete wetting regimes, which are characterized by the spreading coefficient. When the swollen polymers are in the partial wetting regime, polymers wet the nanopores by capillary action, resulting in the formation of polymer nanorods. When the swollen polymers are in the complete wetting regime, polymers form wetting layers in the nanopores, resulting in the formation of polymer nanotubes. The solubility parameters of polymers and solvents are also used to predict the wetting behavior of swollen polymers in cylindrical geometry.     

‘Star‐like’ defects in Cd‐annealed CdZnTe crystals—an experimental study of their origin and formation mechanism

We conducted low‐temperature annealing experiments at temperatures slightly above and below the melting point of Te to clarify the effects of the state of Te inclusions (solid or liquid) upon the formation of ‘star‐like’ defects in Cd‐annealed CdZnTe (CZT). We also carried out post‐growth annealing experiments with and without using Cd vapor to clarify the mechanism of formation of such defects. We demonstrated that these ‘star‐like’ defects are due to the reaction between in‐diffused Cd atoms and the molten Te inclusions, but we found no observable ‘one‐to‐one’ correlation between ‘star‐like’ defects and Te inclusions. The non‐uniform distribution of Te inclusions in the CZT matrix could account for this phenomenon since the punching distance of the dislocations depends on the volume fraction of inclusions within the matrix.     

Effects of rapid thermal annealing on the morphology and optical property of ultrathin InSb film deposited on SiO2/Si substrate

Ultrathin InSb films on SiO2/Si substrates are prepared by radio frequency(RF) magnetron sputtering and rapid thermal annealing(RTA) at 300,400,and 500℃,respectively.X-ray diffraction(XRD) indicates that InSb film treated by RTA at 500℃,which is higher than its melting temperature(about 485℃),shows a monocrystalline-like feature.A high-resolution transmission electron microscopy(HRTEM) micrograph shows that melt recrystallization of InSb film on SiO2/Si(111) substrate is along the(111) planes.The transmittances of InSb films decrease and the optical band gaps redshift from 0.24 eV to 0.19 eV with annealing temperature increasing from 300℃ to 500℃,which is indicated by Fourier transform infrared spectroscopy(FTIR) measurement.The observed changes demonstrate that RTA is a viable technique for improving characteristics of InSb films,especially the melt-recrystallized film treated by RTA at 500℃.