Boundary control and estimation of reaction–diffusion equations on the sphere under revolution symmetry conditions

ABSTRACT

Recently, the problem of designing boundary controllers and observers for unstable linear constant-coefficient reaction–diffusion equation on N-balls has been solved by means of the backstepping method. However, the extension of these results to spatially varying coefficients is far from trivial. This work deals with radially varying reaction coefficients under revolution symmetry conditions on a sphere (the three-dimensional case). Under these conditions, the equations become singular in the radius. When applying the backstepping method, a similar type of singularity appears in the backstepping control and observer kernel equations. However, with a simple scaling transformation, we are able to reduce the singular equation to a regular equation, which turns out to be the same kernel equations appearing when using the one-dimensional backstepping method. In addition, the scaling transformation allows us to prove stability in the H ¹ space.     

Influence of Annealing on the Properties of Explosively Welded Titanium Grade 1—AW7075 Aluminum Alloy Bimetals

Explosive welding of titanium Grade 1 to AW7075 aluminum alloy arranged in parallel setup was performed. The annealing of produced bimetals at the temperatures of 450, 500 and 550 °C for times ranging from 20 to 100 h was carried out after explosive welding. The produced bimetal was characteristic by its wavy interface typical for that bonding process. Increase in the microhardness at the interface was recorded due to work hardening. Delamination of titanium Grade 1 flyer sheet was firstly observed when annealing temperature of 500 °C for 40 h was carried out. Annealing at 550 °C also resulted in delamination of upper sheet. The intermetallic compound (IMC) layer was observed at the interface after annealing of bimetals. The higher the annealing temperature and time, the higher the thickness of continuous IMC layer. The maximum measured thickness of IMC layer averaged 13 µm. Energy dispersive x-ray spectroscopy (EDS) and x-ray diffraction (XRD) analyses revealed that the interface layer is consisted of Al₁₈Ti₂Mg₃ IMC. Microhardness at the interface increased dramatically up to 439 HV0.1 after annealing of bimetal due to the presence of above-mentioned IMC.     

Influence of T4 Heat Treatment on Tribological Behavior of Za27 Alloy Under Lubricated Sliding Condition

The effects of heat treatment on the microstructure, hardness, tensile properties, and tribological behavior of ZA27 alloy were examined. The alloys were prepared by conventional melting and casting route. The heat treatment of samples included the heating up to 370 °C for 3 or 5 h, quenching in water, and natural aging. Lubricated sliding wear test were conducted on as-cast and heat-treated ZA27 samples using block-on-disc machine. The friction and wear behavior of alloys were tested in contact with steel discs using combinations of three levels of load (10, 30, and 50 N) and three levels of linear sliding speeds (0.26, 0.50, and 1.00 m/s). To determine the wear mechanisms, the worn surfaces of the samples were examined by scanning electron microscopy (SEM). The heat treatment resulted in reduction in the hardness and tensile strength but increase in elongation. The heat-treated alloy samples attained improved tribological behavior over the as-cast ones, under all combinations of sliding speeds and contact loads. The rate of improvement increased with duration of solutionizing process before quenching in water. Obtained tribological results were related to the effects of heat treatment on microstructure changes of alloy.     

Detection of lead in Zea mays by dual‐energy X‐ray microtomography at the SYRMEP beamline of the ELETTRA synchrotron and by atomic absorption spectroscopy

This study is related to the application of the X‐ray dual‐energy microradiography technique together with the atomic absorption spectroscopy (AAS) for the detection of lead on Zea mays stem, ear, root, and leaf samples. To highlight the places with lead intake, the planar radiographs taken with monochromatic X‐ray radiation in absorption regime with photon energy below and above the absorption edge of a given chemical element, respectively, are analyzed and processed. To recognize the biological structures involved in the intake, the dual‐energy images with the lead signal have been compared with the optical images of the same Z. mays stem. The ear, stem, root, and leaf samples have also been analyzed with the AAS technique to measure the exact amount of the hyperaccumulated lead. The AAS measurement revealed that the highest intake occurred in the roots while the lowest in the maize ears and in the leaf. It seems there is a particular mechanism that protects the seeds and the leaves in the intake process. Microsc. Res. Tech., 2010. © 2009 Wiley‐Liss, Inc. This article was published online on 1 December 2009. An error was subsequently identified. This notice is included in the online and print version to indicate that both have been corrected 19 February 2010.     

Formation of nanostructured epoxy networks containing polyhedral oligomeric silsesquioxane (POSS) blocks

Nanostructured epoxy networks, based on DGEBA and poly(oxypropylene)diamine (Jeffamine D), containing nano-sized inorganic blocks, polyhedral oligomeric silsesquioxanes (POSS), were investigated. The POSS were incorporated in the network as crosslinks or as pendant units by using octa- or monoepoxy-POSS monomers, respectively, as well as diepoxides with pendant POSS. The authors focused on investigating the relationship between the network formation process and the final product properties. The reactivity of the epoxy-functional POSS monomers, the hybrid systems' time of gelation, the gel fractions and the phase structure of the networks were determined using ¹H or ¹³C NMR spectroscopy, chemorheology experiments, sol-gel analysis and transmission electron microscopy (TEM).All the POSS epoxides tested show a reduced reactivity if compared to their respective model compounds due to sterical crowding in the neighborhood of their functional groups and due to reduced epoxy group mobility. The incorporation of pendant POSS into networks of the type DGEBA-Jeffamine D-monoepoxy-POSS hence took place only in the late reaction stage. Together with the high tendency of these POSS to aggregation, the kinetics favors the formation of small nano-phase-separated POSS domains, which act as physical crosslinks due to their covalent bonds to the organic matrix. At POSS loadings higher than 70%, topological constraint by POSS leads to a strongly reduced elastic chain mobility, thus additionally strongly reinforcing the networks. The network build-up and gelation of the octaepoxy-POSS-Jeffamine D system were slow compared to the reference DGEBA-Jeffamine D network due to a low octaepoxy-POSS reactivity and due to its strong tendency to cyclization reactions with primary amines. The topology of the amino groups is shown to be very important. In contrast to monoepoxy-POSS, the octaepoxy-POSS becomes dispersed as oligomeric junctions (purely chemical crosslinks) of the network in the cured product. The octaepoxide's reinforcing effect is small and is given only by its high functionality and not by its inorganic nature. The functionality effect is reduced by the mentioned cyclizations.