An introduction to the topological derivative

PurposeThis paper provides a self-contained introduction to the mathematical aspects of the topological derivative.Design/methodology/approachFull justifications are given on simple model problems following a modern approach based on the averaged adjoint state technique. Extensions are discussed in relation with the literature on the field.FindingsClosed expressions of topological derivatives are obtained and commented.Originality/valueSeveral cases are covered in a unified and didactic presentation. Some elements of proof are novel.

Effect of Thermally Formed Alumina on Density of AlMgSi Alloys Extrudate Recycled Via Solid State Technique

Solid state recycling of aluminium via hot extrusion is a sustainable technique. The process performed before hot extrusion plays a vital role on the extrudate properties. In this study, the effect of naturally and thermally formed in-situ alumina on the extrudate density were investigated. Fours type of material identified as a solid as-received, non-treated recycle chip, 300 0C thermally treated recycle chip and 500 0C thermally treated recycle chip were prepared for the experiment. Prior to extrusion, the recycle chips were compacted into a chip-based billet, preheated and immediately extruded into a semi-finished product. The density test performed on the chip-based extrudate found that the type of chips influenced the density. The chip-based extrudate made of 300 0C and 500 0C thermally treated chips resulted in higher density than solid as-received and non-treated chips. Chip-based extrudate produced from 500 0C thermally treated chips resulted in density of 2724 kg/m3, which is the highest among the specimen. This density value was 0.7 % higher compared to the solid as-received extrudate. Microstructure examination on the cross-section revealed the alumina entrapped in the chip-based extrudate. The alumina entrapped in 500 0C thermally treated chips specimen was more prone than the non-treated and 300 0C thermally-treated chips. This finding explains the variation in the extrudate density.

ABO4 type scheelite phases in (Ca/Sr)MoO4 - BiVO4 - Bi2Mo3O12 systems: synthesis, structure and optical properties

The cation deficient complex oxides of (Ca/Sr)MoO4 - BiVO4 - Bi2Mo3O12 triple system are promising photocatalysts and pigments. Compounds with general formula of Ca1−1.5x-yBix+yФxMo1-yVyO4 and Sr1−1.5x-yBix+yФxMo1-yVyO4 were synthesized byconvention solid state technique in the range of 550–720 °C. Two wide regions of the solid solutions (ordinary and superstructured scheelite-type phases respectively) were found for each system. The diffuse scatering of homogeneous samples was investigated in the range of 190–1100 nm. Energy gaps calculated with linear approximation of Kubelka-Munk function decreases with bismuth and vanadium content.

Bioactive glass doped with noble metal nanoparticles for bone regeneration: in vitro kinetics and proliferative impact on human bone cell line

This work investigates the bioactivity of novel silver-doped (BG-Ag) and gold-doped (BG-Au) quaternary 46S6 bioactive glasses synthesized via a semi-solid-state technique.

Tribological characteristics of friction stir processed graphite and tin/LM24 surface composites

Friction stir processing (FSP) is an emerging solid-state technique for preparing surface composites using various reinforcements. Ceramics and metallic particles are easily reinforced in a matrix by this technique. Surface composites made from an LM24 alloy reinforced with graphite and tin, with good wettability and material flow owing to the low melting point of tin, were fabricated by FSP at two rotational speeds of 1,400 and 1,000 rpm. Despite its low hardness, the graphite/LM24 surface composite fabricated at a higher rotational speed of 1,400 rpm exhibited better wear resistance. However, its frictional behavior was not significantly affected by the reinforcement. The fabricated surface composites with graphite and tin reinforcement as well as graphite-only reinforcement exhibited contradicting behaviors under sliding wear conditions. The post wear analysis indicated that abrasion, adhesion, layer formation, and delamination occurred on the composite surfaces.