Irreducible cyclic presentations of the trivial group

We produce families of irreducible cyclic presentations of the trivial group. These families comprehensively answer questions about such presentations asked by Dunwoody and by Edjvet, Hammond, and Thomas. Our theorems are purely theoretical, but their derivation is based on practical computations. We explain how we chose the computations and how we deduced the theorems.

Effects of boron-strontium interactions on eutectic modification in Al-10 mass%Si alloys

The effects of boron and strontium interactions on the eutectic silicon in hypoeutectic Al-Si alloys have been studied. Samples were prepared from an AI-I 0 mass%Si base alloy with different Al-B additions, alone and in combination with strontium. In alloys containing no strontium, boron additions do not cause modification of the eutectic silicon, while in strontium containing alloys, boron additions reduce the level of modification of the eutectic silicon. Thermal analysis parameters and eutectic silicon microstructures were investigated with respect to the Sr to B ratio. In order to modify the eutectic silicon, a Sr/B ratio exceeding 0.4 is required.

Comparing social security programs with leisure and bequests

This paper compares social security programs in the AK model with leisure and bequests. It will show that the unfunded program with contribution-dependent benefits has smaller distortions than programs (funded or unfunded alike) with contribution-independent benefits. (C) 2002 Elsevier Science B.V. All rights reserved.

Eutectic modification of Al-Si alloys with rare earth metals

The effects of different concentrations of individual additions of rare earth metals (La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu) on eutectic modification in Al-10mass%Si has been studied by thermal analysis and optical microscopy. According to the twin-plane re-entrant edge (TPRE) and impurity induced twinning mechanism, rare earth metals with atomic radii of about 1.65 times larger than that of silicon, are possible candidates for eutectic modification. All of the rare earth elements caused a depression of the eutectic growth temperature, but only Eu modified the eutectic silicon to a fibrous morphology. At best, the remaining elements resulted in only a small degree of refinement of the plate-like silicon. The samples were also quenched during the eutectic arrest to examine the eutectic solidification modes. Many of the rare-earth additions significantly altered the eutectic solidification mode from that of the unmodified alloy. It is concluded that the impurity induced twinning model of modification, based on atomic radius alone, is inadequate and other mechanisms are essential for the modification process. Furthermore, modification and the eutectic nucleation and growth modes are controlled independently of each other.

Eutectic solidification and its role in casting porosity formation

Understanding and controlling the eutectic solidification process in Al-Si alloys permits prediction of the formation of casting porosity, eventually leading to methods for its control and elimination. In addition, it enables control of eutectic structure, silicon morphology, and eutectic grain size to further improve the alloy properties. This paper presents the current understanding of eutectic solidification in hypoeutectic Al-Si foundry alloys and the relationship between eutectic solidification and porosity formation. New concepts in engineering eutectic solidification are also explored.

Aluminium phosphide as a eutectic grain nucleus in hypoeutectic Al-Si alloys

Aluminium phosphide (AlP) particles arc often suggested to be the nucleation site for eutectic silicon in Al-Si alloys, since both the crystal structure and lattice parameter of AlP (crystal structure: cubic K(4) over bar m; lattice parameter: 5.421 Angstrom) are close to that of silicon (cubic Fd3m, 5.431 Angstrom), and the melting point is higher than the Al-Si eutectic temperature. However, the crystallographic relationships between AlP particles and the surrounding eutectic silicon are seldom reported due to the difficulty in analysing the AlP particles, which react with water during sample preparation for polishing. in this study, the orientation relationships between AlP and Si are analysed by transmission electron microscopy using focused ion-beam milling for sample preparation to investigate the nucleation mechanism of eutectic silicon on AlP. The results show a clear and direct lattice relationship between centrally located AlP particles and the surrounding silicon in the hypoeutectic Al-Si alloy.

Experimenting with infinite groups, I

A group is termed parafree if it is residually nilpotent and has the same nilpotent quotients as a given free group. Since free groups are residually nilpotent, they are parafree. Nonfree parafree groups abound and they all have many properties in common with free groups. Finitely presented parafree groups have solvable word problems, but little is known about the conjugacy and isomorphism problems. The conjugacy problem plays an important part in determining whether an automorphism is inner, which we term the inner automorphism problem. We will attack these and other problems about parafree groups experimentally, in a series of papers, of which this is the first and which is concerned with the isomorphism problem. The approach that we take here is to distinguish some parafree groups by computing the number of epimorphisms onto selected finite groups. It turns out, rather unexpectedly, that an understanding of the quotients of certain groups leads to some new results about equations in free and relatively free groups. We touch on this only lightly here but will discuss this in more depth in a future paper.

Migration of crystals during the filling of semi-solid castings

In cold-chamber high-pressure die castings (HPDC), the microstructure consists of coarse externally solidified crystals (ESCs) that are commonly observed in the central region of cross sections. In the present work, controlled laboratory scale casting experiments have been conducted with particular emphasis on the flow and solidification conditions. An A356 aluminum alloy was used to produce castings by pouring semi-solid metal through a steel die. Microstructures similar to those encountered in HPDC have been produced and the resulting microstructure is found to depend on the melt and die temperature: (1) the fraction of ESCs determines the extent of migration to the central region; (2) a maximum packing determines the area fraction of ESCs in the center; and (3) the die temperature affects the position of the ESCs-a higher die temperature can induce a displaced ESC distribution. It is found that the n-figration of crystals to the central region requires a flow, which is constrained at all melt/die interfaces. Furthermore, potential lift mechanisms are discussed. An assessment of the Saffman lift force on individual particles shows it has no significant effect on the migration of ESCs.

Enhancing the ratio of molecular ions to non-covalent compounds in the electrospray interface of LC-MS in quantitative analysis

A common problem encountered during the development of MS methods for the quantitation of small organic molecules by LGMS is the formation of non-covalently bound species or adducts in the electrospray interface. Often the population of the molecular ion is insignificant compared to those of all other forms of the analyte produced in the electrospray, making it difficult to obtain the sensitivity required for accurate quantitation. We have investigated the effects of the following variables: orifice potential, nebulizer gas flow, temperature, solvent composition and the sample pH on the relative distributions of ions of the types MH+, MNa+, MNH+, and 2MNa(+), where M represents a 4 small organic molecule: BAY 11-7082 ((E)-3-[4-methylphenylsulfonyl]-2-propenenitrile). Orifice potential, solvent composition and the sample pH had the greatest influence on the relative distributions of these ions, making these parameters the most useful for optimizing methods for the quantitation of small molecules.

Combining Sr and Na additions in hypoeutectic Al-Si foundry alloys

From recent published data, it is still unclear whether combining additions of Na and Sr have synergistic effects or deleterious interactions, This paper clarifies the interactions between these two modifiers and investigates the effects of such interactions on alloy solidification and castability. It was found that combined additions of Sr and Na do not appear to cause improvement of the modification of the eutectic microstructure even after only a short period after addition. Na addition may promote Sr vaporization and/or oxidation kinetically. leading to a quicker loss of both modifiers, which is blamed for the rapid loss of the modification effect during melt holding. Quenching trials during the eutectic arrest indicate that addition of Sr into Na-modified melts does not alter the eutectic solidification behaviour The effect of Na on eutectic solidification dominates, and the eutectic is observed to evolve with a significant dependency on the thermal gradient, Combining Sr and Na additions produced no beneficial effects on porosity and casting defects. (c) 2005 Elsevier B.V. All rights reserved.

Iron-rich intermetallic phases and their role in casting defect formation in hypoeutectic Al-Si alloys

Iron is the most common and detrimental impurity in aluminum casting alloys and has long been associated with an increase in casting defects. While the negative effects of iron are clear, the mechanism involved is not fully understood. It is generally believed to be associated with the formation of Fe-rich intermetallic phases. Many factors, including alloy composition, melt superheating, Sr modification, cooling, rate, and oxide bifilms, could play a role. In the present investigation, the interactions between iron and each individual element commonly present in aluminum casting alloys, were investigated using a combination of thermal analysis and interrupted quenching tests. The Fe-rich intermetallic phases were characterized using optical microscope, scanning electron microscope, and electron probe microanalysis (EPMA), and the results were compared with the predictions by Thermocalc. It was found that increasing the iron content changes the precipitation sequence of the beta phase, leading to the precipitation of coarse binary beta platelets at a higher temperature. In contrast, manganese, silicon, and strontium appear to suppress the coarse binary beta platelets, and Mn further promotes the formation of a more compact and less harmful a phase. They are therefore expected to reduce the negative effects of the phase. While reported in the literature, no effect of P on the amount of beta platelets was observed. Finally, attempts are made to correlate the Fe-rich intermetallic phases to the formation of casting defects. The role of the beta phase as a nucleation site for eutectic Si and the role of the oxide bifilms and AIP as a heterogeneous substrate of Fe intermetallics are also discussed.

Segregation of particles and its influence on the morphology of the eutectic silicon phase in Al-7 wt.% Si alloys

A new modification phenomenon is reported for Al-Si alloys, where the Al-Si eutectic is refined by segregated TiB2 particles. The TiB2 particles are pushed to the Al-Si phase boundary during solidification of the eutectic and it is believed that at high concentrations the TiB2 particles restrict solute redistribution causing refinement of the Si. (c) 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Iron-related porosity in Al-Si-(Cu) foundry alloys

An experimental program has been undertaken to explore the effect of iron concentration on porosity levels in Al-Si alloy sand castings. The effect of iron concentrations above, below and equal to the critical iron content for alloys with either 5 or 9% Si and either 0, 1 or 3% Cu has been determined. Increasing iron concentrations were found to increase porosity in all alloys except the copper-containing Al-5% Si alloys which displayed a porosity minimum at the critical iron content. Porosity was observed to be higher in the Al-9% Si castings than the Al-5% Si castings. Differences in the primary phase volume fraction and morphology may explain this observation. The results of this experimental work do not support the existing published theories that have been proposed to explain the effect the iron on porosity. An alternative theory is therefore developed. (c) 2006 Elsevier B.V. All rights reserved.

A rheological assessment of the effect of trace level Ni additions on the solidification of Sn-0.7Cu

The influence of trace level Ni additions on the eutectic solidification mode of Sn-0.7Cu has been studied using continuous torque experiments during solidification. The solid fraction at which resistance to paddle rotation at the thermal centre of the sample occurs is related to the spatial distribution of solid during solidification. The results indicate that a transition in solidification mode occurs in the range 0-300 ppm Ni. Growth occurs antiparallel to heat flow from near the mould walls in the Ni-free alloy, while equiaxed growth from distributed centres dominates in alloys containing at least 300 ppm Ni. (c) 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.