Irrational behavior of algebraic discrete valuations

We study algebraic discrete valuations dominating normal local domains of dimension two. We construct a family of examples to show that the Hilbert-Samuel function of the associated graded ring of the valuation can fail to be asymptotically of the form: quasi-polynomial plus a bounded function. We also show that the associated multiplicity can be irrational, or even transcendental

Action, reflection and learning in team coaching

The aim of the chapter is to examine the role of a coach in supporting reflection, learning and taking action in a team or a group. The chapter will begin by exploring the role of a coach or adviser in learning groups such as action learning sets where the role of the coach is to ask questions to encourage the team to consider and reflect on their current situation. (Marquardt et al., 2009). This is compared and contrasted to the role of a team coach working with a team to achieve common team outcomes in a way that combines performance and processes (Hackman & Wageman, 2005). The concept of learning as a social process in both interventions and the role of the coach in supporting the process of reflection and dialogue for the purpose of gaining new insights are explored. Hence, one of the purposes of the chapter is to develop a sharper understanding of what distinguishes action learning from team coaching, as well as some of the overlaps between them. It must be noted that as the action learning facilitator is commonly referred to as the ‘coach’ this term has been used here interchangeably with group coaching. The distinction between the two interventions are addressed later in the chapter

Application of artificial intelligence to modelling of materials performance and processing

This paper reviews the state-of-the-art in artificial intelligence research pertinent to metallurgical and materials science. The frameworks of two broad schools of AI research, namely, the Expert Systems (ES) and Artificial Neural Network (ANN) have been discussed with specific reference to their various notable applications in the area of materials research. Finally, we present NML's own efforts in this area, where a hybrid framework comprising ES and ANN is being developed for future use

The metallicity dependence of envelope inflation in massive stars

Recently it has been found that models of massive stars reach the Eddington limit in their interior, which leads to dilute extended envelopes. We perform a comparative study of the envelope properties of massive stars at different metallicities, with the aim to establish the impact of the stellar metallicity on the effect of envelope inflation. We analyse published grids of core-hydrogen burning massive star models computed with metallicities appropriate for massive stars in the Milky Way, the LMC and the SMC, the very metal poor dwarf galaxy I Zwicky 18, and for metal-free chemical composition. Stellar models of all the investigated metallicities reach and exceed the Eddington limit in their interior, aided by the opacity peaks of iron, helium and hydrogen, and consequently develop inflated envelopes. Envelope inflation leads to a redward bending of the zero-age main sequence and a broadening of the main sequence band in the upper part of the Hertzsprung-Russell diagram. We derive the limiting L/M-values as function of the stellar surface temperature above which inflation occurs, and find them to be larger for lower metallicity. While Galactic models show inflation above ~29 Msun, the corresponding mass limit for Population III stars is ~150 Msun. While the masses of the inflated envelopes are generally small, we find that they can reach 1-100 Msun in models with effective temperatures below ~8000 K, with higher masses reached by models of lower metallicity. Envelope inflation is expected to occur in sufficiently massive stars at all metallicities, and is expected to lead to rapidly growing pulsations, high macroturbulent velocities, and might well be related to the unexplained variability observed in Luminous Blue Variables like S Doradus and Eta Carina.Comment: 16 pages (with Appendix), accepted in A&

Sustaining supercooled mixed phase via resonant oscillations of the order parameter

We investigate the dynamics of a first order transition when the order parameter field undergoes resonant oscillations, driven by a periodically varying parameter of the free energy. This parameter could be a background oscillating field as in models of pre-heating after inflation. In the context of condensed matter systems, it could be temperature $T$, or pressure, external electric/magnetic field etc. We show that with suitable driving frequency and amplitude, the system remains in a type of mixed phase, without ever completing transition to the stable phase, even when the oscillating parameter of the free energy remains below the corresponding critical value (for example, with oscillating temperature, $T$ always remains below the critical temperature $T_c$). This phenomenon may have important implications. In cosmology, it will imply prolonged mixed phase in a first order transition due to coupling with background oscillating fields. In condensed matter systems, it will imply that using oscillating temperature (or, more appropriately, pressure waves) one may be able to sustain liquids in a mixed phase indefinitely at low temperatures, without making transition to the frozen phase.Comment: 17 pages, 7 figures, Expanded version with more detail

Plasma Technology in Ferroalloy Processing

Plasma technology has come a long way since the early reported applications to metallurgy by Sir W. Siemens(1878) and H. Moissan(1897) about a century back(1). Major attraction of using plasma in metallurgical smelting oper-ations, especially in the last two to three decades, have emerged from its ability to deliver high grade heat to any environment independently of oxygen potential. Further more, compact unit of high throughput, due to high power flux and higher reaction rates attained, and ability to handle cheaper fine feed without causing pollution problems have been the other important attractions. Although, the development of plasma technology in the area of nonferrous extractivepetallurgy is still confined to the laboratory and pilot plant research stage, applications in ferrous metallurgy have entered the stage of commercialization. Table 1' lists some of the high capacity iron and steel installations. Ferroalloys production, using carbothermic smelting reduction of oxide ores and by remelting of ferro-alloys fines, has been a major driving force in fostering the development of plasma technology, As indicated in Table 1, both ferro manganese and ferro chromiuin are being produced at present on industrial scale. Research and development in the production of other ferroalloys, e.g. ferro silicon, ferro vanadium, ferro molybdenum, is in an advanced stage. A brief review is presented in this paper on the applicat-ion of plasma technology for ferroalloys production. We begin with the definition of plasma in general, followed by a discussion on various plasma furnaces, process funda-mentals, i.e. chemistry and transport phenomena in plasma environment, and energy conSiderations involved in plasma smelting. Finally, the advantages of the technology, vis-a-vis the conventional processing using submerged arc fur-nace, and relevance of the technology in 'the Indian con-text are brought into focus. Specific examples of ferro-alloys are cited wherever possible. The reader may refer to the reviews [1-6] for detail

Low-metallicity massive single stars with rotation. Evolutionary models applicable to I Zwicky 18

Massive rotating single stars with an initial metal composition appropriate for the dwarf galaxy I Zw 18 ([Fe/H]=$-$1.7) are modelled during hydrogen burning for initial masses of 9-300 M$_{\odot}$ and rotational velocities of 0-900 km s$^{-1}$. Internal mixing processes in these models were calibrated based on an observed sample of OB-type stars in the Magellanic Clouds. Even moderately fast rotators, which may be abundant at this metallicity, are found to undergo efficient mixing induced by rotation resulting in quasi chemically-homogeneous evolution. These homogeneously-evolving models reach effective temperatures of up to 90 kK during core hydrogen burning. This, together with their moderate mass-loss rates, make them Transparent Wind Ultraviolet INtense stars (TWUIN star), and their expected numbers might explain the observed HeII ionizing photon flux in I Zw 18 and other low-metallicity HeII galaxies. Our slowly rotating stars above $\sim$80 M$_{\odot}$ evolve into late B- to M-type supergiants during core hydrogen burning, with visual magnitudes up to 19$^{\mathrm{m}}$ at the distance of I Zw 18. Both types of stars, TWUIN stars and luminous late-type supergiants, are only predicted at low metallicity. Massive star evolution at low metallicity is shown to differ qualitatively from that in metal-rich environments. Our grid can be used to interpret observations of local star-forming dwarf galaxies and high-redshift galaxies, as well as the metal-poor components of our Milky Way and its globular clusters.Comment: accepted for publication in A\&

Phosphorus: A Boon or Curse for the Environment?

Phosphorus, a limiting nutrient of biosphere, exists as dissolved inorganic phosphorus (DIP), dissolved organic phosphorus (DOP), particulate inorganic phosphorus (PIP) and particulate organic phosphorus (POP) in water of soil as well as ponds, lakes, etc. The only available phosphorus for plants are DIP, while the other forms need to be converted to DIP by the decomposing microorganisms of the soil. The heavy metals (such as arsenic and chromium), which are the menace of both terrestrial and aquatic environment, are taken up by the plants and animals causing toxicity at physiological level. However, the metal (Cr and As) toxicity can be mitigated competitively by phosphorus, since the latter is a structural analogue. Since, phosphorus is an essential nutrient, plants prefer it over Cr or As. At the same time, if excess of phosphorus is applied in the soil in the form of fertilisers, it gets discharged into the water bodies (ponds, lakes, etc.) through agricultural runoff, causing eutrophication followed by harming the health of the water bodies. This can be further mitigated by employing the phenomenon of luxury uptake by the aquatic plants such as Pistia stratiotes