Knot Theory: from Fox 3-colorings of links to Yang-Baxter homology and Khovanov homology

This paper is an extended account of my "Introductory Plenary talk at Knots in Hellas 2016" conference We start from the short introduction to Knot Theory from the historical perspective, starting from Heraclas text (the first century AD), mentioning R.Llull (1232-1315), A.Kircher (1602-1680), Leibniz idea of Geometria Situs (1679), and J.B.Listing (student of Gauss) work of 1847. We spend some space on Ralph H. Fox (1913-1973) elementary introduction to diagram colorings (1956). In the second section we describe how Fox work was generalized to distributive colorings (racks and quandles) and eventually in the work of Jones and Turaev to link invariants via Yang-Baxter operators, here the importance of statistical mechanics to topology will be mentioned. Finally we describe recent developments which started with Mikhail Khovanov work on categorification of the Jones polynomial. By analogy to Khovanov homology we build homology of distributive structures (including homology of Fox colorings) and generalize it to homology of Yang-Baxter operators. We speculate, with supporting evidence, on co-cycle invariants of knots coming from Yang-Baxter homology. Here the work of Fenn-Rourke-Sanderson (geometric realization of pre-cubic sets of link diagrams) and Carter-Kamada-Saito (co-cycle invariants of links) will be discussed and expanded. Dedicated to Lou Kauffman for his 70th birthday.Comment: 35 pages, 31 figures, for Knots in Hellas II Proceedings, Springer, part of the series Proceedings in Mathematics & Statistics (PROMS

Unsteady effects during resistance tests on a ship model in a towing tank

It is known that there are oscillations in the wave resistance during the constantvelocity phase of a towing-tank resistance test on a ship model. In this work, the unsteady thin-ship resistance theory has been applied to this case. The results have been compared with experiment data obtained using a towing carriage the velocity history of which can be programmed. It is demonstrated here that generally excellent correlation exists between the theory and the experiments. In particular, one can predict the influence of Froude number, rate of acceleration, and type of smoothing of the acceleration on the characteristics of the oscillations. These characteristics include the amplitude, rate of decay, frequency, and phasing of the oscillations in the curve of wave resistance versus time

Reframing the concept of alternative livelihoods

Alternative livelihood project (ALP) is a widely used term for interventions that aim to reduce the prevalence of activities deemed to be environmentally damaging by substituting them with lower impact livelihood activities that provide at least equivalent benefits. ALPs are widely implemented in conservation, but in 2012, an International Union for Conservation of Nature resolution called for a critical review of such projects based on concern that their effectiveness was unproven. We focused on the conceptual design of ALPs by considering their underlying assumptions. We placed ALPs within a broad category of livelihood-focused interventions to better understand their role in conservation and their intended impacts. We dissected 3 flawed assumptions about ALPs based on the notions of substitution, the homogenous community, and impact scalability. Interventions based on flawed assumptions about people's needs, aspirations, and the factors that influence livelihood choice are unlikely to achieve conservation objectives. We therefore recommend use of a sustainable livelihoods approach to understand the role and function of environmentally damaging behaviors within livelihood strategies; differentiate between households in a community that have the greatest environmental impact and those most vulnerable to resource access restrictions to improve intervention targeting; and learn more about the social–ecological system within which household livelihood strategies are embedded. Rather than using livelihood-focused interventions as a direct behavior-change tool, it may be more appropriate to focus on either enhancing the existing livelihood strategies of those most vulnerable to conservation-imposed resource access restrictions or on use of livelihood-focused interventions that establish a clear link to conservation as a means of building good community relations. However, we recommend that the term ALP be replaced by the broader term livelihood-focused intervention. This avoids the implicit assumption that alternatives can fully substitute for natural resource-based livelihood activities

Revealing heterogeneous nucleation of primary Si and eutectic Si by AlP in hypereutectic Al-Si alloys

The heterogeneous nucleation of primary Si and eutectic Si can be attributed to the presence of AlP. Although P, in the form of AlP particles, is usually observed in the centre of primary Si, there is still a lack of detailed investigations on the distribution of P within primary Si and eutectic Si in hypereutectic Al-Si alloys at the atomic scale. Here, we report an atomic-scale experimental investigation on the distribution of P in hypereutectic Al-Si alloys. P, in the form of AlP particles, was observed in the centre of primary Si. However, no significant amount of P was detected within primary Si, eutectic Si and the Al matrix. Instead, P was observed at the interface between the Al matrix and eutectic Si, strongly indicating that P, in the form of AlP particles (or AlP ‘patch’ dependent on the P concentration), may have nucleated on the surface of the Al matrix and thereby enhanced the heterogeneous nucleation of eutectic Si. The present investigation reveals some novel insights into heterogeneous nucleation of primary Si and eutectic Si by AlP in hypereutectic Al-Si alloys and can be used to further develop heterogeneous nucleation mechanisms based on adsorption