Semi-invariants of symmetric quivers of tame type

A symmetric quiver $(Q,\sigma)$ is a finite quiver without oriented cycles $Q=(Q_0,Q_1)$ equipped with a contravariant involution $\sigma$ on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form on a representation $V$ of $Q$. We shall say that $V$ is orthogonal if is symmetric and symplectic if $$ is skew-symmetric. Moreover, we define an action of products of classical groups on the space of orthogonal representations and on the space of symplectic representations. So we prove that if $(Q,\sigma)$ is a symmetric quiver of tame type then the rings of semi-invariants for this action are spanned by the semi-invariants of determinantal type $c^V$ and, when matrix defining $c^V$ is skew-symmetric, by the Pfaffians $pf^V$. To prove it, moreover, we describe the symplectic and orthogonal generic decomposition of a symmetric dimension vector

Drying of complex suspensions

We investigate the 3D structure and drying dynamics of complex mixtures of emulsion droplets and colloidal particles, using confocal microscopy. Air invades and rapidly collapses large emulsion droplets, forcing their contents into the surrounding porous particle pack at a rate proportional to the square of the droplet radius. By contrast, small droplets do not collapse, but remain intact and are merely deformed. A simple model coupling the Laplace pressure to Darcy's law correctly estimates both the threshold radius separating these two behaviors, and the rate of large-droplet evacuation. Finally, we use these systems to make novel hierarchical structures.Comment: 4 pages, 4 figure

Colloid-stabilized emulsions: behaviour as the interfacial tension is reduced

We present confocal microscopy studies of novel particle-stabilized emulsions. The novelty arises because the immiscible fluids have an accessible upper critical solution temperature. The emulsions have been created by beginning with particles dispersed in the single-fluid phase. On cooling, regions of the minority phase nucleate. While coarsening these nuclei become coated with particles due to the associated reduction in interfacial energy. The resulting emulsion is arrested, and the particle-coated interfaces have intriguing properties. Having made use of the binary-fluid phase diagram to create the emulsion we then make use of it to study the properties of the interfaces. As the emulsion is re-heated toward the single-fluid phase the interfacial tension falls and the volume of the dispersed phase drops. Crumpling, fracture or coalescence can follow. The results show that the elasticity of the interfaces has a controlling influence over the emulsion behaviour.Comment: Submitted for the proceedings of the 6th Liquid Matter Conference, held in Utrecht (NL) in July 200

Cluster algebras of type A2(1)A_2^{(1)}

In this paper we study cluster algebras \myAA of type $A_2^{(1)}$. We solve the recurrence relations among the cluster variables (which form a T--system of type $A_2^{(1)}$). We solve the recurrence relations among the coefficients of \myAA (which form a Y--system of type $A_2^{(1)}$). In \myAA there is a natural notion of positivity. We find linear bases \BB of \myAA such that positive linear combinations of elements of \BB coincide with the cone of positive elements. We call these bases \emph{atomic bases} of \myAA. These are the analogue of the "canonical bases" found by Sherman and Zelevinsky in type $A_{1}^{(1)}$. Every atomic basis consists of cluster monomials together with extra elements. We provide explicit expressions for the elements of such bases in every cluster. We prove that the elements of \BB are parameterized by \ZZ^3 via their $\mathbf{g}$--vectors in every cluster. We prove that the denominator vector map in every acyclic seed of \myAA restricts to a bijection between \BB and \ZZ^3. In particular this gives an explicit algorithm to determine the "virtual" canonical decomposition of every element of the root lattice of type $A_2^{(1)}$. We find explicit recurrence relations to express every element of \myAA as linear combinations of elements of \BB.Comment: Latex, 40 pages; Published online in Algebras and Representation Theory, springer, 201

Blaming Bill Gates AGAIN! Misuse, overuse and misunderstanding of performance data in sport

Recently in Sport, Education and Society, Williams and Manley (2014) argued against the heavy reliance on technology in professional Rugby Union and elite sport in general. In summary, technology is presented as an elitist, ‘gold standard’ villain that management and coaches use to exert control and by which players lose autonomy, identity, motivation, social interactions and expertise. In this article we suggest that the sociological interpretations and implications offered by Williams and Manley may be somewhat limited when viewed in isolation. In doing so, we identify some core methodological issues in Williams and Manley’s study and critically consider important arguments for utilising technology; notably, to inform coach decision making and generate player empowerment. Secondly, we present a different, yet perhaps equally concerning, practice-oriented interpretation of the same results but from alternative coaching and expertise literature. Accordingly, we suggest that Williams and Manley have perhaps raised their alarm prematurely, inappropriately and on somewhat shaky foundations. We also hope to stimulate others to consider contrary positions, or at least to think about this topic in greater detail. More specifically, we encourage coaches and academics to think carefully about what technology is employed, how and why, and then the means by which these decisions are discussed with and, preferably, sold to players. Certainly, technology can significantly enhance coach decision making and practice, while also helping players to optimise their focus, empowerment and independence in knowing how to achieve their personal and collective goals

Emergence of the nematic electronic state in FeSe

We present a comprehensive study of the evolution of the nematic electronic structure of FeSe using high resolution angle-resolved photoemission spectroscopy (ARPES), quantum oscillations in the normal state and elastoresistance measurements. Our high resolution ARPES allows us to track the Fermi surface deformation from four-fold to two-fold symmetry across the structural transition at ~87 K which is stabilized as a result of the dramatic splitting of bands associated with dxz and dyz character. The low temperature Fermi surface is that a compensated metal consisting of one hole and two electron bands and is fully determined by combining the knowledge from ARPES and quantum oscillations. A manifestation of the nematic state is the significant increase in the nematic susceptibility as approaching the structural transition that we detect from our elastoresistance measurements on FeSe. The dramatic changes in electronic structure cannot be explained by the small lattice effects and, in the absence of magnetic fluctuations above the structural transition, points clearly towards an electronically driven transition in FeSe stabilized by orbital-charge ordering.Comment: Latex, 8 pages, 4 figure

Structure of nanoparticles embedded in micellar polycrystals

We investigate by scattering techniques the structure of water-based soft composite materials comprising a crystal made of Pluronic block-copolymer micelles arranged in a face-centered cubic lattice and a small amount (at most 2% by volume) of silica nanoparticles, of size comparable to that of the micelles. The copolymer is thermosensitive: it is hydrophilic and fully dissolved in water at low temperature (T ~ 0{\deg}C), and self-assembles into micelles at room temperature, where the block-copolymer is amphiphilic. We use contrast matching small-angle neuron scattering experiments to probe independently the structure of the nanoparticles and that of the polymer. We find that the nanoparticles do not perturb the crystalline order. In addition, a structure peak is measured for the silica nanoparticles dispersed in the polycrystalline samples. This implies that the samples are spatially heterogeneous and comprise, without macroscopic phase separation, silica-poor and silica-rich regions. We show that the nanoparticle concentration in the silica-rich regions is about tenfold the average concentration. These regions are grain boundaries between crystallites, where nanoparticles concentrate, as shown by static light scattering and by light microscopy imaging of the samples. We show that the temperature rate at which the sample is prepared strongly influence the segregation of the nanoparticles in the grain-boundaries.Comment: accepted for publication in Langmui

Effect of Fermi Surface Topology on Inter-Layer Magnetoresistance in Layered Multiband Systems: Application to LaFeAsO1-xFx

In layered single band systems, the interlayer conductivity depends on the orientation of the in-plane magnetic field and takes maximum values when the magnetic field is perpendicular to flat regions of the Fermi surface. Extending this known results to multi-band systems, we propose an experiment to extract information about their Fermi surface topology. We discuss application of the formula to a FeAs-based superconductor, LaFeAsO$_{1-x}$F$_x$. We show that the magnetically ordered state in the parent compound is clearly distinguished from the paramagnetic state by the oscillation period in the interlayer conductivity. We demonstrate that evolution of the Fermi surface topology by changing the doping concentration is reflected to the interlayer conductivity oscillation patterns.Comment: 12 pages, 6 figures, corrected Fig.6, added clarifications and refs, to appear in J. Phys. Soc. Jp

The spectrum of BPS branes on a noncompact Calabi-Yau

We begin the study of the spectrum of BPS branes and its variation on lines of marginal stability on O_P^2(-3), a Calabi-Yau ALE space asymptotic to C^3/Z_3. We show how to get the complete spectrum near the large volume limit and near the orbifold point, and find a striking similarity between the descriptions of holomorphic bundles and BPS branes in these two limits. We use these results to develop a general picture of the spectrum. We also suggest a generalization of some of the ideas to the quintic Calabi-Yau.Comment: harvmac, 45 pp. (v2: added references

Balancing employee needs, project requirements and organisational priorities in team deployment

The 'people and performance' model asserts that performance is a sum of employee ability, motivation and opportunity (AMO). Despite extensive evidence of this people-performance link within manufacturing and many service sectors, studies within the construction industry are limited. Thus, a recent research project set out to explore the team deployment strategies of a large construction company with the view of establishing how a balance could be achieved between organisational strategic priorities, operational project requirements and individual employee needs and preferences. The findings suggested that project priorities often took precedence over the delivery of the strategic intentions of the organisation in meeting employees' individual needs. This approach is not sustainable in the long term because of the negative implications that such a policy had in relation to employee stress and staff turnover. It is suggested that a resourcing structure that takes into account the multiple facets of AMO may provide a more effective approach for balancing organisational strategic priorities, operational project requirements and individual employee needs and preferences more appropriately in the future