Comparing and characterizing some constructions of canonical bases from Coxeter systems

The Iwahori-Hecke algebra $\mathcal{H}$ of a Coxeter system $(W,S)$ has a "standard basis" indexed by the elements of $W$ and a "bar involution" given by a certain antilinear map. Together, these form an example of what Webster calls a pre-canonical structure, relative to which the well-known Kazhdan-Lusztig basis of $\mathcal{H}$ is a canonical basis. Lusztig and Vogan have defined a representation of a modified Iwahori-Hecke algebra on the free $\mathbb{Z}[v,v^{-1}]$-module generated by the set of twisted involutions in $W$, and shown that this module has a unique pre-canonical structure satisfying a certain compatibility condition, which admits its own canonical basis which can be viewed as a generalization of the Kazhdan-Lusztig basis. One can modify the parameters defining Lusztig and Vogan's module to obtain other pre-canonical structures, each of which admits a unique canonical basis indexed by twisted involutions. We classify all of the pre-canonical structures which arise in this fashion, and explain the relationships between their resulting canonical bases. While some of these canonical bases are related in a trivial fashion to Lusztig and Vogan's construction, others appear to have no simple relation to what has been previously studied. Along the way, we also clarify the differences between Webster's notion of a canonical basis and the related concepts of an IC basis and a $P$-kernel.Comment: 32 pages; v2: additional discussion of relationship between canonical bases, IC bases, and P-kernels; v3: minor revisions; v4: a few corrections and updated references, final versio

Configurational order-disorder induced metal-nonmetal transition in B13_{13}C2_{2} studied with first-principles superatom-special quasirandom structure method

Due to a large discrepancy between theory and experiment, the electronic character of crystalline boron carbide B$_{13}$C$_{2}$ has been a controversial topic in the field of icosahedral boron-rich solids. We demonstrate that this discrepancy is removed when configurational disorder is accurately considered in the theoretical calculations. We find that while ordered ground state B$_{13}$C$_{2}$ is metallic, configurationally disordered B$_{13}$C$_{2}$, modeled with a superatom-special quasirandom structure method, goes through a metal to non-metal transition as the degree of disorder is increased with increasing temperature. Specifically, one of the chain-end carbon atoms in the CBC chains substitutes a neighboring equatorial boron atom in a B$_{12}$ icosahedron bonded to it, giving rise to a B$_{11}$C$^{e}$(BBC) unit. The atomic configuration of the substitutionally disordered B$_{13}$C$_{2}$ thus tends to be dominated by a mixture between B$_{12}$(CBC) and B$_{11}$C$^{e}$(BBC). Due to splitting of valence states in B$_{11}$C$^{e}$(BBC), the electron deficiency in B$_{12}$(CBC) is gradually compensated

Optimal Pacing for Running 400 m and 800 m Track Races

Physicists seeking to understand complex biological systems often find it rewarding to create simple "toy models" that reproduce system behavior. Here a toy model is used to understand a puzzling phenomenon from the sport of track and field. Races are almost always won, and records set, in 400 m and 800 m running events by people who run the first half of the race faster than the second half, which is not true of shorter races, nor of longer. There is general agreement that performance in the 400 m and 800 m is limited somehow by the amount of anaerobic metabolism that can be tolerated in the working muscles in the legs. A toy model of anaerobic metabolism is presented, from which an optimal pacing strategy is analytically calculated via the Euler-Lagrange equation. This optimal strategy is then modified to account for the fact that the runner starts the race from rest; this modification is shown to result in the best possible outcome by use of an elementary variational technique that supplements what is found in undergraduate textbooks. The toy model reproduces the pacing strategies of elite 400 m and 800 m runners better than existing models do. The toy model also gives some insight into training strategies that improve performance.Comment: 14 pages, 4 figures, submitted to the American Journal of Physic

Electronic structure and chemical bonding of nc-TiC/a-C nanocomposites

The electronic structure of nanocrystalline (nc-) TiC/amorphous C nanocomposites has been investigated by soft x-ray absorption and emission spectroscopy. The measured spectra at the Ti 2p and C 1s thresholds of the nanocomposites are compared to those of Ti metal and amorphous C. The corresponding intensities of the electronic states for the valence and conduction bands in the nanocomposites are shown to strongly depend on the TiC carbide grain size. An increased charge-transfer between the Ti 3d-eg states and the C 2p states has been identified as the grain size decreases, causing an increased ionicity of the TiC nanocrystallites. It is suggested that the charge-transfer occurs at the interface between the nanocrystalline TiC and the amorphous C matrix and represents an interface bonding which may be essential for the understanding of the properties of nc-TiC/amorphous C and similar nanocomposites.Comment: 13 pages, 6 figures, 1 table; http://link.aps.org/doi/10.1103/PhysRevB.80.23510

Phase composition and transformations in magnetron-sputtered (Al,V)2O3 coatings

Coatings of (Al1-xVx)2O3, with x ranging from 0 to 1, were deposited by pulsed DC reactive sputter deposition on Si(100) at a temperature of 550 {\deg}C. XRD showed three different crystal structures depending on V-metal fraction in the coating: {\alpha}-V2O3 rhombohedral structure for 100 at.% V, a defect spinel structure for the intermediate region, 63 - 42 at.% V. At lower V-content, 18 and 7 at.%, a gamma-alumina-like solid solution was observed, shifted to larger d-spacing compared to pure {\gamma}-Al2O3. The microstructure changes from large columnar faceted grains for {\alpha}-V2O3 to smaller equiaxed grains when lowering the vanadium content toward pure {\gamma}-Al2O3. Annealing in air resulted in formation of V2O5 crystals on the surface of the coating after annealing to 500 {\deg}C for 42 at.% V and 700 {\deg}C for 18 at.% V metal fraction respectively. The highest thermal stability was shown for pure {\gamma}-Al2O3-coating, which transformed to {\alpha}-Al2O3 after annealing to 1100{\deg} C. Highest hardness was observed for the Al-rich oxides, ~24 GPa. The latter decreased with increasing V-content, larger than 7 at.% V metal fraction. The measured hardness after annealing in air decreased in conjunction with the onset of further oxidation of the coatings

Surface Morphology of Unused and Used HydromerR-Coated Intravenous Catheters

HydromerR-coated polyurethane (Erythroflex)R catheters, unused, or intravenously inserted for 2-20 days, were studied by scanning electron microscopy (SEM). Both unfixed and fixed (2% glutar-aldehyde in phosphate buffer), and air-or critical-point dried (CPD) specimens were investigated. The catheter segments were sputter-coated with approx. 20 nm gold and studied at an accelerating voltage of 20 kV. The specimens were examined for surface depositions, thickness and structure of the HydromerR layers, and occurrence of adhering and embedded bacteria. The outer HydromerR layer showed, in the un-used specimens, scratches and fissures, as well as adhering foreign bodies. In used specimens, the layer was swollen, with cracks (like dried earth ), and, occasionally , amorphous substances and coccoid bacteria were seen adhering. Damage to the layer, or even its total disappearance was also noted in some specimens. The inner (luminal) HydromerR layer was, in unused specimens, clean and slightly wavy. In used catheters, it was thicker, possibly swollen, with small, isolated or agglomerated protrusions, like a lunar landscape . Adhering platelets and amorphous substances were also occasionally seen. The results suggest that the HydromerR is a fragile material in both its dry and wet forms. Thus, the HydromerR-coated catheters should neither be stored in flexible packs, nor inserted by the Seldinger technique. The findings do not support the belief that the HydromerR-coating can prevent either thrombus formation, or intraluminal occlusion of the in-situ catheters

A unified cluster expansion method applied to the configurational thermodynamics of cubic TiAlN

We study the thermodynamics of cubic Ti1-xAlxN using a unified cluster expansion approach for the alloy problem. The purely configurational part of the alloy Hamiltonian is expanded in terms of concentration and volume dependent effective cluster interactions. By separate expansions of the chemical fixed-lattice, and local lattice relaxation terms of the ordering energies, we demonstrate how the screened generalized perturbation method can be fruitfully combined with a concentration dependent Connolly-Williams cluster expansion method. Utilising the obtained Hamiltonian in Monte Carlo simulations we access the free energy of Ti1-xAlxN alloys and construct the isostructural phase diagram. The results show surprising similarities with the previously obtained mean-field results: The metastable c-TiAlN is subject to coherent spinodal decomposition over a larger part of the concentration range, e.g. from x >= 0.33 at 2000 K.Comment: 21 pages, 7 figure