Note on a conjecture of toft

A conjecture of Toft [17] asserts that any 4-critical graph (or equivalently, every 4-chromatic graph) contains a fully odd subdivision ofK ₄. We show that if a graphG has a degree three nodev such thatG-v is 3-colourable, then eitherG is 3-colourable or it contains a fully oddK ₄. This resolves Toft's conjecture in the special case where a 4-critical graph has a degree three node, which is in turn used to prove the conjecture for line-graphs. The proof is constructive and yields a polynomial algorithm which given a 3-degenerate graph either finds a 3-colouring or exhibits a subgraph that is a fully odd subdivision ofK ₄. (A graph is 3-degenerate if every subgraph has some node of degree at most three.)     

Instability of Bose-Einstein condensates moving in optical lattices

We investigate the Landau damping of Bogoliubov excitations in a dilute Bose gas moving in an optical lattice at a finite temperature. Using a 1D tight-binding model, we explicitly obtain the Landau damping rate, the sign of which determines the stability of the condensate. We find that the sign changes at a certain velocity, which is exactly the same as the critical velocity determined by the Landau criterion of superfluidity. This coincidence reveals the microscopic mechanism of the Landau instability.     

Identification of dislocations and their influence on the recombination of charge carriers in gallium nitride

The relation between the density of etch pits revealed in GaN by etching in a KOH/NaOH eutectic and the density of dislocations determined by transmission electron microscopy (TEM) is studied along with the relation between the density of dislocations and the density of dark spot defects observed in GaN by microcathodoluminescence (MCL) and electron-beam-induced current (EBIC). It is demonstrated that selective etching is a reliable rapid method for the determination of the type and density of dislocations in GaN in the range 10⁶–10⁸ cm^?2, while MCL and EBIC can be used for the rapid nondestructive determination of the density of dislocations in the range 10⁶–10⁸ cm^?2. It is also found that some deep electron and hole traps are related to dislocations.     

WZW–Poisson manifolds

We observe that a term of the WZW-type can be added to the Lagrangian of the Poisson σ-model in such a way that the algebra of the first class constraints remains closed. This leads to a natural generalization of the concept of Poisson geometry. The resulting “WZW–Poisson” manifold M is characterized by a bivector Π and by a closed three-form H such that 1/2[Π,Π]_Schouten=H,ΠΠΠ.     

Macrodefect-Free Materials: Modification of Interfaces in Cement Composites by Polymer Grafting

MDF materials are chemically bonded ceramic materials free of the macrodefects typical of hydraulic cement-based materials. MDF materials arising through reactions of sulfo-aluminate-ferrite belitic (SAFB) clinkers and/or Portland cements (PC) with two types of water-soluble polymer (hydroxy-propylmethyl cellulose {HPMC}, polyphosphate glass {poly-P}) are discussed. Mixes of low energy SAFB clinkers with Portland cement, HPMC and, especially poly-P comprise promising cross-linked compositions additional to the better known MDF materials formed from high alumina cement with polyvinylalcohol/acetate. The principles of co-ordination of P and C atoms (of the polymer) with Al and Fe atoms (originating from the cement) are highlighted from spectroscopic information on next-nearest-neighbour interactions, along with the effects of second co-ordination spheres. Polymers modify the interface through functional bonding/grafting of polymer chains onto the surfaces of cement grains. Both the cross-linked atomic structure and the interface coincide well with the model of functional polymers and represent a new type of atomic-level structure in polymer-modified cements. Interpretation is based on previous magnetic resonance and thermal analysis studies. The compactness of Al(Fe)-O-P cross-links reduces transport through the interfaces, increasing the interfacial interactions and resisting the unfavourable uptake of moisture and carbonation.     

Modeling hyperelastic behavior of rubber: A novel invariant‐based and a review of constitutive models

A constitutive phenomenological model completing the Gent‐Thomas concept is carried out to formulate laws governing the hyperelastic behavior of incompressible rubber materials. It is shown that the phenomenological Gent‐Thomas model (1958) and the constrained chain model (1992) give similar precise results at small to moderate deformation. On the other hand, comparisons of the outcome of the proposed model with that of the molecular model from the combined concepts of Flory‐Erman and Boyce‐Arruda (2000), and with those of the phenomenological models of Ogden (1982), Yeoh‐Fleming (1997), Pucci‐Saccomandi (2002) and Beda (2005) are made. Residual inconveniences raised by attractive continuum models in rubber elasticity literature have been successfully overcome. Results from both the statistical and phenomenological mechanics concepts are compared with the data of some useful classical materials (rubbers of Treloar, Rivlin‐Saunders, Pak‐Flory and Yeoh‐Fleming). The results permit one to see salient equivalence of the two theories for a more reliable prediction of stress‐stretch response for all states of any mode of deformation. A complete and exhaustive analysis of the Mooney plot that combines small and very large extension‐compression has been quite essential in assessing the validity of models. A method of identification of material parameters is presented and data of the simple tension suffice for the determination of the parameter values. It is shown that the ordinary identification procedures, such as the usual least squares, a very much used numerical method in materials investigation, can be unsuitable in some cases of hyperelastic modeling. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1713–1732, 2007     

Investigating laser rapid manufacturing for Inconel-625 components

This paper presents an investigation of laser rapid manufacturing (LRM) for Inconel-625 components. LRM is an upcoming rapid manufacturing technology, it is similar to laser cladding at process level with different end applications. In general, laser-cladding technique is used to deposit materials on the substrate either to improve the surface properties or to refurbish the worn out parts, while LRM is capable of near-net shaping the components by layer-by-layer deposition of the material directly from CAD model. In the present study, a high-power continuous wave (CW) CO₂ laser system, integrated with a co-axial powder-feeding system and a three-axis workstation were used. The effect of processing parameters during LRM of Inconel-625 was studied and the optimum set of parameters for the maximum deposition rate was established employing Orthogonal L9 array of Taguchi technique. Results indicated that the powder feed rate and the scan speed contributed about 56% and 26%, respectively to the deposition rate, while the influence of laser power was limited to 10% only. Fabricated components were subjected to non-destructive testing (like—ultrasonic testing, dye-penetrant testing), tensile testing, impact testing, metallographic examinations and micro-hardness measurement. The test results revealed defect-free material deposition with improved mechanical strength without sacrificing the ductility.     

Nanostructures in calcia stabilized hafnia thin films observed by PAC as a function of temperature

The hyperfine quadrupole interaction at Hf sites in films and powders of 14 mol% CaO–HfO₂ and 20 mol% CaO–HfO₂ has been determined as a function of temperature. Results indicate the formation of a cubic solid solution and other microstructures assigned to the ?₁ (CaHf₄O₉) and ?₂ (Ca₆Hf₁₉O₄₄) phases. Dynamical effects on the electric field gradient reveal the existence of oxygen vacancies movements in the solid solution. The thermal behavior of the relaxation constant observed in films allowed the determination of activation energies of 0.54 eV and 0.70 eV for the 14 mol% and 20 mol% CaO doped hafnias, respectively. The influence of the microdomains and the stability of the cubic solid solution are discussed.