Assessing the Importance of Cation Size in the Tetragonal-Cubic Phase Transition in Lithium-Garnet Electrolytes**

Lithium garnets are promising solid-state electrolytes for next-generation lithium-ion batteries. These materials have high ionic conductivity, a wide electrochemical window and stability with Li metal. However, lithium garnets have a maximum limit of seven lithium atoms per formula unit (e.g., La₃Zr₂Li₇O₁₂), before the system transitions from a cubic to a tetragonal phase with poor ionic mobility. This arises from full occupation of the Li sites. Hence, the most conductive lithium garnets have Li between 6–6.55 Li per formula unit, which maintains the cubic symmetry and the disordered Li sub-lattice. The tetragonal phase, however, forms the highly conducting cubic phase at higher temperatures, thought to arise from increased cell volume and entropic stabilisation permitting Li disorder. However, little work has been undertaken in understanding the controlling factors of this phase transition, which could enable enhanced dopant strategies to maintain room temperature cubic garnet at higher Li contents. Here, a series of nine tetragonal garnets were synthesised and analysed by variable temperature XRD to understand the dependence of site substitution on the phase transition temperature. Interestingly the octahedral site cation radius was identified as the key parameter for the transition temperature with larger or smaller dopants altering the transition temperature noticeably. A site substitution was, however, found to make little difference irrespective of significant changes to cell volume.     

Central recirculation zone analysis in an unconfined tangential swirl burner with varying degrees of premixing

Swirl-stabilised combustion is one of the most widely used techniques for flame stabilisation, uses ranging from gas turbine combustors to pulverised coal-fired power stations. In gas turbines, lean premixed systems are of especial importance, giving the ability to produce low NOx systems coupled with wide stability limits. The common element is the swirl burner, which depends on the generation of an aerodynamically formed central recirculation zone (CRZ) and which serves to recycle heat and active chemical species to the root of the flame as well as providing low-velocity regions where the flame speed can match the local flow velocity. Enhanced mixing in and around the CRZ is another beneficial feature. The structure of the CRZ and hence that of the associated flames, stabilisation and mixing processes have shown to be extremely complex, three-dimensional and time dependent. The characteristics of the CRZ depend very strongly on the level of swirl (swirl number), burner configuration, type of flow expansion, Reynolds number (i.e. flowrate) and equivalence ratio. Although numerical methods have had some success when compared to experimental results, the models still have difficulties at medium to high swirl levels, with complex geometries and varied equivalence ratios. This study thus focuses on experimental results obtained to characterise the CRZ formed under varied combustion conditions with different geometries and some variation of swirl number in a generic swirl burner. CRZ behaviour has similarities to the equivalent isothermal state, but is strongly dependent on equivalence ratio, with interesting effects occurring with a high-velocity fuel injector. Partial premixing and combustion cause more substantive changes to the CRZ than pure diffusive combustion.     

Synthesis and characterization of a new fluorogenic substrate for alpha-galactosidase

Alpha-galactosidase A hydrolyzes the terminal alpha-galactosyl moieties from glycolipids and glycoproteins in lysosomes. Mutations in α-galactosidase cause lysosomal accumulation of the glycosphingolipid, globotriaosylceramide, which leads to Fabry disease. Small-molecule chaperones that bind to mutant enzyme proteins and correct their misfolding and mistrafficking have emerged as a potential therapy for Fabry disease. We have synthesized a red fluorogenic substrate, resorufinyl α-d-galactopyranoside, for a new α-galactosidase enzyme assay. This assay can be measured continuously at lower pH values, without the addition of a stop solution, due to the relatively low pK _a of resorufin (~6). In addition, the assay emits red fluorescence, which can significantly reduce interferences due to compound fluorescence and dust/lint as compared to blue fluorescence. Therefore, this new red fluorogenic substrate and the resulting enzyme assay can be used in high-throughput screening to identify small-molecule chaperones for Fabry disease. Zhen-Dan Shi and Omid Motabar contributed equally to this work     

Thermochemistry of Binding of Lead(II) and Cadmium(II) by Saccharides in Aqueous Solution

Solution calorimetry was used to determine enthalpies and stability constants for binding of lead(II) or cadmium(II) by galacturonic acid and several monosaccharides in aqueous solution. New values for enthalpies of solution in water are reported for galacturonic acid and maltose monohydrate. The interaction of water solvent with the reactants is the largest factor in the binding process.     

Resolution and uniqueness of estimated parameters of a model of thin filament regulation in solution

The estimation of chemical kinetic rate constants for any non-trivial model is complex due to the nonlinear effects of second order chemical reactions. We developed an algorithm to accomplish this goal based on the Damped Least Squares (DLS) inversion method and then tested the effectiveness of this method on the McKillop–Geeves (MG) model of thin filament regulation. The kinetics of MG model is defined by a set of nonlinear ordinary differential equations (ODEs) that predict the evolution of troponin–tropomyosin–actin and actin–myosin states. The values of the rate constants are estimated by integrating these ODEs numerically and fitting them to a series of stopped-flow pyrene fluorescence transients of myosin-S1 fragment binding to regulated actin in solution. The accuracy and robustness of the estimated rate constants are evaluated for DLS and two other methods, namely quasi-Newton (QN) and simulated annealing (SA). The comparison of these methods revealed that SA provides the best estimates of the model parameters because of its global optimization scheme. However it converges slowly and does quantify the uniqueness of the estimated parameters. On the other hand the QN method converges rapidly but only if the initial guess of the parameters is close to the optimum values, otherwise it diverges. Overall, the DLS method proves to be the most convenient method. It converges fast and was able to provide excellent estimates of kinetic parameters. Furthermore, DLS provides the model resolution matrix, which quantifies the interdependence of model parameters thereby evaluating the uniqueness of their estimated values. This property is essential for estimating of the dependence of the model parameters on experimental conditions (e.g. Ca²⁺ concentration) when it is assessed from noisy experimental data such as pyrene fluorescence from stopped-flow transients. The advantages of the DLS method observed in this study should be further examined in other physicochemical systems to firmly establish the observed effectiveness of DSL vs. the other parameter estimation methods.     

On the Ramsey number of the triangle and the cube

The Ramsey number r(K ₃,Q _n ) is the smallest integer N such that every red-blue colouring of the edges of the complete graph K _N contains either a red n-dimensional hypercube, or a blue triangle. Almost thirty years ago, Burr and Erd?s conjectured that r(K ₃,Q _n )=2 ⁿ⁺¹?1 for every n∈?, but the first non-trivial upper bound was obtained only recently, by Conlon, Fox, Lee and Sudakov, who proved that r(K ₃,Q _n )?7000·2 ⁿ . Here we show that r(K ₃,Q _n )=(1+o(1))2 ⁿ⁺¹ as n→∞.     

A pair of Fibonacci-like polynomials arising from a special mapping

We study here a pair of sequences of polynomials that arise from a particular iterated mapping on the plane. We show how these sequences come about, and give some of their interesting mathematical properties.