A *-product on SL(2) and the corresponding nonstandard (\mathfrak{s}\mathfrak{l}({\text{2}}))

We obtain Zakrzewski's deformation of Fun SL(2) through the construction of a *-product on SL(2). We then give the deformation of dual to this, as well as a Poincaré basis for both algebras.Aspirant au Fonds National belge de la Recherche Scientifique. Partially supported by EEC contract SC1-0105-C.     

Serre-type relations for special linear Lie superalgebras

It is pointed out that, for m, n 2, the naive Serre presentation corresponding to the simplest Cartan matrix of sl(m, n) does not define the Lie superalgebra sl(m, n) but a larger algebra s(m, n) of which sl(m, n) is a nontrivial quotient. The supplementary relations for the generators are found and the definition of the q-deformed universal enveloping algebra of sl(m, n) is modified accordingly.     

Quantum groups and diagonalization of the braid generator

It is shown that the braid generator is diagonalizable on arbitrary tensor product modules V V, V an irreducible module for a quantum group. A generalization of the Reshetikhin form for the braid generator is thereby obtained in the general case. As an application, a general closed formula is determined for link polynomials.     

环形装置中三维MHD平衡与稳定性的计算机模拟

一、引 言 在聚变研究中,环形等离子体的磁约束起着重要作用。目前托卡马克研究的进展令人鼓舞,其理论与实验比较符合,定标关系清楚。但是无论从聚变的最终目标来看,还是从实验的安排考虑,完全轴对称的几何形状给各方面部带来许多不便。人们希望知道如果把环形几何中加进直线段,或者把圆环改成不具有对称性的环形,会对等离子体约束产生何种影响?     

Quenching of Flame Propagation with Heat Loss

The steady propagation of a planar laminar premixed flame, with a one-step exothermic reaction and linear heat loss, is studied. The corresponding travelling wave equations are solved numerically. The dependence of the flame velocity on the heat loss parameter is determined and compared with known results obtained by asymptotic expansion and other approximations. Due to the introduction of an ignition temperature the problem can be reduced to a bounded interval (of length L) and the graph of flame speed versus heat loss parameter can be parametrised by L. The numerical method is tested in the case of a step function nonlinearity when the exact solution of the differential equations can also be calculated.     

Sustainable,fire‐resistant phthalonitrile‐based glass fiber composites

The sustainable resveratrol‐based phthalonitrile was used in the preparation of E‐glass fiber‐reinforced phthalonitrile composite panels fabricated by hot pressed prepreg consolidation with bis[4‐(3‐aminophenoxy)phenyl]sulfone (m‐BAPS) as the curing additive. This amorphous monomer exhibited excellent viscosities at temperatures below 200 °C, which is applicable to standard processing conditions. Rheometric measurements were used to evaluate the cure of the composite as a function of the postcure conditions. The composite retains >95% of its room temperature storage modulus up to 450 °C based on these postcuring parameters. More importantly, flammability performance of the composite—which was determined in terms of ignitability, heat release, and mass loss rate—excels over other state‐of‐the‐art polymer/glass composites. Even under the most extreme heat fluxes (e.g., 100 kW⋅m⁻²), the composite performs exceptionally well suggesting that resveratrol‐based phthalonitrile composites can be used in fire‐resistant applications. Published 2018.^† J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 1128–1132     

Phosphoryl‐Rich Flame‐Retardant Ions (FRIONs): Towards Safer Lithium‐Ion Batteries

The functionalized catecholate, tetraethyl (2,3‐dihydroxy‐1,4‐phenylene)bis(phosphonate) (H₂‐DPC), has been used to prepare a series of lithium salts Li[B(DPC)(oxalato)], Li[B(DPC)₂], Li[B(DPC)F₂], and Li[P(DPC)₃]. The phosphoryl‐rich character of these anions was designed to impart flame‐retardant properties for their use as potential flame‐retardant ions (FRIONs), additives, or replacements for other lithium salts for safer lithium‐ion batteries. The new materials were fully characterized, and the single‐crystal structures of Li[B(DPC)(oxalato)] and Li[P(DPC)₃] have been determined. Thermogravimetric analysis of the four lithium salts show that they are thermally stable up to around 200 °C. Pyrolysis combustion flow calorimetry reveals that these salts produce high char yields upon combustion.     

Attainment of Emulsions with Liquid Crystal from Marigold Oil Using the Required HLB Method

Development of new formulations for topical use and cosmetic and pharmaceutical delivery agents has increased the complexity of emulsified systems. Liquid crystals, known since the nineteenth century are the third phase of an emulsion, being responsible for increasing its stability and the solubility of substances poorly soluble in water, or the oily phase, modulating the release of drugs imprisoned in its structure and promoting hydration of the skin surface. In the present work we developed oil/water emulsions, making use of Marigold oil (Calendula officinalis L) and ethoxylated fat alcohols as surfactant. The required HLB value for marigold oil was determined to be 6.0. The surfactants were associated in lipophilic/hydrophilic pairs. The lipophilic surfactants were Ceteth‐2 and Steareth‐2 and the hydrophilic surfactants were Steareth‐20, Ceteareth‐20, Ceteareth‐5, and Ceteth‐10. To identify the liquid crystalline phases, the emulsions were analyzed by polarized light microscopy. The physical stability was evaluated by rheology and zeta potential analysis. All emulsions presented lamellar liquid crystal structures. Results showed that this type of surfactant is able to produce liquid crystal in the system, with slight difference in appearance, influencing the physical stability, according to the methods applied.     

Analytical predictions of shapes of laminar diffusion flames in microgravity and earth gravity

Flame shape is an important observed characteristic of flames that can be used to scale flame properties such as heat release rates and radiation. Flame shape is affected by fuel type, oxygen levels in the oxidiser, inverse burning and gravity. The objective of this study is to understand the effect of high oxygen concentrations, inverse burning, and gravity on the predictions of flame shapes. Flame shapes are obtained from recent analytical models and compared with experimental data for a number of inverse and normal ethane flame configurations with varying oxygen concentrations in the oxidiser and under earth gravity and microgravity conditions. The Roper flame shape model was extended to predict the complete flame shapes of laminar gas jet normal and inverse diffusion flames on round burners. The Spalding model was extended to inverse diffusion flames. The results show that the extended Roper model results in reasonable predictions for all microgravity and earth gravity flames except for enhanced oxygen normal diffusion flames under earth gravity conditions. The results also show trends towards cooler flames in microgravity that are in line with past experimental observations. Some key characteristics of the predicted flame shapes and parameters needed to describe the flame shape using the extended Roper model are discussed.     

A hybrid level set method for modelling detonation and combustion problems in complex geometries

We present an accurate and fast wave tracking method that uses parametric representations of tracked fronts, combined with modifications of level set methods that use narrow bands. Our strategy generates accurate computations of the front curvature and other geometric properties of the front. We introduce data structures that can store discrete representations of the location of the moving fronts and boundaries, as well as the corresponding level set fields, that are designed to reduce computational overhead and memory storage. We present an algorithm we call stack sweeping to efficiently sort and store data that is used to represent orientable fronts. Our implementation features two reciprocal procedures, a forward ‘front parameterization’ that constructs a parameterization of a front given a level set field and a backward ‘field construction’ that constructs an approximation of the signed normal distance to the front, given a parameterized representation of the front. These reciprocal procedures are used to achieve and maintain high spatial accuracy. Close to the front, precise computation of the normal distance is carried out by requiring that displacement vectors from grid points to the front be along a normal direction. For front curves in two dimensions, a cubic interpolation scheme is used, and G ¹ surface parameterization based on triangular patches is used for the three-dimensional implementation to compute the distances from grid points near the front. To demonstrate this new, high accuracy method we present validations and show examples of combustion-like applications that include detonation shock dynamics, material interface motions in a compressible multi-material simulation and the Stephan problem associated with dendrite solidification.