An ignition-temperature model with two free interfaces in premixed flames†

In this paper we consider an ignition-temperature zero-order reaction model of thermo-diffusive combustion. This model describes the dynamics of thick flames, which have recently received considerable attention in the physical and engineering literature. The model admits a unique (up to translations) planar travelling wave solution. This travelling wave solution is quite different from those usually studied in combustion theory. The main qualitative feature of this travelling wave is that it has two interfaces: the ignition interface where the ignition temperature is attained and the trailing interface where the concentration of deficient reactants reaches zero. We give a new mathematical framework for studying the cellular instability of such travelling front solutions. Our approach allows the analysis of a free boundary problem to be converted into the analysis of a boundary value problem having a fully nonlinear system of parabolic equations. The latter is very suitable for both mathematical and numerical analysis. We prove the existence of a critical Lewis number such that the travelling wave solution is stable for values of Lewis number below the critical one and is unstable for Lewis numbers that exceed this critical value. Finally, we discuss the results of numerical simulations of a fully nonlinear system that describes the perturbation dynamics of planar fronts. These simulations reveal, in particular, some very interesting ‘two-cell’ steady patterns of curved combustion fronts.     

Synergistic Peptide and Gold Catalysis: Enantioselective Addition of Branched Aldehydes to Allenamides

The combination of a peptide catalyst and a gold catalyst is presented for enantioselective addition reactions between branched aldehydes and allenamides. The two catalysts act in concert to provide γ,δ-enamide aldehydes bearing a fully substituted, benzylic stereogenic center – a structural motif common in many natural products and therapeutically active compounds – with good yields and enantioselectivities. The reaction tolerates a variety of alkyl and alkoxy substituted aldehydes and the products can be elaborated into several chiral building blocks bearing either 1,4- or 1,5- functional group relationships. Mechanistic studies showed that the conformational features of the peptide are important for both the catalytic efficiency and stereochemistry, while a balance of acid/base additives is key for ensuring formation of the desired product over undesired side reactions.     

用Matlab比较双缝干涉和双缝衍射

运用Matlab软件,对双缝衍射和双缝干涉、单缝衍射的光强分布和谱线特征进行了数值模拟,绘出实验中难以观察到的光强分布图,比较出双缝衍射与双缝干涉及单缝衍射的联系与区别。     

ECONOMICALLY OPTIMAL MARINE RESERVES WITHOUT SPATIAL HETEROGENEITY IN A SIMPLE TWO‐PATCH MODEL

Bioeconomic analyses of spatial fishery models have established that marine reserves can be economically optimal (i.e., maximize sustainable profit) when there is some type of spatial heterogeneity in the system. Analyses of spatially continuous models and models with more than two discrete patches have also demonstrated that marine reserves can be economically optimal even when the system is spatially homogeneous. In this note we analyze a spatially homogeneous two‐patch model and show that marine reserves can be economically optimal in this case as well. The model we study includes the possibility that fishing can damage habitat. In this model, marine reserves are necessary to maximize sustainable profit when dispersal between the patches is sufficiently high and habitat is especially vulnerable to damage.     

A Quantitative Regularity Estimate for Nonnegative Supersolutions of Uniformly Parabolic Equations

This note establishes an interior quantitative lower bound for nonnegative supersolutions of fully nonlinear uniformly parabolic equations. The result may be interpreted as a quantitative version of a growth lemma established by Krylov and Safonov for nonnegative supersolutions of linear uniformly parabolic equations in nondivergence form. Our approach is different, and follows from an application of a reverse Holder inequality. The result is the parabolic analogue of an elliptic regularity estimate established by Caffarelli, Souganidis, and Wang in the stochastic homogenization of fully nonlinear uniformly elliptic equations.     

纳米磁流体动态散斑干涉场的奇异场分布

通过对由纳米磁流体运动引起的双扫描激光散斑干涉光场及其变化做拉盖尔-高斯滤波下的傅里叶变换,获得动态散斑干涉图对应的光学涡旋分布及变化特征。分析认为,光学涡旋分布及变化对应着由纳米磁微粒及其团族的运动所引起的动态散斑变化。当纳米磁微粒聚集到分散的过程中,动态激光散斑光场的奇异场分布发生相应变化,说明了磁流体运动过程对应涡旋密度有先大后小,再由小变大的两个变化;并且光学涡旋密度高,对应较小颗粒的散斑场,磁流体处于稳态的状况;光学涡旋密度低,对应较大颗粒的散斑场,对应着磁流体激烈的运动。研究结果体现了奇异场分布变化和纳米磁流体动后趋稳的过程存在对应关系。     

铅镉重金属离子在铋膜电极上的相互影响

采用原位镀铋电极的方式,以玻碳电极为工作电极,通过改变Cd2+和Pb2+的比例,考察不同Pb2+和Cd2+浓度条件下,两者同时存在时的相互影响。实验发现,Cd2+和Pb2+同时存在时,存在相互的影响,特别是对于Cd2+的检测,由于Pb2+较正的析出电位,对于Cd2+的析出有一定的辅助作用。考察了Cd2+和Pb2+单独存在时的分析性能,Pb2+沉积时间为60 s时,在1~80μg/L范围内呈线性关系,检出限为0.5μg/L;Cd2+的沉积时间为120 s,在1~25μg/L和30~200μg/L范围内有良好的线性关系,检出限为1.0μg/L。考察了铋膜电极在不同实际水样中对Pb2+和Cd2+的分析,获得了较好的一致性。     

A Fully Non-fused Ring Acceptor with Planar Backbone and Near-IR Absorption for High Performance Polymer Solar Cells

Fused-ring electron acceptors have made significant progress in recent years, while the development of fully non-fused ring acceptors has been unsatisfactory. Here, two fully non-fused ring acceptors, o-4TBC-2F and m-4TBC-2F, were designed and synthesized. By regulating the location of the hexyloxy chains, o-4TBC-2F formed planar backbones, while m-4TBC-2F displayed a twisted backbone. Additionally, the o-4TBC-2F film showed a markedly red-shifted absorption after thermal annealing, which indicated the formation of J-aggregates. For fabrication of organic solar cells (OSCs), PBDB-T was used as a donor and blended with the two acceptors. The o-4TBC-2F-based blend films displayed higher charge mobilities, lower energy loss and a higher power conversion efficiency (PCE). The optimized devices based on o-4TBC-2F gave a PCE of 10.26 %, which was much higher than those based on m-4TBC-2F at 2.63 %, and it is one of the highest reported PCE values for fully non-fused ring electron acceptors.     

EMI shielding and dynamic mechanical analysis of graphene oxide-carbon nanotube-acrylonitrile butadiene styrene hybrid composites

Carbon nanomaterials such as carbon nanotubes (CNTs), graphene and their hybrid have been studied extensively. Despite having excellent properties of CNTs and graphene have not yet been fully realized in the polymer composites. During fabrication agglomeration of CNTs and restacking of graphene is a serious concern that results in the degradation of properties of nanomaterials into the final composites. To improve the dispersion of CNTs and restacking graphene, in the present research work, we focused on the hybridization of graphene oxide and CNTs. Multiwalled carbon nanotubes (MWCNTs), functionalized carbon nanotubes (FCNTs), and graphene oxide-carbon nanotubes (GCNTs) reinforced acrylonitrile butadiene styrene (ABS) composites were prepared separately by vacuum filtration followed by hot compression molding. Further, dynamic mechanical analysis (DMA), and electromagnetic interference (EMI) shielding properties of ABS composites reinforced carbon nanofillers were investigated. The dynamic mechanical properties of polymers strongly depend on the adhesion of fillers and polymer, entanglement density of polymer chains in the presence of carbon fillers. The dynamic mechanical characteristics such as storage, loss modulus, and damping factor of prepared composites were significantly affected by the incorporation of MWCNTs, FCNTs, and GCNTs. Maximum EMI shielding effectiveness of −49.6 dB was achieved for GCNT-ABS composites which were highest compared to MWCNTs-ABS composites (−38.6 dB) and FCNTs-ABS composites (−36.7 dB) in the Ku band (12.4–18 GHz). These results depict the great potential of GCNTs-ABS composites to be used in various applications of efficient heat dissipative EMI shielding materials for electronic devices.