Homogenisation and spectral convergence of a periodic elastic composite with weakly compressible inclusions

A two-phase elastic composite with weakly compressible elastic inclusions is considered. The homogenised two-scale limit problem is found, via a version of the method of two-scale convergence, and analysed. The microscopic part of the two-scale limit is found to solve a Stokes type problem and shown to have no microscopic oscillations when the composite is subjected to body forces that are microscopically irrotational. The composites spectrum is analysed and shown to converge, in an appropriate sense, to the spectrum of the two-scale limit problem. A characterisation of the two-scale limit spectrum is given in terms of the limit macroscopic and microscopic behaviours.     

A set oriented definition of finite-time Lyapunov exponents and coherent sets

The problem of phase space transport, which is of interest from both the theoretical and practical point of view, has been investigated extensively using geometric and probabilistic methods. Two important tools to study this problem that have emerged in recent years are finite-time Lyapunov exponents (FTLE) and the Perron–Frobenius operator. The FTLE measures the averaged local stretching around reference trajectories. Regions with high stretching are used to identify phase space transport barriers. One probabilistic method is to consider the spectrum of the Perron–Frobenius operator of the flow to identify almost-invariant densities. These almost-invariant densities are used to identify almost invariant sets. In this paper, a set-oriented definition of the FTLE is proposed which is applicable to phase space sets of finite size and reduces to the usual definition of FTLE in the limit of infinitesimal phase space elements. This definition offers a straightforward connection between the evolution of probability densities and finite-time stretching experienced by phase space curves. This definition also addresses some concerns with the standard computation of the FTLE. For the case of autonomous and periodic vector fields we provide a simplified method to calculate the set-oriented FTLE using the Perron–Frobenius operator. Based on the new definition of the FTLE we propose a simple definition of finite-time coherent sets applicable to vector fields of general time-dependence, which are the analogues of almost-invariant sets in autonomous and time-periodic vector fields. The coherent sets we identify will necessarily be separated from one another by ridges of high FTLE, providing a link between the framework of coherent sets and that of codimension one Lagrangian coherent structures. Our identification of coherent sets is applied to three examples.     

A mathematical model of hotspot condensed phase ignition in the presence of a competitive endothermic reaction

We consider the propagation of a combustion front resulting from the gasless combustion of a condensed state fuel. The propagation of the front, essentially a premixed laminar flame, is supported by an exothermic reaction subject to possible heat loss through a competitive endothermic reaction. The dynamics of the endothermic process inducing the heat loss strongly depend on the temperature and the local fuel concentration. Through an analysis based on high activation energy, the steady-state values of the final burnt temperature as well as the burning velocity are obtained, and the control parameters are identified. Using a linear perturbation method, we assess the stability of the propagating front and obtain a condition for oscillatory behaviour. The critical parameter values for the transition from steady to oscillatory burning speeds are identified. The results represent a generalization of those obtained by Matkowsky and Sivashinsky to include the effects of heat loss induced by a competitive endothermic reaction.     

Central Sets and Radii of the Zero-Divisor Graphs of Commutative Rings

For a commutative ring R with identity, the zero-divisor graph, Γ(R), is the graph with vertices the nonzero zero-divisors of R and edges between distinct vertices x and y whenever xy = 0. This article gives a proof that the radius of Γ(R) is 0, 1, or 2 if R is Noetherian. The center union {0} is shown to be a union of annihilator ideals if R is Artinian. The diameter of Γ(R) can be determined once the center is identified. If R is finite, then the median is shown to be a subset of the center. A dominating set of Γ(R) is constructed using elements of the center when R is Artinian. It is shown that for a finite ring R ? ?₂ × F for some finite field F, the domination number of Γ(R) is equal to the number of distinct maximal ideals of R. Other results on the structure of Γ(R) are also presented.     

Additive‐dependent iptycene incorporation in polyanilines: Insights into the pentiptycene clipping effect and the polymerization mechanism

Despite the long history of polyaniline chemistry, backbone‐substituted polyanilines are limited. Here, we report the synthesis of pentiptycene‐incorporated polyanilines through acidic aniline oxidative polymerization with three pentiptycene derivatives, TA, DA, and TP, as nucleate additives. The reactivity of TA > DA ? TP, as evidenced by structural and property analysis of the corresponding polyaniline products, demonstrates a radical coupling mechanism and the formation of Dewar π‐complex intermediates for the chain propagation. In addition, the iptycene substituent effect on enhancing the electrochemical stability and charge storage capability of polyaniline are discussed with a clip model, namely, the threading of neighboring polyaniline chains through the U‐ and V‐shaped cavities of pentiptycene restricts lateral motions of the polymer chains and promotes interchain conductivity. Density function theory (DFT) calculations suggest a larger clipping effect for the U versus V cavities. Both the conclusion of a terminal planar p‐phenylenediamine (ppda) group being the key component of an effective nucleate and the concept of interchain clipping for enhanced electrochemical performance should facilitate the design and synthesis of novel polyanilines for electronic applications.     

Raising the bar on-bead: Efficient on-resin synthesis of α-conotoxin LvIA

α4/7-Conotoxin LvIA is an isoform-selective inhibitor of the α3β2 nicotinic acetylcholine receptor. An efficient strategy for the synthesis of this toxin is critical to advancing its utility as a probe for receptor function and as a potential pharmaceutical lead target. On-resin methods for peptide synthesis offer potential synthetic advantages; however, strategies for on-resin formation of multiple disulfides have historically been low-yielding. Here, we harness the reactivity of the Allocam protecting group and employ a 3-amino acid spacer strategy to synthesize α4/7-conotoxin LvIA via three different on-resin strategies, each of which results in an isolated yield higher than previous fully on-resin approaches.     

Scalable Biosynthesis of the Seaweed Neurochemical,Kainic Acid

Kainic acid, the flagship member of the kainoid family of natural neurochemicals, is a widely used neuropharmacological agent that helped unravel the key role of ionotropic glutamate receptors, including the kainate receptor, in the central nervous system. Worldwide shortages of this seaweed natural product in the year 2000 prompted numerous chemical syntheses, including scalable preparations with as few as six‐steps. Herein we report the discovery and characterization of the concise two‐enzyme biosynthetic pathway to kainic acid from l ‐glutamic acid and dimethylallyl pyrophosphate in red macroalgae and show that the biosynthetic genes are co‐clustered in genomes of Digenea simplex and Palmaria palmata. Moreover, we applied a key biosynthetic α‐ketoglutarate‐dependent dioxygenase enzyme in a biotransformation methodology to efficiently construct kainic acid on the gram scale. This study establishes both the feasibility of mining seaweed genomes for their biotechnological prowess.     

Acyclic 1,4-stereocontrol via reductive 1,3-transpositions

One-pot reduction/allylic diazene rearrangement of lactic acid- and mandelic acid-derived alpha,beta-unsaturated tosyl hydrazones leads to 1,4-syn- or 1,4-anti-E-2-alkenyl arrays in high yield and diastereoselectivity. Either the syn or the anti diastereomer can be prepared by choosing the appropriate alkene stereoisomer of the hydrazone. The E-alkenes led to the 1,4-syn isomers, while the Z-alkenes led to the 1,4-anti isomers, both with > or =20:1 diastereoselectivity.     

Biocatalytically oligomerized epicatechin with potent and specific anti-proliferative activity for human breast cancer cells

Catechins, naturally occurring flavonoids derived from wine and green tea, are known to exhibit multiple health benefits. Epigallocatechin gallate (EGCG) is one of the most widely investigated catechins, but its efficacy in cancer therapy is still inconsistent and limited. The poor stability of EGCG has contributed to the disparity in the reported anti-cancer activity and other beneficial properties. Here we report an innovative enzymatic strategy for the oligomerization of catechins (specifically epicatechin) that yields stable, water-soluble oligomerized epicatechins with enhanced and highly specific anti-proliferative activity for human breast cancer cells. This one-pot oxidative oligomerization is carried out in ambient conditions using Horseradish Peroxidase (HRP) as a catalyst yielding water-soluble oligo(epicatechins). The oligomerized epicatechins obtained exhibit excellent growth inhibitory effects against human breast cancer cells with greater specificity towards growth-inhibiting cancer cells as opposed to normal cells, achieving a high therapeutic differential. Our studies indicate that water-soluble oligomeric epicatechins surpass EGCG in stability, selectivity and efficacy at lower doses.     

Analysis of formaldehyde formation in wastewater using on-fiber derivatization-solid-phase microextraction-gas chromatography-mass spectrometry

A method has been developed for the quantification of the formation of formaldehyde during the advanced oxidation treatment (AOT) of wastewater destined for reuse. This method uses solid-phase microextraction (SPME) with on-fiber derivatization followed by gas chromatography-mass spectrometry (GC-MS) analysis. Based on calculated method detection limits (MDL) and ambient background levels, the method reporting (MRL) limit for formaldehyde was set at 10 microg/L. Precision for formaldehyde using this technique resulted in 23% relative standard deviation (RSD), while the internal standard, acetone-d(6), was only 6%. This method was used to evaluate the formation of formaldehyde in bench scale UV-AOT experiments using natural organic matter (NOM) fortified reagent water and tertiary treated wastewater effluent. Results suggest that the formation of formaldehyde increases in both the reagent water and wastewater matrices with increasing UV exposure and hydrogen peroxide concentrations, with overall higher concentrations of formaldehyde in the wastewater samples. No appreciable amount of formaldehyde formation was observed when UV was applied in the absence of hydrogen peroxide in both matrices tested.