Damage models for multi-component systems

A series system of n components is subject to a damage process. The damage to each component is cumulative and when it exceeds a certain threshold the component, and hence the device, fails. For various optimality criteria related to system lifetime and system reliability, we find the optimal allocation of resources among the components where the total resources are limited and the allocation of the resources determines the threshold level of each component. Various inventory-type applications are noted.     

Analytical study of diffusive relativistic shock acceleration

Particle acceleration in relativistic shocks is studied analytically in the test-particle, small-angle scattering limit, for an arbitrary velocity-angle diffusion function D. The particle spectral index s is found to be sensitive to D, particularly downstream and at certain angles. The analysis, confirmed numerically, justifies and generalizes previous results for isotropic diffusion. It can be used to test collisionless shock models and to observationally constrain D. For example, strongly forward- or backward-enhanced diffusion downstream is ruled out by gamma-ray burst afterglow observations.     

Long-range electronic-to-vibrational energy transfer from nanocrystals to their surrounding matrix environment

A radiationless transition process of long-range, resonance interconversion of electronic-to-vibrational energy transfer (EVET) is discovered between the band-gap excitation of nanocrystal quantum dots to matrix vibrational overtone modes using fluorescence lifetime measurements. A theoretical analysis based on long-range dipole-dipole nonadiabatic couplings, being distinct from the traditional adiabatic or "static-coupling" pictures, is given and is in qualitative agreement with experiments. EVET should be considered in matrix choices for near-infrared optoelectronic applications of nanocrystals.     

A combinatorial method for solution-phase synthesis of labeled bivalent beta-turn mimics

Piperidine-functionalized, 1,4-disubstituted-1,2,3-triazoles of generic structure 1 were conceived as "minimalist" mimics of peptidic beta-turn structures. Key features of these molecules include (i) the possibility of incorporating amino acid side chains corresponding to many of the protein amino acids; (ii) a close correspondence of separations of these side chains to i + 1 to i + 2 residues in turns; (iii) facile adjustment of the side-chain vectors on docking while only influencing two critical degrees of freedom; and (iv) some electrostatic polarity. Fifteen monomers of this type were made via copper-mediated cycloaddition reactions. Solution-phase methodologies were devised to assemble these monomers into bivalent compounds in high purity states (typically >85%) so that they could be used in first-pass biological assays without further purification. The skeleton for forming these bivalent compounds is triazine-based. There is a third site which allowed for introduction of a fluorescent label (library of compounds 2) or an alkyne-functionalized triethylene glycol chain (library of compounds 3) included to promote water-solubility and to allow incorporation of probes via copper-mediated cycloaddition reactions. In the event, two 135-membered libraries were prepared, one consisting of compounds 2 and the other of 3. No protecting groups or coupling agents were required; these attributes of the method were important to allow most of the products to be obtained in over 85% purities. The fluorescein-tagged library of compounds 2 was screened in a fluorescence-activated cell sorting (FACS) assay using cells transfected to overexpress one of the following neurotrophin receptors: TrkA, TrkC, and p75. Preliminary findings indicate four compounds 2gm, 2gn, 2gi, and 2gj bound the TrkA receptor selectively; all of these contain a threonine-lysine turn mimic. Thus, a pharmacological probe for the TrkA receptor has been developed.     

Measure theoretical entropy of covers

In this paper we introduce three notions of measure theoretical entropy of a measurable cover in a measure theoretical dynamical system. Two of them were already introduced in [R] and the new one is defined only in the ergodic case. We then prove that these three notions coincide, thus answering a question posed in [R], and recover a variational inequality (proved in [GW]) and a proof of the classical variational principle based on a comparison between the entropies of covers and partitions.     

Forces between mica surfaces, prepared in different ways, across aqueous and nonaqueous liquids confined to molecularly thin films

We have measured normal and lateral interactions across a range of different liquids between mica surfaces using a surface force balance (SFB). The mica surfaces were prepared either by melt cutting using Pt wire and standard procedures in our laboratories or by tearing sheets (that had not been exposed to Pt) off from a freshly cleaved sheet of mica. AFM micrographs revealed the substantial absence of Pt nanoparticles on the melt cut and torn-off mica surfaces. Normal-force versus surface-separation (D) profiles and shear force versus D measurements for purified water (no added salt), for concentrated aqueous NaCl solutions, and for cyclohexane revealed that in all cases the behavior of the highly confined liquids between melt-cut and between torn-off mica sheets was identical within experimental scatter. These results demonstrate directly that interactions measured between melt-cut mica surfaces as routinely prepared using established procedures in our laboratories and in other laboratories are free of the effect of any Pt contamination.     

Multiphase thermoplastic hybrid for controlled release of antimicrobial essential oils in active packaging film

Active packaging, a new technology concept in the field of food packaging, has been introduced in recent years in order to provide quality and safety, as well as extend the shelf life of food products. Antimicrobial (AM) agents can be incorporated directly into the active packaging and migrate in a controlled manner to the headspace between the food and the package, inhibiting bacteria growth on the food surface. Naturally derived AM agent, such as essential oils (EOs), has received considerable attention for food preservation purposes, because of their effective AM activity against various bacteria and fungi. In the present study, AM active film systems based on polypropylene/polyamide blends, montmorillonite nanoclays, and thymol EO were produced to investigate the feasibility of controlling the release rate of thymol from food packaging systems. Selective localization of thymol in a specific phase in the system that derives from thermodynamic affinity was assumed to be useful in controlling its migration rate from the film to the headspace. EO retention in the film under two different time conditions was measured by spectroscopic analysis. The release rate of EO was determined using Gas chromatography technique and analyzed by diffusion model approach. Inhibition of bacterial growth was periodically tested for Listeria and Escherichia coli bacteria. This study confirms the thermodynamic affinity of polyamide phase with thymol that has a positive effect in retaining the EO. Results show controlled AM behavior of the active packaging films, based on various blend compositions. Copyright © 2016 John Wiley & Sons, Ltd.     

More results in polychromatic Ramsey theory

We study polychromatic Ramsey theory with a focus on colourings of [ω ₂]². We show that in the absence of GCH there is a wide range of possibilities. In particular each of the following is consistent relative to the consistency of ZFC: (1) 2 ^ω = ω ₂ and \(\omega _2 \to ^{poly} (\alpha )_{\aleph _0 - bdd}^2 \) for every α <ω ₂; (2) 2 ^ω = ω ₂ and \(\omega _2 \nrightarrow ^{poly} (\omega _1 )_{2 - bdd}^2 \).