Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.     

Synthesis,self-assembly,and photomechanical actuator performance of a sequence-defined polyviologen crosslinker

ABSTRACT

Although it is well known that viologen radical cations can self-assemble into stacks or complexes on account of radical-radical pairing interactions, it has only recently been demonstrated that reduction of main-chain polyviologens integrated into hydrogel networks can trigger actuation. In these earlier examples, hydrogels comprising oligoethylene glycol-based polyviologens and poly(ethylene glycol) were functionalized with terminal azide groups to prepare ‘click’-based gels. Here, we report a new structural design for the functional polyviologen that consists of main-chain viologen subunits separated by hexamethylene groups instead of glycols and is capped at each end with styrene groups. Activation of this viologen-based macrocrosslinker was achieved using chemical- and photoreduction methods and its ability to undergo intramolecular chain-folding was monitored by absorption spectroscopy. Acrylate-based organogels and hydrogels were also prepared and a comparison was carried out to assess the actuator performance in each gel in terms of the rate of contraction and changes in stiffness.     

Gibbsian dynamics and ergodicity of magnetohydrodynamics and related systems forced by random noise

The magnetohydrodynamics system consists of the Navier-Stokes equations from fluid mechanics, coupled with the Maxwell’s equations from electromagnetism through multiples of non-linear terms involving derivatives. Following the approach of [1 Weinan, E., Mattingly, J. C., Sinai, Y. (2001). Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation. Commun. Math. Phys. 224:83–106. DOI:10.1007/s002201224083.[Crossref], [Web of Science ®] , [Google Scholar]], we prove the existence of a unique invariant measure in case the forcing terms consist of the cylindrical Wiener processes with only low modes. Its proof requires taking advantage of the structure of the non-linear terms carefully and is extended to various other related models such as the magnetohydrodynamics-Boussinesq system from fluid mechanics in atmosphere and oceans, as well as the magneto-micropolar fluid system from the theory of microfluids.     

On the Optimal Design of Wall-to-Wall Heat Transport

We consider the problem of optimizing heat transport through an incompressible fluid layer. Modeling passive scalar transport by advection-diffusion, we maximize the mean rate of total transport by a divergence-free velocity field. Subject to various boundary conditions and intensity constraints, we prove that the maximal rate of transport scales linearly in the r.m.s. kinetic energy and, up to possible logarithmic corrections, as the one-third power of the mean enstrophy in the advective regime. This makes rigorous a previous prediction on the near optimality of convection rolls for energy-constrained transport. On the other hand, optimal designs for enstrophy-constrained transport are significantly more difficult to describe: we introduce a “branching” flow design with an unbounded number of degrees of freedom and prove it achieves nearly optimal transport. The main technical tool behind these results is a variational principle for evaluating the transport of candidate designs. The principle admits dual formulations for bounding transport from above and below. While the upper bound is closely related to the “background method,” the lower bound reveals a connection between the optimal design problems considered herein and other apparently related model problems from mathematical materials science. These connections serve to motivate designs. © 2019 Wiley Periodicals, Inc.     

Photoluminescence of Seven-Coordinate Zirconium and Hafnium Complexes with 2,2′-Pyridylpyrrolide Ligands

Luminescent seven-coordinated zirconium and hafnium complexes bearing three mono-anionic 2,2′-pyridylpyrrolide ligands and one chloride were synthesized. Solid-state structures and the dynamic behaviors in solution were probed by X-ray crystallography and variable temperature ¹H NMR experiments, respectively. Absorption spectroscopy and time-dependent density functional theory (TD-DFT) calculations supported a hybrid of ligand-to-metal charge transfer (LMCT)/ligand-to-ligand charge transfer (LLCT) for the visible light absorption band. The complexes (^MePMP^Me)₃MCl (M=Zr, Hf, ^MePMP^Me=3,5-dimethyl-2-(2-pyridyl)pyrrolide) are emissive in solution at room temperature upon irradiation with visible light due to a combination of phosphorescence and fluorescence characterized by excited state lifetimes in the μs and low to sub-ns timescale, respectively. Electrochemical experiments revealed that the zirconium complex possesses a reversible redox event under highly reducing condition (−2.29 V vs. Fc^+/0).     

Synthesis,anticancer activity,toxicity evaluation and molecular docking studies of novel phenylaminopyrimidine—(thio)urea hybrids as potential kinase inhibitors

Thirty-two novel urea/thiourea compounds as potential kinase inhibitor were designed, synthesized and evaluated for their cytotoxic activity on breast (MCF7), colon (HCT116) and liver (Huh7) cancer cell lines. Compounds 10, 19 and 30 possessing anticancer activity with IC₅₀ values of 0.9, 0.8 and 1.6 μM respectively on Huh7 cells were selected for further studies. These hit compounds were tested against liver carcinoma panel. Real time cell electronic sensing assay was used to evaluate the effects of the compounds 10, 19 and 30 on the growth pattern of liver cancer cells. Apoptotic cell death and cell cycle analysis upon treatment of liver carcinoma cells with hit compounds were determined. A significant apoptotic cell death was detected upon treatment of Huh7 and Mahlavu cells with compound 30 after 48 h of treatment. Additionally, compound 10 caused cell cycle arrest at G0/G1 phase. Mutagenicity of hit compounds was evaluated. Assertively, these compounds were not found to be mutagenic on Salmonella typhimurium strains TA98 and TA100. To understand the binding modes of the synthesized compounds, molecular docking studies were performed using the crystal data of VEGFR and Src-kinase enzymes in correlation with anticancer activities.     

Resonance Energy Transfer in a Genetically Engineered Polypeptide Results in Unanticipated Fluorescence Intensity

The fluorescence intensity of a C-terminal acceptor chromophore, N-(7-dimethylamino-4-methyl coumarin (DACM), increased proportionally with 280 nm irradiation of an increasing number of donor tryptophan residues located on a β-sheet forming polypeptide. The fluorescence intensity of the acceptor chromophore increased even as the length of the β-sheet edge approached 256 Å, well beyond the Förster radius for the tryptophan–acceptor chromophore pair. The folding of the peptides under investigation was verified by circular dichroism (CD) and deep UV resonance Raman experiments. Control experiments showed that the enhancement of DACM fluorescence occurred concomitantly with peptide folding. In other control experiments, the DACM fluorescence intensity of the solutions of tryptophan and DACM did not show any enhancement of DACM fluorescence with increasing tryptophan concentrations. Formation of fibrillar aggregates of the substrate peptides prepared for the fluorescence studies was undetectable by thioflavin T (ThT) fluorescence.     

Ab initio simulations of liquid electrolytes for energy conversion and storage

Understanding physicochemical properties of liquid electrolytes is essential for predicting and optimizing device performance for a wide variety of emerging energy technologies, including photoelectrochemical water splitting, supercapacitors, and batteries. In this work, we review recent progress and open challenges in predicting structural, dynamical, and electronic properties of the liquids using first-principles approaches. We briefly summarize the basic concepts of first-principles molecular dynamics (FPMD), and we discuss how FPMD methods have enriched our understanding of a number of liquids, including aqueous solutions, organic electrolytes and ionic liquids. We also discuss technical challenges in extending FPMD simulations to the study of liquid electrolytes in more complex environments, including the interface between electrolytes and electrodes, which is a key component in many energy storage and conversion systems.