Generalizing reduction-based algebraic multigrid

Algebraic multigrid (AMG) methods are often robust and effective solvers for solving the large and sparse linear systems that arise from discretized PDEs and other problems, relying on heuristic graph algorithms to achieve their performance. Reduction-based AMG (AMGr) algorithms attempt to formalize these heuristics by providing two-level convergence bounds that depend concretely on properties of the partitioning of the given matrix into its fine- and coarse-grid degrees of freedom. MacLachlan and Saad (SISC 2007) proved that the AMGr method yields provably robust two-level convergence for symmetric and positive-definite matrices that are diagonally dominant, with a convergence factor bounded as a function of a coarsening parameter. However, when applying AMGr algorithms to matrices that are not diagonally dominant, not only do the convergence factor bounds not hold, but measured performance is notably degraded. Here, we present modifications to the classical AMGr algorithm that improve its performance on matrices that are not diagonally dominant, making use of strength of connection, sparse approximate inverse (SPAI) techniques, and interpolation truncation and rescaling, to improve robustness while maintaining control of the algorithmic costs. We present numerical results demonstrating the robustness of this approach for both classical isotropic diffusion problems and for non-diagonally dominant systems coming from anisotropic diffusion.     

Selective CO2 Reduction to Ethylene Mediated by Adaptive Small-molecule Engineering of Copper-based Electrocatalysts

Electrochemical CO₂ reduction reaction (CO₂RR) over Cu catalysts exhibits enormous potential for efficiently converting CO₂ to ethylene (C₂H₄). However, achieving high C₂H₄ selectivity remains a considerable challenge due to the propensity of Cu catalysts to undergo structural reconstruction during CO₂RR. Herein, we report an in situ molecule modification strategy that involves tannic acid (TA) molecules adaptive regulating the reconstruction of a Cu-based material to a pathway that facilitates CO₂ reduction to C₂H₄ products. An excellent Faraday efficiency (FE) of 63.6 % on C₂H₄ with a current density of 497.2 mA cm⁻² in flow cell was achieved, about 6.5 times higher than the pristine Cu catalyst which mainly produce CH₄. The in situ X-ray absorption spectroscopy and Raman studies reveal that the hydroxyl group in TA stabilizes Cu^δ+ during the CO₂RR. Furthermore, theoretical calculations demonstrate that the Cu^δ+/Cu⁰ interfaces lower the activation energy barrier for *CO dimerization, and hydroxyl species stabilize the *COH intermediate via hydrogen bonding, thereby promoting C₂H₄ production. Such molecule engineering modulated electronic structure provides a promising strategy to achieve highly selective CO₂ reduction to value-added chemicals.     

Solid state NMR studies of photoluminescent cadmium chalcogenide nanoparticles

Solid state (113)Cd, (77)Se, (13)C and (31)P NMR have been used to study a number of Cd chalcogenide nanoparticles synthesized in tri-n-octyl-phosphine (TOP) with different compositions and architectures. The pure CdSe and CdTe nanoparticles show a dramatic, size-sensitive broadening of the (113)Cd NMR line, which can be explained in terms of a chemical shift distribution arising from multiple Cd environments. From (13)C NMR, it has been discovered that TOP, or its derivatives such as TOPO (trioctylphosphine oxide), is rapidly moving about the surface of the nanoparticles, indicating that it is relatively weakly bound as compared to other materials used as surface ligands, such as hexadecylamine. (31)P NMR of the nanoparticles shows at least five species arising from coordination of the ligands to different surface sites. (113)Cd NMR of CdSeTe alloy and layered nanoparticles has provided crucial information which, in conjunction with results from other techniques (especially optical characterization), has made it possible to develop a detailed picture of the composition and structure of these materials: (i) a true CdSeTe homogeneous alloy nanoparticle, (ii) a nanoparticle segregated into an alloy core region rich in Te, with a CdSeTe (close to 1 : 1 Se : Te) alloy shell and (iii) a CdSe/CdTe/CdSe layered nanoparticle in which the CdTe layer contains a small amount of Se and which forms a Quantum Dot Quantum Well (QDQW) system. The results demonstrate that solid state NMR is a vital tool in the arsenal of characterisation techniques available for nanomaterials.     

Field due to a point source in a layer over an inhomogenous medium

Summary A point source at an interface between a homogeneous layer of finite depth and an inhomogeneous half-space is considered. The transmitted wave and the dispersion relation for the Love waves is calculated analytically. The authors of this paper have agreed to not receive the proofs for correction.     

Free energy landscape of receptor-mediated cell adhesion

Receptor-mediated cell adhesion plays a critical role in cell migration, proliferation, signaling, and survival. A number of diseases, including cancer, show a strong correlation between integrin activation and metastasis. A better understanding of cell adhesion is highly desirable for not only therapeutic but also a number of tissue engineering applications. While a number of computational models and experimental studies have addressed the issue of cell adhesion to surfaces, no model or theory has adequately addressed cell adhesion at the molecular level. In this paper, the authors present a thermodynamic model that addresses receptor-mediated cell adhesion at the molecular level. By incorporating the entropic, conformational, solvation, and long- and short-range interactive components of receptors and the extracellular matrix molecules, they are able to predict adhesive free energy as a function of a number of key variables such as surface coverage, interaction distance, molecule size, and solvent conditions. Their method allows them to compute the free energy of adhesion in a multicomponent system where they can simultaneously study adhesion receptors and ligands of different sizes, chemical identities, and conformational properties. The authors' results not only provide a fundamental understanding of adhesion at the molecular level but also suggest possible strategies for designing novel biomaterials.     

Thermostability of Cromobacterium viscosum lipase in AOT/isooctane reverse micelle

The thermostability of Cromobacterium viscosum lipase (EC 3.1.1.3) entrapped in AOT (sodium bis-[2-ethylhexyl] sulfosuccinate) reverse micelles was increased by the addition of short-chain polyethylene glycol (PEG 400). Two different approaches were considered: (1) the determination of half-life time and (2) the mechanistic analysis of deactivation kinetics. The half-life of lipase entrapped in AOT/isooctane reverse micelles with PEG 400 at 60 degrees C was 28 h, ninefold higher than that in reverse micelles without PEG 400. The lipase entrapped in both reverse micellar systems followed a series-type deactivation mechanism involving two first-order steps. The deactivation constant for the first step at 60 degrees C in PEG containing reverse micelles was 0.055 h!1, 11-fold lower than that in reverse micelles without PEG, whereas it remained almost constant for the second step. The inactivation energy of the lipase entrapped in reverse micelles with and without PEG 400 was 88.12 and 21.97 kJ/mol, respectively.     

Fe3O4@SiO2@l‐arginine@Pd(0): a new magnetically retrievable heterogeneous nanocatalyst with high efficiency for C–C bond formation

The surface of Fe₃O₄@SiO₂ nanoparticles was modified using l ‐arginine as a green and available amino acid to trap palladium nanoparticles through a strong interaction between the metal nanoparticles and functional groups of the amino acid. The proposed green synthetic method takes advantage of nontoxic reagents through a simple procedure. Characterization of Fe₃O₄@SiO₂@l ‐arginine@Pd(0) was done using Fourier transform infrared spectroscopy, thermogravimetric analysis, scanning electron microscopy, energy‐dispersive X‐ray spectroscopy, X‐ray diffraction, vibrating sample magnetometry and inductively coupled plasma analysis. The catalytic activity of Fe₃O₄@SiO₂@l ‐arginine@Pd(0) as a new nanocatalyst was investigated in C – C coupling reactions. Waste‐free, use of green medium, efficient synthesis leading to high yield of products, eco‐friendly and economic catalyst, excellent reusability of the nanocatalyst and short reaction time are the main advantages of the method presented. Copyright © 2016 John Wiley & Sons, Ltd.     

A new simple synthesis of poly(thiophene-methine)s

Acid-promoted polycondensation of 3,4-(ethylenedioxy)thiophene-2-carbaldehyde leads to a conjugated heavily p-doped poly(thiophene-methine), which can be dedoped leading to a low band-gap neutral polymer.     

Global Aspects of Age-Structured Cigarette Smoking Model

Smoking impacts health and as a result creates several problems related to age which means smoking has a strong correlation with age. Keeping this problem in view, we consider the global asymptotic properties of age-structured smoking model. First, we formulate the model and present the existence and uniqueness of solution. Then we discuss the equilibrium points and construct the Lyapunov function to examine global stability of the free smoking and positive smoking equilibrium points. Finally, we fixed the age factor and use the non-standard finite difference (NSFD) scheme for numerical solutions and compare our results obtained with RK4 and ODE45 graphically with the help of MATLAB.     

Unsteady wake vortices in jets in cross-flow

Abstract  

The current flow visualization study investigates unsteady wake vortices of jets in cross-flow in order to (1) advance the understanding of their origin and characteristics and (2) explore various excitation techniques for organizing and accentuating them. An isolated circular jet passed through a nozzle and entered the cross-flow normal to the wall. Free stream velocities up to 5 m/s and jet-to-cross-flow velocity ratio range between 1 and 10 were covered. While mechanical perturbation did not result in any significant periodic organization of the wake vortices, the database obtained for the unperturbed flow provided further insight into their behavior. The key finding was that the wake vortices always originated from the lee-side of the jet where the jet efflux boundary layer and the wall boundary layer intersected. In no case these vortices were seen to form either from the wall boundary layer or the jet shear layer at downstream locations. After formation the wake vortex twists and stretches as it convects downstream with the base still attached to the near-wall region on the jet’s lee side. The top remains connected to the underside of the jet where the tracer particles dissipate due to high turbulence in the shear layer.