Algebraic Multigrid Preconditioning for Finite Element Solution of Inhomogeneous Elastic Inclusion Problems in Articular Cartilage

In studying biomechanical deformation in articular cartilage, the presence of cells (chondrocytes) necessitates the consideration of inhomogeneous elasticity problems in which cells are idealized as soft inclusions within a stiff extracellular matrix. An analytical solution of a soft inclusion problem is derived and used to evaluate iterative numerical solutions of the associated linear algebraic system based on discretization via the finite element method, and use of an iterative conjugate gradient method with algebraic multigrid preconditioning (AMG-PCG). Accuracy and efficiency of the AMG-PCG algorithm is compared to two other conjugate gradient algorithms with diagonal preconditioning (DS-PCG) or a modified incomplete LU decomposition (Euclid-PCG) based on comparison to the analytical solution. While all three algorithms are shown to be accurate, the AMG-PCG algorithm is demonstrated to provide significant savings in CPU time as the number of nodal unknowns is increased. In contrast to the other two algorithms, the AMG-PCG algorithm also exhibits little sensitivity of CPU time and number of iterations to variations in material properties that are known to significantly affect model variables. Results demonstrate the benefits of algebraic multigrid preconditioners for the iterative solution of assembled linear systems based on finite element modeling of soft elastic inclusion problems and may be particularly advantageous for large scale problems with many nodal unknowns.     

Four-dimensional parameter estimation of plane waves using swarming intelligence

This paper proposes an efficient approach for four-dimensional(4D) parameter estimation of plane waves impinging on a 2-L shape array. The 4D parameters include amplitude, frequency and the two-dimensional(2D) direction of arrival,namely, azimuth and elevation angles. The proposed approach is based on memetic computation, in which the global optimizer, particle swarm optimization is hybridized with a rapid local search technique, pattern search. For this purpose,a new multi-objective fitness function is used. This fitness function is the combination of mean square error and the correlation between the normalized desired and estimated vectors. The proposed hybrid scheme is not only compared with individual performances of particle swarm optimization and pattern search, but also with the performance of the hybrid genetic algorithm and that of the traditional approach. A large number of Monte–Carlo simulations are carried out to validate the performance of the proposed scheme. It gives promising results in terms of estimation accuracy, convergence rate, proximity effect and robustness against noise.     

On Quantum Markov Chains on Cayley Tree III: Ising Model

In this paper, we consider the classical Ising model on the Cayley tree of order \(k\) ( \(k\ge 2\) ), and show the existence of the phase transition in the following sense: there exists two quantum Markov states which are not quasi-equivalent. It turns out that the found critical temperature coincides with the classical critical temperature.     

Size effect on phonon transport in two-dimensional silicon film

Phonon transport in two-dimensional silicon film is investigated and frequency dependent Boltzmann transport equation is solved numerically using discrete ordinate method. The transient effects of phonon transport in the film are incorporated in the analysis. The influence of film size on phonon transport is examined through equivalent equilibrium temperature in the film. It is found that increasing film thickness enhances phonon scattering and dispersion in the film while increasing equivalent equilibrium temperature. The rate of equivalent equilibrium temperature increase is high in the early heating period ( \(\hbox {t} \le 50\,\hbox {ps}\) ) and the rate of temperature increase becomes gradual in the film as the heating period progresses.     

Spin-polarized current generated by magneto-electrical gating

We theoretically study spin-polarized current through a single electron tunneling transistor (SETT), in which a quantum dot (QD) is coupled to non-magnetic source and drain electrodes via tunnel junctions, and gated by a ferromagnetic (FM) electrode. The I–V characteristics of the device are investigated for both spin and charge currents, based on the non-equilibrium Green's function formalism. The FM electrode generates a magnetic field, which causes a Zeeman spin-splitting of the energy levels in the QD. By tuning the size of the Zeeman splitting and the source–drain bias, a fully spin-polarized current is generated. Additionally, by modulating the electrical gate bias, one can effect a complete switch of the polarization of the tunneling current from spin-up to spin-down current, or vice versa.     

New approaches to photocatalytic reaction of low concentrations of arylamines in alcohols

Photocatalytic interactions of a series of arylamines, for example 1,4-phenylenediamine, 1,2-phenylenediamine, 4-aminophenol, and 2-aminophenol, at low concentrations in typical primary alcohols have been investigated in the presence of anatase TiO₂ nanopowder. GC?CMS analysis of the irradiated solutions showed that, except for 1,2-phenylenediamine, 10?mmol/l alcoholic solutions of the arylamines gave predominately the corresponding imines. Irradiation of 2-aminophenol under these conditions, led to oxidation and dimerization to 2-amino-3H-phenoxazin-3-one.     

Synthesis and characterization of functionalized ordered hexagonal nanoporous carbon nitride with melamine-based dendrimer amines

Mesoporous carbon nitride (MCN-1) and functionalized MCN-1 with melamine-based dendrimer amine (MDA-MCN-1) have been synthesized. These materials are characterized by means of nitrogen adsorption–desorption isotherms, thermogravimetric analysis (TGA), Fourier transform infrared (FT-IR) spectroscopy, small-angle X-ray scattering (SAXS), wide angle X-ray diffraction (XRD) pattern and Energy dispersive X-ray (EDX). Two bands at 1,434 and 1,550 cm^?1 in FT-IR spectrum of MDA-MCN-1 are clear evidence of an aromatic triazine ring and confirm that the melamine-based dendrimer is formed. The pore diameter is centered at 4.74 nm with a relatively high BET surface area of 102.2 m² g^?1 and a pore volume of 0.12 cm³ g^?1. TGA curves show that samples (MCN-1 and MDA-MCN-1) have high thermal stability compared to the earlier species. The carbon-to-nitrogen ratio calculated from the EDX analysis significantly decreases from 3.87–4.35 to 1.26 in MDA-MCN-1 than MCN-1 material. This indicates that MDA-MCN-1 has high nitrogen content and active adsorption sites in comparison to MCN-1 species.     

Aqueous media preparation of 2-amino-4,6-diphenylnicotinonitriles using cellulose sulfuric acid as an efficient catalyst

A convenient approach to the synthesis of 2-amino-4,6-diphenylnicotinonitriles via four-component reaction of aromatic aldehydes, acetophenone derivatives, malononitrile and ammonium acetate is described. The reactions were done in water as solvent using cellulose sulfuric acid as catalyst. This simple protocol offer advantages such as shorter reaction times, simple work-up procedure, excellent yields and catalyst recovery.     

Computational electrochemistry: aqueous two-electron reduction potentials for substituted quinones

The electrode potentials of some quinone derivatives in aqueous solution have been calculated. The calculations are carried out at the Hartree–Fock and B3LYP levels with the inclusion of entropic and thermochemical corrections to yield free energies of redox reactions. The Polarisable Continuum Model (PCM) is used to describe the solvent. The average error of calculation of electrode potentials is less than 0.03 V and is decreased compared to the average error of methods presented previously. The role of relaxation energies and frequency calculations in improving the results has been investigated.     

Charge-transport in crystalline organic semiconductors with liquid crystalline order

We report the design and synthesis of a liquid crystalline material exhibiting highly ordered smectic phases and high charge carrier-mobility; by a process known as "paramorphosis" highly ordered smectic phases can be transferred to the amorphous crystalline state on crystallisation without the formation of significant crystal grain boundaries and deep traps.