Temporal Homogenization of Linear ODEs,with Applications to Parametric Super-Resonance and Energy Harvest

We consider the temporal homogenization of linear ODEs of the form \({\dot{x}=Ax+\epsilon P(t)x+f(t)}\), where P(t) is periodic and \({\epsilon}\) is small. Using a 2-scale expansion approach, we obtain the long-time approximation \({x(t)\approx {\rm exp}(At) \left( \Omega(t)+\int_0^t {\rm exp}(-A \tau) f(\tau) {\rm d}\tau \right)}\), where \({\Omega}\) solves the cell problem \({\dot{\Omega}=\epsilon B \Omega + \epsilon F(t)}\) with an effective matrix B and an explicitly-known F(t). We provide necessary and sufficient conditions for the accuracy of the approximation (over a \({{\mathcal{O}}(\epsilon^{-1})}\) time-scale), and show how B can be computed (at a cost independent of \({\epsilon}\)). As a direct application, we investigate the possibility of using RLC circuits to harvest the energy contained in small scale oscillations of ambient electromagnetic fields (such as Schumann resonances). Although a RLC circuit parametrically coupled to the field may achieve such energy extraction via parametric resonance, its resistance R needs to be smaller than a threshold \({\kappa}\) proportional to the fluctuations of the field, thereby limiting practical applications. We show that if n RLC circuits are appropriately coupled via mutual capacitances or inductances, then energy extraction can be achieved when the resistance of each circuit is smaller than \({n\kappa}\). Hence, if the resistance of each circuit has a non-zero fixed value, energy extraction can be made possible through the coupling of a sufficiently large number n of circuits (\({n\approx 1000}\) for the first mode of Schumann resonances and contemporary values of capacitances, inductances and resistances). The theory is also applied to the control of the oscillation amplitude of a (damped) oscillator.     

Effect of sol–gel pH on XRD peak broadening,lattice strain,ferroelectric domain orientation,and optical bandgap of nanocrystalline Pb1.1(Zr0.52Ti0.48)O3

Nanocrystalline Pb_1.1(Zr_0.52Ti_0.48)O₃ (PZT) samples were prepared using a citrate–nitrate sol–gel process near the morphotropic phase boundary. The effect of pH on the lattice parameters (tetragonality and lattice constants), crystal structure [strain broadening, relative phase content, ferroelectric domain (FD) orientation and nanocrystallite size], microstructure (grain size and particle morphology) and optical bandgap was investigated. The samples were characterized using X-ray diffraction (XRD), the size strain plot (SSP) method, Fourier-transform infrared spectroscopy, and the classical Tauc relation. The particle morphology was investigated using field-emission scanning electron microscopy. The XRD results revealed a perovskite structure and coexisting tetragonal and rhombohedral phases for all PZT samples. Lattice strain and peak broadening were determined from SSP and XRD results. The behavior of these parameters was in agreement for all pH values. The optical bandgap for PZT was estimated from UV-vis absorption spectra. We found that for PZT the maximum relative tetragonal phase content, c/a ratio, and FD orientation along the a-axis occurred at pH 4.     

Design and synthesis of phenoxymethybenzoimidazole incorporating different aryl thiazole-triazole acetamide derivatives as α-glycosidase inhibitors

Molecular Diversity - A novel series of phenoxymethybenzoimidazole derivatives (9a-n) were rationally designed, synthesized, and evaluated for their α-glycosidase inhibitory activity. All...     

Reverse micelle-mediated dispersive liquid-liquid microextraction of 2,4-dichlorophenoxyacetic acid and 4-chloro-2-methylphenoxyacetic acid

A supramolecular solvent consisting of reverse micelles of decanoic acid, dispersed in a continuous phase of tetrahydrofuran:water, was proposed as an efficient microextraction technique for extraction of selected chlorophenoxy acid herbicides from water samples prior to high-performance liquid chromatography UV determination. The disperser solvent (1.0 mL tetrahydrofuran) containing 20 mg decanoic acid was rapidly injected into 10.0 mL of water sample. After centrifugation, the reverse micelle-rich phase (25 ± 0.5 μL) was floated at top of the home-designed centrifuge tube. The solvent was collected and 20 μL of it was injected into high-performance liquid chromatography for analysis. The results showed that the in situ solvent formation and extraction process can be completed in a few seconds. Under the optimal conditions, limits of detection of the method for 4-chloro-2-methylphenoxyacetic acid and 2,4-dichlorophenoxyacetic acid were in the range of 0.5-0.8 μg L(-1) and the repeatability of the proposed method, expressed as relative standard deviation, varied in the range of 2.5-3.2%. Linearity was found to be in the range of 1-200 μg L(-1) and the preconcentration factors were between 148 and 157. The mean percentage recoveries exceeded 92.0% for all the spiking levels in real water samples.     

Photoswitchable nanoparticles for triggered tissue penetration and drug delivery

We report a novel nanoparticulate drug delivery system that undergoes reversible volume change from 150 to 40 nm upon phototriggering with UV light. The volume change of these monodisperse nanoparticles comprising spiropyran, which undergoes reversible photoisomerization, and PEGylated lipid enables repetitive dosing from a single administration and enhances tissue penetration. The photoswitching allows particles to fluoresce and release drugs inside cells when illuminated with UV light. The mechanism of the light-induced size switching and triggered-release is studied. These particles provide spatiotemporal control of drug release and enhanced tissue penetration, useful properties in many disease states including cancer.     

Electron–hole transition in a spherical quantum dot confined at the center of a cylindrical nano-wire: Comparison of isotropic and anisotropic effective mass

Electronic structure of an InAs spherical quantum dot placed at the center of a GaAs cylindrical nano-wire is investigated. The Schrodinger equation within the effective mass approximation is solved and the energy eigenvalues and transition energies are calculated as a function of quantum dot and nano-wire radii using the finite element method. The two types of heavy holes, hhI and hhII, with isotropic and anisotropic effective masses are considered, respectively. The effect of spherical and nano-wire confining potentials, the size of the dot and the nano-wire on ground and first excited state energies of the electron, heavy hole I and heavy hole II are investigated. The results show that the electron and heavy holes energies decrease as the dot and the nano-wire radii increase. The emitted wavelength of transitions between el-hhI and el-hhII are also calculated and compared. The results show that the anisotropy of the effective mass has great effect on the emitted wavelength.     

On the fixed point of (ψ−φ)-weak and generalized (ψ−φ)-weak contraction mappings

Let $(X,d)$ be a complete metric space, and $T:X?X$ be a $(\psi ?\phi )$-weak or generalized $(\psi ?\phi )$-weak contraction mapping, where $\psi ,\phi :[0,+\infty )?[0,+\infty )$ are two mappings with ${\psi }^{?1}\left(0\right)={\phi }^{?1}\left(0\right)=0$, $\underset{n\to \infty }{lim}{t}_n=0$, if $\underset{n\to \infty }{lim}\phi \left(t_n\right)=0$ and $\psi$ is continuous or $\psi$ is monotone nondecreasing with $\phi \left(a\right)>\psi \left(a\right)?\psi (a?)$ for all $a>0$. Then $T$ has a unique fixed point. Our results extend the previous results given by Rhoades (2001) [3], Dutta and Choudhury (2008) [4], Doric (2009) [5] and Popescu (2011) [6].     

Efficient and green synthesis of dihydropyrimido[4,5-b]quinolinetriones using MWCNTs@TEPA/Co (II) as a novel and eco-friendly catalyst

A new heterogeneous nanocatalyst [MWCNTs@TEPA/Co (II)] was successfully prepared using multiwall carbon nanotubes (MWCNTs) as a suitable and efficient support for covalent anchoring of tetraethylene pentaamine (TEPA)/Co (II). The new heterogeneous catalyst was prepared through an easy and applicable method, and characterized by various techniques such as Fourier transform-infrared, thermogravimetric analysis, energy-dispersive X-ray spectroscopy, mapping, field emission-scanning electron microscopy, inductively coupled plasma-optical emission spectrometry and Brunauer−Emmett−Teller. Synthesized catalyst was used efficiently for the preparation of dihydropyrimido [4,5-b]quinolinetrione derivatives via the four-components reaction of barbituric acid, dimedone, aryl aldehyde and amines under thermal conditions. The nanostructure catalyst was easily recovered by filtration and reused several times without noticeable loss of its catalytic activity. Low amounts of catalyst (0.005 g), short reaction times and green conditions are some merits of the presented method.     

Thermal Degradation Kinetics and Modeling Study of Ultra High Molecular Weight Polyethylene (UHMWP)/Graphene Nanocomposite

The incorporation of nanofillers such as graphene into polymers has shown significant improvements in mechanical characteristics, thermal stability, and conductivity of resulting polymeric nanocomposites. To this aim, the influence of incorporation of graphene nanosheets into ultra-high molecular weight polyethylene (UHMWPE) on the thermal behavior and degradation kinetics of UHMWPE/graphene nanocomposites was investigated. Scanning electron microscopy (SEM) analysis revealed that graphene nanosheets were uniformly spread throughout the UHMWPE’s molecular chains. X-Ray Diffraction (XRD) data posited that the morphology of dispersed graphene sheets in UHMWPE was exfoliated. Non-isothermal differential scanning calorimetry (DSC) studies identified a more pronounced increase in melting temperatures and latent heat of fusions in nanocomposites compared to UHMWPE at lower concentrations of graphene. Thermogravimetric analysis (TGA) and derivative thermogravimetric (DTG) revealed that UHMWPE’s thermal stability has been improved via incorporating graphene nanosheets. Further, degradation kinetics of neat polymer and nanocomposites have been modeled using equations such as Friedman, Ozawa–Flynn–Wall (OFW), Kissinger, and Augis and Bennett’s. The "Model-Fitting Method” showed that the auto-catalytic nth-order mechanism provided a highly consistent and appropriate fit to describe the degradation mechanism of UHMWPE and its graphene nanocomposites. In addition, the calculated activation energy (E_a) of thermal degradation was enhanced by an increase in graphene concentration up to 2.1 wt.%, followed by a decrease in higher graphene content.