Linearized Asymptotic Stability for Fractional Differential Equations

We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. As a consequence we extend Lyapunov's first method to fractional differential equations by proving that if the spectrum of the linearization is contained in the sector \{\lambda \in \C : |\arg \lambda| > \frac{\alpha \pi}{2}\} where $\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable

Delayed hepatic uptake of multi-phosphonic acid poly(ethylene glycol) coated iron oxide measured by real-time Magnetic Resonance Imaging

We report on the synthesis, characterization, stability and pharmacokinetics of novel iron based contrast agents for magnetic resonance imaging (MRI). Statistical copolymers combining multiple phosphonic acid groups and poly(ethylene glycol) (PEG) were synthesized and used as coating agents for 10 nm iron oxide nanocrystals. In vitro, protein corona and stability assays show that phosphonic acid PEG copolymers outperform all other coating types examined, including low molecular weight anionic ligands and polymers. In vivo, the particle pharmacokinetics is investigated by monitoring the MRI signal intensity from mouse liver, spleen and arteries as a function of the time, between one minute and seven days after injection. Iron oxide particles coated with multi-phosphonic acid PEG polymers are shown to have a blood circulation lifetime of 250 minutes, i.e. 10 to 50 times greater than that of recently published PEGylated probes and benchmarks. The clearance from the liver takes in average 2 to 3 days and is independent of the core size, coating and particle stability. By comparing identical core particles with different coatings, we are able to determine the optimum conditions for stealth MRI probes.Comment: 19 pages 8 figures, RSC Advances, 201

Filtered Reaction Rate Modelling in Moderate and High Karlovitz Number Flames: an a Priori Analysis

Abstract: Direct numerical simulations (DNS) of statistically planar flames at moderate and high Karlovitz number (Ka) have been used to perform an a priori evaluation of a presumed-PDF model approach for filtered reaction rate in the framework of large eddy simulation (LES) for different LES filter sizes. The model is statistical and uses a presumed shape, based here on a beta-distribution, for the sub-grid probability density function (PDF) of a reaction progress variable. Flamelet tabulation is used for the unfiltered reaction rate. It is known that presumed PDF with flamelet tabulation may lead to over-prediction of the modelled reaction rate. This is assessed in a methodical way using DNS of varying complexity, including single-step chemistry and complex methane/air chemistry at equivalence ratio 0.6. It is shown that the error is strongly related to the filter size. A correction function is proposed in this work which can reduce the error on the reaction rate modelling at low turbulence intensities by up to 50%, and which is obtained by imposing that the consumption speed based on the modelled reaction rate matches the exact one in the flamelet limit. A second analysis is also conducted to assess the accuracy of the flamelet assumption itself. This analysis is conducted for a wide range of Ka, from 6 to 4100. It is found that at high Ka this assumption is weaker as expected, however results improve with larger filter sizes due to the reduction of the scatter produced by the fluctuations of the exact reaction rate

Achieving sub-diffraction imaging through bound surface states in negative-refracting photonic crystals at the near-infrared

We report the observation of imaging beyond the diffraction limit due to bound surface states in negative refraction photonic crystals. We achieve an effective negative index figure-of-merit [-Re(n)/Im(n)] of at least 380, ~125x improvement over recent efforts in the near-infrared, with a 0.4 THz bandwidth. Supported by numerical and theoretical analyses, the observed near-field resolution is 0.47 lambda, clearly smaller than the diffraction limit of 0.61 lambda. Importantly, we show this sub-diffraction imaging is due to the resonant excitation of surface slab modes, allowing refocusing of non-propagating evanescent waves

Designing a novel heterostructure AgInS₂@MIL-101(Cr) photocatalyst from PET plastic waste for tetracycline degradation

Semiconductor-containing porous materials with a well-defined structure could be unique scaffolds for carrying out selective organic transformations driven by visible light. We herein introduce for the first time a heterostructure of silver indium sulfide (AgInS(2)) ternary chalcogenide and a highly porous MIL-101(Cr) metal–organic framework (MOF) synthesised from polyethylene terephthalate plastic waste. Our results demonstrate that AgInS(2) nanoparticles were uniformly attached to each lattice plane of the octahedral MIL-101(Cr) structure, resulting in a nanocomposite with a high distribution of semiconductors in a porous media. We also demonstrate that the nanocomposite with up to 40% of AgInS(2) doping exhibited excellent catalytic activity for tetracycline degradation under visible light irradiation (∼99% tetracycline degraded after 4 h) and predominantly maintained its performance after five cycles. These results could promote a new material circularity pathway to develop new semiconductors that can be used to protect water from further pollution

One-pot preparation of alumina-modified polysulfone-graphene oxide nanocomposite membrane for separation of emulsion-oil from wastewater

In recent years, polysulfone-based nanocomposite membranes have been widely used for contaminated water treatment because they comprise properties such as high thermal stability and chemical resistance. In this study, a polysulfone (PSf) nanocomposite membrane was fabricated using the wet-phase inversion method with the fusion of graphene oxide (GO) and alumina (Al2O3) nanoparticles. We also showed that GO-Al2O3 nanoparticles were synthesised successfully by using a one-pot hydrothermal method. The nanocomposite membranes were characterised by Fourier transform infrared (FT-IR), scanning electron microscopy (SEM), nitrogen adsorption-desorption isotherms, energy-dispersive X-ray spectroscopy (EDX), thermogravimetric analysis (TGA), and water contact angle. The loading of GO and Al2O3 was investigated to improve the hydrophilic and oil rejection of the matrix membrane. It was shown that by using 1.5 wt.% GO-Al2O3 loaded in polysulfone, ~74% volume of oil was separated from the oil/water emulsion at 0.87 bar and 30 min. This figure was higher than that of the process using the unmodified membrane (PSf/GO) at the same conditions, in which only ~60% volume of oil was separated. The pH, oil/water emulsion concentration, separation time, and irreversible fouling coefficient (FRw) were also investigated. The obtained results suggested that the GO-Al2O3 nanoparticles loaded in the polysulfone membrane might have potential use in oily wastewater treatment applications