A new numerical algorithm to solve fractional differential equations based on operational matrix of generalized hat functions

In this paper, we propose a new numerical algorithm for solving linear and non linear fractional differential equations based on our newly constructed integer order and fractional order generalized hat functions operational matrices of integration. The linear and nonlinear fractional order differential equations are transformed into a system of algebraic equations by these matrices and these algebraic equations are solved through known computational methods. Further some numerical examples are given to illustrate and establish the accuracy and reliability of the proposed algorithm. The results obtained, using the scheme presented here, are in full agreement with the analytical solutions and numerical results presented elsewhere.     

Pressure-induced phase transitions in some AnS (An = Th,U, Np,Pu) Compounds

Pressure-induced structural phase transitions at high-pressure in monosulfides of thorium, uranium, neptunium and plutonium (AnS) have been studied theoretically by an inter-ionic potential theory with modified ionic charge introduced to include the Coulomb screening effect due to localized ‘f’ electrons. These AnS compounds undergo a phase transition from sodium chloride (NaCl) to cesium chloride (CsCl) structure at a very high-pressure. The present theoretical investigation carried out up to 120?GPa reveals that these compounds undergo NaCl–CsCl phase transitions at 100, 81, 75 and 105?GPa for ThS, US, NpS and PuS, respectively. The first-order pressure derivatives calculated from the present theory agree well with observed data.     

Global Dynamics of a Multi-group SEIR Epidemic Model with Infection Age

National Natural Science Foundation of China (No. 12022113),Henry Fok Foundation for Young Teachers, China (No. 171002), Outstanding Young Talents Support Plan of Shanxi Province, Science and Engineering Research Board (SERB for short), India(No. ECR/2017/002786), UGC-BSR Research Start-Up-Grant, India (No. F.30-356/2017(BSR)), and Senior Research Fellowship from the Council of Scientific and Industrial Research (CSIR for short),India (No. 09/1131(0006)/2017-EMR-I).     

3D printed titanium micro-bore columns containing polymer monoliths for reversed-phase liquid chromatography

The potential of 3D selective laser melting (SLM) technology to produce compact, temperature and pressure stable titanium alloy chromatographic columns is explored. A micro bore channel (0.9 mm I.D. × 600 mm long) was produced within a 5 × 30 × 30 mm titanium alloy (Ti–6Al–4V) cuboid, in form of a double handed spiral. A poly(butyl methacrylate-co-ethyleneglycoldimethacrylate) (BuMA-co-EDMA) monolithic stationary phase was thermally polymerised within the channel for application in reversed-phase high-performance liquid chromatography. The prepared monolithic column was applied to the liquid chromatographic separation of intact proteins and peptides. Peak capacities of 69–76 (for 6–8 proteins respectively) were observed during isothermal separation of proteins at 44 °C which were further increased to 73–77 using a thermal step gradient with programmed temperature from 60 °C to 35 °C using an in-house built direct-contact heater/cooler platform based upon matching sized Peltier thermoelectric modules. Rapid temperature gradients were possible due to direct-contact between the planar metal column and the Peltier module, and the high thermal conductivity of the titanium column as compared to a similar stainless steel printed column. The separation of peptides released from a digestion of E.coli was also achieved in less than 35 min with ca. 40 distinguishable peaks at 210 nm.     

High pressure effect on structural and mechanical properties of some LnO (Ln=Sm, Eu, Yb) compounds

The structural and mechanical properties of LnO (Ln=Sm, Eu, Yb) compounds have been investigated using a modified interionic potential theory, which includes the effect of Coulomb screening. We predicted a structural phase transition from NaCl (B₁)- to CsCl (B₂)-type structure and elastic properties in LnO compounds at very high pressure. The anomalous properties of these compounds have been correlated in terms of the hybridisation of f-electrons of the rare earth ion with conduction band and strong mixing of f-states of lanthanides with the p-orbital of neighbouring chalcogen ion. For EuO, the calculated transition pressure, bulk modulus and lattice parameter are close to the experimental data. The nature of bonds between the ions is predicted by simulating the ion-ion (Ln-Ln and Ln-O) distances at high pressure. The second order elastic constants along with shear modulus and Young's modulus, elastic anisotropy and Poisson's ratio are also presented for these oxides.     

UV-switchable polyoxometalate sandwiched between TiO2 and metal nanoparticles for enhanced visible and solar light photococatalysis

To improve the photocatalytic efficiency of TiO(2)-based nanomaterials, we demonstrate a facile, generalized, highly localized reduction approach to the decoration of TiO(2)-polyoxometalate composites with a range of metal nanoparticles including Cu, Ag, Pt, and Au. The synthesis of nanocomposite photococatalysts reported in this study has been achieved by utilizing the unique ability of the TiO(2)-bound PTA (phosphotungstic acid) molecules (a polyoxometalate, POM) to act as a highly localized UV-switchable reducing agent that specifically reduces metal ions to their nanoparticulate forms directly and only onto the TiO(2) surface. This leads to the metal contaminant-free synthesis of TiO(2)-PTA-metal nanocomposites, which is a significant advantage of the proposed approach. The study further demonstrates that polyoxometalates are regenerable photoactive molecules with outstanding electron-transfer ability and the deposition of metal nanoparticles on the TiO(2)-PTA cocatalytic surface can have a dramatic effect on increasing the overall photocatalytic performance of the composite system. Moreover, it is observed that the photococatalytic performance of the TiO(2)-PTA-metal nanoparticles can be fine tuned by choosing the composition of metal nanoparticles in the nanocomposite. Interestingly, the photococatalysts reported here are found to be active under visible and simulated solar-light conditions. The underlying reaction mechanism for enhanced solar-light photococatalysis has been proposed.     

Functionalization/passivation of porous graphitic carbon with di-tert-amylperoxide

Porous graphitic carbon (PGC) particles were functionalized/passivated in situ in packed beds at elevated temperature with neat di-tert-amylperoxide (DTAP) in a column oven. The performance of these particles for high performance liquid chromatography (HPLC) was assayed before and after this chemistry with the following analytes: benzene, toluene, ethyl benzene, n-propyl benzene, n-butyl benzene, p-xylene, phenol, 4-methylphenol, phenetole, 3,5-xylenol, and anisole. After the first functionalization/passivation, the retention factors, k, of these compounds decreased by about 5% and the number of theoretical plates (N) increased by ca. 15%. These values of k then remained roughly constant after a second functionalization/passivation but a further increase in N was noticed. In addition, after each of the reactions, the peak asymmetries decreased by ca. 15%, for a total of ca. 30%. The columns were then subjected twice to methanol at 100°C for 5h at 1 mL/min. After these stability tests, the values of k remained roughly constant, the number of plates increased, which is favorable, and the asymmetries rose and then declined, where they remained below the initial values for the unfunctionalized columns. Functionalized and unfunctionalized particles were characterized by scanning electron microscopy and BET measurements, which showed no difference between the functionalized and unfunctionalized materials, and X-ray photoelectron spectroscopy and time-of-flight secondary ion mass spectrometry (ToF-SIMS), where ToF-SIMS suggested some chemical differences between the functionalized and unfunctionalized materials. In particular ToF-SIMS suggested that the expected five-carbon fragments from DTAP exist at higher concentrations on DTAP-functionalized PGC. First principle calculations on model graphitic surfaces suggest that the first addition of a DTAP radical to the surface proceeds in an approximately isothermal or slightly favorable fashion, but that subsequent DTAP additions are then increasingly thermodynamically favorable. Thus, this analysis suggests that the direct functionalization/passivation of PGC with DTAP is plausible. Chemometric analyses of the chromatographic and ToF-SIMS data are also presented.     

High-pressure behaviour and elastic properties of heavy rare-earth Gd monopnictides

Pressure-induced structural phase transition of gadolinium monopnictides GdX (X=As and Sb) has been studied theoretically using an inter-ionic potential theory. This method has been found quite satisfactory in case of the pnictides of rare-earth and describes the crystal properties in the framework of rigid-ion model. We have modified the ionic charge so that it may include the Coulomb-screening effect by the delocalization of f electron of the rare-earth ion. The anomalous structural properties of these compounds with many f electrons have been interpreted in terms of the hybridization of f electrons with the conduction band and strong mixing of f states of Gd ion with the p orbital of neighbouring pnictogen ion. Both the compounds are found to undergo from their initial NaCl (B₁) structure to body centered tetragonal (BCT) structure at high pressure and agree well with the experimental results. The BCT structure is viewed as distorted CsCl structure and is highly anisotropic with c/a=0.82–0.85. The nature of bonds between the ions is predicted by simulating the ion–ion (Gd–Gd and Gd–X) distance at high pressure. Elastic properties of these compounds have also been studied with their second-order elastic constants.     

Biogasification of community-derived biomass and solid wastes in a pilot-scale solcon® reactor

Applied Biochemistry and Biotechnology - The Institute of Gas Technology has developed a novel, solids-concentrating (SOLCON®) bioreactor to convert a variety of individual or mixed feedstocks...