A unified approach to the mathematical analysis of generalized RKPM,gradient RKPM,and GMLS

It is well-known that the conventional reproducing kernel particle method (RKPM) is unfavorable when dealing with the derivative type essential boundary conditions [1], [2], [3]. To remedy this issue a group of meshless methods in which the derivatives of a function can be incorporated in the formulation of the corresponding interpolation operator will be discussed. Formulation of generalized moving least squares (GMLS) on a domain and GMLS on a finite set of points will be presented. The generalized RKPM will be introduced as the discretized form of GMLS on a domain. Another method that helps to deal with derivative type essential boundary conditions is the gradient RKPM which incorporates the first gradients of the function in the reproducing equation. In present work the formulation of gradient RKPM will be derived in a more general framework. Some important properties of the shape functions for the group of methods under consideration are discussed. Moreover error estimates for the corresponding interpolants are derived. By generalizing the concept of corrected collocation method, it will be seen that in the case of employing each of the proposed methods to a BVP, not only the essential boundary conditions involving the function, but also the essential boundary conditions which involve the derivatives could be satisfied exactly at particles which are located on the boundary.     

Using Coal Fly Ash and Wastewater for Microwave Synthesis of LTA Zeolite

The reuse of industrial wastes from a coal‐fired power plant and a plasma electrolytic oxidation process was attempted to realize a zero discharge. The batch composition was adjusted by adding sodium hydroxide and sodium aluminate. A single‐mode microwave oven equipped with reflux condenser was used for crystallization under atmospheric pressure. The synthesized samples were characterized by X‐ray diffraction, scanning electron microscopy, BET, thermogravimetric analysis, and cation‐exchange capacity (CEC) measurement. Analytical results indicated that Na‐A zeolite with a defined maximum crystallinity could be successfully synthesized by hydrothermal treatment of fly ash with wastewater. Due to the high CEC, the product can be applied for gas purification and soil remediation processes.     

Two-dimensional elasticity solution for transient response of simply supported beams under moving loads

A semi-analytical analysis for the transient elastodynamic response of an arbitrarily thick simply supported beam due to the action of an arbitrary moving transverse load is presented, based on the linear theory of elasticity. The solution of the problem is derived by means of the powerful state space technique in conjunction with the Laplace transformation with respect to the time coordinate. The inversion of Laplace transform has been carried out numerically using Durbin??s approach based on Fourier series expansion. Special convergence enhancement techniques are invoked to completely eradicate spurious oscillations and obtain uniformly convergent solutions. Detailed numerical results for the transient vibratory responses of concrete beams of selected thickness parameters are obtained and compared for three types of harmonic moving concentrated loads: accelerated, decelerated and uniform. The effects of the load velocity, pulsation frequency and beam aspect ratio on the dynamic response are examined. Also, comparisons are made against solutions based on Euler?CBernoulli and Timoshenko beam models. Limiting cases are considered, and the validity of the model is established by comparison with the solutions available in the existing literature as well as with the aid of a commercial finite element package.     

Preparation and characterization of photocatalytic titania–alumina composite membranes by sol–gel methods

Titania–alumina composite membranes containing 10 and 20 mol% alumina were prepared by two different sol–gel methods; co-hydrolysis and separately peptized. The samples were characterized by different techniques. XRD results showed that for the composite membranes the anatase to rutile transformation temperature was increased by 200 and 300 °C. According to specific surface area results, alumina effectively increased the specific surface area of composite membranes compared to pure titania membranes. Microstructure of composite supported membranes was considered by scanning electron microscopy and showed a crack-free layer with 1 μm thickness. The photocatalytic activity of composite samples showed that alumina addition up to an optimum amount can slightly affect the photocatalytic activity of titania.     

Preparation of synthesized sulfide polymer through phase-transfer catalyzed polycondensation of ethylene dibromide and sodium tetrasulfide: characterization,thermal and rheological properties

Sulfide polymers were obtained through the interfacial polymerization of sodium tetrasulfide and ethylene dibromide. The polymerization process was carried out under interfacial condition using two phase-transfer catalysts: methyl-tributyl ammonium bromide and methyl-tributyl ammonium chloride. The polymer characteristics were examined by attenuated total reflectance- fourier transform infrared spectroscopy, elemental analysis (CHNS/O) and X-ray diffraction methods. Thermal characteristics were investigated by differential scanning calorimetry and thermogravimetric analysis methods. The rheological behavior of the synthesized sulfide polymer during curing reaction, and isothermal time dependency of elastic storage modulus, G^′, at different temperatures and constant shear frequency was studied using a stress-controlled rheometer. Moreover, the solvent resistance of synthesized polymer was investigated through the swelling method.     

An analysis of carbone monoxide distribution in large tunnel fires

Fire events and the related toxicants such as CO are responsible for many fatalities in the current century. These hazardous events are much more dangerous when they occur in enclosed spaces. In the present study, a theoretical relation is developed for horizontal distribution of CO in a large tunnel fire. Then, the developed criterion is used to study the effect of some rudimentary parameters such as the heat release rate (HRR) of fire and tunnel’s aspect ratio (AR) on CO and temperature stratification. Theoretical results of various heat release rates and aspect ratios for horizontal distribution of CO are compared with numerical results using fire dynamics simulator (FDS5.5). It is found that big fires have higher rates of CO concentration decay in comparison to the smaller ones due to higher air entrainment into the travelling plume. It is indicated that the smoke travelling at higher values of tunnel AR, dilutes faster. Moreover, using FDS5.5, the relevant variations in temperature and CO concentration are discussed for tunnel angles ranging from ?20° to 20°.     

A Highly Flexible Green Synthesis of 3,4,5-Substituted Furan-2(5H)-ones Using Nano-CdZr4(PO4)6 as Catalyst under Microwave Irradiation

A concise and efficient method for the synthesis of 3,4,5-substituted furan-2 (5H)-ones was achieved through a three-component reaction of amines, dialkyl acetylene dicarboxylate, and aromatic aldehydes using nano-CdZr₄(PO₄)₆ as catalyst under microwave irradiation. This method has several advantages such as, high efficiency, short reaction times, simple workup, and recyclability of the catalyst up to seven runs without considerable loss of activity.