On using mesh-based and mesh-free methods in problems defined by Eringen’s non-local integral model: issues and remedies

With the recent success of nonlocal theories in modeling of engineering problems involving small intrinsic length scales, such as modeling of crack propagation, this paper addresses issues pertaining to cost-ineffectiveness of Eringen’s integral model. The cost effectiveness of the computation may be considered as a twofold issue; one pertaining to the non-local model and another pertaining to the numerical tool. First of all, we shall show that during the solution of problems with Eringen’s non-local integral model, there is no need to consider the integral model for the whole computational domain. In fact, the problems may be solved by just using the integral model close to the boundaries, i.e. a boundary layer effect, or around the points with singularities. In this paper we propose a partitioning strategy to remarkably reduce the computational cost. This may be considered as a gateway for solving some types of two-scale problems, e.g. those with macro/micro and nano scales, in which the small scale effects are localized just at parts of the domain. To demonstrate the efficiency of the numerical tools, we examine the performance of the finite element method (FEM), the element free Galerkin method (EFG) and the finite point method (FPM). This paves the way for using mesh-free methods in the solution of problems with non-local integral models. Examples with smooth and non-smooth solutions are considered for examining the efficiency of the methods. It will be shown that, by considering the boundary layer effect, the FEM and FPM will be efficient enough for being used in problems defined by Eringen’s non-local integral model.

     

Dynamical behavior and network analysis of an extended Hindmarsh–Rose neuron model

Nonlinear Dynamics - In this paper, the extended Hindmarsh–Rose neuron model, which considers the slow intracellular exchange of calcium ions between its store and the cytoplasm, is studied....     

Quantitative Analysis of Holmium Ion by a Ho3+ Ion‐Selective Sensor Based on a Symmetric Thio‐Schiff's Base

A poly(vinyl chloride) (PVC) membrane sensor for holmium ions was fabricated based on N‐[(Z)‐1‐(2‐thienyl)‐ methylidene]‐N‐[4‐(4‐{[(Z)‐1‐(2‐thienyl)methylidene]amino} phenoxy)phenyl] amine (TPA) as a new ion carrier, acetophenon (AP) as plasticizing solvent mediator and sodium tetraphenyl borate (NaTPB) as an anion excluder. The electrode shows a good selectivity towards Ho³⁺ ions respect to other inorganic cations, including alkali, alkaline earth, transition and heavy metal ions. The constructed sensor displays a Nernstian behavior (19.5±0.3 mV/decade) over the concentration range of 1.0×10⁻⁶ to 1.0×10⁻² mol·L⁻¹ with the detection limit of the electrode being 4.6×10⁻⁷ mol·L⁻¹ and very short response time (ca. 5 s). It has a useful working pH range of 3.2–9.8 for at least 8 weeks. The electrode was successfully applied as an indicator electrode for the potentiometric titration of a Ho³⁺ solution with EDTA and holmium determination in some alloys. The proposed sensor accuracy was studied by the determination of Ho³⁺ in mixtures of three different ions.     

Nano-TiO_2:An eco-friendly alternative for the synthesis of quinoxalines

Nano-TiO₂ as an eco-friendly and efficient nanocatalyst was applied for quinoxaline preparation with improved yield.In this protocol,diketones and 1,2-diamines were condensed in the presence of catalyst at room temperature.     

Determination of the effective atomic and mass numbers for mixture and compound materials in high energy photon interactions

In consideration the radiological properties of materials and studying the scattering processes in atomic and nuclear physics, the effective atomic and mass numbers is widely employed. These numbers have been calculated for any mixed or composite materials in interaction with high energy photons (Linac in radiation therapy). A pair equation in terms of these numbers is obtained. The first equation has been derived from the conservation of mass energy law and the second by minimizing the binding energy from the semiempirical mass formula (Myers and Swiatecki formula) that gives a relation between atomic and mass numbers for stable nuclei approximately. By these equations one can obtain the effective atomic and mass numbers for any compound or mixed materials uniquely. These numbers are calculated for some materials and compared with the other studies.     

A convenient synthesis of bis(indolyl)alkanes under ultra sonic irradiation using silica-supported Preyssler nano particles

Bis(indolyl)alkanes have been synthesised in excellent yields in the presence of catalytic amount of silica-supported Preyssler nano particles as green, reusable and efficient catalyst under ultra sonic irradiation.     

The selective aerobic oxidation of methylaromatics to benzaldehydes using a unique combination of two heterogeneous catalysts

A unique combination of a supported cobalt complex and the first example of supported NHPI in acetic acid gives a surprisingly stable heterogeneous catalytic system for the selective aerobic oxidation of methylaromatics to benzaldehydes at atmospheric pressure.