A meshless method based on the dual reciprocity method for one‐dimensional stochastic partial differential equations

This article describes a new meshless method based on the dual reciprocity method (DRM) for the numerical solution of one‐dimensional stochastic heat and advection–diffusion equations. First, the time derivative is approximated by the time–stepping method to transforming the original stochastic partial differential equations (SPDEs) into elliptic SPDEs. The resulting elliptic SPDEs have been approximated with the new method, which is a combination of radial basis functions (RBFs) method and the DRM method. We have used inverse multiquadrics (IMQ) and generalized IMQ (GIMQ) RBFs, to approximate functions in the presented method. The noise term has been approximated at the source points, at each time step. The developed formulation is verified in two test problems with investigating the convergence and accuracy of numerical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 292–306, 2016     

B-, N-doped and BN codoped C60 heterofullerenes for environmental monitoring of NO and NO2: a DFT study

ABSTRACT

Using density functional theory calculations, we investigate the gas sensing performance of B-, N-doped and BN-codoped C₆₀ fullerenes towards NO and NO₂ molecules. The calculated adsorption energies and net charge-transfer values indicate that NO and NO₂ molecules have a stronger interaction with the BN-codoped fullerenes compared to the B- or N-doped ones. It is also found that the electronic properties of the BN-codoped C₆₀ exhibit a larger sensitivity towards NO and NO₂ molecules. An increase in the concentration of doped/co-doped B and N atoms tends to weaken the gas sensing ability of these systems.     

Prediction and characterisation of a chalcogen···π interaction with acetylene as a potential electron donor in XHS···HCCH and XHSe···HCCH (X = F,Cl, Br,CN, OH,OCH3, NH2, CH3) σ-hole complexes

It is well-known that many covalently bonded atoms of group VI have specific positive regions of electrostatic potential (σ-holes) through which they can interact with Lewis bases. This interaction is called ‘chalcogen bond’ by analogy with halogen bond and hydrogen bond. In this study, ab initio calculations are performed to predict and characterise chalcogen···π interactions in XHS···HCCH and XHSe···HCCH complexes, where X = F, Cl, Br, CN, OH, OCH₃, NH₂, CH₃. For the complexes studied here, XHS(Se) and HCCH are treated as a Lewis acid and a Lewis base, respectively. The CCSD(T)/aug-cc-pVTZ interaction energies of this type of σ-hole bonding range from ?1.18 to ?4.83 kcal/mol. The calculated interaction energies tend to increase in magnitude with increasing positive electrostatic potential on the extension of X–S(Se) bond. The stability of chalcogen···π complexes is attributed mainly to electrostatic and correlation effects. The nature of chalcogen···π interactions is unveiled by means of the atoms in molecules, natural bond orbital, and electron localisation function analyses.     

Tuning of carbon bonds by substituent effects: an ab initio study

ABSTRACT

An ab initio study, at the MP2/aug-cc-pVTZ level of theory, is performed to study σ-hole bond in binary XH₃C···CNY complexes, where X = CN, F, NO₂, CCH and Y = H, OH, NH₂, CH₃, C₂H₅, Li. This type of interaction is labelled as ‘carbon bond’, since a covalently bonded carbon atom acts as the Lewis acid in these systems. The geometrical and energetic parameters of the resulting complexes are analysed in details. The interaction energies of these complexes are between ?4.97 kJ/mol in (HCC)H₃C···CNH and ?23.07 kJ/mol in (O₂N)H₃C···CNLi. It is found that the electrostatic interaction plays a key role in the overall stabilisation of these carbon-bonded complexes. To deepen the understanding of the nature of the carbon-bonding, the molecular electrostatic potential, natural bond orbital, quantum theory of atoms in molecules and non-covalent interaction index analyses are also used. Our results indicate that the carbon bond is favoured over the C-H···C hydrogen bond in the all complexes considered and may suggest the possible important roles of the C···C interactions in the crystal growth and design.     

The Interaction of Polyphenol Flavonoids with β-lactoglobulin: Molecular Docking and Molecular Dynamics Simulation Studies

The interaction of quercetin, quercitrin, and rutin, as natural polyphenolic compounds, with β-lactoglobulin (BLG) using molecular docking and molecular dynamics simulation methods was examined. Molecular docking studies showed that quercetin and quercitrin were bounded to the internal cavity of protein, while rutin was bounded to the entrance of the cavity because of its large structural volume. It was found that there were one-, three-, and four-hydrogen bond interactions between BLG and quercetin, quercitrin, and rutin respectively. This showed that with an increase in the number of OH groups in the flavonoid structure, there was an increase in the number of hydrogen bond interactions. The binding constants for the binding of quercetin, quercitrin, and rutin to BLG were 1.2 × 10⁶, 1.9 × 10⁶, and 7.4 × 10⁴ M^?1 respectively. The results of molecular dynamics simulation showed that the root mean square deviation (RMSD) of non-liganded BLG and BLG–ligand complexes reached equilibration after 3500 ps. The study of the radius of gyration revealed that BLG and BLG–ligand complexes were stabilized around 2500 ps, and unlike the two other complexes, there was no conformational change for BLG–quercetin. Finally, analyzing the RMS fluctuations suggested that the structure of the ligand binding site remained approximately rigid during simulation.     

Voltammetric determination of hydroxylamine in water samples using a 1-benzyl-4-ferrocenyl-1H-[1,2,3]-triazole/carbon nanotube-modified glassy carbon electrode

A modified glassy carbon electrode has been constructed using a 1-benzyl-4-ferrocenyl-1H-[1,2,3]-triazole along with multiwalled carbon nanotubes. The electrochemical behaviour of modified electrode has been investigated by cyclic voltammetry. Electrocatalytic activity of the modified electrode was investigated for the oxidation of hydroxylamine in 0.1 M phosphate-buffered solution of pH 8. The modified electrode showed electrocatalytic response to the oxidation of hydroxylamine at the potential of 330 mV. The linear range and detection limit for the detection of hydroxylamine in the optimum condition were found to be 4.0?×?10^?7 to 6.75?×?10^?4 M and 28.0?±?1.0 nM, respectively. Finally, the method was employed for the determination of hydroxylamine in water samples.     

Exploring the origin of tip‐enhanced Raman scattering; preparation of efficient TERS probes with high yield

Tip‐enhanced Raman scattering (TERS) spectroscopy is a promising technique for nanoscale chemical analysis. However, there are several challenges preventing widespread application of this technology, including reproducible fabrication of efficient TERS probes. These problems reflect a lack of clear understanding of the origins of, and the parameters influencing TERS. It is believed that the coating characteristics at the apex of the tip have a major effect on the near‐field optical enhancement and thus the TERS activity of a metalized probe. Here we show that the aspect ratio of the tip can play a significant role in the efficiency of TERS probes. We argue that the electrostatic field arising from the lightning‐rod effect has a substantial role in the observed TERS effect. This argument is supported by ‘edge‐enhanced Raman scattering’ which is shown for a noble metal film. Furthermore, it is reported that an associated tip‐surface‐enhanced Raman scattering effect can be achieved by using a TERS‐inactive metalized probe on a surface‐enhanced Raman spectroscopy‐inactive roughened surface. This observation can be explained by an interparticle enhancement of the electromagnetic field. Copyright © 2011 John Wiley & Sons, Ltd.     

An efficient meshfree point collocation moving least squares method to solve the interface problems with nonhomogeneous jump conditions

We are going to study a simple and effective method for the numerical solution of the closed interface boundary value problem with both discontinuities in the solution and its derivatives. It uses a strong‐form meshfree method based on the moving least squares (MLS) approximation. In this method, for the solution of elliptic equation, the second‐order derivatives of the shape functions are needed in constructing the global stiffness matrix. It is well‐known that the calculation of full derivatives of the MLS approximation, especially in high dimensions, is quite costly. In the current work, we apply the diffuse derivatives using an efficient technique. In this technique, we calculate the higher‐order derivatives using the approximation of lower‐order derivatives, instead of calculating directly derivatives. This technique can improve the accuracy of meshfree point collocation method for interface problems with nonhomogeneous jump conditions and can efficiently estimate diffuse derivatives of second‐ and higher‐orders using only linear basis functions. To introduce the appropriate discontinuous shape functions in the vicinity of interface, we choose the visibility criterion method that modifies the support of weight function in MLS approximation and leads to an efficient computational procedure for the solution of closed interface problems. The proposed method is applied for elliptic and biharmonic interface problems. For the biharmonic equation, we use a mixed scheme, which replaces this equation by a coupled elliptic system. Also the application of the present method to elasticity equation with discontinuities in the coefficients across a closed interface has been provided. Representative numerical examples demonstrate the accuracy and robustness of the proposed methodology for the closed interface problems. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1031–1053, 2015     

Determination of a control parameter in a one-dimensional parabolic equation using the method of radial basis functions

In this work, the method of radial basis functions is used for finding the solution of an inverse problem with source control parameter. Because a much wider range of physical phenomena are modelled by nonclassical parabolic initial-boundary value problems, theoretical behavior and numerical approximation of these problems have been active areas of research. The radial basis functions (RBF) method is an efficient mesh free technique for the numerical solution of partial differential equations. The main advantage of numerical methods which use radial basis functions over traditional techniques is the meshless property of these methods. In a meshless method, a set of scattered nodes are used instead of meshing the domain of the problem. The results of numerical experiments are presented and some comparisons are made with several well-known finite difference schemes.