A proper orthogonal decomposition variational multiscale meshless interpolating element-free Galerkin method for incompressible magnetohydrodynamics flow

In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element-free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced-order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced-order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two-dimensional cases.     

Asymptotic stabilization of a class of nonlinear SDEs

Nonlinear Dynamics - In this paper, we investigate the asymptotic stability of the probability density function (pdf) of the states of a class of nonlinear SDEs. We use the Detailed-balance...     

A unified model for electrostatic sensors in fluid media

Nonlinear Dynamics - We present a unified model of electrostatic sensors comprising cantilever microbeam resonators in fluid media. The model couples Euler–Bernoulli beam equation to the...     

Cover Image

Pd-PEPPSI type complexes are widely used as precatalyst in a variety of organic reactions, including the Negishi, Kumada and Suzuki-Miyaura cross-coupling reactions. The aim of this research is to determine potential proposed reaction pathways 1, 2, or 2′ (See Schemes 1 and S1–S4 ) for Pd-PEPPSI precatalyst activation in the presence of ethylene glycol as a solvent also in the gas phase at Cam-B3LYP-D3 method nominated among eight DFT methods examined. There is also investigation into the impact of promoter bases (NaOEt, NaOⁱPr, NaO^tBu) on precatalyst activation of Pd-PEPPSI. Eventually, the most favorable proposed reaction pathway and promoter base for reducing Pd(II) to Pd(0) are predicted computationally. Notably, our findings are consistent with the organ Pd-PEPPSI type complexes that offer increased catalytic activity and provide basic information in the presence of solvents designing the monoligated Pd(0)-solvent.     

Equational Compactness of G-sheaves

Purity and equational compactness play a role at least in the Theories of Modules, Acts, Model, and Category. Adámek and Rosický have studied them categorically, Rothmaler model-theoretically, and some authors, including Banaschewski, Gould, and Normak have studied these notions on G-acts. We take both the group G and the set A in the definition of a G-act to be sheaves and study equationally compact G-sheaves. We get different kinds of equationally compact G-sheaves, study them and their interrelations, give some conditions for their proper behavior, and generalize some of the existing results.     

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     

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.     

One-pot synthesis of functionalized 4-oxo-2-thioxo-1,3-thiazinanes from primary amines,CS2, and itaconic anhydride

An efficient synthesis of 2-(3-alkyl-4-oxo-2- thioxo-1,3-thiazinan-5-yl)acetic acids is described via a three-component reaction between primary amines, CS₂, and itaconic anhydride.     

Direct numerical method for an inverse problem of a parabolic partial differential equation

A coefficient inverse problem of the one-dimensional parabolic equation is solved by a high-order compact finite difference method in this paper. The problem of recovering a time-dependent coefficient in a parabolic partial differential equation has attracted considerable attention recently. While many theoretical results regarding the existence and uniqueness of the solution are obtained, the development of efficient and accurate numerical methods is still far from satisfactory. In this paper a fourth-order efficient numerical method is proposed to calculate the function u(x,t) and the unknown coefficient a(t) in a parabolic partial differential equation. Several numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method.