Meshless local Petrov-Galerkin (MLPG) approximation to the two dimensional sine-Gordon equation

During the past few years, the idea of using meshless methods for numerical solution of partial differential equations (PDEs) has received much attention throughout the scientific community, and remarkable progress has been achieved on meshless methods. The meshless local Petrov-Galerkin (MLPG) method is one of the “truly meshless” methods since it does not require any background integration cells. The integrations are carried out locally over small sub-domains of regular shapes, such as circles or squares in two dimensions and spheres or cubes in three dimensions. In this paper the MLPG method for numerically solving the non-linear two-dimensional sine-Gordon (SG) equation is developed. A time-stepping method is employed to deal with the time derivative and a simple predictor-corrector scheme is performed to eliminate the non-linearity. A brief discussion is outlined for numerical integrations in the proposed algorithm. Some examples involving line and ring solitons are demonstrated and the conservation of energy in undamped SG equation is investigated. The final numerical results confirm the ability of proposed method to deal with the unsteady non-linear problems in large domains.     

Effect of Aqueous Ablation Environment on the Characteristics of ZnO Nanoparticles Produced by Laser Ablation

Effect of ablation environment on the nature of ZnO nanoparticles produced by laser ablation method in liquid medium is investigated experimentally. High purity Zn plate was irradiated by the fundamental beam of a Q-switch Nd-YAG laser in cetyltrimethylammonium bromide (CTAB), acetone, sodium dodecyl sulfate and water. Produced nanoparticles were characterized by UV–Vis absorption spectroscopy, transmission electron microscopy, scanning electron microscopy, X-ray diffraction spectrum, and fourier transform infrared spectroscopy. Results show that the highest rate of ablation occurs in CTAB. Largest nanoparticles are produced in acetone, and crystallinity of nanoparticles produced in CTAB is higher than other samples. CTAB surfactant changed the morphology of ZnO nanoparticles.     

A greedy meshless local Petrov–Galerkin methodbased on radial basis functions

The meshless local Petrov–Galerkin (MLPG) method with global radial basis functions (RBF) as trial approximation leads to a full final linear system and a large condition number. This makes MLPG less efficient when the number of data points is increased. We can overcome this drawback if we avoid using more points from the data site than absolutely necessary. In this article, we equip the MLPG method with the greedy sparse approximation technique of (Schaback, Numercail Algorithms 67 (2014), 531–547) and use it for numerical solution of partial differential equations. This scheme uses as few neighbor nodal values as possible and allows to control the consistency error by explicit calculation. Whatever the given RBF is, the final system is sparse and the algorithm is well‐conditioned. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 847–861, 2016     

Synthesis of dimethyl 4-thiazolidinylphosphine oxides via addition of dimethylphosphine oxide to 3-thiazolines

The addition of dimethylphosphine oxide and its trimethylsiloxyphosphorus(III) derivative, generated in situ, to 3-thiazolines was found to yield dimethyl 4-thiazolidinylphosphine oxides via three different synthetic routes. The structures of two products were confirmed by X-ray analysis; common features include approximate envelope conformations of the five-membered rings and hydrogen bonding of the form N–H· · ·O=P. © 1997 John Wiley & Sons, Inc. Heteroatom Chem 8 : 207–215, 1997.     

New Form of the T-Duality Due to the Stability of a Compact Dimension

We study behaviors of a compact dimension and the T-duality, in the presence of the wrapped closed bosonic strings. When the closed strings interact and form another system of strings, the radius of compactification increases. This modifies the T-duality, which we call it as T-duality-like. Some effects of the T-duality-like will be studied.     

Photoluminescence of ZnO nanoparticles generated by laser ablation in deionized water

Zinc oxide (ZnO) nanoparticles were synthesized using pulsed laser ablation of a Zn metal plate in deionized water without using surfactant. The beam of a Q-switched Nd:YAG laser of 1064-nm and 532-nm wavelengths at 6-ns pulse width and different fluences is employed to irradiate the solid target in water. Transmission electron microscopy images revealed that the size of the ZnO nanoparticles formed by the 532-nm wavelength laser beam is smaller than that of the nanoparticles generated by the 1064-nm wavelength laser beam. The room-temperature photoluminescence spectra of the ZnO nanoparticles show intense violet emission along with emission in blue and green bands. The excellent ultraviolet emission indicates that the ZnO nanostructures have a low defect concentration.