A new four-step Runge–Kutta type method with vanished phase-lag and its first, second and third derivatives for the numerical solution of the Schrödinger equation

The construction of new four-step Runge–Kutta type method of sixth algebraic order with vanished phase-lag and its first, second and third derivatives is presented in this paper. We present a comparative error and stability analysis for the produced new method. In order to test the efficiency of the obtained method, an application to the resonance problem of the Schrödinger equation is described.     

Elastic–plastic analysis of two-dimensional functionally graded materials under thermal loading

The two-dimensional functionally graded materials, (2D-FGMs) have been recently introduced in order to significantly reduce the thermal stresses in machine elements that subjected to sever thermal loading. To the author’s knowledge no work was found that investigates the elastic–plastic stress analysis for 2D-FGMs. In the current work, a 3D finite element model of 2D-FGM plates made of ZrO₂, 6061-T6 and Ti-6Al-4V with temperature dependent material properties has been proposed to perform such analysis. An elastic plastic stress–strain relation based on the rule of mixture of the 2D-FGM has been introduced in the model. Also, a 3D finite element model of conventional FGM plates, of ZrO₂/Ti-6Al-4V and ZrO₂/6061-T6, with temperature dependent material properties has been proposed for the investigation of these plates too. Then, elastic–plastic stress analysis of the considered four plates (two conventional FGMs and two 2D-FGMs) under the same transient cyclic heating and cooling was carried out. It was found that heat conductivity of the metallic constituents of FGM has great effect on the temperature distributions that resulting from the thermal loads. Minimum temperatures variation and minimum stresses can be obtained using ZrO₂/6061-T6/Ti-6Al-4V 2D-FGM. Also, the results indicate that only ZrO₂/6061-T6/Ti-6Al-4V 2D-FGM can stand with the adopted sever thermal loading without fracture or plastic deformations.     

Infrared spectral signatures of CDCP1-induced effects in colon carcinoma cells

Metastasis is the major cause of death by cancer. Indeed, metastatic colonies can reactivate and become life threatening, sometimes months or years after the initial diagnosis and surgery of the primary tumor. Therefore, there is a crucial need to develop methods for diagnosis of tumor cells that exhibit high metastatic potential. Here, we addressed the capability of vibrational spectroscopy for investigating the effects induced by CDCP1 expression in colon carcinoma cells. This transmembrane protein has been suggested to play a key role in metastasis by its pleiotropic function. We focused on a cellular model constituted by the cell lines SW480 and SW620 derived respectively from the primary tumor and a lymph node metastasis of the same patient. Induced CDCP1 expression in SW480 led to marked changes in cell morphology. Whereas SW480 form a cell layer, the SW480/CDCP1 cells exhibited reduced cell-to-cell contact. On collagen I, SW480 was more spread and filopodia were observed. In contrast, SW480/CDCP1 cells exhibited lower spreading with no formation of filopodia. Synchrotron Fourier transform infrared microspectroscopy experiments were performed on this cellular model. High quality spectroscopic information at sub-cellular resolution, provided by the use of the synchrotron source in infrared microspectroscopy, was recorded on numerous individual cells. Multivariate analysis of spectra recorded using principal component analysis indicated a highest intensity increase of the 970 and 1080 cm(-1) bands, and a modest intensity increase of the 1240 cm(-1) band in the SW480/CDCP1 cells. These bands were correlated with an increased content of phosphorylated proteins as confirmed by in situ labelling using a monoclonal antibody directed against phosphorylated tyrosines. Altogether, these results demonstrate that the vibrational technique used in this study exhibits the capability to characterize spectral signatures of CDCP1-induced effects in colon carcinoma cells. This study may open new avenues for rapid diagnosis of cells with a metastatic potential.     

A new four-step hybrid type method with vanished phase-lag and its first derivatives for each level for the approximate integration of the Schrödinger equation

In this paper we present a new methodology for the development of four-step hybrid type methods of sixth algebraic order with vanished phase-lag and its derivatives. The methodology is based on the vanishing of the phase-lag and its derivatives on its level of the hybrid method. We present a comparative error and stability analysis for the produced new method. The efficiency of the new obtained methods is examined by application to the resonance problem of the Schrödinger equation.     

New open modified trigonometrically-fitted Newton-Cotes type multilayer symplectic integrators for the numerical solution of the Schrödinger equation

In this paper we present new modified open Newton Cotes integrators and we develop a new modified trigonometrically-fitted open Newton-Cotes method. We study the connection between the new proposed schemes, the differential methods and the symplectic integrators. although The research on multistep symplectic integrators is very poor, although, much research has been done on one step symplectic integrators and several of then have obtained based on symplectic geometry. In this paper a new open modified numerical algorithm of Newton-Cotes type is produced. We present the new obtained method as symplectic multilayer integrator. The new obtained symplectic schemes are applied for the solution of the resonance problem of the radial Schrödinger Equation. The results show the efficiency of the new proposed algorithm.     

Folding model description of reactions with exotic nuclei

Microscopic folding calculations based upon the effective M3Y nucleon-nucleon interaction and the nuclearmatter densities of the interacting nuclei have been carried out to explain recently measured experimental data of the ⁶He+¹²⁰Sn elastic scattering cross section at four different laboratory energies near the Coulomb barrier. The extracted reaction cross sections are also considered.