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.     

Analysis of <Superscript>8</Superscript>B Proton Halo Nucleus Scattered from <Superscript>12</Superscript>C and <Superscript>58</Superscript>Ni at Different Energies

Angular distributions in the elastic scattering of ⁸B from ¹²C and ⁵⁸Ni targets at different energies have been analyzed in the framework of the double-folding (DF) optical model. The real central part of the nuclear optical potential is obtained by folding the M3Y effective interaction with the cluster density distribution of the ⁸B nucleus. The experimental angular distributions have been successfully reproduced. This confirms the validity of the cluster structure of the ⁸B nucleus.     

New three-stages symmetric six-step finite difference method with vanished phase-lag and its derivatives up to sixth derivative for second order initial and/or boundary value problems with periodical and/or oscillating solutions

In this paper, for the first time in the literature, we develop a symmetric three-stages six-step method with the following characteristics; the method

1. 1.
   is a symmetric hybrid (multistages) six-step method,
    
2. 2.
   is of three-stages,
    
3. 3.
   is of twelfth algebraic order,
    
4. 4.
   has vanished the phase-lag and
    
5. 5.
   has vanished the derivatives of the phase-lag up to order six.
    

A detailed theoretical, numerical and computational analysis is also presented. The above analyses consist of:

• the construction of the new six-step pair,
• the presentation of the computed local truncation error of the new six-step pair,
• the comparative error analysis of the new six-step pair with other six-step pairs of the same family which are:

  • the classical six-step pair of the family (i.e. the six-step pair with constant coefficients),
  • the recently proposed six-step pair of the same family with vanished phase-lag and its first derivative,
  • the recently proposed six-step pair of the same family with vanished phase-lag and its first and second derivatives,
  • the recently proposed six-step pair of the same family with vanished phase-lag and its first, second and third derivatives,
  • the recently proposed six-step pair of the same family with vanished phase-lag and its first, second, third and fourth derivatives and finally,
  • the recently proposed six-step pair of the same family with vanished phase-lag and its first, second, third, fourth and fifth derivatives
• the stability and the interval of periodicity analysis for the new obtained six-step pair and finally
• the investigation of the accuracy and computational efficiency of the new developed six-step pair for the solution of the Schrödinger equation.

The theoretical, numerical and computational achievements lead to the conclusion that the new produced three-stages symmetric six-step pair is more efficient than other known or recently developed finite difference pairs of the literature.

     

Sol–gel synthesis of NiFe2O4 with PVA matrices and their catalytic activities for one-step hydroxylation of benzene into phenol

Nickel ferrite (NiFe₂O₄) was synthesized using citric acid (CA) as a chelating agent and varying amounts of polyvinyl alcohol (PVA) as powder binder via a combustion process. The influence of PVA/NiFe₂O₄ blend composition on the phase, crystal structure, and morphology has been investigated by X-ray diffraction (XRD), scanning electron microscopy, and Fourier transform infrared spectroscopy, respectively. The probable assignments of the thermal degradation products of PVA/NiFe₂O₄ were studied by complementary thermogravimetric analysis and differential thermal analysis. The PVA/NiFe₂O₄ crystals preferentially oriented along the (311) plane as revealed by XRD, owing to diffusion of α-Fe₂O₃ particles into the lattice matrix where the rate of diffusion increased significantly with the PVA concentration increase from 0.1 to 0.3 mol%. A vibrational doublet at 1,644 and 1,609 cm^?1 for the ≡Fe–O–COOH complex was emitted in the spectra of PVA-impregnated NiFe₂O₄ to assure the attachment of Fe(III) to the chelating agents CA/PVA. Thermal kinetic consideration based on Coats–Redfern and Horowitz–Metzger equations at subsequent decomposition steps of CA/PVA/NiFe₂O₄ illustrated that the values of activation free energy ΔG* increase significantly, indicating the non-spontaneous behavior. The one-step direct hydroxylation of benzene toward phenol has been extensively investigated using hydrogen peroxide as an oxidant.     

Analysis of Elastic 16O + 40Ca Refractive Scattering at 214 MeV

Physics of Atomic Nuclei - The elastic scattering of 16O+40Ca system at the incident energy 214 MeV has been analyzed within the optical model (OM) potential using the phenomenological Woods-Saxon...     

Preparation,spectral and thermal properties of new Isoflavone derivatives: mesomorphic properties and DFT studies

The four new homologous series of symmetric Isoflavon dimers were synthesised using varied alkyl/aryl diamines in linear sense. The chemical structures of the molecules were characterised by IR, NMR and CHNS analysis. Further, Liquid crystalline properties were verified using the combination of differential scanning calorimetry (DSC) and polarised optical microscope (POM). The molecular systems studied here reveal that LC property depends on the length of the middle connecting diamine spacer along with terminal alkyl spacer. The lower members favour to exhibit smectic A phase, whereas higher members exhibit nematic mesophase. The nature of LC property behaviours is supported by molecular geometries studied by DFT calculations.