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81.
S.A. Safwan A.S. Asmaa Nagwa El meshed M.H. Hekmat TH.M. El-Sherbini S.H. Allam 《Superlattices and Microstructures》2010
Within the effective mass approximation, we investigated theoretically the ground-state energy of a single particle and the binding energy of the neutral donor impurity (D0) affected by a lateral electric field in a parabolic quantum dot (QD). The results show that the electron and the hole ground-state energy and the band to band transition energies shift to lower values (red shift) by increasing the field intensity. The quantum Stark shift (QSS) for the electron increases rapidly in the quasi spherical QD (QSQD) by increasing the lateral field, whereas for the hole it increases monotony. In the cylindrical QDs (CQDs), we found that the QSS for electron and hole increase monotonically. The quantum size, lateral electric field and impurity position effect on the binding energy of neutral donor (D0) is studied. Unexpected behavior of D0 in quantum well limit (QW), the binding energy of D0 is increasing (blue shift) with increasing QD radius R at the presence of a lateral electric field. It appears that for a fixed size of the QD, the off-center binding energy decreases when the impurity ion is displaced from the center to the QD borders, while it is shifted to lower energy with increasing the field. 相似文献
82.
Sami I. Muslih Om P. Agrawal Dumitru Baleanu 《International Journal of Theoretical Physics》2010,49(8):1746-1752
This paper presents a fractional Schrödinger equation and its solution. The fractional Schrödinger equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives to obtain the fractional Euler-Lagrange equations of motion. We present the Lagrangian for the fractional Schrödinger equation of order α. We also use a fractional Klein-Gordon equation to obtain the fractional Schrödinger equation which is the same as that obtained using the fractional variational principle. As an example, we consider the eigensolutions of a particle in an infinite potential well. The solutions are obtained in terms of the sines of the Mittag-Leffler function. 相似文献
83.
The Fourier transform method is used to solve fractional Poisson’s equation with Riesz fractional derivative of order α. It is shown that the solution is given in terms of the fractional dimensional space D. Gauss law for the electrostatic problem is given and the total electric flux is obtained in terms of α and D. 相似文献
84.
85.
O. Abdulaziz A. Sami Bataineh I. Hashim 《Journal of Applied Mathematics and Computing》2010,33(1-2):61-81
In this paper, the homotopy analysis method (HAM) and its modification (MHAM) are applied to solve the nonlinear time- and space-fractional modified Korteweg-de Vries (fmKdV). The fractional derivatives are described by Caputo’s sense. Approximate and exact analytical solutions of the fmKdV are obtained. The MHAM in particular overcomes the computing difficulty encountered in HAM. Convergence theorems for both the homogeneous and non-homogeneous cases are given. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the approach. 相似文献
86.
The extended tanh method with a computerized symbolic computation is used for constructing the traveling wave solutions of coupled nonlinear equations arising in physics. The obtained solutions include solitons, kinks and plane periodic solutions. The applied method will be used to solve the generalized coupled Hirota Satsuma KdV equation. 相似文献
87.
Illia Krasnou Elena Melenevskaya Alexander Filippov Vladimir Aseyev Sami Hietala 《Journal of Macromolecular Science: Physics》2013,52(3):500-510
Aqueous solutions of complexes formed between poly(vinylpyrrolidone) (PVP), as a matrix polymer, and fullerene C60 were investigated. The effect of the external hydrodynamic field on the supermolecular assemblies formed by the complexes was analyzed. Despite the low content in the complexes (1.5 mass%), fullerene significantly modified the viscosity of aqueous PVP. Thus, the dynamic viscosity of the PVP/C60 complexes grew faster than that of the pure PVP upon increasing the PVP/C60 concentration. The difference in viscosities is especially pronounced for semidilute solutions. As a possible explanation, it is assumed that fullerenes act as crosslinks, in addition to the physical entanglements of the PVP macromolecules, which appear in the vicinity of the crossover concentration. Shear flow corresponding to the high shear rates destroyed fullerene‐induced intermolecular crosslinks in PVP/C60 solutions. 相似文献
88.
From a microscopic point of view, various natural and engineering materials consist of individual grains, whose motion strongly influence the macroscopic material behaviour. Exemplarily, one may look at the development of shear zones in natural granular materials, such as sand, occurring as a result of local grain dislocations and the transition of the granulate from a denser to a looser packing. The intuitive modelling approach for granular assemblies is consequently the consideration of each grain as a rigid particle. In a numerical framework, this leads to the Discrete Element Method (DEM), wherein the motion of each particle can be obtained solving Newton's equations for each particle. The present contribution discusses the basic fundaments of modelling granular material on the microscopic scale by use of the DEM. Special interest is taken to the constitutive choice of the governing particle-to-particle contact forces, as they have to account for plastic material behaviour as well as for assumptions concerning particle shape, size and distribution. As engineering problems are regularly described on the macroscale by means of continuum mechanics, a homogenisation strategy transfers the information from the microscale towards continuum quantities via volume averaging. Therefore, characteristic Representative Elementary Volumes (REV) are constructed by an ensemble of particles, where each particle can be chosen as the centre of a REV. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
89.
Sami Mustapha 《偏微分方程通讯》2013,38(1-2):245-275
Abstract We study the regularity of the free boundary in the two membranes problem. We prove that around any point the free boundary is either a C 1, α surface or a cusp, as in the obstacle problem. We also prove C 1, 1 regularity for the pair of functions solving the problem. 相似文献
90.
In this work, we consider the problem of a half space in the context of the theory of generalized thermoelasticity with one relaxation time. Realistically, the boundary conditions of the problem are considered to be stochastic. Laplace transform technique is used to solve the problem. The boundary conditions are considered to be of a type white noise. The inverse transforms are obtained in an approximate manner using asymptotic expansions valid for small values of time. Numerical results are given and represented graphically. Finally, a comparison with the ideal case when the boundary conditions are deterministic is carried out. 相似文献