Non-Euclidean Analogues of Plane Waves

Ab initio band theory approach to electron energy loss near edge structures

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100104595 ◽

1988 ◽

Vol 46 ◽

pp. 506-507

Author(s):

Xudong Weng ◽

O.F. Sankey ◽

Peter Rez

Keyword(s):

Ab Initio ◽

Local Density ◽

Interpolation Method ◽

Atomic Orbital ◽

Plane Waves ◽

Large Set ◽

Theory Approach ◽

Band Theory ◽

Atomic Orbitals ◽

Pseudopotential Calculations

Single electron band structure techniques have been applied successfully to the interpretation of the near edge structures of metals and other materials. Among various band theories, the linear combination of atomic orbital (LCAO) method is especially simple and interpretable. The commonly used empirical LCAO method is mainly an interpolation method, where the energies and wave functions of atomic orbitals are adjusted in order to fit experimental or more accurately determined electron states. To achieve better accuracy, the size of calculation has to be expanded, for example, to include excited states and more-distant-neighboring atoms. This tends to sacrifice the simplicity and interpretability of the method.In this paper. we adopt an ab initio scheme which incorporates the conceptual advantage of the LCAO method with the accuracy of ab initio pseudopotential calculations. The so called pscudo-atomic-orbitals (PAO's), computed from a free atom within the local-density approximation and the pseudopotential approximation, are used as the basis of expansion, replacing the usually very large set of plane waves in the conventional pseudopotential method. These PAO's however, do not consist of a rigorously complete set of orthonormal states.

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REFLECTION OF PLANE WAVES FROM A FREE SURFACE OF A POROTHERMOELASTIC SOLID HALF-SPACE

Journal of Porous Media ◽

10.1615/jpormedia.v16.i10.60 ◽

2013 ◽

Vol 16 (10) ◽

pp. 945-957 ◽

Cited By ~ 6

Author(s):

Baljeet Singh

Keyword(s):

Free Surface ◽

Half Space ◽

Plane Waves

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Propagation and Reflection of Plane Waves in a Rotating Magneto-Elastic Fibre-Reinforced Semi Space with Surface Stress

Mechanics and Mechanical Engineering ◽

10.2478/mme-2018-0074 ◽

2020 ◽

Vol 22 (4) ◽

pp. 939-958

Author(s):

Indrajit Roy ◽

D. P. Acharya ◽

Sourav Acharya

Keyword(s):

Surface Stress ◽

Incident Angle ◽

Plane Waves ◽

Three Dimensional ◽

Elastic Fibre ◽

Amplitude Ratios ◽

Governing Equations ◽

Rotation Surface ◽

Wave Velocities ◽

Magnetic Field Rotation

AbstractThe present paper investigates the propagation of quasi longitudinal (qLD) and quasi transverse (qTD) waves in a magneto elastic fibre-reinforced rotating semi-infinite medium. Reflections of waves from the flat boundary with surface stress have been studied in details. The governing equations have been used to obtain the polynomial characteristic equation from which qLD and qTD wave velocities are found. It is observed that both the wave velocities depend upon the incident angle. After imposing the appropriate boundary conditions including surface stress the resultant amplitude ratios for the total displacements have been obtained. Numerically simulated results have been depicted graphically by displaying two and three dimensional graphs to highlight the influence of magnetic field, rotation, surface stress and fibre-reinforcing nature of the material medium on the propagation and reflection of plane waves.

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Electromagnetic waves

10.1093/oso/9780198786399.003.0033 ◽

2018 ◽

Author(s):

Nathalie Deruelle ◽

Jean-Philippe Uzan

Keyword(s):

Plane Wave ◽

Electromagnetic Waves ◽

Maxwell Equations ◽

Plane Waves ◽

Geometrical Optics ◽

Particle Detection ◽

Spatial Coordinates ◽

A Charge

This chapter examines solutions to the Maxwell equations in a vacuum: monochromatic plane waves and their polarizations, plane waves, and the motion of a charge in the field of a wave (which is the principle upon which particle detection is based). A plane wave is a solution of the vacuum Maxwell equations which depends on only one of the Cartesian spatial coordinates. The monochromatic plane waves form a basis (in the sense of distributions, because they are not square-integrable) in which any solution of the vacuum Maxwell equations can be expanded. The chapter concludes by giving the conditions for the geometrical optics limit. It also establishes the connection between electromagnetic waves and the kinematic description of light discussed in Book 1.

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