4.4 Article

From Eikonal to Antieikonal Approximations: Competition of Scales in the Framework of Schrodinger and Classical Wave Equation

Journal

Publisher

ASME
DOI: 10.1115/1.4054153

Keywords

Schrodinger equations; wave equations; Maxwell equations; fractional calculus; cloud computing

Funding

  1. European Commission [823934]
  2. Ministerio de Economia, Industria y Competitividad
  3. Ministerio de Ciencia, Innovacion y Universidades of Spanish Government [ESP2016-79135-R]
  4. Marie Curie Actions (MSCA) [823934] Funding Source: Marie Curie Actions (MSCA)

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We describe certain limits associated with the Schrodinger equation, the classical wave equation, and Maxwell equations. These limits are determined by the competition of two fundamental scales. We particularly focus on the competition between an exploratory wavelength and the scale of fluctuations in the propagation media, as well as the propagation of electromagnetic waves in media with self-similar structures. This study requires large-scale computations, which can be achieved in the framework of cloud computing.
We present a description of certain limits associated with the Schrodinger equation, the classical wave equation, and Maxwell equations. Such limits are mainly characterized by the competition of two fundamental scales. More precisely: (1) The competition of an exploratory wavelength and the scale of fluctuations is associated with the media where the propagation takes place. From that, the universal behaviors arise eikonal and anti-eikonal. (2) In the context above, it is specially relevant and promising the study of propagation of electromagnetic waves in a media with a self-similar structure, like a fractal one. These systems offer the suggestive scenario where the eikonal and anti-eikonal behaviors are simultaneous. This kind of study requires large and massive computations that are mainly possible in the framework of the cloud computing. Recently, we started to carry out this task. (3) Finally and as a collateral aspect, we analyze the Planck constant in the interval 0 <= h <= infinity.

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