scholarly journals An evolution equation approach to the Klein–Gordon operator on curved spacetime

2019 ◽  
Vol 1 (2) ◽  
pp. 215-261 ◽  
Author(s):  
Jan Dereziński ◽  
Daniel Siemssen
Keyword(s):  
Evolution Equation ◽  
Equation Approach ◽  
Curved Spacetime ◽  
Klein Gordon

Klein-Gordon equation approach to nonlinear split-ring resonator based metamaterials: One-dimensional systems

2011 ◽  
Vol 84 (15) ◽  
Author(s):  
Pradipta Giri ◽  
Kamal Choudhary ◽  
Arnab Sen Gupta ◽  
A. K. Bandyopadhyay ◽  
Arthur R. McGurn
Keyword(s):  
Gordon Equation ◽  
Ring Resonator ◽  
Split Ring Resonator ◽  
Equation Approach ◽  
Split Ring ◽  
One Dimensional ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Evolution-equation approach to seismic image, and data, continuation

Wave Motion ◽  
2008 ◽  
Vol 45 (7-8) ◽  
pp. 952-969 ◽  
Author(s):  
Anton A. Duchkov ◽  
Maarten V. de Hoop ◽  
Antônio Sá Barreto
Keyword(s):  
Evolution Equation ◽  
Equation Approach ◽  
Seismic Image

A phase-equation approach to boundary–layer instability theory: Tollmien-Schlichting waves

1995 ◽  
Vol 304 ◽  
pp. 185-212 ◽  
Author(s):  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Evolution Equation ◽  
Modulational Instability ◽  
Reaction Diffusion Equations ◽  
Large Reynolds Number ◽  
Two Dimensional ◽  
Equation Approach ◽  
Phase Equation ◽  
Tollmien Schlichting

Our concern is with the evolution of large-amplitude Tollmien-Schlichting waves in boundary-layer flows. In fact, the disturbances we consider are of a comparable size to the unperturbed state. We shall describe two-dimensional disturbances which are locally periodic in time and space. This is achieved using a phase equation approach of the type discussed by Howard & Kopell (1977) in the context of reaction-diffusion equations. We shall consider both large and O(1) Reynolds number flows though, in order to keep our asymptotics respectable, our finite-Reynolds-number calculation will be carried out for the asymptotic suction flow. Our large-Reynolds-number analysis, though carried out for Blasius flow, is valid for any steady two-dimensional boundary layer. In both cases the phase-equation approach shows that the wavenumber and frequency will develop shocks or other discontinuities as the disturbance evolves. As a special case we consider the evolution of constant frequency/wavenumber disturbances and show that their modulational instability is controlled by Burgers equation at finite-Reynolds-number and by a new integro-differential evolution equation at large-Reynolds-numbers. For the large Reynolds number case the evolution equation points to the development of a spatially localized singularity at a finite time.

scholarly journals Discreteness of Curved Spacetime from GUP

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Ahmad Adel Abutaleb
Keyword(s):  
Dirac Equation ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Curved Spacetime ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Heisenberg's Uncertainty Principle ◽  
Area And Volume

Diverse theories of quantum gravity expect modifications of the Heisenberg's uncertainty principle near the Planck scale to a so-called Generalized uncertainty principle (GUP). It was shown by some authors that the GUP gives rise to corrections to the Schrodinger , Klein-Gordon, and Dirac equations. By solving the GUP corrected equations, the authors arrived at quantization not only of energy but also of box length, area, and volume. In this paper, we extend the above results to the case of curved spacetime (Schwarzschild metric). We showed that we arrived at the quantization of space by solving Dirac equation with GUP in this metric.

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