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Understanding the Atom and the Nucleus
Published in Robert E. Masterson, Nuclear Engineering Fundamentals, 2017
Scientists believe that space at the Planck scale can be described by a seething sea of virtual black holes or multidimensional manifolds (called Calabi–Yau manifolds) that determine the statistical probability distributions that the particles in nuclear reactors obey. Many Nobel Prize winners even believe that our 3D universe is sitting on a “brane” which is contained within a higher dimensional universe in which the force of gravity is stronger than it is in ours. The theory of strings, which is the most complete theory of physical reality ever developed, is based in part on these and other innovative ideas. In the next few chapters, we would like to illustrate how these concepts can be used to design and build a nuclear power plant. Normally, classical nuclear engineering is not approached in this way.
W-shaped, dark and grey solitary waves in the nonlinear Schrödinger equation competing dual power-law nonlinear terms and potentials modulated in time and space
Published in Journal of Modern Optics, 2019
Mati Youssoufa, Ousmanou Dafounansou, Alidou Mohamadou
The soliton concept and the presence of solitons in various physical phenomena have drawn a good deal of attention during the last five decades (1,2). Nonlinear equations which admit solitonic solutions can describe phenomena such as the propagation of optical pulses in nonlinear media, the stability and dynamics of molecules, propagation through ferromagnetic nanotubes, Bose–Einstein condensates (BEC), and string theory (D-Brane) (3). These equations generally describe completely integrable models (in the sense of Liouville or Inverse Scattering Transform) (4,5). We can cite among others the nonlinear Schrodinger equation (NLSE) known as Gross–Pitaevski equation, Korteweg de Vries equation and Boussinesq equation. However, some of these nonlinear equations are non-integrable. For example, the Burger–Korteweg de Vries which describes nonlinear waves in the media with dispersion and dissipation. The higher-order NLSE with modulating coefficients is also non-integrable. Some investigations reveal that the dynamic of solutions for non-integrable equations can be much richer and complex. Many exciting theories have also been developed for these types of systems, such as the Vakhitov–Kolokolov criterion for linear stability of solitary waves, the exponential asymptotic method for calculating non-local solitary waves, and the theories for fractal scatterings in solitary wave interactions (1,6).