摘要 :
The deformation structure of the eveneven ytterbium, hafnium and tungsten nuclei is investigated in framework of the collective model, the single-particle Schr?dinger fluid model and the cranked Nilsson model. Accordingly, we have...
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The deformation structure of the eveneven ytterbium, hafnium and tungsten nuclei is investigated in framework of the collective model, the single-particle Schr?dinger fluid model and the cranked Nilsson model. Accordingly, we have calculated the rotational and vibrational energies, the nuclear moments of inertia, the total ground-state energy, the quadrupole moment, the liquid drop (LD) energy, the Strutinsky inertia, the LD inertia, the volume conservation factor ω0/ω0 ~0, the smoothed energy, the Bardeen, Cooper and Schrieffer (BCS) energy and the G-value of the ytterbium: ~(170)Yb, ~(172)Yb and ~(174)Yb, hafnium: ~(176)Hf, ~(178)Hf and ~(180)Hf and tungsten: ~(182)W, ~(184)W and ~(186)W nuclei as functions of the deformation parameters β, γ, which are assumed to vary in the ranges (-0.50 ≤ β ≤ 0.50) and (0° ≤ γ ≤ 60°). Also, two polynomials in β are obtained to produce results in good agreement with the corresponding results for the total ground-state energy and the quadrupole moment of the mentioned nine nuclei.
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摘要 :
We consider the logarithmic Schro"\dinger equations with damping, also called the Schro"\dinger--Langevin equation. On a periodic domain, this equation possesses plane wave solutions that are explicit. We prove that these solution...
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We consider the logarithmic Schro"\dinger equations with damping, also called the Schro"\dinger--Langevin equation. On a periodic domain, this equation possesses plane wave solutions that are explicit. We prove that these solutions are asymptotically stable in Sobolev regularity. In the case without damping, we prove that for almost all values of the nonlinear parameter, these solutions are stable in high Sobolev regularity for arbitrary long times when the solution is close to a plane wave. We also show and discuss numerical experiments illustrating our results.
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