We consider the dynamics on a quantum graph as the limit of the dynamics generated by a one-particle Hamiltonian in R-2 with a potential having a deep strict minimum on the graph, when the width of the well shrinks to...
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We consider the dynamics on a quantum graph as the limit of the dynamics generated by a one-particle Hamiltonian in R-2 with a potential having a deep strict minimum on the graph, when the width of the well shrinks to zero. For a generic graph we prove convergence outside the vertices to the free dynamics on the edges. For a simple model of a graph with two edges and one vertex, we prove convergence of the dynamics to the one generated by the Laplacian with Dirichlet boundary conditions in the vertex.
This paper is concerned with the stability characteristics of nonlinear surface waves propagating along a left-handed substrate (LHM) and a non-linear dielectric cover. These characteristics have been simulated numeri...
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This paper is concerned with the stability characteristics of nonlinear surface waves propagating along a left-handed substrate (LHM) and a non-linear dielectric cover. These characteristics have been simulated numerically by using the perturbation method. The growth rate of perturbation is computed by solving the dispersion equation of perturbation. I found that the stability of nonlinear surface waves is affected by the frequency dependence of the electric permittivity εh and magnetic permeability μh of the LHM. The spatial evolution of the steady state field amplitude is determined by using computer simulation method. The calculations show that with increasing the effective refractive index nx at fixed saturation parameter μp, the field distribution is sharpened and concentrated in the nonlinear medium. The waves are stable of forward and backward behavior. At higher values of nx, attenuated backward waves are observed.
Photochemical reactions related to the Ge lone-pair center (GLPC) that are induced by KrF excimer laser photons in H2-loaded Ge-doped SiO2 glass have been investigated. Without the H2 loading, the Ge electron center (...
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Photochemical reactions related to the Ge lone-pair center (GLPC) that are induced by KrF excimer laser photons in H2-loaded Ge-doped SiO2 glass have been investigated. Without the H2 loading, the Ge electron center (GEC) and the positively charged GLPC were induced by the laser irradiation. In the H2-loaded sample, the GEC, the Ge E′ center, and the germyl radical (GR) were induced by the irradiation, while the positively charged GLPC was not observed after the irradiation. If the H2-loaded sample was thermally annealed after the photon irradiation, the concentration of the photo-induced GEC decreased monotonically with an increase in the annealing temperature. On the other hand, the concentration of the GR increased up to the annealing temperature of 160 °C, and it decreased at higher temperatures. Without the pre-irradiation, the induction of the GR was not observed even in the H2-loaded sample. From these results, it is concluded that the positively charged GLPC is terminated with a hydrogen atom in the H2-loaded sample and then becomes the GR by trapping an electron thermally released from the GEC.
We show that localized (non-evanescent) solutions to Maxwell equations exist, which propagate without distortion along normal waveguides with Superluminal speed.
We show that localized (non-evanescent) solutions to Maxwell equations exist, which propagate without distortion along normal waveguides with Superluminal speed.
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