We survey recent results on ground and bound state solutions E:?→R^3 of the problem {▽(▽×E)+}λE=|E|^(P-2)E in Ω,v×E=0 on Ω on a bounded Lipschitz domain ??R^3,where?×denotes the curl operator in R...We survey recent results on ground and bound state solutions E:?→R^3 of the problem {▽(▽×E)+}λE=|E|^(P-2)E in Ω,v×E=0 on Ω on a bounded Lipschitz domain ??R^3,where?×denotes the curl operator in R^3.The equation describes the propagation of the time-harmonic electric field R{E(χ)e^(iwt)}in a nonlinear isotropic material ? withλ=-μεω~2≤0,where μ andεstand for the permeability and the linear part of the permittivity of the material.The nonlinear term|E|^(P-2)E with 2<p≤2*=6 comes from the nonlinear polarization and the boundary conditions are those for?surrounded by a perfect conductor.The problem has a variational structure;however the energy functional associated with the problem is strongly indefinite and does not satisfy the Palais-Smale condition.We show the underlying difficulties of the problem and enlist some open questions.展开更多
The structure-property relationships in Ba0.4Sr0.6Ti1-ySiyO3 with y=0.00,0.01,0.02,0.05,0.10 and 0.20 ceramics have been studied by using X-ray diffraction,electron microscopy and dielectric spectroscopy.An increase o...The structure-property relationships in Ba0.4Sr0.6Ti1-ySiyO3 with y=0.00,0.01,0.02,0.05,0.10 and 0.20 ceramics have been studied by using X-ray diffraction,electron microscopy and dielectric spectroscopy.An increase of Si concentration is not favorable for the stability of the perovskite structure,which results in the formation of BaTiSiO5 secondary phase.The dielectric peaks of samples are suppressed,broadened and shifted to low temperature with increasing Si concentration.Permittivity and Q value are reduced gradually with increasing Si concentration,due to growing of second BaTiSiO5 phase.The tunability(T) still remains ～18.0% under 60 kV/cm biasing for the samples with y-0.10.The best combination of microwave dielectric properties are obtained for the composition of y=0.10:-=531,Q=391(at 1.610 GHz) and T=17.7%.展开更多
In this paper, the nonlinear interaction of ultra-high power laser beam with fusion plasma at relativistic regime in the presence of obliquely external magnetic field has been studied. Imposing an external magnetic fi...In this paper, the nonlinear interaction of ultra-high power laser beam with fusion plasma at relativistic regime in the presence of obliquely external magnetic field has been studied. Imposing an external magnetic field on plasma can modify the density profile of the plasma so that the thermal conductivity of electrons reduces which is considered to be the decrease of the threshold energy for ignition. To achieve the fusion of Hydrogen–Boron(HB) fuel,the block acceleration model of plasma is employed. Energy production by HB isotopes can be of interest, since its reaction does not generate radioactive tritium. By using the inhibit factor in the block model acceleration of plasma and Maxwell's as well as the momentum transfer equations, the electron density distribution and dielectric permittivity of the plasma medium are obtained. Numerical results indicate that with increasing the intensity of the external magnetic field, the oscillation of the laser magnetic field decreases, while the dielectric permittivity increases. Moreover, the amplitude of the electron density becomes highly peaked and the plasma electrons are strongly bunched with increasing the intensity of external magnetic field. Therefore, the magnetized plasma can act as a positive focusing lens to enhance the fusion process. Besides, we find that with increasing θ-angle(from oblique external magnetic field) between 0 and 90°, the dielectric permittivity increases, while for θ between 90° and 180°, the dielectric permittivity decreases with increasing θ.展开更多
基金supported by the National Science Centre of Poland (Grant No. 2013/09/B/ST1/01963)
文摘We survey recent results on ground and bound state solutions E:?→R^3 of the problem {▽(▽×E)+}λE=|E|^(P-2)E in Ω,v×E=0 on Ω on a bounded Lipschitz domain ??R^3,where?×denotes the curl operator in R^3.The equation describes the propagation of the time-harmonic electric field R{E(χ)e^(iwt)}in a nonlinear isotropic material ? withλ=-μεω~2≤0,where μ andεstand for the permeability and the linear part of the permittivity of the material.The nonlinear term|E|^(P-2)E with 2<p≤2*=6 comes from the nonlinear polarization and the boundary conditions are those for?surrounded by a perfect conductor.The problem has a variational structure;however the energy functional associated with the problem is strongly indefinite and does not satisfy the Palais-Smale condition.We show the underlying difficulties of the problem and enlist some open questions.
基金supported by the National Basic Research Program of China ("973" Project) (Grant No. 2009CB623302)
文摘The structure-property relationships in Ba0.4Sr0.6Ti1-ySiyO3 with y=0.00,0.01,0.02,0.05,0.10 and 0.20 ceramics have been studied by using X-ray diffraction,electron microscopy and dielectric spectroscopy.An increase of Si concentration is not favorable for the stability of the perovskite structure,which results in the formation of BaTiSiO5 secondary phase.The dielectric peaks of samples are suppressed,broadened and shifted to low temperature with increasing Si concentration.Permittivity and Q value are reduced gradually with increasing Si concentration,due to growing of second BaTiSiO5 phase.The tunability(T) still remains ～18.0% under 60 kV/cm biasing for the samples with y-0.10.The best combination of microwave dielectric properties are obtained for the composition of y=0.10:-=531,Q=391(at 1.610 GHz) and T=17.7%.
文摘In this paper, the nonlinear interaction of ultra-high power laser beam with fusion plasma at relativistic regime in the presence of obliquely external magnetic field has been studied. Imposing an external magnetic field on plasma can modify the density profile of the plasma so that the thermal conductivity of electrons reduces which is considered to be the decrease of the threshold energy for ignition. To achieve the fusion of Hydrogen–Boron(HB) fuel,the block acceleration model of plasma is employed. Energy production by HB isotopes can be of interest, since its reaction does not generate radioactive tritium. By using the inhibit factor in the block model acceleration of plasma and Maxwell's as well as the momentum transfer equations, the electron density distribution and dielectric permittivity of the plasma medium are obtained. Numerical results indicate that with increasing the intensity of the external magnetic field, the oscillation of the laser magnetic field decreases, while the dielectric permittivity increases. Moreover, the amplitude of the electron density becomes highly peaked and the plasma electrons are strongly bunched with increasing the intensity of external magnetic field. Therefore, the magnetized plasma can act as a positive focusing lens to enhance the fusion process. Besides, we find that with increasing θ-angle(from oblique external magnetic field) between 0 and 90°, the dielectric permittivity increases, while for θ between 90° and 180°, the dielectric permittivity decreases with increasing θ.
