1,275 research outputs found

    The Construction of a Partially Regular Solution to the Landau-Lifshitz-Gilbert Equation in R2\mathbb{R}^2

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    We establish a framework to construct a global solution in the space of finite energy to a general form of the Landau-Lifshitz-Gilbert equation in R2\mathbb{R}^2. Our characterization yields a partially regular solution, smooth away from a 2-dimensional locally finite Hausdorff measure set. This construction relies on approximation by discretization, using the special geometry to express an equivalent system whose highest order terms are linear and the translation of the machinery of linear estimates on the fundamental solution from the continuous setting into the discrete setting. This method is quite general and accommodates more general geometries involving targets that are compact smooth hypersurfaces.Comment: 43 pages, 2 figure

    Superthermal photon bunching in terms of simple probability distributions

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    We analyze the second-order photon autocorrelation function g(2)g^{(2)} with respect to the photon probability distribution and discuss the generic features of a distribution that result in superthermal photon bunching (g(2)>2g^{(2)}>2). Superthermal photon bunching has been reported for a number of optical microcavity systems that exhibit processes like superradiance or mode competition. We show that a superthermal photon number distribution cannot be constructed from the principle of maximum entropy, if only the intensity and the second-order autocorrelation are given. However, for bimodal systems an unbiased superthermal distribution can be constructed from second-order correlations and the intensities alone. Our findings suggest modeling superthermal single-mode distributions by a mixture of a thermal and a lasing like state and thus reveal a generic mechanism in the photon probability distribution responsible for creating superthermal photon bunching. We relate our general considerations to a physical system, a (single-emitter) bimodal laser, and show that its statistics can be approximated and understood within our proposed model. Furthermore the excellent agreement of the statistics of the bimodal laser and our model reveal that the bimodal laser is an ideal source of bunched photons, in the sense that it can generate statistics that contain no other features but the superthermal bunching

    Energy transfer mechanism in Gd_2(SiO_4)O:Ce scintillators

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    The scintillation decay of cerium-doped gadolinium oxyorthosilicate Gd_2(SiO_4)O:Ce is lengthened by the energy transfer from Gd to Ce. To investigate the role of the Gd in the scintillation processes, the Gd was partially replaced by optically inactive rare earth elements, Y and Lu, and the effective transfer rates from Gd to Ce were measured as a function of Gd and Ce concentrations using UV- and gamma-ray excitations. The data clearly indicate the dilution of the Gd by the Y and the Lu further lengthens the migration time through the Gd in the energy transfer process from Gd to Ce

    Energy Transfer Mechanism In Gd_2(SiO_4)O:Ce Scintillators

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    The scintillation decay of cerium-doped gadolinium oxyorthosilicate Gd_2(SiO_4)O:Ce is lengthened by the energy transfer from Gd to Ce. To investigate the role of the Gd in the scintillation processes, the Gd was partially replaced by optically inactive rare earth elements, Y and Lu, and the effective transfer rates from Gd to Ce were measured as a function of Gd and Ce concentrations using UV- and gamma-ray excitations. The data clearly indicate the dilution of the Gd by the Y and the Lu further lengthens the migration time through the Gd in the energy transfer process from Gd to Ce

    Light emission mechanism of Lu_2(SiO_4)O:Ce

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    Lutetium oxyorthosilicate Lu_2(SiO_4)O has two crystallographically independent lutetium sites. When it is doped with Ce, the dopant Ce is assumed to occupy two different sites, and thus the existence of two activation centers is proposed. UV and gamma-ray excited spectra clearly indicate that two activation centers exist in cerium-doped lutetium oxyorthosilicate Lu_2(SiO_4)O:Ce (LSO)
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