Self-referenced method for the Judd–Ofelt parametrisation of the Eu3+ excitation spectrum

Judd-Ofelt theory presents a centrepiece in spectroscopy of lanthanides since it explains and predicts 4f absorptions and emissions from only 3 intensity parameters. A self-referenced method for calculating Judd–Ofelt intensity parameters from the excitation spectra of Eu3+-activated luminescent materials is proposed in this study along with a description of the parametrisation procedure and free user-friendly web application. It uses the integrated intensities of the 7F0→5D2, 7F0→5D4, and 7F0→5L6 transitions in the excitation spectrum for calculations and the integrated intensity of the 7F0→5D1 magnetic dipole transition for calibration. This approach allows a simple derivation of the Ω6 intensity parameter, which is difficult to calculate precisely by Krupke’s parametrisation of the emission spectrum and, therefore, frequently omitted in published research papers. Compared to the parametrisation of absorption spectra, the described method is more accurate, can be applied to any material form, and requires a single excitation spectrum.

From classical theory to spin 2 gravity

We consider here the simple derivation of the Einstein equations by Fock. Then, we approach the way from the spin 1 fields to the spin 2 fields for massive and massless particles and we derive the gravity equations from this base. In conclusion, we discuss the principle of equivalence in classical Einstein theory and in the Schwinger spin 2 gravity

Generalized Optical Theorem and Point Sources

A simple derivation of the general form of the optical theorem (GOT) is given for the case of a conservative scatterer in a homogeneous lossless medium, suitable for describing point sources and an observation region close to the scatterer. The presentation is based on the use of the operator approach and scalar wave equation in the limit of vanishingly small absorption. This approach does not require asymptotic estimates of rapidly oscillating integrals, does not use the integration of fluxes, which leads to the loss of information about the energy conservation law, and allows a natural generalization to the case of polarized radiation, as well as more complex multi-part fields. Such GOT generalizes the results known in the mathematical literature for models to the case of any conservative (real) scattering potential and arbitrary sources.

Celestial fields on the string and the Schwarzian action

This paper describes the motion of a classical Nambu-Goto string in three-dimensional anti-de Sitter spacetime in terms of two ‘celestial’ fields on the worldsheet. The fields correspond to retarded and advanced boundary times at which null rays emanating from the string reach the boundary. The formalism allows for a simple derivation of the Schwarzian action for near-AdS2 embeddings.

A Continuous Bayesian Model for the Stimulation COVID-19 Epidemic Dynamics

It is of great theoretical and application value to accurately forecast the spreading dynamics of COVID-19 epidemic. We first proposed and established a Bayesian model to predict the epidemic spreading behavior. In this model, the infection probability matrix is estimated according to the individual contact frequency in certain population group. This infection probability matrix is highly correlated with population geographic distribution, population age structure and so on. This model can effectively avoid the prediction malfunction by using the traditional ordinary differential equation methods such as SIR (susceptible, infectious and recovered) model and so on. Meanwhile, it would forecast the epidemic distribution and predict the epidemic hot spots geographically at different time. According to the results revealed by Bayesian model, the effect of population geographical distribution should be considered in the prediction of epidemic situation, and there is no simple derivation relationship between the threshold of group immunity and the virus reproduction numberR0. If we further consider the virus mutation effect and the antibody attenuation effect, with a large global population spatial distribution, it will be difficult for us to eliminate Covid-19 in a short time even with vaccination endeavor. Covid-19 may exist in human society for a long time, and the epidemic caused by re-infection is characterized by a wild-geometric && low- probability distribution with no epidemic hotspots.

Microscopic Numerical Simulations of Epidemic Models on Networks

Mathematical models of the spread of epidemic diseases are studied, paying special attention to networks. We treat the Susceptible-Infected-Recovered (SIR) model and the Susceptible-Exposed-Infectious-Recovered (SEIR) model described by differential equations. We perform microscopic numerical simulations for corresponding epidemic models on networks. Comparing a random network and a scale-free network for the spread of the infection, we emphasize the role of hubs in a scale-free network. We also present a simple derivation of the exact solution of the SIR model.

From teaching experience. VIII. Grid ornaments

After 7 symmetry groups of borders, 17 symmetry groups of grid ornaments are the next step on the way to 230 space symmetry groups in the university course of crystallography. A simple derivation of grid ornaments is proposed, combining the search for 10 flat clusters and their translations in 5 parallelogram grids. Analysis of grid ornaments in the urban landscape (artistic mosaics, wall claddings, floorings, etc.) draws students to the actual problem of the prevalence of 230 space symmetry groups in minerals.