National and subnational short-term forecasting of COVID-19 in Germany and Poland during early 2021

We compare forecasts of weekly case and death numbers for COVID-19 in Germany and Poland based on 15 different modelling approaches. These cover the period from January to April 2021 and address numbers of cases and deaths one and two weeks into the future, along with the respective uncertainties. We find that combining different forecasts into one forecast can enable better predictions. However, case numbers over longer periods were challenging to predict. Additional data sources, such as information about different versions of the SARS-CoV-2 virus present in the population, might improve forecasts in the future

Nanostructured birefringent and gradient-index micro-optical elements

The main goal of this thesis is the numerical and experimental verification of the concept of the structured micro-optical elements fabricated with the modified stackand- draw technique. This technology, based on the well-known method of photonic crystal fibres (PCFs) production, allows the fabrication of nanostructured GRIN microlenses, form birefringent nanostructured materials and diffractive optical elements (DOEs). The principle of operation of the nanostructured GRIN (nGRIN) microlenses as well as the form birefringent nanostructured material can be explained by an effective medium theory (EMT). Both the approach based on the Maxwell-Garnet formula used for a description of nanostructured GRIN microlenses and the second-order EMT needed to account for birefringence properties are introduced. Numerical simulations of a Gaussian beam focusing and collimation (within GRIN microlenses) are performed using a FDTD method. The modelling results show that nGRIN microlenses can be described using the notion of the effective permittivity (or the effective refractive index) also in the case of the Gaussian beam illumination. Futhermore, Gaussian beam propagation within nGRIN microlenses can be approximately described by the paraxial scalar theory of the GRIN medium despite a high refractive index gradient. The concept of a so-called large-diameter nGRIN microlens with a quantised refractive index profile is introduced. Numerical simulations, performed using fast Fourier transform beam propagation method (FFT-BPM), show that focusing properties of the large-diameter quantised nGRIN microlens are similar to the focusing characteristic of the corresponding ideal continuous GRIN microlens. Both simulation and experimental results show that the fabricated large-diameter quantised nGRIN microlens has good chromatic properties in a range 633nm - 850nm. The successful fabrication of the prototype birefringent nanostructured element and a few diffractive checkerboards structures with different feature sizes is also reported. Applicability of the second-order EMT in the case of the fabricated birefringent material is verified both numerically, using the FDTD method, and experimentally. Diffractive patterns produced by DOEs are shown.Engineering and Physical Sciences Research Council (EPSRC)Foundation for Polish Science (FNP)European Regional Development Fund, Operational Program Innovative Policy 2007-201

Diffractive optics development using a modified stack-and-draw technique

Kivachuk V. S. Managed chaos and its consequences - 2 (evolution and prospects

National and subnational short-term forecasting of COVID-19 in Germany and Poland during early 2021

We compare forecasts of weekly case and death numbers for COVID-19 in Germany and Poland based on 15 different modelling approaches. These cover the period from January to April 2021 and address numbers of cases and deaths one and two weeks into the future, along with the respective uncertainties. We find that combining different forecasts into one forecast can enable better predictions. However, case numbers over longer periods were challenging to predict. Additional data sources, such as information about different versions of the SARS-CoV-2 virus present in the population, might improve forecasts in the future