Forecasts of Covid-19 evolution by nearest epidemic trajectories detection.

Robust method of short-term forecast of Covid-19 epidemic in small administrative units (districts) is proposed. By identifying similar sections of epidemic evolutions in the past it is possible to obtain short-term forecast of epidemic in given district. Examples of one and two-weeks forecasts for three cities in Poland during third epidemic wave (March and April 2021) are shown. Difference between epidemic evolutions in third wave and previous waves caused by Covid B.1.1.7 UK variant is observed. Proposed algorithm allows one to manage epidemic locally by entering or releasing anti-Covid restrictions in groups of small administrative units.

Microscale's relationship between Young's modulus and tissue density. Prediction of displacements.

The study presents an experimental verification of Wagner et al.'s relationship in microscale and proposes a modification of this relationship. For this purpose, 11 cubic specimens were microcomputed tomography scanned and mechanically tested with the displacement full-field measurements using a digital image correlation system. Then, numerical simulations of the compression tests were performed using a finite elements method. The Young's modulus distributions assigned to the finite elements models were calculated using both of Wagner et al.'s relationships: original and modified. Comparison of the experimental and numerical results indicated the accuracy of numerical solutions for both relationships.

Prediction of Young׳s modulus of trabeculae in microscale using macro-scale׳s relationships between bone density and mechanical properties.

According to the literature, there are many mathematical relationships between density of the trabecular bone and mechanical properties obtained in macro-scale testing. In micro-scale, the measurements provide only the ranges of Young׳s modulus of trabeculae, but there are no experimentally tested relationships allowing the calculation of the distribution of Young׳s modulus of trabeculae within these experimental ranges. This study examined the applicability of relationships between bone density and mechanical properties obtained in macro-scale testing for the calculation of Young׳s modulus distribution in micro-scale. Twelve cubic specimens from eleven femoral heads were cut out and micro-computed tomography (micro-CT) scanned. A mechanical compression test and Digital Image Correlation (DIC) measurements were performed to obtain the experimental displacement and strain full-field evaluation for each specimen. Five relationships between bone density and Young׳s modulus were selected for the test; those were given by Carter and Hayes (1977), Ciarelli et al. (2000), Kaneko et al. (2004), Keller (1994) for the human femur, and Li and Aspden, 1997. Using these relationships, five separate finite element (FE) models were prepared, with different distribution of Young׳s modulus of trabeculae for each specimen. In total, 60 FE analyses were carried out. The obtained displacement and strain full-field measurements from numerical calculations and experiment were compared. The results indicate that the highest accuracy of the numerical calculation was obtained for the Ciarelli et al. (2000) relationship, where the relative error was 17.87% for displacements and 50.94 % for strains. Therefore, the application of the Ciarelli et al. (2000) relationship in the microscale linear FE analysis is possible, but mainly to determine bone displacement.

Numerical modelling and verification of Polish ventricular assist device.

The developed multiscale model of blood chamber of POLVAD (Polish ventricular assist device) was introduced. The tension test for polymer and digital image correlation (DIC) were performed for verification of the strains and displacements obtained in the numerical model of POLVAD_EXT. The numerical simulations were carried out in conditions given in the experiment to compare the results obtained on external surfaces of blood chamber of the POLVAD_EXT. The examined polymer applied in the POLVADs is sensitive to changes of temperature and this observation is considered in all prepared numerical models. The comparison of experimental and numerical results shows acceptable coincidence. There are some heterogeneous distributions of strains in experiment with respect to analysis of computed parameters. The comparison of two versions of blood chambers (POLVAD and POLVAD_EXT) in numerical analysis shows that POLVAD_EXT construction is better with respect to analysis of strain and stress. The maximum values of computed parameters are located in the regions between connectors on the internal surfaces of blood chambers of POLVAD.

Zitterbewegung (trembling motion) of electrons in semiconductors: a review.

We review recent research on Zitterbewegung (ZB, trembling motion) of electrons in semiconductors. A brief history of the subject is presented, the trembling motion in semi-relativistic and spin systems is considered and its main features are emphasized. ZB of charge carriers in monolayer and bilayer graphene as well as in carbon nanotubes is elaborated in some detail. We describe the effects of an external magnetic field on ZB using monolayer graphene as an example. The nature of electron ZB in crystalline solids is explained. We also review various simulations of the trembling motion in a vacuum and in semiconductors, and mention ZB-like wave phenomena in sonic and photonic periodic structures. An attempt is made to quote all the relevant literature on the subject.