LDOS of electron pair and the role of the Pauli exclusion principle.

The local density of states (LDOS) for a pair of non-relativistic electrons, influenced by repulsive Coulomb forces, is expressed in term of one-dimensional integrals over Whittaker functions. The computation of the electron pair's LDOS relies on a two-particle Green's function (GF), a generalization of the one-particle GF applicable to a charged particle in an attractive Coulomb potential. By incorporating electron spins and considering the Pauli exclusion principle, the resulting LDOS consists of two components: one originating from an exchange-even two-particle GF and the other from an exchange-odd two-particle GF.

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.

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.

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.

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.

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.