On the problem of relativistic particles motion in strong magnetic field and dense matter

We consider a problem of electron motion in different media and magnetic field. It is shown that in case of nonmoving medium and constant homogenious magnetic field the electron energies are quantized. We also discuss the general problem of eigenvectors and eigenvalues of a given class of Hamiltonians. We examine obtained exact solutions for the particular case of the electron motion in a rotating neutron star with account for matter and magnetic field effects. We argue that all of these considerations can be usefull for astrophysical applications

Practical analytical solutions for benchmarking of 2-D and 3-D geodynamic Stokes problems with variable viscosity

Geodynamic modeling is often related with challenging computations involving solution of the Stokes and continuity equations under the condition of highly variable viscosity. Based on a new analytical approach we have developed particular analytical solutions for 2-D and 3-D incompressible Stokes flows with both linearly and exponentially variable viscosity. We demonstrate how these particular solutions can be converted into 2-D and 3-D test problems suitable for benchmarking numerical codes aimed at modeling various mantle convection and lithospheric dynamics problems. The Main advantage of this new generalized approach is that a large variety of benchmark solutions can be generated, including relatively complex cases with open model boundaries, non-vertical gravity and variable gradients of the viscosity and density fields, which are not parallel to the Cartesian axes. Examples of respective 2-D and 3-D MatLab codes are provided with this paper

Neutrino magnetic moment and neutrino energy quantization in rotating media

After a brief discussion on neutrino electromagnetic properties, we consider the problem of neutrino energy spectra in different media. It is shown that in two particular cases (i.e., neutrino propagation in a) transversally moving with increasing speed medium and b) rotating medium) neutrino energies are quantized. These phenomena can be important for astrophysical applications, for instance, for physics of rotating neutron stars.Comment: 7 pagex in LaTex, to appear in Proceedings of the XXIII Recontres de Physique de la Vallee D'Aoste on "Results and Perspectives in Particle Physics" (La Thuile, Italy, March 1-7, 2009