Sequential limiting in continuous and discontinuous Galerkin methods for the Euler equations

We present a new approach to enforcing local maximum principles in finite element schemes for the compressible Euler equations. In contrast to synchronized limiting techniques for systems of conservation laws, the density, momentum, and total energy are constrained in a sequential manner which guarantees positivity preservation for the pressure and internal energy. After the density limiting step, the total energy and momentum are adjusted to incorporate the irreversible effect of density changes. Then the corresponding antidiffusive corrections are limited to satisfy inequality constraints for the total and kinetic energy. The same element-based limiting strategy is employed in the context of continuous and discontinuous Galerkin methods. The sequential nature of the new limiting procedure makes it possible to achieve crisp resolution of contact discontinuities while using sharp local bounds in the energy constraints. A numerical study is performed for piecewise-linear finite element discretizations of 1D and 2D test problems

Evolution of non-collinear magnetic state of exchange biased ferromagnet/normal metal/ferromagnet/superconductor heterostructure in magnetic field studied by polarized neutron reflectometry

By using waveguide enhanced polarized neutron reflectometry we have characterized the magnetic state of exchange biased CoO x(20 nm)/Co(4 nm)/Nb(5 nm)/Co(2 nm)/Nb(25 nm)/Al₂O₃ system. Measurement allowed to determine the dependence of the inclination angles of magnetic moment of the both Co layers as a function of applied field. According to the measurement the soft Co(2 nm) layer magnetization turns towards external field in magnetic fields as small as 20 Oe. In contrast direction of magnetic moment of Co(4 nm) layer cannot be altered in magnetic fields as high as 2 kOe