Problems on electrorheological fluid flows

We develop a model of an electrorheological fluid such that the fluid is considered as an anisotropic one with the viscosity depending on the second invariant of the rate of strain tensor, on the module of the vector of electric field strength, and on the angle between the vectors of velocity and electric field. We study general problems on the flow of such fluids at nonhomogeneous mixed boundary conditions, wherein values of velocities and surface forces are given on different parts of the boundary. We consider the cases where the viscosity function is continuous and singular, equal to infinity, when the second invariant of the rate of strain tensor is equal to zero. In the second case the problem is reduced to a variational inequality. By using the methods of a fixed point, monotonicity, and compactness, we prove existence results for the problems under consideration. Some efficient methods for numerical solution of the problems are examined.Comment: Presented to the journal "Discrete and Continuous Dynamical Systems, Series

Adaptive multilevel methods for obstacle problems

The authors consider the discretization of obstacle problems for second-order elliptic differential operators by piecewise linear finite elements. Assuming that the discrete problems are reduced to a sequence of linear problems by suitable active set strategies, the linear problems are solved iteratively by preconditioned conjugate gradient iterations. The proposed preconditioners are treated theoretically as abstract additive Schwarz methods and are implemented as truncated hierarchical basis preconditioners. To allow for local mesh refinement semilocal and local a posteriors error estimates are derived, providing lower and upper estimates for the discretization error. The theoretical results are illustrated by numerical computations

Adaptive multilevel-methods for obstacle problems in three space dimensions

We consider the discretization of obstacle problems for second order elliptic differential operators in three space dimensions by piecewise linear finite elements. Linearizing the discrete problems by suitable active set strategies, the resulting linear sub-problems are solved iteratively by preconditioned cg-iterations. We propose a variant of the BPX preconditioner and prove an O(j) estimate for the resulting condition number To allow for local mesh refinement we derive semi-local and local a posteriori error estimates. The theoretical results are illustrated by numerical computations

Applications of Abundance Data and Requirements for Cosmochemical Modeling

Understanding the evolution of the universe from Big Bang to its present state requires an understanding of the evolution of the abundances of the elements and isotopes in galaxies, stars, the interstellar medium, the Sun and the heliosphere, planets and meteorites. Processes that change the state of the universe include Big Bang nucleosynthesis, star formation and stellar nucleosynthesis, galactic chemical evolution, propagation of cosmic rays, spallation, ionization and particle transport of interstellar material, formation of the solar system, solar wind emission and its fractionation (FIP/FIT effect), mixing processes in stellar interiors, condensation of material and subsequent geochemical fractionation. Here, we attempt to compile some major issues in cosmochemistry that can be addressed with a better knowledge of the respective element or isotope abundances. Present and future missions such as Genesis, Stardust, Interstellar Pathfinder, and Interstellar Probe, improvements of remote sensing instrumentation and experiments on extraterrestrial material such as meteorites, presolar grains, and lunar or returned planetary or cometary samples will result in an improved database of elemental and isotopic abundances. This includes the primordial abundances of D, ^3He, ^4He, and ^7Li, abundances of the heavier elements in stars and galaxies, the composition of the interstellar medium, solar wind and comets as well as the (highly) volatile elements in the solar system such as helium, nitrogen, oxygen or xenon

Non-isothermal model for the direct isotropic/smectic-A liquid crystalline transition

An extension to a high-order model for the direct isotropic/smectic-A liquid crystalline phase transition was derived to take into account thermal effects including anisotropic thermal diffusion and latent heat of phase-ordering. Multi-scale multi-transport simulations of the non-isothermal model were compared to isothermal simulation, showing that the presented model extension corrects the standard Landau-de Gennes prediction from constant growth to diffusion-limited growth, under shallow quench/undercooling conditions. Non-isothermal simulations, where meta-stable nematic pre-ordering precedes smectic-A growth, were also conducted and novel non-monotonic phase-transformation kinetics observed.Comment: First revision: 20 pages, 7 figure

Atomic Scale Control of Spin Current Transmission at Interfaces

Ferromagnet/heavy metal bilayers represent a central building block for spintronic devices where the magnetization of the ferromagnet can be controlled by spin currents generated in the heavy metal. The efficiency of spin current generation is paramount. Equally important is the efficient transfer of this spin current across the ferromagnet/heavy metal interface. Here, we show theoretically and experimentally that for Ta as heavy metal the interface only partially transmits the spin current while this effect is absent when Pt is used as heavy metal. This is due to magnetic moment reduction at the interface caused by 3d–5d hybridization effects. We show that this effect can be avoided by atomically thin interlayers. On the basis of our theoretical model we conclude that this is a general effect and occurs for all 5d metals with less than half-filled 5d shell