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

Dynamics of perpendicular recording heads

3D modeling and inductance measurements were used to design an ultra-high frequency perpendicular system. Kerr microscopy and spin-stand experiments with focused ion beam (FI-B) trimmed perpendicular heads and perpendicular media directly verified the high frequency concepts

Observation of Non-Exponential Orbital Electron Capture Decays of Hydrogen-Like 140^{140}Pr and 142^{142}Pm Ions

We report on time-modulated two-body weak decays observed in the orbital electron capture of hydrogen-like $^{140}$Pr$^{59+}$ and $^{142}$Pm$^{60+}$ ions coasting in an ion storage ring. Using non-destructive single ion, time-resolved Schottky mass spectrometry we found that the expected exponential decay is modulated in time with a modulation period of about 7 seconds for both systems. Tentatively this observation is attributed to the coherent superposition of finite mass eigenstates of the electron neutrinos from the weak decay into a two-body final state.Comment: 12 pages, 5 figure

Cyclic projectors and separation theorems in idempotent convex geometry

Semimodules over idempotent semirings like the max-plus or tropical semiring have much in common with convex cones. This analogy is particularly apparent in the case of subsemimodules of the n-fold cartesian product of the max-plus semiring it is known that one can separate a vector from a closed subsemimodule that does not contain it. We establish here a more general separation theorem, which applies to any finite collection of closed semimodules with a trivial intersection. In order to prove this theorem, we investigate the spectral properties of certain nonlinear operators called here idempotent cyclic projectors. These are idempotent analogues of the cyclic nearest-point projections known in convex analysis. The spectrum of idempotent cyclic projectors is characterized in terms of a suitable extension of Hilbert's projective metric. We deduce as a corollary of our main results the idempotent analogue of Helly's theorem.Comment: 20 pages, 1 figur

Application of the RMF mass model to the r-process and the influence of mass uncertainties

A new mass table calculated by the relativistic mean field approach with the state-dependent BCS method for the pairing correlation is applied for the first time to study r-process nucleosynthesis. The solar r-process abundance is well reproduced within a waiting-point approximation approach. Using an exponential fitting procedure to find the required astrophysical conditions, the influence of mass uncertainty is investigated. R-process calculations using the FRDM, ETFSI-Q and HFB-13 mass tables have been used for that purpose. It is found that the nuclear physical uncertainty can significantly influence the deduced astrophysical conditions for the r-process site. In addition, the influence of the shell closure and shape transition have been examined in detail in the r-process simulations.Comment: to be published in Phys. Rev. C, 22 pages, 9 figure

Semiring and semimodule issues in MV-algebras

In this paper we propose a semiring-theoretic approach to MV-algebras based on the connection between such algebras and idempotent semirings - such an approach naturally imposing the introduction and study of a suitable corresponding class of semimodules, called MV-semimodules. We present several results addressed toward a semiring theory for MV-algebras. In particular we show a representation of MV-algebras as a subsemiring of the endomorphism semiring of a semilattice, the construction of the Grothendieck group of a semiring and its functorial nature, and the effect of Mundici categorical equivalence between MV-algebras and lattice-ordered Abelian groups with a distinguished strong order unit upon the relationship between MV-semimodules and semimodules over idempotent semifields.Comment: This version contains some corrections to some results at the end of Section