Local measurements of velocity fluctuations and diffusion coefficients for a granular material flow

Measurements were made of two components of the average and fluctuating velocities, and of the local self-diffusion coefficients in a flow of granular material. The experiments were performed in a 1 m-high vertical channel with roughened sidewalls and with polished glass plates at the front and the back to create a two-dimensional flow. The particles used were glass spheres with a nominal diameter of 3 mm. The flows were high density and were characterized by the presence of long-duration frictional contacts between particles. The velocity measurements indicated that the flows consisted of a central uniform regime and a shear regime close to the walls. The fluctuating velocities in the transverse direction increased in magnitude from the centre towards the walls. A similar variation was not observed for the streamwise fluctuations. The self-diffusion coefficients showed a significant dependence on the fluctuating velocities and the shear rate. The velocity fluctuations were highly anistropic with the streamwise components being 2 to 2.5 times the transverse components. The self-diffusion coefficients for the streamwise direction were an order-of-magnitude higher than those for the transverse direction. The surface roughness of the particles led to a decrease in the self-diffusion coefficients

A constitutive model for the forces of a magnetic bearing including eddy currents

A multiple magnet bearing can be developed from N individual electromagnets. The constitutive relationships for a single magnet in such a bearing is presented. Analytical expressions are developed for a magnet with poles arranged circumferencially. Maxwell's field equations are used so the model easily includes the effects of induced eddy currents due to the rotation of the journal. Eddy currents must be included in any dynamic model because they are the only speed dependent parameter and may lead to a critical speed for the bearing. The model is applicable to bearings using attraction or repulsion

Nonlinear dynamics of attractive magnetic bearings

The nonlinear dynamics of a ferromagnetic shaft suspended by the force of attraction of 1, 2, or 4 independent electromagnets is presented. Each model includes a state variable feedback controller which has been designed using the pole placement method. The constitutive relationships for the magnets are derived analytically from magnetic circuit theory, and the effects of induced eddy currents due to the rotation of the journal are included using Maxwell's field relations. A rotor suspended by four electro-magnets with closed loop feedback is shown to have nine equilibrium points within the bearing clearance space. As the rotor spin speed increases, the system is shown to pass through a Hopf bifurcation (a flutter instability). Using center manifold theory, this bifurcation can be shown to be of the subcritical type, indicating an unstable limit cycle below the critical speed. The bearing is very sensitive to initial conditions, and the equilibrium position is easily upset by transient excitation. The results are confirmed by numerical simulation

Calculation of resonances in the Coulomb three-body system with two disintegration channels in the adiabatic hyperspherical approach

The method of calculation of the resonance characteristics is developed for the metastable states of the Coulomb three-body (CTB) system with two disintegration channels. The energy dependence of K-matrix in the resonance region is calculated with the use of the stabilization method. Resonance position and partial widths are obtained by fitting the numerically calculated K(E)-matrix with the help of the generalized Breit-Wigner formula.Comment: Latex, 11 pages with 5 figures and 2 table

Crystal field states of Kondo lattice heavy fermions CeRuSn3 and CeRhSn3

Inelastic neutron scattering experiments have been carried out to determine the crystal field states of the Kondo lattice heavy fermions CeRuSn3 and CeRhSn3. Both the compounds crystallize in LaRuSn3-type cubic structure (space group Pm-3n) in which the Ce atoms occupy two distinct crystallographic sites with cubic (m-3) and tetragonal (-4m.2) point symmetries. The INS data of CeRuSn3 reveal the presence of a broad excitation centered around 6-8 meV which is accounted by a model based on crystal electric field (CEF) excitations. On the other hand, the INS data of isostructural CeRhSn3 reveal three CEF excitations around 7.0, 12.2 and 37.2 meV. The neutron intensity sum rule indicates that the Ce ions at both cubic and tetragonal Ce sites are in Ce3+ state in both CeRuSn3 and CeRhSn3. The CEF level schemes for both the compounds are deduced. We estimate the Kondo temperature T_K = 3.1(2) K for CeRuSn3 from neutron quasielastic linewidth in excellent agreement with that determined from the scaling of magnetoresistance which gives T_K = 3.2(1) K. For CeRhSn3 the neutron quasielastic linewidth gives T_K = 4.6 K. For both CeRuSn3 and CeRhSn3, the ground state of Ce3+ turns out to be a quartet for the cubic site and a doublet for the tetragonal site.Comment: 12 pages, 13 figures, 2 tables, to appear in Phys. Rev.

Computations of Three-Body Continuum Spectra

We formulate a method to solve the coordinate space Faddeev equations for positive energies. The method employs hyperspherical coordinates and analytical expressions for the effective potentials at large distances. Realistic computations of the parameters of the resonances and the strength functions are carried out for the Borromean halo nucleus 6He (n+n+alpha) for J = 0+, 0-, 1+, 1-, 2+,2-. PACS numbers: 21.45.+v, 11.80.Jy, 31.15.Ja, 21.60.GxComment: 10 pages, 3 postscript figures, LaTeX, epsf.sty, corrected misprints in the caption of Fig.

The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions

We show that for two dimensional manifolds M with negative Euler characteristic there exists subsets of the space of smooth Riemannian metrics which are invariant and either parabolic or backwards-parabolic for the 2nd order RG flow. We also show that solutions exists globally on these sets. Finally, we establish the existence of an eternal solution that has both a UV and IR limit, and passes through regions where the flow is parabolic and backwards-parabolic