Friction measuring apparatus Patent

Kinetic and static friction force measurement between magnetic tape and magnetic head surface

Comment on "What does the Letelier-Gal'tsov metric describe?"

We show that the Letelier-Gal'tsov (LG) metric describing multiple crossed strings in relative motion does solve the Einstein equations, in spite of the discontinuity uncovered recently by Krasnikov [gr-qc/0502090] provided the strings are straight and moving with constant velocities.Comment: 3 page

Stored mafic/ultramafic crust and early Archean mantle depletion

Both early and late Archean rocks from greenstone belts and felsic gneiss complexes exhibit positive epsilon(Nd) values of +1 to +5 by 3.5 Ga, demonstrating that a depleted mantle reservoir existed very early. The amount of preserved pre-3.0 Ga continental crust cannot explain such high epsilon values in the depleted residue unless the volume of residual mantle was very small: a layer less than 70 km thick by 3.0 Ga. Repeated and exclusive sampling of such a thin layer, especially in forming the felsic gneiss complexes, is implausible. Extraction of enough continental crust to deplete the early mantle and its destructive recycling before 3.0 Ga ago requires another implausibility, that the sites of crustal generation of recycling were substantially distinct. In contrast, formation of mafic or ultramafic crust analogous to present-day oceanic crust was continuous from very early times. Recycled subducted oceanic lithosphere is a likely contributor to present-day hotspot magmas, and forms a reservoir at least comparable in volume to continental crust. Subduction of an early mafic/ultramafic oceanic crust and temporary storage rather than immediate mixing back into undifferentiated mantle may be responsible for the depletion and high epsilon(Nd) values of the Archean upper mantle

Limit Theorems For Quantum Walks Associated with Hadamard Matrices

We study a one-parameter family of discrete-time quantum walk models on the line and in the xy-plane associated with the Hadamard walk. Weak convergence in the long-time limit of all moments of the walker's pseudo-velocity on the line and in the xy-plane is proved. Symmetrization on the line and in the xy-plane is theoretically investigated, leading to the resolution of the Konno-Namiki-Soshi conjecture in the special case of symmetrization of the unbiased Hadamard walk on the line . A necessary condition for the existence of a phenomenon known as localization is given