1,208 research outputs found
Rough cut tool path planning for B-spline surfaces using convex hull boxes
The objective of this paper is to present a non-uniform layered rough cut plan for B-spline surfaces using convex hull boxes. The tool path plan generated by this method will rapidly remove most redundant material from stock material without overcutting. First, a B-spline surface is decomposed into piecewise Bezier surfaces, of which the convex hull boxes form an approximate model for rough cutting. Then, according to the top planes of those convex hull boxes, the stock material is divided into layers of different thickness. The cavity contour for each layer is obtained using a simplified union Boolean operation on convex hull boxes. Finally, from the top down, each layer is processed like a 2D pocket die cavity. The algorithm is implemented on a personal computer. It is shown that the rough cut plan is very efficient since no computation for solving nonlinear equations is needed, and no overcutting occurs since B-spline surfaces are protected by the convex hull property of Bezier surfaces
A characteristic free criterion of birationality
One develops {\em ab initio} the theory of rational/birational maps over
reduced, but not necessarily irreducible, projective varieties in arbitrary
characteristic. A numerical invariant of a rational map is introduced, called
the Jacobian dual rank. It is proved that a rational map in this general setup
is birational if and only if the Jacobian dual rank attains its maximal
possible value. Even in the "classical" case where the source variety is
irreducible there is some gain for this invariant over the degree of the map as
it is, on one hand, intrinsically related to natural constructions in
commutative algebra and, on the other hand, is effectively straightforwardly
computable. Applications are given to results so far only known in
characteristic zero. In particular, the surprising result of Dolgachev
concerning the degree of a plane polar Cremona map is given an alternative
conceptual angle.Comment: 24 page
Proximity effect and strong coupling superconductivity in nanostructures built with an STM
We present high resolution tunneling spectroscopy data at very low
temperatures on superconducting nanostructures of lead built with an STM. By
applying magnetic fields, superconductivity is restricted to length scales of
the order of the coherence length. We measure the tunneling conductance and
analyze the phonon structure and the low energy DOS. We demonstrate the
influence of the geometry of the system on the magnetic field dependence of the
tunneling density of states, which is gapless in a large range of fields. The
behavior of the features in the tunneling conductance associated to phonon
modes are explained within current models.Comment: 4 figures, 4 page
Inherent Inhomogeneities in Tunneling Spectra of BSCCO Crystals in the Superconducting State
Scanning Tunneling Spectroscopy on cleaved BSCCO(2212) single crystals reveal
inhomogeneities on length-scales of 30 . While most of the surface
yields spectra consistent with a d-wave superconductor, small regions show a
doubly gapped structure with both gaps lacking coherence peaks and the larger
gap having a size typical of the respective pseudo-gap for the same sample.Comment: 4 pages, 4 figure
Structural and electrical properties of c-axis oriented Y1-xCaxBa2(Cu1-yZny)3O7-delta thin films grown by pulsed laser deposition
Ca- and Zn-subsituted Y1-xCaxBa2(Cu1-yZny)O7-delta (x = 0, 0.05 and y = 0,
0.02, 0.04, 0.05) thin films were grown on SrTiO3 (100) substrates using the
pulsed laser deposition (PLD) technique. Effects of various growth parameters
on the quality of the film were studied via X-ray diffraction (XRD), atomic
force microscopy (AFM), and in-plane resistivity, rhoab(T), measurements. The
deposition temperature and oxygen partial pressure were gradually increased to
820C and 1.20 mbar respectively. Films grown under these conditions exhibited
good c-axis orientation (primarily limited by the grain size) and low values of
the extrapolated residual resistivity, rho(0), at zero temperature. The planar
hole content, p, was determined from the room temperature thermopower, S[290K],
measurements and the effects of oxygen annealing were also studied. Fully
oxygenated samples were found to be overdoped with p ~ 0.195. The
Superconducting transition temperature Tc(p), and rho(T,p) showed the expected
systematic variations with changing Zn content.Comment: Submitted to Physica C (2003
Low-Frequency Optical Conductivity in Inhomogeneous d-wave Superconductors
Motivated by the recent optical conductivity experiments on
Bi_2Sr_2CaCu_2O_{8+delta} films, we examine the possible origin of
low-frequency dissipation in the superconducting state. In the presence of
spatial inhomogeneity of the local phase stiffness rho_s, it is shown that some
spectral weight is removed from omega=0 to finite frequencies and contribute to
dissipation. A case where both rho_s and the local normal fluid density are
inhomogeneous is also considered. We find an enhanced dissipation at low
frequency if the two variations are anti-correlated.Comment: To appear in Phys. Rev.
Temperature dependence of Vortex Charges in High Temperature Superconductors
Using a model Hamiltonian with d-wave superconductivity and competing
antiferromagnetic (AF) interactions, the temperature (T) dependence of the
vortex charge in high T_c superconductors is investigated by numerically
solving the Bogoliubov-de Gennes equations. The strength of the induced AF
order inside the vortex core is T dependent. The vortex charge could be
negative when the AF order with sufficient strength is present at low
temperatures. At higher temperatures, the AF order may be completely suppressed
and the vortex charge becomes positive. A first order like transition in the T
dependent vortex charge is seen near the critical temperature T_{AF}. For
underdoped sample, the spatial profiles of the induced spin-density wave and
charge-density wave orders could have stripe like structures at T < T_s, and
change to two-dimensional isotropic ones at T > T_s. As a result, a vortex
charge discontinuity occurs at T_s.Comment: 5 pages, 5 figure
Power spectrum of many impurities in a d-wave superconductor
Recently the structure of the measured local density of states power spectrum
of a small area of the \BSCCO (BSCCO) surface has been interpreted in terms of
peaks at an "octet" of scattering wave vectors determined assuming weak,
noninterfering scattering centers. Using analytical arguments and numerical
solutions of the Bogoliubov-de Gennes equations, we discuss how the
interference between many impurities in a d-wave superconductor alters this
scenario. We propose that the peaks observed in the power spectrum are not the
features identified in the simpler analyses, but rather "background" structures
which disperse along with the octet vectors. We further consider how our
results constrain the form of the actual disorder potential found in this
material.Comment: 5 pages.2 figure
Anisotropic transport in unidirectional lateral superlattice around half-filling of the second Landau level
We have observed marked transport anisotropy in short period (a=92 nm)
unidirectional lateral superlattices around filling factors nu=5/2 and 7/2:
magnetoresistance shows a sharp peak for current along the modulation grating
while a dip appears for current across the grating. By altering the ratio a/l
(with l=sqrt{hbar/eB_perp} the magnetic length) via changing the electron
density n_e, it is shown that the nu=5/2 anisotropic features appear in the
range 6.6 alt a/l alt 7.2 varying their intensities, becoming most conspicuous
at a/l simeq 6.7. The peak/dip broadens with temperature roughly preserving its
height/depth up to 250 mK. Tilt experiments reveal that the structures are
slightly enhanced by an in-plane magnetic field B_| perpendicular to the
grating but are almost completely destroyed by B_| parallel to the grating. The
observations suggest the stabilization of a unidirectional charge-density-wave
or stripe phase by weak external periodic modulation at the second Landau
level.Comment: REVTeX, 5 pages, 3 figures, Some minor revisions, Added notes and
reference
Ground State and Spectral Properties of a Quantum Impurity in d-Wave Superconductors
The variational approach of Gunnarsson and Sch\"onhammer to the Anderson
impurity model is generalized to study d-wave superconductors in the presence
of dilute spin-1/2 impurities. We show that the local moment is screened when
the hybridization exceeds a nonzero critical value at which the ground state
changes from a spin doublet to a spin singlet. The electron spectral functions
are calculated in both phases. We find that while a Kondo resonance develops
above the Fermi level in the singlet phase, the spectral function exhibits a
low-energy spectral peak below the Fermi level in the spin doublet phase. The
origin of such a ``virtual Kondo resonance'' is the existence of low-lying
collective excitations in the spin-singlet sector. We discuss our results in
connection to recent spectroscopic experiments on Zn doped high-T
superconductors.Comment: 5 pages, 4figures, revised versio
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