From Golden Spirals to Constant Slope Surfaces

In this paper, we find all constant slope surfaces in the Euclidean 3-space, namely those surfaces for which the position vector of a point of the surface makes constant angle with the normal at the surface in that point. These surfaces could be thought as the bi-dimensional analogue of the generalized helices. Some pictures are drawn by using the parametric equations we found.Comment: 11 pages, 8 figure

Influence of qubit displacements on quantum logic operations in a silicon-based quantum computer with constant interaction

The errors caused by qubit displacements from their prescribed locations in an ensemble of spin chains are estimated analytically and calculated numerically for a quantum computer based on phosphorus donors in silicon. We show that it is possible to polarize (initialize) the nuclear spins even with displaced qubits by using Controlled NOT gates between the electron and nuclear spins of the same phosphorus atom. However, a Controlled NOT gate between the displaced electron spins is implemented with large error because of the exponential dependence of exchange interaction constant on the distance between the qubits. If quantum computation is implemented on an ensemble of many spin chains, the errors can be small if the number of chains with displaced qubits is small

Temperature effects on the 15-85-micron spectra of olivines and pyroxenes

Far-infrared spectra of laboratory silicates are normally obtained at room temperature even though the grains responsible for astronomical silicate emission bands seen at wavelengths >20 micron are likely to be at temperatures below ~150 K. In order to investigate the effect of temperature on silicate spectra, we have obtained absorption spectra of powdered forsterite and olivine, along with two orthoenstatites and diopside clinopyroxene, at 3.5+-0.5 K and at room temperature (295+-2K). To determine the changes in the spectra the resolution must be increased from 1 to 0.25 cm^-1 at both temperatures since a reduction in temperature reduces the phonon density, thereby reducing the width of the infrared peaks. Several bands observed at 295 K split at 3.5 K. At 3.5 K the widths of isolated single bands in olivine, enstatites and diopside are ~ 90% of their 295 K-widths. However, in forsterite the 3.5-K-widths of the 31-, 49- and 69-micron bands are, respectively, 90%, 45% and 31% of their 295 K widths. Due to an increase in phonon energy as the lattice contracts, 3.5-K-singlet peaks occur at shorter wavelengths than do the corresponding 295-K peaks; the magnitude of the wavelength shift increases from \~ 0-0.2 micron at 25 micron to ~0.9 micron at 80 micron. Changes in the relative absorbances of spectral peaks are also observed. The temperature dependence of lambda_pk and bandwidth shows promise as a means to deduce characteristic temperatures of mineralogically distinct grain populations. In addition, the observed changes in band strength with temperature will affect estimates of grain masses and relative mineral abundances inferred using room-temperature laboratory data.Comment: 11 pages, 7 figures including figures 3a and 3b. includes latex and eps files. Accepted by MNRAS on 15th March 200

Magnetic structure of Ba(TiO)Cu4_4(PO4_4)4_4 probed using spherical neutron polarimetry

The antiferromagnetic compound Ba(TiO)Cu$_4$(PO$_4$)$_4$ contains square cupola of corner-sharing CuO$_4$ plaquettes, which were proposed to form effective quadrupolar order. To identify the magnetic structure, we have performed spherical neutron polarimetry measurements. Based on symmetry analysis and careful measurements we conclude that the orientation of the Cu$^{2+}$ spins form a non-collinear in-out structure with spins approximately perpendicular to the CuO$_4$ motif. Strong Dzyaloshinskii-Moriya interaction naturally lends itself to explain this phenomenon. The identification of the ground state magnetic structure should serve well for future theoretical and experimental studies into this and closely related compounds.Comment: 9 pages, 4 figure

The supercluster--void network III. The correlation function as a geometrical statistic

We investigate properties of the correlation function of clusters of galaxies using geometrical models. On small scales the correlation function depends on the shape and the size of superclusters. On large scales it describes the geometry of the distribution of superclusters. If superclusters are distributed randomly then the correlation function on large scales is featureless. If superclusters and voids have a tendency to form a regular lattice then the correlation function on large scales has quasi-regularly spaced maxima and minima of decaying amplitude; i.e., it is oscillating. The period of oscillations is equal to the step size of the grid of the lattice. We calculate the power spectrum for our models and compare the geometrical information of the correlation function with other statistics. We find that geometric properties (the regularity of the distribution of clusters on large scales) are better quantified by the correlation function. We also analyse errors in the correlation function and the power spectrum by generating random realizations of models and finding the scatter of these realizations.Comment: MNRAS LaTex style, 12 pages, 7 PostScript figures embedded, accepted by MNRA