Search

We develop a novel sampling theorem for functions defined on the three-dimensional rotation group SO(3) by connecting the rotation group to the three-torus through a periodic extension. Our sampling theorem requires $4L^3$ samples to capture all of the information content of a signal band-limited at $L$, reducing the number of required samples by a factor of two compared to other equiangular sampling theorems. We present fast algorithms to compute the associated Fourier transform on the rotation group, the so-called Wigner transform, which scale as $O(L^4)$, compared to the naive scaling of $O(L^6)$. For the common case of a low directional band-limit $N$, complexity is reduced to $O(N L^3)$. Our fast algorithms will be of direct use in speeding up the computation of directional wavelet transforms on the sphere. We make our SO3 code implementing these algorithms publicly available., Comment: 5 pages, 2 figures, minor changes to match version accepted for publication. Code available at http://www.sothree.org

A potassium alumina borosilicate glass with the composition 13K2O*13Al2O3*16B2O3*43SiO2*15Fe2O3-x was melted using Fe2O3 as raw material. The melt was dumped from a Pt-crucible with a downpipe in water which resulted in the formation of phase separated droplets with a size of around 100 - 150 nm. In this droplets, magnetite crystals with a size of around 10-20 nm were observed. These magnetite nanoparticles with superparamagnetic behaviour are arranged to larger aggregates. This leads to a higher effective magnetic radius. According to magnetisation measurements the particles show hysteresis. The ratio of remanent vs. saturation magnetisation is not as high as it is necessary for uniaxial anisotropy. It is possible to elude the phase separations by cooking the pulverized glass in concentrated sodium hydroxide. Additional temperature dependent magnetorelaxometry (TMRX) measurements show in the distribution of the relaxation of magnetic moments over the course of temperature two peaks at 13 and 39 K. According to an interparticle distance smaller than 5 dC (the core diameter) could that be a result of strong magnetic interactions. Other magnetic relaxation processes also explain this measured effect., Comment: submitted to Journal of Nanoparticle Research

In this work we compare previously measured energy barriers over the course of temperature with the results of simulations of the behaviour of the energy barriers. For the measurements the temperature dependent magnetorelaxation method (TMRX) was used. For the simulations of the energy barrier distribution we have used the real particles properties such as anisotropy and core size volume of the fractions of two magnetically fractionated ferrofluids. There is a good agreement between the simulated behaviour and the experimental obtained results. The influence of the particle volume concentration and agglomeration on the energy barrier distribution has been investigated. Finally the simulations confirm a previously published explanation for an experimentally obtained relaxation effect., Comment: submitted to Journal of Magnetism and Magnetic Materials

In applications for high-Tc superconducting DC-SQUIDs such as biomagnetism, nondestructive evaluation and the relaxation of magnetic nanoparticles, it is important to maintain reliable sensor performance over an extended time period. We designed and produced DC-SQUID gradiometers based on YBCO thin films which are inductively coupled to a flux transformer to achieve a higher sensitivity. The gradiometers are protected against ambient atmosphere and humidity by SiO2 and amorphous YBCO layers. The noise properties of the sensor in flip-chip configuration, especially in unshielded environments, are shown. We present a comparison of TBCCO thin films on buffered sapphire or LaAlO3 substrates for the flux transformer in shielded and unshielded environments. We reach a low white field gradient noise of 72 fT/(cm sqrt(Hz)) with the TBCCO on LaAlO3 flux transformer. The electric properties of the gradiometers (critical current IC, normal state resistance RN and the transfer function VPhi) were measured over a period of one year and do not show significant signs of degradation., Comment: 9 pages, 8 figures, ISEC 2007