Reconstruction of Mercury’s internal magnetic field beyond the octupole

The reconstruction of Mercury’s internal magnetic field enables us to take a look into the inner heart of Mercury. In view of the BepiColombo mission, Mercury’s magnetosphere is simulated using a hybrid plasma code and the multipoles of the internal magnetic field are estimated from the virtual spacecraft data using three distinct reconstruction methods: the truncated singular value decomposition, the Tikhonov regularization and Capon’s minimum variance projection. The study shows that a precise determination of Mercury’s internal field beyond the octupole, up to the dotriacontapole is possible and that Capon’s method provides the same high performance as the Tikhonov regularization, which is superior to the performance of the truncated singular value decomposition.

Observation and Inversion of Aerosol Particle Size Distribution over Yinchuan Area

Particle size distribution is one of the important microphysical parameters to characterize the aerosol properties. The aerosol optical depth is used as the function of wavelength to study the particle size distribution of whole atmospheric column. However, the inversion equation of the particle size distribution from the aerosol optical depth belongs to the Fredholm integral equation of the first kind, which is usually ill-conditioned. To overcome this drawback, the integral equation is first discretized directly by using the complex trapezoid formula. Then, the corresponding parameters are selected by the L curve method. Finally the truncated singular value decomposition regularization method is employed to regularize the discrete equation and retrieve the particle size distribution. To verify the feasibility of the algorithm, the aerosol optical depths taken by a sun photometer CE318 over Yinchuan area in four seasons, as well as hazy, sunny, floating dusty and blowing dusty days, were used to retrieve the particle size distribution. In order to verify the effect of truncated singular value decomposition algorithm, the Tikhonov regularization algorithm was also adopted to retrieve the aerosol PSD. By comparing the errors of the two regularizations, the truncated singular value decomposition regularization algorithm has a better retrieval effect. Moreover, to understand intuitively the sources of aerosol particles, the backward trajectory was used to track the source. The experiment results show that the truncated singular value decomposition regularization method is an effective method to retrieve the particle size distribution from aerosol optical depth.

COMPRESSION OF PINWISE NUCLIDE CONCENTRATIONS IN CMS5

Pinwise nuclide number density (ND) data from the lattice physics code CASMO5 is compressed using a preconditioned truncated singular value decomposition (TSVD) to reduce storage requirements. Previously only assembly-average or single-pin NDs were optionally saved in the CMS5 few-group cross section library. However, backend analysis has prompted the desire to have pin-by-pin NDs available in the library for use by the SNF code. Adding this data set significantly increases the size of the library, particularly for lattices modeled in full assembly geometry (that is, not in half or octant symmetry). To reduce the required storage, the SVD is used to approximate the entire data with a reduced basis. In the four test cases, compression ratios of 2.7 to 8.5 were achieved for the PWR cases, with maximum errors less than 0.1%. However, the rodded BWR segment proved more difficult, with an average compression ratio of 1.6. One advantage of this technique is that the compression ratio is higher for full-symmetry cases, where the need for the compression is also highest.

Truncated singular value decomposition in ripped photo recovery

Singular value decomposition (SVD) is one of the most useful matrix decompositions in linear algebra. Here, a novel application of SVD in recovering ripped photos was exploited. Recovery was done by applying truncated SVD iteratively. Performance was evaluated using the Frobenius norm. Results from a few experimental photos were decent.