The fast multipole method (FMM) has been regarded as one of the top 10 algorithms in scientific computing that were developed in the 20th century. Combined with the FMM, the boundary element method (BEM) can now solve large-scale problems with several million degrees of freedom on a desktop computer within hours. This opened up a wide range of applications for the BEM that has been hindered for...

In vortex-like spin arrangements, multiple spins can combine into emergent multipole moments. Such multipole moments have broken space-inversion and time-reversal symmetries, and can therefore exhibit linear magnetoelectric (ME) activity. Three types of such multipole moments are known: toroidal; monopole; and quadrupole moments. So far, however, the ME activity of these multipole moments has o...

Identifying the relativistic multipole moments of a spacetime of an astrophysical object that has been constructed numerically is of major interest, both because the multipole moments are intimately related to the internal structure of the object, and because the construction of a suitable analytic metric that mimics a numerical metric should be based on the multipole moments of the latter one ...

We discuss the concept and implementation of fast multipole algorithms on a regular structured grid. In doing so, the discrte analogue of the continuous fundamental solution is evaluated numerically. We discuss the concept and implementation of fast multipole algorithms on a regular structured grid. In doing so, the discrte analogue of the continuous fundamental solution is evaluated numericall...

We derive model independent, non-perturbative supersymmetric sum rules for the magnetic and electric multipole moments of any theory with N = 1 supersymmetry. We find that in any irreducible N = 1 supermultiplet the diagonal matrix elements of the l-multipole moments are completely fixed in terms of their off-diagonal matrix elements and the diagonal (l− 1)-multipole moments. † e-mail: giannak@...

Chemical bonding at the active site of hen egg-white lysozyme (HEWL) is analyzed on the basis of Bader's quantum theory of atoms in molecules [QTAIM; Bader (1994), Atoms in Molecules: A Quantum Theory. Oxford University Press] applied to electron-density maps derived from a multipole model. The observation is made that the atomic displacement parameters (ADPs) of HEWL at a temperature of 100 K ...

In this paper, the problem of finding an axisymmetric stationary spacetime from a specified set of multipole moments, is studied. The condition on the multipole moments, for existence of a solution, is formulated as a convergence condition on a power series formed from the multipole moments. The methods in this paper can also be used to give approximate solutions to any order as well as estimat...

In this paper, we express the Newman–Penrose constants in terms of the Geroch–Hansen multipole moments for stationary spacetimes. These expressions are translation-invariant combinations of the multipole moments up to quadrupole order, which do not normally vanish.

The observed spectra and X-ray luminosities of millisecond pulsars in 47 Tuc can be interpreted in the context of theoretical models based on strong, small scale multipole fields on the neutron star surface. For multipole fields that are relatively strong as compared to the large scale dipole field, the emitted X-rays are thermal and likely result from polar cap heating associated with the retu...