We analyze radiation reaction for synchrotron radiation by computing, via a multipole expansion, the near field and derive from it the Lorentz four-force, which we evaluate on the world-line of the charge. We find that the temporal component of the self four-force agrees with the radiated power, which one calculates in the radiation zone. This is the case for each mode in the multipole decompos...

We present in this paper a new kernel-independent fast multipole method (FMM), named as FKI-FMM, for pairwise particle interactions with translation-invariant kernel functions. FKI-FMM creates, using numerical techniques, sufficiently accurate and compressive representations of a given kernel function over multi-scale interaction regions in the form of a truncated Fourier series. It provides al...

We studied possibility of application of the multipole vectors decomposition of the cosmic microwave background (CMB) maps for detection signatures of non-trivial topology of the universe. Using 10 simulations we analysed distribution of the multipole vectors on the sky for the low order multipoles and probability distribution function of the statistics based on the sum of the dot products of t...

This paper presents an algorithm for the rapid evaluation of the vector spline in two dimensions. The algorithm is based on the fast multipole method and has an asymptotic CPU time estimate of O(N), where N is the number of data points. The main idea of the algorithm is to combine a cluster of evaluation kernels at diierent data sources into a single kernel in the form of a multipole expansion ...

The problem of oblique wave scattering of a Rayleigh wave by a cylindrical cavity in an elastic half-space is solved using the multipole expansion method. Whereas in the analogous water-wave problem a single scalar field is expressed as an infinite multipole expansion, and in the Rayleigh wave case with normal incidence two scalar fields suffice, here we require three coupled scalar multipole e...

This paper is concerned with the fast multipole boundary element method (FMBEM) in two dimensional frequency domain elastodynamics. The fast multipole method (FMM) is derived by the Galerkin vector in the elastodynamic field. The elastodynamic field is expressed as the sum of the longitudinal and transverse wave fields, and the Galerkin vector FMM is simply derived from the scalar wave FMM. Mul...

Parasitic extraction techniques are used to estimate signal delay in VLSI chips. Inductance extraction is a critical component of the parasitic extraction process in which on-chip inductive effects are estimated with high accuracy. In earlier work [1], we described a parallel software package for inductance extraction called ParIS, which uses a novel preconditioned iterative method to solve the...

This paper introduces two techniques for approximating the Biot–Savart integral for deforming elliptical Gaussian functions. The primary motivation is to develop a high spatial accuracy vortex method. The first technique is a regular perturbation of the streamfunction in the small parameter = a−1 a+1 , where a2 is the aspect ratio of the basis function. This perturbative technique is suitable f...

We calculate electrostatic multipole moments of C60 up to l=18 using the quantum-mechanical charge distribution with icosahedral symmetry obtained from ab initio calculations. It is found that the second nonzero moment (l=10) is comparable to the first nonzero moment (l=6). The values of several low-order multipole moments are almost 10 times smaller than those found from the charge distributio...

A new charge analysis is presented that gives an accurate description of the electrostatic potential from the charge distribution in molecules. This is achieved in three steps: first, the total density is written as a sum of atomic densities; next, from these atomic densities a set of atomic multipoles is defined; finally, these atomic multipoles are reconstructed exactly by distributing charge...