Related papers: Harmonic Function Expansion of Nearly Oblate Syste…

We use the weighted integral form of spherical Bessel functions, and introduce a new analytical set of complete and biorthogonal potential--density basis functions. The potential and density functions of the new set have finite central…

An algorithm for providing analytical solutions to Schr\"{o}dinger's equation with non-exactly solvable potentials is elaborated. It represents a symbiosis between the logarithmic expansion method and the techniques of the superymmetric…

Imposing Huygens' Principle in a 4D Wightman QFT puts strong constraints on its algebraic and analytic structure. These are best understood in terms of ``biharmonic fields'', whose properties reflect the presence of infinitely many…

By using the technique of supersymmetric quantum mechanics, we study a quasi exactly solvable extension of the N-particle rational Calogero model with harmonic confining interaction. Such quasi exactly solvable many particle system, whose…

We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is…

Different steps leading to the new functional for pairing based on natural orbitals and occupancies proposed in ref. [D. Lacroix and G. Hupin, arXiv:1003.2860] are carefully analyzed. Properties of quasi-particle states projected onto good…

Biorthonormal basis function expansions are widely used in galactic dynamics, both to study problems in galactic stability and to provide numerical algorithms to evolve collisionless stellar systems. They also provide a compact and…

Multipolar expansions are a foundational tool for describing basis functions in quantum mechanics, many-body polarization, and other distributions on the unit sphere. Progress on these topics is often held back by complicated and competing…

We develop potential theory for $m$-subharmonic functions with respect to a Hermitian metric on a Hermitian manifold. First, we show that the complex Hessian operator is well-defined for bounded functions in this class. This allows to…

We start from a study of the density-potential relation for classical homeoids in terms of an asymptotic expansion for small deviations from spherical symmetry. We then show that such expansion is a useful device that allows us to construct…

We establish the plurisubharmonicity of the envelope of the Poisson functional on almost complex manifolds. That is, we generalize the corresponding result for complex manifolds and almost complex manifolds of complex dimension two.

Physical systems and signals are often characterized by complex functions of frequency in the harmonic-domain. The extension of such functions to the complex frequency plane has been a topic of growing interest as it was shown that specific…

In orbital-free density functional theory (OFDFT), an equation exists for $\psi = \sqrt n$, the square root of the ground state electron density $n$. We show that $\psi$ cannot be expanded as a linear combination of elements of a complete…

We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent the solution as the sum of a volume potential and a double layer potential. Rather than…

For weighted $L^1$ space on the unit sphere of $\RR^{d+1}$, in which the weight functions are invariant under finite reflection groups, a maximal function is introduced and used to prove the almost everywhere convergence of orthogonal…

We consider the non-linear Poisson-Boltzmann theory for a single cylindrical or spherical macro-ion in symmetric 1:1, together with asymmetric 1:2 and 2:1 electrolytes. We focus on the regime where $\kappa a $, the ratio of the macro-ion…

The finite basis optimized effective potential (OEP) method within density functional theory is examined as an ill-posed problem. It is shown that the generation of nonphysical potentials is a controllable manifestation of the use of…

Spherical harmonics (SH) have been extensively used as a basis for analyzing the morphology of particles in granular mechanics. The use of SH is facilitated by mapping the particle coordinates onto a unit sphere, in practice often a…

A condition for the synchronizability of a pair of PDE systems, coupled through a finite set of variables, is commonly the existence of internal synchronization or internal coherence in each system separately. The condition was previously…

Given a charge and current distribution with compact support, the associated potentials and fields are generally not integrable in the classical sense. However, it is convenient to be able to define their Fourier transform in order to…