Related papers: Conjugate points along spherical harmonics
This study presents a study of equilibrium points, periodic orbits, stabilities, and manifolds in a rotating plane symmetric potential field. It has been found that the dynamical behaviour near equilibrium points is completely determined by…
We prove sectional and Ricci-type comparison theorems for the existence of conjugate points along sub-Riemannian geodesics. In order to do that, we regard sub-Riemannian structures as a special kind of variational problems. In this setting,…
We consider the multicomponent Smoluchowski coagulation equation under non-equilibrium conditions induced either by a source term or via a constant flux constraint. We prove that the corresponding stationary non-equilibrium solutions have a…
We consider Backus's problem in geophysics. This consists in reconstructing a harmonic potential outside the Earth when the intensity of the related field is measured on the Earth's surface. Thus, the boundary condition is (severely)…
A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order O(L^5), where 2L…
Using the generalised set of fluid equations that include the `Coriolis force' along with the centrifugal and pressure gradient forces, we have reanalysed the class of self similar solutions, with the pseudo-Newtonian potential. We find…
We resolve the paradox that although magnetic collimation of an isotropic solar wind results in an enhancement of its proton flux along the polar directions, several observations indicate a wind proton flux peaked at the equator. To that…
When superimposing the potentials of external fields on the Coulomb potential of the hydrogen atom a saddle point appears, which is called the Stark saddle point. For energies slightly above the saddle point energy one can find classical…
We study the correlation between the total number of critical points of random spherical harmonics and the number of critical points with value in any interval $I \subset \mathbb{R}$. We show that the correlation is asymptotically zero,…
We study the two-point correlation function of density perturbations in a spherically symmetric void universe model which does not employ the Copernican principle. First we solve perturbation equations in the inhomogeneous universe model…
The loss of criticality in the form of weak first-order transitions or the end of the conformal window in gauge theories can be described as the merging of two fixed points that move to complex values of the couplings. When the complex…
In this article, we prove the existence of common fixed points for a pair of maps on a $q$-spherically complete $T_0$-ultra-quasi-metric space. The present article is a generalization, in the assymmetric setting of the paper of Rao et…
We derive an efficient algorithm to find solutions to Euler's concordant form problem and rational points on elliptic curves associated with this problem.
The limit of energies of a sequence of harmonic maps as their annular domains approach the boundary of moduli space depends upon the boundary point approached. The infinite energy case is associated with limits of images containing ruled…
In this paper, we introduce three new iterative methods for finding a common point of the set of fixed points of a symmetric generalized hybrid mapping and the set of solutions of an equilibrium problem in a real Hilbert space. Each method…
The magnetic field outside the earth is in good approximation a harmonic vector field determined by its values at the earth's surface. The direction problem seeks to determine harmonic vector fields vanishing at infinity and with prescribed…
We provide symmetrization results in the form of mass concentration comparisons for fractional singular elliptic equations in bounded domains, coupled with homogeneous external Dirichlet conditions. Two types of comparison results are…
There are many ways to generate a set of nodes on the sphere for use in a variety of problems in numerical analysis. We present a survey of quickly generated point sets on $\mathbb{S}^2$, examine their equidistribution properties,…
Mesoscopic particles immersed in a critical fluid experience long-range Casimir forces due to critical fluctuations. Using field theoretical methods, we investigate the Casimir interaction between two spherical particles and between a…
This work introduces a new set of orbital elements to fully represent the zonal harmonics problem around an oblate celestial body. This new set of orbital elements allows to obtain a complete linear system for the unperturbed problem and,…