A Vector Equilibrium Problem for Symmetrically Located Point Charges on a Sphere
نویسندگان
چکیده
We study the equilibrium measure on two-dimensional sphere in presence of an external field generated by $$r+1$$ equal point charges that are symmetrically located around north pole. The support is known as droplet. droplet has a motherbody which we characterize means vector problem (VEP) for r measures complex plane. model undergoes two transitions reflected first component minimizer VEP, namely can be finite interval containing 0, union intervals, or full half-line. case corresponds to with disjoint components, and it analyzed genus one Riemann surface.
منابع مشابه
Genetic-algorithm energy minimization for point charges on a sphere.
We demonstrate that a new approach for optimizing atomic structures is very eeective for attacking the Thomson problem of nding the lowest energy connguration of N point charges on a unit sphere. Our approach uses a genetic algorithm, combined with a \cut and paste" scheme of mating , that eeciently explores the diierent low energy structures. 1 Not only have we reproduced the known results 2{5...
متن کاملFuzzy Vector Equilibrium Problem
In the present paper, we introduce and study a fuzzy vector equilibrium problem and prove some existence results with and without convexity assumptions by using some particular forms of results of textit{Kim} and textit{Lee} [W.K. Kim and K.H. Lee, Generalized fuzzy games and fuzzy equilibria, Fuzzy Sets and Systems, 122 (2001), 293-301] and textit{Tarafdar} [E. Tarafdar, Fixed point theorems i...
متن کاملOn Vector Equilibrium Problem with Generalized Pseudomonotonicity
In this paper, first a short history of the notion of equilibrium problem in Economics and Nash$acute{'}$ game theory is stated. Also the relationship between equilibrium problem among important mathematical problems like optimization problem, nonlinear programming, variational inequality problem, fixed point problem and complementarity problem is given. The concept of generalized pseudomonoton...
متن کاملfuzzy vector equilibrium problem
in the present paper, we introduce and study a fuzzy vector equilibrium problem and prove some existence results with and without convexity assumptions by using some particular forms of results of textit{kim} and textit{lee} [w.k. kim and k.h. lee, generalized fuzzy games and fuzzy equilibria, fuzzy sets and systems, 122 (2001), 293-301] and textit{tarafdar} [e. tarafdar, fixed point theorems i...
متن کاملMinimal Energy of 100 Point Charges on the Unit Sphere
Before 1909, atoms were thought to consist of a diffuse positive charge surrounded by electrons (the “plum pudding” model). In order to predict the properties of the elements on the periodic table with this model, the distribution of electrons on a sphere had to be studied. This problem was named after Thomson, the originator of the plum pudding model and the first to study it. In 1909, Rutherf...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Constructive Approximation
سال: 2022
ISSN: ['0176-4276', '1432-0940']
DOI: https://doi.org/10.1007/s00365-022-09566-5