scholarly journals Uniqueness of bubbling solutions of mean field equations with non-quantized singularities

2020 ◽  
pp. 2050038
Author(s):  
Lina Wu ◽  
Lei Zhang
Keyword(s):  
Riemann Surface ◽  
Compact Riemann Surface ◽  
Mean Field ◽  
Field Equations ◽  
Field Type ◽  
Dirac Mass ◽  
Mean Field Equations ◽  
The Mean ◽  
Chern Simons

For singular mean field equations defined on a compact Riemann surface, we prove the uniqueness of bubbling solutions if some blowup points coincide with the singularities of the Dirac data. If the strength of the Dirac mass at each blowup point is not a multiple of [Formula: see text], we prove that bubbling solutions are unique. This paper extends previous results of Lin-Yan [C. S. Lin and S. S. Yan, On the mean field type bubbling solutions for Chern–Simons–Higgs equation, Adv. Math. 338 (2018) 1141–1188] and Bartolucci et al. [D. Bartolucci, A. Jevnikar, Y. Lee and W. Yang, Uniqueness of bubbling solutions of mean field equations, J. Math. Pures Appl. (9) 123 (2019) 78–126].

Solution of the mean field equations for spontaneous fission

1987 ◽  
Vol 35 (3) ◽  
pp. 1007-1027 ◽  
Author(s):  
G. Puddu ◽  
J. W. Negele
Keyword(s):  
Spontaneous Fission ◽  
Mean Field ◽  
Field Equations ◽  
Mean Field Equations ◽  
The Mean

scholarly journals INFINITE-TENSION STRINGS AT d>1

1993 ◽  
Vol 08 (06) ◽  
pp. 557-572 ◽  
Author(s):  
D.V. BOULATOV
Keyword(s):  
Matrix Model ◽  
Continuum Limit ◽  
Mean Field ◽  
Bethe Lattice ◽  
Point Of View ◽  
Simple Application ◽  
Field Equations ◽  
Mean Field Equations ◽  
The Mean ◽  
The One

A matrix model describing surfaces embedded in a Bethe lattice is considered. From the mean field point of view, it is equivalent to the Kazakov-Migdal induced gauge theory and therefore, at N=∞ and d>1, the latter can be interpreted as a matrix model for infinite-tension strings. We show that, in the naive continuum limit, it is governed by the one-matrix model saddle point with an upside-down potential. To derive mean field equations, we consider the one-matrix model in external field. As a simple application, its explicit solution in the case of the inverted W potential is given.

scholarly journals Some Predictions from the Mean Field Equations of Magnetoconvection

1980 ◽  
Vol 33 (1) ◽  
pp. 47 ◽  
Author(s):  
N Riahi
Keyword(s):  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Field Equations ◽  
Layer Method ◽  
Mean Field Equations ◽  
Boundary Layer Method ◽  
The Mean ◽  
Chandrasekhar Number ◽  
Large Rayleigh Number

Nonlinear magnetic convection is investigated by the mean field approximation. The boundary layer method is used assuming large Rayleigh number R for different ranges of the Chandrasekhar number Q. The heat flux F is determined for wavenumbers CXn which optimize F. It is shown that there are a finite number of modes in the ranges Q ~ R2/3 and R2/3 ~ Q ~ R, and that the number of modes increases with increasing Q in the former range and decreases with increasing Q in the latter range. For Q = 0(R2/3) there are infinitely many modes, and F is proportional to Rl/3 While the optimal F is independent of Q for Q ~ Rl/2, it is found to decrease with increasing Q in the range Rl/2 ~ Q ~ R and eventually to become of 0(1) as Q -> OCR), and the layer becomes stable.

Sign in / Sign up

Export Citation Format

Share Document