Existence and non-existence of solutions of the mean field equations on flat tori

Let [Formula: see text] be a closed Riemannian surface, [Formula: see text] be an isometric group acting on it. Denote a positive integer [Formula: see text], where [Formula: see text] is the number of all distinct points of the set [Formula: see text]. A sufficient condition for existence of solutions to the mean field equation [Formula: see text] is given. This recovers results of Ding–Jost–Li–Wang, Asian J. Math. (1997) 230–248 when [Formula: see text] or equivalently [Formula: see text], where Id is the identity map.

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Solution of the mean field equations for spontaneous fission

Physical Review C ◽

10.1103/physrevc.35.1007 ◽

1987 ◽

Vol 35 (3) ◽

pp. 1007-1027 ◽

Cited By ~ 9

Author(s):

G. Puddu ◽

J. W. Negele

Keyword(s):

Spontaneous Fission ◽

Mean Field ◽

Field Equations ◽

Mean Field Equations ◽

The Mean

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Explicit Solutions to the mean field equations on hyperelliptic curves of genus two

Differential Geometry and its Applications ◽

10.1016/j.difgeo.2017.08.005 ◽

2018 ◽

Vol 56 ◽

pp. 173-186

Author(s):

Jia-Ming (Frank) Liou

Keyword(s):

Mean Field ◽

Hyperelliptic Curves ◽

Explicit Solutions ◽

Field Equations ◽

Mean Field Equations ◽

The Mean ◽

Genus Two

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On the Mean Field Equations of Motion in the Theories with Unstable Vacuum

Fortschritte der Physik/Progress of Physics ◽

10.1002/prop.2190360202 ◽

1988 ◽

Vol 36 (2) ◽

pp. 97-105 ◽

Cited By ~ 2

Author(s):

I. L. Buchbinder ◽

E. S. Fradkin

Keyword(s):

Equations Of Motion ◽

Mean Field ◽

Field Equations ◽

Mean Field Equations ◽

The Mean

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INFINITE-TENSION STRINGS AT d>1

Modern Physics Letters A ◽

10.1142/s0217732393000581 ◽

1993 ◽

Vol 08 (06) ◽

pp. 557-572 ◽

Cited By ~ 4

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.

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Some Predictions from the Mean Field Equations of Magnetoconvection

Australian Journal of Physics ◽

10.1071/ph800047 ◽

1980 ◽

Vol 33 (1) ◽

pp. 47 ◽

Cited By ~ 3

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.

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