Existence of solutions for some weighted mean field equations in dimension N

2020 ◽  
Vol 100 ◽  
pp. 106010 ◽  
Author(s):  
Shengbing Deng
Keyword(s):  
Existence Of Solutions ◽  
Mean Field ◽  
Field Equations ◽  
Weighted Mean ◽  
Mean Field Equations

scholarly journals Existence of Solutions to Mean Field Equations on Graphs

2020 ◽  
Vol 377 (1) ◽  
pp. 613-621
Author(s):  
An Huang ◽  
Yong Lin ◽  
Shing-Tung Yau
Keyword(s):  
Existence Of Solutions ◽  
Mean Field ◽  
Field Equations ◽  
Mean Field Equations

scholarly journals THE RELATIVISTIC MEAN-FIELD EQUATIONS OF THE ATOMIC NUCLEUS

2012 ◽  
Vol 24 (04) ◽  
pp. 1250008 ◽  
Author(s):  
SIMONA ROTA NODARI
Keyword(s):  
Nuclear Physics ◽  
Existence Of Solutions ◽  
Mean Field Theory ◽  
Mean Field ◽  
Static Case ◽  
Concentration Compactness ◽  
Field Equations ◽  
Relativistic Mean Field ◽  
Dirac Equations ◽  
Mean Field Equations

In nuclear physics, the relativistic mean-field theory describes the nucleus as a system of Dirac nucleons which interact via meson fields. In a static case and without nonlinear self-coupling of the σ meson, the relativistic mean-field equations become a system of Dirac equations where the potential is given by the meson and photon fields. The aim of this work is to prove the existence of solutions of these equations. We consider a minimization problem with constraints that involve negative spectral projectors and we apply the concentration-compactness lemma to find a minimizer of this problem. We show that this minimizer is a solution of the relativistic mean-field equations considered.

scholarly journals Mean field equations on a closed Riemannian surface with the action of an isometric group

2020 ◽  
Vol 31 (09) ◽  
pp. 2050072
Author(s):  
Yunyan Yang ◽  
Xiaobao Zhu
Keyword(s):  
Field Equation ◽  
Positive Integer ◽  
Existence Of Solutions ◽  
Mean Field ◽  
Riemannian Surface ◽  
Sufficient Condition ◽  
Field Equations ◽  
Mean Field Equations ◽  
The Mean ◽  
Mean Field Equation

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.

Precipitation in small systems—II. Mean field equations more effective than population balance

1996 ◽  
Vol 51 (19) ◽  
pp. 4423-4436 ◽  
Author(s):  
S. Manjunath ◽  
K.S. Gandhi ◽  
R. Kumar ◽  
Doraiswami Ramkrishna
Keyword(s):  
Mean Field ◽  
Population Balance ◽  
Field Equations ◽  
Small Systems ◽  
Mean Field Equations

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

Mean field equations with probability measure in 2D-turbulence

2014 ◽  
Vol 63 (S1) ◽  
pp. 255-264 ◽  
Author(s):  
Tonia Ricciardi ◽  
Gabriella Zecca
Keyword(s):  
Probability Measure ◽  
Mean Field ◽  
Field Equations ◽  
2D Turbulence ◽  
Mean Field Equations

scholarly journals Distributed Control of Clustered Populations of Thermostatic Loads in Multi-Area Systems: A Mean Field Game Approach

Energies ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 6483
Author(s):  
Vincenzo Trovato ◽  
Antonio De Paola ◽  
Goran Strbac
Keyword(s):  
Power System ◽  
Frequency Response ◽  
Mean Field ◽  
Cost Effective ◽  
Support Network ◽  
Field Equations ◽  
Mean Field Game ◽  
Flexible Resources ◽  
Mean Field Equations ◽  
The Impact

Thermostatically controlled loads (TCLs) can effectively support network operation through their intrinsic flexibility and play a pivotal role in delivering cost effective decarbonization. This paper proposes a scalable distributed solution for the operation of large populations of TCLs providing frequency response and performing energy arbitrage. Each TCL is described as a price-responsive rational agent that participates in an integrated energy/frequency response market and schedules its operation in order to minimize its energy costs and maximize the revenues from frequency response provision. A mean field game formulation is used to implement a compact description of the interactions between typical power system characteristics and TCLs flexibility properties. In order to accommodate the heterogeneity of the thermostatic loads into the mean field equations, the whole population of TCLs is clustered into smaller subsets of devices with similar properties, using k-means clustering techniques. This framework is applied to a multi-area power system to study the impact of network congestions and of spatial variation of flexible resources in grids with large penetration of renewable generation sources. Numerical simulations on relevant case studies allow to explicitly quantify the effect of these factors on the value of TCLs flexibility and on the overall efficiency of the power system.

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